Research ArticleA Fast Imaging Technique Applied to 2D ElectricalResistivity Data

Raffaele Martorana and Patrizia Capizzi

Dipartimento di Scienze della Terra e del Mare University of Palermo Via Archirafi 26 90123 Palermo Italy

Correspondence should be addressed to Raffaele Martorana raffaelemartoranaunipait

Received 22 November 2013 Revised 16 February 2014 Accepted 2 March 2014 Published 2 April 2014

Academic Editor Filippos Vallianatos

Copyright copy 2014 R Martorana and P Capizzi This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

A new technique is proposed to process 2D apparent resistivity datasets in order to obtain a fast and contrasted resistivity imageuseful for a rapid data check in field or as a starting model to constrain the inversion procedure In the past some modifications tothe back-projection algorithm as well as the use of filtering techniques for the sensitivitymatrix were proposed An implementationof this technique is proposed here considering a two-step approach Initially a damped least squares solution is obtained after a fullmatrix inversion of the linearized geoelectrical problem Furthermore on the basis of the results a subsequent filtering algorithmis applied to the Jacobian matrix aiming at reducing smoothness and the linearized damped least square inversion is repeated toget the final resultThis fast imaging technique aims at increasing the resistivity contrasts and practically since it does not require aparameter set optimization it can be used to easily obtain fast and preliminary resultsThe proposed technique is tested on syntheticdata the objective of which is to find the optimal parameter set Finally two field cases are discussed and the comparison betweenback-projection and inversion is shown

1 Introduction

Besides the well-known inversion techniques there are othertechniques that aim to obtain approximate representations ofthe subsoil in shorter times compared to those required bythe ldquoclassicalrdquo iterative methods

These methodologies give approximated images of theresistivity patterns in the subsoil in which zones of highor low resistivity are approximately represented Howeverthe resulting resistivity values are generally very differentfrom the real ones and the resistivity gradient is generallymuch lower than the corresponding gradient obtained by theinverted models

A probabilistic methodology called probability tomog-raphy was developed by Patella [1] for the SP method andthen extended to resistivity measures [2] in which theinterpretative model obtained is an image reconstruction ofthe most probable location of electrical charges induced bythe primary source over buried resistivity discontinuities

In previous papers [3ndash5] a filtered back-projection resis-tivity technique was described that was based on a convolu-tion of the experimental data with a filter function calculatedon the basis of the sensitivity factors of each voxel onthe various resistivity data The calculation of the influencefactors in a discrete set of representative points (centers of thevoxels to be utilized for the back-projection) is based on theintegral of the influence density function on the volume ofeach voxel [6]

2 The Back-Projection ResistivityTechnique (BPRT)

The back-projection resistivity technique (BPRT) can beapplied to a set of apparent resistivity measures to quicklyobtain an approximate image of the resistivity distributionof the investigated volume This technique is based onthe consideration that a resistivity perturbation in a pointelement (voxel) of a bounded region produces a change in

Hindawi Publishing CorporationInternational Journal of GeophysicsVolume 2014 Article ID 846024 9 pageshttpdxdoiorg1011552014846024

2 International Journal of Geophysics

voltagemdashthus an apparent resistivity anomalymdashat the surfaceof the region according to a sensitivity coefficient Thevalue of the coefficient is dependent on the position of thevoxel considered in respect of both the current and thevoltage dipoles in agreement with the sensitivity theorem ofGeselowitz [7] This consideration suggests that it is possibleto correlate all the measured resistivity values weighted bythe appropriate sensitivity coefficients to each voxel of theinvestigated volume [8] and to estimate the resistivity valueof each cell of the model using a weighted summation of theapparent resistivity measurements This method allows us toidentify zones of ldquohighrdquo and ldquolowrdquo resistivity in the subsoil[9] The main disadvantage of these techniques is that theresistivity values of the resulting image can greatly differ fromthe actual subsurface resistivities

Barber et al [10] developed a method of back-projectionof measures along equipotential lines This approximationsimplifies the reconstruction process by assuming a linearrelationship between electrical measurements and the resis-tivity distribution This results in a fast single step imagereconstruction algorithm The image is formed by the back-projection of the boundary measurements normalized to thecase of uniform resistivity Barber and Brown [11] modifiedthe reconstruction by normalizing both sides of the back-projection equation using a reference data set The conse-quence of this strategy however is that the reconstructionproduces differential images rather than static images andthus only the normalized change in conductivity can bedetermined

Barber [12] derived a new formulation for the back-projection reconstruction algorithm in which the measure-ment data are first transformed and then back-projectedThefiltration stage of the ldquofiltered back-projectionrdquo method isachieved by premultiplication of the data measured and isfollowed by the back-projection operation

Kotre [13 14] used a linearized sensitivity matrix to carryout a similar data normalization strategy However ratherthan normalizing this matrix with the uniform referencedata set Kotre [13] normalized each column of the matrix(corresponding to each individual cell) with the sum of thesensitivity coefficients for all apparent resistivity measures

Let us consider a set of 119873 measures carried out onthe surface of a homogeneous medium characterized by abackground resistivity 120588119887 All data are referenced on thesurface by means of the positions of the four electrodes usedThe investigated volume can be discretized in119872 small voxelsIf the 119894th voxel has an anomalous resistivity 120588

1015840

119894= 120588119887 + 120597120588119894 all

the apparent resistivitymeasures are influenced In particularthe value of the 119895th resistivity measure will be 120588

1015840

119886119895= 120588119887 + 120597120588119886119895

As long as 120597120588119894 is small it can be assumed that the relation islinear so that 120597120588119886119895 prop 120597120588119894

The proportionality can then be defined by a sensitivitycoefficient that correlates the 119894th voxel to the 119895th measure

119878119894119895 =

120597120588119886119895

120597120588119894

(1)

By considering the resistivity anomaly in the single element interms of logarithmic difference between the perturbed valueof the element and the background resistivity we establishthat perturbation 119875119894(119909 119910 119911) can be expressed as

119875119894 (119909 119910 119911) = ln (120588119887 + 120597120588119894 (119909 119910 119911)) minus ln (120588119887)

= ln[1 +120597120588119894 (119909 119910 119911)

120588119887

]

asymp120597120588119894 (119909 119910 119911)

120588119887

(2)

where 120597120588119894(119909 119910) ≪ 120588119887By taking the superposition principle into due considera-

tion the relative change in the apparent resistivity is given bythe sum of the contributions of all the voxels [13 15]

120597120588119886119895 =

119872

sum

119894=1

119878119894119895120597120588119894 (3)

The perturbation of the apparent resistivity in respect of ahomogeneous body can then be expressed as

120597120588119886119895

120588119887

=

sum119872

119894=1119878119894119895120597120588119894

sum119872

119894=1119878119894119895 sdot 120588119887

(4)

Using the matrix notation we can write

120588a = B sdot 120588t (5)

where 120588a is the vector (120575120588119886120588119887) of the relative differences ofapparent resistivity 120588t is the vector (120575120588120588119887) of the relativeresistivity changes in the model elements and B is the matrixof the following terms

119861119894119895 =

119878119894119895

sum119872

119894=1119878119894119895

where 119894 = 1 119872 119895 = 1 119873 (6)

The BPRT is based on the estimation of the resistivity of eachcell of the model by means of the approximate inversion of(5)

3 Procedure Proposed

The procedure proposed in this work consists of four steps

(1) evaluation of sensitivity matrix B(2) inversion of matrix B using a damped LSQR solution

(3) recalculation of a filtered JacobianmatrixB1015840

obtainedby means of a correlation filter

(4) inversion of the filtered sensitivity matrix

31 Evaluation of the Sensitivity Matrix In the case ofa homogeneous half-space B can easily be calculated byestimating 119878119894119895 terms by integrating the sensitivity functionderived from the Frechet derivate [16] over each voxel

International Journal of Geophysics 3

0minus2minus4minus6minus8

10 15 20 25 30 35 40 45 50

x (m)

x (m)

98 100 102 104 106 108 110 112 114 116 118 120

(Ωm)

z(m

)

Figure 1 Back-projection obtained using transposed matrix BTsimulating a 2D model with a resistive square body (1000Ωm)buried in a homogeneous medium (100Ωm)

In fact if the pole-pole array is considered with a currentelectrode 1198621(0 0 0) and a potential electrode 1198751(119886 0 0) asmall change in resistivity 120575120588 within an elemental volume 120575120591

having (119909 119910 119911) coordinates causes a potential variation 120575120601 in1198751 given by [17]

120575120601

120575120588

= int119881

1

41205872

(119909 minus 119886)2+ 1199102+ 1199112

[1199092 + 1199102 + 1199112]32

[(119909 minus 119886)2+ 1199102 + 1199112]

32119889119909 119889119910119889119911

(7)

in which the term within the integral is the Frechet 3Dderivative The Frechet 3D derivative for a four-electrodearray can be obtained by adding together the contribution ofeach potential electrode-current electrode pair

Equation (7) has the same form as the equation foundby Roy and Apparao [6] to calculate the potential differencecreated by a small volume element centered at (119909 119910 119911) with apole-pole array on the surface of a homogenous earth

In this way B only depends on the positions of theelectrodes and on the discretization model

Between the electrodes in near surface zones the sensi-tivity function can be negative [18] So when the size of thecell is smaller than one-half of the unit electrode spacingthe terms of 119878 can oscillate between positive and negativefactors with very large absolute values near the electrode As aconsequence the BPRT becomes instable near the electrodes

To partially overcome this problem [5] the normalizationof the terms of matrix B is made by dividing each term 119878119894119895 bythe sum of the absolute values of all the coefficients related tothe 119895th measure

Consider

119861119894119895 =

119878119894119895

sum119872

119894=1

10038161003816100381610038161003816119878119894119895

10038161003816100381610038161003816

(8)

In this way the effects of the oscillation of the sensitivityfunction near the electrodes are strongly attenuated withoutthere being a significant loss of resolution

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

minus2

minus4

minus6

minus8

(a)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

minus2

minus4

minus6

minus8

(b)

0 5 10 15 20 25 30 35

50 100 150 200 250 300 350

z(m

)

x (m)

(Ωm)

0

minus2

minus4

minus6

minus8

(c)

Figure 2 Results of the one-step damped least-square inversionobtained by using different damping factors 120582 on a 2D modelwith two equal square bodies (1000Ωm) buried in a homogeneousmedium (100Ωm) at different depths (a) 120582= 0003 (b) 120582= 003 and(c) 120582 = 03

32 Inversion of the Sensitivity Matrix Inversion of thesensitivity matrix B in (4) constitutes the basis of the BPRTwhen estimating 120588t However the analytical solution of (5)is not trivial and the process is often instable Approximatesolutions [5 13 18] have been proposed that substitute theinverted matrix Bminus1 with the transposed matrix BT Figure 1shows an example of back-projection obtained using BTApparent resistivities have been calculated by simulating aresistive square body (1000Ωm) buried in a homogeneousmedium (100Ωm) It stands to reason that back-projectedimages are also smoothed Furthermore the estimated tomo-graphic resistivity contrasts are generally very low in respectof the real ones Since matrix B is generally ill-conditionedand is not square a more accurate solution for the inversionadopted here is a damped least-squares solution [19ndash21]

120588119899= 1205880 + [BTB + 120582119865maxI]

minus1

BT(120588a minus 1205880) (9)

where 1205880 is the initial homogeneous background resistivityvector 120582 is a damping factor 119865max is the biggest value of themain diagonal values of the matrix [BTB] and I is a unity

4 International Journal of Geophysics

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

10 15 20 25 30 35

N(120588a)

N(120588)

120588amin 120588min120588amax120588max(Ωm)

Figure 3 Pattern of the normalizing119873(120588119890) function applied to a setof apparent resistivity values and to the corresponding set of first-step resistivity values

0010203040506070809

1

0 01 02 03 04 05 06 07 08 09 1High correlation Low correlation

120594 = 50120594 = 20

120594 = 10 120594 = 8

120594 = 5

120594 = 3

120594 = 2

120594 = 1

120594 = 05

120594 = 01

|N(120588) minus N(120588a )|

Φ(120588a120588)

Figure 4 Pattern of filtering function Φ at different values ofparameter 120594

diagonal matrix of the same size as [BTB] In this way thesquare matrix [BTB] is regularized to obtain an approximatesolution

For a nonzero value of 120582 an inverse can be calculatedalthough its condition number and hence the stability of theinversion depend on the value of damping factor 120582 for largevalues the image obtained can result as being too smooth andblurred however if 120582 is too small inversion can produce verynoisy images

Figure 2 shows the results of the one-step damped least-square inversion of synthetic data calculated for a modelhaving two square bodies with resistivity equal to 1000Ωmburied at different depths in a homogeneous medium of100Ωm resistivity Synthetic tests showed that for 120582 le

001 the back-projected images were generally noised andfurthermore artifacts are present due to the instability of theprocess As 120582 increases noise attenuates while the resistivitygradient decreases Therefore if damping is too high (120582 ge

01) the image becomes too smooth and blurred All thesynthetic tests carried out with 2D data suggested that a goodcompromise for 2D inversions is to choose 120582 asymp 003

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

minus2

minus4

minus6

minus8

(a)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

minus2

minus4

minus6

minus8

(b)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

minus2

minus4

minus6

minus8

60 80 100 120 140 160 180 200 220(Ωm)

(c)

Figure 5 Results of filtered Jacobian damped LSQR imagingobtained by varying correction parameter 120594 (a) 120594 = 05 (b) 120594 = 5and (c) 120594 = 50 The model is the same as that in Figure 2

33 Recalculation of the Sensitivity Matrix Using a Corre-lation Filter (Gradient Enhancing) The subsequent step ofthe imaging technique proposed is a recalculation of thesensitivity matrix B This is substituted by a matrix B1015840 inwhich each term is calculated by applying a correlation filter

1198611015840

119894119895= 119861119894119895 sdot Φ [120588119886119895 120588119895] (10)

The aim of filtering is to attenuate term 119861119894119895 linking the119894th voxel and the 119895th resistivity datum when the first-stepresistivity value of the 119894th voxel and the apparent resistivityvalue of the 119895th datum show a low correlation

In order to correctly estimate a correlation value betweendata sets of different kinds both sets of experimental data(apparent resistivities and first-step resistivities) are previ-ously normalized using the following normalizing function

119873(120588119890) = 2(ln 120588119890 minus ln 120588119890min

ln 120588119890max minus ln 120588119890min) minus 1 (11)

where 120588119890 is the datum (it can be 120588119886 or 120588) and 120588119890min and 120588119890maxare respectively the minimum and the maximum values

Figure 3 shows the pattern of the normalizing function119873(120588119890) applied to a set of data measures and to the first-step

International Journal of Geophysics 5

15 20 25 30 35 40 45

x (m)z

(m)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

(a)

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

(b)

Figure 6 Results of filtered Jacobian dampedLSQR imaging obtained by varying the depth of an anomalous square body (a)A resistive squarebody (1000Ωm) in a homogeneous medium (100Ωm) and (b) a conductive square body (10Ωm) in a homogenous medium (100Ωm)

resistivity values In this way 119873(120588119890) ranges from minus1 (for aminimum resistivity) to 1 (for a maximum)

The filtering function Φ(120588119886 120588) is then defined as follows

Φ(120588119886 120588) = 119890minus120594(12)|119873(120588) minus119873(120588

119886)| (12)

where 120594 is a correction parameter that controls the grade ofattenuation of terms 119861119894119895

In this way Φ(120588119886 120588) varies from 119890minus120594 (if the correlation

between 120588119886 and 120588 is the lowest) to 1 (if the correlation is thehighest)

Figure 4 shows the pattern of the filtering function fordifferent values of parameter 120594The lower the correlation thelower is the value of Φ(120588119886 120588) (the attenuation being higher)Furthermore the higher the value of 120594 the higher is thegradient of attenuation

34 Inversion of the Filtered Matrix B1015840 Finally each sensitiv-ity coefficient is recalculated by means of (10) and using thedamped least-squares inversion now considering the filteredmatrix B1015840 instead of B

120588119899= 1205880 + [B1015840TB + 120582119865maxI]

minus1

B1015840T (120588a minus 1205880) (13)

In Figure 5 the influence of varying correction parameter120594 on the back-projection is shown The sharpness of thenew tomographic image depends on the value of correction

parameter 120594 generally if 120594 le 1 the image obtained isgenerally too smooth As 120594 increases the anomalous bodiesbecome more contrasted However when 120594 is greater than10 images become noised and the anomalies break down inseveral parts

All the synthetic tests carried out with 2D data suggestedthat a good compromise for 2D inversions is to choose 120594 asymp 5

In spite of the long presentation the four steps are in factvery quick to carry out when using an automatic procedurewith a simple notebook

4 Results of Some Tests on Synthetic Models

The procedure proposed was tested on synthetic dataobtained by simulating pseudosections of different arrayscarried out on several simple 2D discrete models All thesynthetic tests stressed that the estimated shapes depths andresistivity contrasts of the anomalous bodies depend on thekind of array used Results seem to suggest that the bestestimation is obtained by using the Wenner-Schlumbergerarray Hereafter only the results obtained using this latterarray will be discussed

For each model the minimum electrode distance wasfixed at 1m and apparent resistivity measures were calculatedconsidering that order 119899 varied between 1 and 10 and that thepotential electrode distance MN was equal to 1 2 and 3m

6 International Journal of Geophysics

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

120588 = 2Ωm

120588 = 10Ωm

120588 = 20Ωm

120588 = 50Ωm

120588 = 80Ωm

120588 = 120Ωm

120588 = 200Ωm

120588 = 500Ωm

120588 = 1000Ωm

120588 = 5000Ωm

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

Figure 7 Results of filtered Jacobian damped LSQR imaging obtained by varying the resistivity of an anomalous square body buried in ahomogeneous medium (100Ωm) from 2Ωm to 5000Ωm

Several tests were carried out by changing the dimen-sions the position and the depth of the targets and by varyingthe values of the above defined parameters

The results obtained by varying the depth (from 1 to 3m)of a square target (3m times 3m) are shown in Figure 6 In ahomogeneous medium (120588 = 100Ωm) a resistive (1000ΩmFigure 6(a)) or conductive (10Ωm Figure 6(b)) squaredprism is placed under the profile at varying depths Theresolution and the contrast of the obtained image obviouslydecrease with depth As a consequence the anomalous bodyis still recognizable until a depth of about 25m

Figure 7 shows the tomographic images obtained startingfrom square-sized targets inwhich the resistivity of the targets

varies from 2Ωm to 5000Ωm In cases of very low resistivitythe tomographic shape does not fit the real shape Thecorrelation between the tomographic images and the modelsincreases with the resistivity of the target Specifically thedifference between the real top of the target and the estimatedone decreases

Finally the results of a more complex model are shownApparent resistivity measures were simulated starting from amodel consisting of four prisms of different shapes and resis-tivities buried in a homogeneous medium Figure 8 showsa comparison between back-projection using transposedmatrix B (Figure 8(a)) the image obtained by the techniquehere proposed using a damped least-squares solution of

International Journal of Geophysics 7

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(a)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(b)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(c)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

(d)

Figure 8 Back-projection fast imaging and inversions on datasimulated starting from amodel with four prisms of different shapesand resistivities (resp 1000Ωm the resistive ones and 10Ωm theconductive ones) buried in a homogeneous medium (100Ωm) Acomparison ismade between the back-projection obtained using thetransposed of matrix B (a) the image obtained by a damped least-squares solution of the filtered sensitivity matrix (b) the standardleast-squares constrain inversion (c) and robust data constraininversion (d) The color scales are the same

the filtered sensitivity matrix (Figure 8(b)) and two inver-sions carried out using the RES2DINV software respectivelywith a standard least-squares constrain (Figure 8(c)) andwith a robust data constrain algorithm (Figure 8(d)) Resultsof back-projections are strongly smoothed and dependenton the lateral position of the anomalous body in respectof the section Furthermore the resistivity contrast is verylow if compared to the real one Instead the damped least-squares solution of the filtered sensitivity matrix allowsa less smoothed and more accurate representation of thetargets which show higher resistivity contrasts and morecorrect shapes especially if referred to the resistive targets

The resistivity range showed is considerablywider than that ofthe back-projection and it is near the range of values obtainedin the inversions Nonuniqueness involved in standard least-squares constrain procedure implies that invertedmodels canpresent artifacts linked to the choice of inversion parametersThe image obtained by the damped least-squares solution ofthe filtered sensitivity matrix is instead less influenced bythe choice of parameters and does not produce significantartifacts

5 Test on Experimental Measures

The reliability of the proposed method was tested in severalarchaeological and environmental casesThe results of two ofthese are discussed below

Figure 9 shows a test on a set of geoelectrical measurescarried out on the plane of Himera [22] to detect buriedarcheological structures A 2D dipole-dipole resistivity sur-vey was carried out using 64 electrodes spaced 05m apartand with order 119899 from 1 to 9

ERT results showed clear resistive localized anomalieswhich are connected with wall-like relicsThis was confirmedby an archeological excavation near the profile in which thestructure of a building in line with geoelectrical anomalieswas located In fact the survey direction was perpendicularto that of the buried archaeological structures Furthermorethe low background resistivity values shown by the inversionwere interpreted as representing river deposits having differ-ent moisture characteristics

The comparison between the fast imaging and the robustinversion shows that the structures detected by the fastimaging technique have very similar shapes to those of theinversion

The second case regards an area on the outskirts ofMarsala (Western Sicily) where many sandstone quarries arepresent [23] some of which are abandoned In this area themain outcropping formation is the Calcarenite di Marsalawhich has been exploited for a long time as building stone

A geophysical model of the subsoil was designed usingdetailed geological information and the geometrical shapesof some galleries that were physically investigated Thisallowed us to compare synthetic and experimental dataIn the survey here presented the filtered Jacobian dampedLSQR model shows three resistive anomalies correspondingto three buried tunnels one of which was actually inspectedIn Figure 10 the grey lines represent the positions and theshapes of the galleries The fast imaging model (Figure 10(a))shows three resistive anomalies in correspondence with thegalleries even though it shows a lower resistivity contrast andsmoother boundaries compared with the inversion model(Figure 10(b))

6 Conclusions

An in-depth discussion on this topic involves taking intoconsideration not only the type of synthetic andor real(sharp or smooth boundary) model to be used but alsothe equivalence problem which is always relevant However

8 International Journal of Geophysics

21

3 4

A998400A

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

201000

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1 2 34

(m)

(Ωm)

A998400A

(b)

1000

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

1 2 3 4

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

(m) A998400A

(Ωm)

(c)

Figure 9 Results of a dipole-dipole survey carried out on the plane of Himera to detect buried archeological structures (a) Map of thearchaeological excavation (the black arrow indicates the position of the survey) (b) Filtered Jacobian damped LSQR imaging (c) Standardleast-squares constrain inversion The black numbers indicate some resistive localized anomalies which are well related to wall-like relics(red numbers)

0 5 10 15 20 25 30 35 40 45 50

10

5

0

x (m)

z(m

)

1500 1750 2000 2250 2500 2750 3000(Ωm)

(a)

0 5 10 15 20 25 30 35 40 45 50

10

5

0

x (m)

z(m

)

1500 1750 2000 2250 2500 2750 3000(Ωm)

(b)

Figure 10 Results of the geoelectrical survey carried out on the test site of Marsala (Italy) (a) filtered Jacobian damped LSQR imaging (b)standard least-squares constrain inversion The superimposed black lines represent the real shapes of the tunnels

the simulations and field data here presented stress thatthe filtered Jacobian damped LSQR imaging can be a validtool when looking for a fast approach to the tomographicrepresentation of geoelectrical data

The modification of the back-projection equation pro-posed above indeed leads to tomographic images that havehigher resistivity contrasts than those obtained using stan-dard back-projection methods Furthermore filtering of thesensitivity matrix with the correlation filter proposed andtested above reduces smoothness in the final tomographicrepresentation

The values chosen for the parameters of the filtered Jaco-bian damped LSQR imaging (a damping parameter value 120582 asymp

003 in the first matrix inversion and a correction parameter120594 asymp 5 in the filtering procedure) worked sufficiently wellwith both synthetic and field data In all those cases where

sharp-boundary models were sufficiently representative (ietunnels voids archaeological remains etc) the procedurehere presented seemed to be efficient enough to give reliableimages of the subsoil

Further simulations on noised data (not presented in thispaper) showed that back-projected images are not particu-larly influenced by noise In fact they tend to highlight onlythe main structures while masking small anomalies that areprobably caused by noise

In conclusion the quickness of the technique togetherwith its almost total independence from choice of parametersand from data noise suggests that proposed procedurecan be a useful as well as a fast technique of approxi-mate image reconstruction It can therefore be carried outdirectly in the field for a first and fast preliminary resultFurthermore these could be used as a startingmodel instead

International Journal of Geophysics 9

of the homogenous model or the pseudosection to constrainthe inversion procedure

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D Patella ldquoIntroduction to ground surface self-potentialtomographyrdquo Geophysical Prospecting vol 45 no 4 pp 653ndash681 1997

[2] P Mauriello and D Patella ldquoResistivity anomaly imaging byprobability tomographyrdquo Geophysical Prospecting vol 47 no 3pp 411ndash429 1999

[3] P Cosentino D Luzio RMartorana and L Terranova ldquoTomo-graphic techniques for pseudo-section representationrdquo in Pro-ceedings of the 1st Meeting of Environmental and EngineeringGeophysical Society pp 485ndash488 Turin Italy 1995

[4] P Cosentino and D Luzio ldquoTomographic pseudo-inversion ofresistivity profilesrdquo Annali di Geofisica vol 40 no 5 pp 1127ndash1144 1997

[5] P Cosentino D Luzio and R Martorana ldquoTomographic resis-tivity 3D mapping filter coefficients and depth correctionrdquo inProceedings of the 4thMeeting of Environmental and EngineeringGeophysical Society pp 279ndash282 European Section BarcelonaSpain 1998

[6] A Roy andAApparao ldquoDepth of investigation in direct currentmethodsrdquo Geophysics vol 36 no 5 pp 943ndash959 1971

[7] D B Geselowitz ldquoAn application of electrocardiographic leadtheory to impedance plethysmographyrdquo IEEE Transactions onBiomedical Engineering vol 18 no 1 pp 38ndash41 1971

[8] D C Barber andA D Seagar ldquoFast reconstruction of resistanceimagesrdquo Clinical Physics and Physiological Measurement vol 8supplement A pp 47ndash54 1987

[9] M Noel and B Xu ldquoArchaeological investigation by electricalresistivity tomography a preliminary studyrdquo Geophysical Jour-nal International vol 107 no 1 pp 95ndash102 1991

[10] C C Barber B H Brown and I L Freeston ldquoImaging spatialdistributions of resistivity using applied potential tomographyrdquoElectronics Letters vol 19 no 22 pp 933ndash935 1983

[11] D C Barber andBH Brown ldquoErrors in reconstruction of resis-tivity images using a linear reconstruction techniquerdquo ClinicalPhysics and Physiological Measurement vol 9 supplement App 101ndash104 1988

[12] D C Barber ldquoImage reconstruction in applied potentialtomographymdashelectrical impedance tomographyrdquo InternalReport Department of Medical Physics and ClinicalEngineering University of Sheffield 1990

[13] C J Kotre ldquoA sensitivity coefficient method for the reconstruc-tion of electrical impedance tomogramsrdquo Clinical Physics andPhysiological Measurement vol 10 no 3 pp 275ndash281 1989

[14] C J Kotre ldquoEIT image reconstruction using sensitivityweighted filtered back-projectionrdquo Physiological Measurementvol 15 supplement 2 pp A125ndashA136 1994

[15] H Shima and T Sakayama ldquoResistivity tomography anapproach to 2-D resistivity inverse problemsrdquo in Proceedingsof the 57th Annual International Meeting Society of ExplorationGeophysicists Expanded Abstracts pp 204ndash207 1987

[16] P R McGillivray and D W Oldenburg ldquoMethods for calcu-lating Frechet derivatives and sensitivities for the non-linearinverse problem a comparative studyrdquo Geophysical Prospectingvol 38 no 5 pp 499ndash524 1990

[17] M H Loke and R D Barker ldquoLeast-squares deconvolution ofapparent resistivity pseudosectionsrdquo Geophysics vol 60 no 6pp 1682ndash1690 1995

[18] H Shima ldquo2-D and 3-D resistivity image reconstruction usingcrosshole datardquo Geophysics vol 57 no 10 pp 1270ndash1281 1992

[19] W Menke Geophysical Data Analysis Discrete Inverse TheoryAcademic Press New York NY USA 1989

[20] Y L Yaoguo Li and D W Oldenburg ldquoApproximate inversemappings in DC resistivity problemsrdquo Geophysical JournalInternational vol 109 no 2 pp 343ndash362 1992

[21] H Dehghani D C Barber and I Basarab-Horwath ldquoIncor-porating a priori anatomical information into image recon-struction in electrical impedance tomographyrdquo PhysiologicalMeasurement vol 20 no 1 pp 87ndash102 1999

[22] P Capizzi P L Cosentino G Fiandaca R Martorana PMessina and S Vassallo ldquoGeophysical investigations at theHimera archaeological site northern Sicilyrdquo Near Surface Geo-physics vol 5 no 6 pp 417ndash426 2007

[23] P Capizzi P L Cosentino G Fiandaca R Martorana and PMessina ldquo2D GPR and geoelectrical modelling tests on man-made tunnels and cavitiesrdquo in Proceedings of the 11th EuropeanMeeting of Environmental and Engineering Geophysics B036Near Surface Palermo Italy 2005

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

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EarthquakesJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

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MineralogyInternational Journal of

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MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

International Journal of Geophysics 3

0minus2minus4minus6minus8

10 15 20 25 30 35 40 45 50

x (m)

x (m)

98 100 102 104 106 108 110 112 114 116 118 120

(Ωm)

z(m

)

Figure 1 Back-projection obtained using transposed matrix BTsimulating a 2D model with a resistive square body (1000Ωm)buried in a homogeneous medium (100Ωm)

In fact if the pole-pole array is considered with a currentelectrode 1198621(0 0 0) and a potential electrode 1198751(119886 0 0) asmall change in resistivity 120575120588 within an elemental volume 120575120591

having (119909 119910 119911) coordinates causes a potential variation 120575120601 in1198751 given by [17]

120575120601

120575120588

= int119881

1

41205872

(119909 minus 119886)2+ 1199102+ 1199112

[1199092 + 1199102 + 1199112]32

[(119909 minus 119886)2+ 1199102 + 1199112]

32119889119909 119889119910119889119911

(7)

in which the term within the integral is the Frechet 3Dderivative The Frechet 3D derivative for a four-electrodearray can be obtained by adding together the contribution ofeach potential electrode-current electrode pair

Equation (7) has the same form as the equation foundby Roy and Apparao [6] to calculate the potential differencecreated by a small volume element centered at (119909 119910 119911) with apole-pole array on the surface of a homogenous earth

In this way B only depends on the positions of theelectrodes and on the discretization model

Between the electrodes in near surface zones the sensi-tivity function can be negative [18] So when the size of thecell is smaller than one-half of the unit electrode spacingthe terms of 119878 can oscillate between positive and negativefactors with very large absolute values near the electrode As aconsequence the BPRT becomes instable near the electrodes

To partially overcome this problem [5] the normalizationof the terms of matrix B is made by dividing each term 119878119894119895 bythe sum of the absolute values of all the coefficients related tothe 119895th measure

Consider

119861119894119895 =

119878119894119895

sum119872

119894=1

10038161003816100381610038161003816119878119894119895

10038161003816100381610038161003816

(8)

In this way the effects of the oscillation of the sensitivityfunction near the electrodes are strongly attenuated withoutthere being a significant loss of resolution

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

minus2

minus4

minus6

minus8

(a)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

minus2

minus4

minus6

minus8

(b)

0 5 10 15 20 25 30 35

50 100 150 200 250 300 350

z(m

)

x (m)

(Ωm)

0

minus2

minus4

minus6

minus8

(c)

Figure 2 Results of the one-step damped least-square inversionobtained by using different damping factors 120582 on a 2D modelwith two equal square bodies (1000Ωm) buried in a homogeneousmedium (100Ωm) at different depths (a) 120582= 0003 (b) 120582= 003 and(c) 120582 = 03

32 Inversion of the Sensitivity Matrix Inversion of thesensitivity matrix B in (4) constitutes the basis of the BPRTwhen estimating 120588t However the analytical solution of (5)is not trivial and the process is often instable Approximatesolutions [5 13 18] have been proposed that substitute theinverted matrix Bminus1 with the transposed matrix BT Figure 1shows an example of back-projection obtained using BTApparent resistivities have been calculated by simulating aresistive square body (1000Ωm) buried in a homogeneousmedium (100Ωm) It stands to reason that back-projectedimages are also smoothed Furthermore the estimated tomo-graphic resistivity contrasts are generally very low in respectof the real ones Since matrix B is generally ill-conditionedand is not square a more accurate solution for the inversionadopted here is a damped least-squares solution [19ndash21]

120588119899= 1205880 + [BTB + 120582119865maxI]

minus1

BT(120588a minus 1205880) (9)

where 1205880 is the initial homogeneous background resistivityvector 120582 is a damping factor 119865max is the biggest value of themain diagonal values of the matrix [BTB] and I is a unity

4 International Journal of Geophysics

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

10 15 20 25 30 35

N(120588a)

N(120588)

120588amin 120588min120588amax120588max(Ωm)

Figure 3 Pattern of the normalizing119873(120588119890) function applied to a setof apparent resistivity values and to the corresponding set of first-step resistivity values

0010203040506070809

1

0 01 02 03 04 05 06 07 08 09 1High correlation Low correlation

120594 = 50120594 = 20

120594 = 10 120594 = 8

120594 = 5

120594 = 3

120594 = 2

120594 = 1

120594 = 05

120594 = 01

|N(120588) minus N(120588a )|

Φ(120588a120588)

Figure 4 Pattern of filtering function Φ at different values ofparameter 120594

diagonal matrix of the same size as [BTB] In this way thesquare matrix [BTB] is regularized to obtain an approximatesolution

For a nonzero value of 120582 an inverse can be calculatedalthough its condition number and hence the stability of theinversion depend on the value of damping factor 120582 for largevalues the image obtained can result as being too smooth andblurred however if 120582 is too small inversion can produce verynoisy images

Figure 2 shows the results of the one-step damped least-square inversion of synthetic data calculated for a modelhaving two square bodies with resistivity equal to 1000Ωmburied at different depths in a homogeneous medium of100Ωm resistivity Synthetic tests showed that for 120582 le

001 the back-projected images were generally noised andfurthermore artifacts are present due to the instability of theprocess As 120582 increases noise attenuates while the resistivitygradient decreases Therefore if damping is too high (120582 ge

01) the image becomes too smooth and blurred All thesynthetic tests carried out with 2D data suggested that a goodcompromise for 2D inversions is to choose 120582 asymp 003

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

minus2

minus4

minus6

minus8

(a)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

minus2

minus4

minus6

minus8

(b)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

minus2

minus4

minus6

minus8

60 80 100 120 140 160 180 200 220(Ωm)

(c)

Figure 5 Results of filtered Jacobian damped LSQR imagingobtained by varying correction parameter 120594 (a) 120594 = 05 (b) 120594 = 5and (c) 120594 = 50 The model is the same as that in Figure 2

33 Recalculation of the Sensitivity Matrix Using a Corre-lation Filter (Gradient Enhancing) The subsequent step ofthe imaging technique proposed is a recalculation of thesensitivity matrix B This is substituted by a matrix B1015840 inwhich each term is calculated by applying a correlation filter

1198611015840

119894119895= 119861119894119895 sdot Φ [120588119886119895 120588119895] (10)

The aim of filtering is to attenuate term 119861119894119895 linking the119894th voxel and the 119895th resistivity datum when the first-stepresistivity value of the 119894th voxel and the apparent resistivityvalue of the 119895th datum show a low correlation

In order to correctly estimate a correlation value betweendata sets of different kinds both sets of experimental data(apparent resistivities and first-step resistivities) are previ-ously normalized using the following normalizing function

119873(120588119890) = 2(ln 120588119890 minus ln 120588119890min

ln 120588119890max minus ln 120588119890min) minus 1 (11)

where 120588119890 is the datum (it can be 120588119886 or 120588) and 120588119890min and 120588119890maxare respectively the minimum and the maximum values

Figure 3 shows the pattern of the normalizing function119873(120588119890) applied to a set of data measures and to the first-step

International Journal of Geophysics 5

15 20 25 30 35 40 45

x (m)z

(m)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

(a)

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

(b)

Figure 6 Results of filtered Jacobian dampedLSQR imaging obtained by varying the depth of an anomalous square body (a)A resistive squarebody (1000Ωm) in a homogeneous medium (100Ωm) and (b) a conductive square body (10Ωm) in a homogenous medium (100Ωm)

resistivity values In this way 119873(120588119890) ranges from minus1 (for aminimum resistivity) to 1 (for a maximum)

The filtering function Φ(120588119886 120588) is then defined as follows

Φ(120588119886 120588) = 119890minus120594(12)|119873(120588) minus119873(120588

119886)| (12)

where 120594 is a correction parameter that controls the grade ofattenuation of terms 119861119894119895

In this way Φ(120588119886 120588) varies from 119890minus120594 (if the correlation

between 120588119886 and 120588 is the lowest) to 1 (if the correlation is thehighest)

Figure 4 shows the pattern of the filtering function fordifferent values of parameter 120594The lower the correlation thelower is the value of Φ(120588119886 120588) (the attenuation being higher)Furthermore the higher the value of 120594 the higher is thegradient of attenuation

34 Inversion of the Filtered Matrix B1015840 Finally each sensitiv-ity coefficient is recalculated by means of (10) and using thedamped least-squares inversion now considering the filteredmatrix B1015840 instead of B

120588119899= 1205880 + [B1015840TB + 120582119865maxI]

minus1

B1015840T (120588a minus 1205880) (13)

In Figure 5 the influence of varying correction parameter120594 on the back-projection is shown The sharpness of thenew tomographic image depends on the value of correction

parameter 120594 generally if 120594 le 1 the image obtained isgenerally too smooth As 120594 increases the anomalous bodiesbecome more contrasted However when 120594 is greater than10 images become noised and the anomalies break down inseveral parts

All the synthetic tests carried out with 2D data suggestedthat a good compromise for 2D inversions is to choose 120594 asymp 5

In spite of the long presentation the four steps are in factvery quick to carry out when using an automatic procedurewith a simple notebook

4 Results of Some Tests on Synthetic Models

The procedure proposed was tested on synthetic dataobtained by simulating pseudosections of different arrayscarried out on several simple 2D discrete models All thesynthetic tests stressed that the estimated shapes depths andresistivity contrasts of the anomalous bodies depend on thekind of array used Results seem to suggest that the bestestimation is obtained by using the Wenner-Schlumbergerarray Hereafter only the results obtained using this latterarray will be discussed

For each model the minimum electrode distance wasfixed at 1m and apparent resistivity measures were calculatedconsidering that order 119899 varied between 1 and 10 and that thepotential electrode distance MN was equal to 1 2 and 3m

6 International Journal of Geophysics

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

120588 = 2Ωm

120588 = 10Ωm

120588 = 20Ωm

120588 = 50Ωm

120588 = 80Ωm

120588 = 120Ωm

120588 = 200Ωm

120588 = 500Ωm

120588 = 1000Ωm

120588 = 5000Ωm

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

Figure 7 Results of filtered Jacobian damped LSQR imaging obtained by varying the resistivity of an anomalous square body buried in ahomogeneous medium (100Ωm) from 2Ωm to 5000Ωm

Several tests were carried out by changing the dimen-sions the position and the depth of the targets and by varyingthe values of the above defined parameters

The results obtained by varying the depth (from 1 to 3m)of a square target (3m times 3m) are shown in Figure 6 In ahomogeneous medium (120588 = 100Ωm) a resistive (1000ΩmFigure 6(a)) or conductive (10Ωm Figure 6(b)) squaredprism is placed under the profile at varying depths Theresolution and the contrast of the obtained image obviouslydecrease with depth As a consequence the anomalous bodyis still recognizable until a depth of about 25m

Figure 7 shows the tomographic images obtained startingfrom square-sized targets inwhich the resistivity of the targets

varies from 2Ωm to 5000Ωm In cases of very low resistivitythe tomographic shape does not fit the real shape Thecorrelation between the tomographic images and the modelsincreases with the resistivity of the target Specifically thedifference between the real top of the target and the estimatedone decreases

Finally the results of a more complex model are shownApparent resistivity measures were simulated starting from amodel consisting of four prisms of different shapes and resis-tivities buried in a homogeneous medium Figure 8 showsa comparison between back-projection using transposedmatrix B (Figure 8(a)) the image obtained by the techniquehere proposed using a damped least-squares solution of

International Journal of Geophysics 7

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(a)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(b)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(c)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

(d)

Figure 8 Back-projection fast imaging and inversions on datasimulated starting from amodel with four prisms of different shapesand resistivities (resp 1000Ωm the resistive ones and 10Ωm theconductive ones) buried in a homogeneous medium (100Ωm) Acomparison ismade between the back-projection obtained using thetransposed of matrix B (a) the image obtained by a damped least-squares solution of the filtered sensitivity matrix (b) the standardleast-squares constrain inversion (c) and robust data constraininversion (d) The color scales are the same

the filtered sensitivity matrix (Figure 8(b)) and two inver-sions carried out using the RES2DINV software respectivelywith a standard least-squares constrain (Figure 8(c)) andwith a robust data constrain algorithm (Figure 8(d)) Resultsof back-projections are strongly smoothed and dependenton the lateral position of the anomalous body in respectof the section Furthermore the resistivity contrast is verylow if compared to the real one Instead the damped least-squares solution of the filtered sensitivity matrix allowsa less smoothed and more accurate representation of thetargets which show higher resistivity contrasts and morecorrect shapes especially if referred to the resistive targets

The resistivity range showed is considerablywider than that ofthe back-projection and it is near the range of values obtainedin the inversions Nonuniqueness involved in standard least-squares constrain procedure implies that invertedmodels canpresent artifacts linked to the choice of inversion parametersThe image obtained by the damped least-squares solution ofthe filtered sensitivity matrix is instead less influenced bythe choice of parameters and does not produce significantartifacts

5 Test on Experimental Measures

The reliability of the proposed method was tested in severalarchaeological and environmental casesThe results of two ofthese are discussed below

Figure 9 shows a test on a set of geoelectrical measurescarried out on the plane of Himera [22] to detect buriedarcheological structures A 2D dipole-dipole resistivity sur-vey was carried out using 64 electrodes spaced 05m apartand with order 119899 from 1 to 9

ERT results showed clear resistive localized anomalieswhich are connected with wall-like relicsThis was confirmedby an archeological excavation near the profile in which thestructure of a building in line with geoelectrical anomalieswas located In fact the survey direction was perpendicularto that of the buried archaeological structures Furthermorethe low background resistivity values shown by the inversionwere interpreted as representing river deposits having differ-ent moisture characteristics

The comparison between the fast imaging and the robustinversion shows that the structures detected by the fastimaging technique have very similar shapes to those of theinversion

The second case regards an area on the outskirts ofMarsala (Western Sicily) where many sandstone quarries arepresent [23] some of which are abandoned In this area themain outcropping formation is the Calcarenite di Marsalawhich has been exploited for a long time as building stone

A geophysical model of the subsoil was designed usingdetailed geological information and the geometrical shapesof some galleries that were physically investigated Thisallowed us to compare synthetic and experimental dataIn the survey here presented the filtered Jacobian dampedLSQR model shows three resistive anomalies correspondingto three buried tunnels one of which was actually inspectedIn Figure 10 the grey lines represent the positions and theshapes of the galleries The fast imaging model (Figure 10(a))shows three resistive anomalies in correspondence with thegalleries even though it shows a lower resistivity contrast andsmoother boundaries compared with the inversion model(Figure 10(b))

6 Conclusions

An in-depth discussion on this topic involves taking intoconsideration not only the type of synthetic andor real(sharp or smooth boundary) model to be used but alsothe equivalence problem which is always relevant However

8 International Journal of Geophysics

21

3 4

A998400A

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

201000

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1 2 34

(m)

(Ωm)

A998400A

(b)

1000

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

1 2 3 4

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

(m) A998400A

(Ωm)

(c)

Figure 9 Results of a dipole-dipole survey carried out on the plane of Himera to detect buried archeological structures (a) Map of thearchaeological excavation (the black arrow indicates the position of the survey) (b) Filtered Jacobian damped LSQR imaging (c) Standardleast-squares constrain inversion The black numbers indicate some resistive localized anomalies which are well related to wall-like relics(red numbers)

0 5 10 15 20 25 30 35 40 45 50

10

5

0

x (m)

z(m

)

1500 1750 2000 2250 2500 2750 3000(Ωm)

(a)

0 5 10 15 20 25 30 35 40 45 50

10

5

0

x (m)

z(m

)

1500 1750 2000 2250 2500 2750 3000(Ωm)

(b)

Figure 10 Results of the geoelectrical survey carried out on the test site of Marsala (Italy) (a) filtered Jacobian damped LSQR imaging (b)standard least-squares constrain inversion The superimposed black lines represent the real shapes of the tunnels

the simulations and field data here presented stress thatthe filtered Jacobian damped LSQR imaging can be a validtool when looking for a fast approach to the tomographicrepresentation of geoelectrical data

The modification of the back-projection equation pro-posed above indeed leads to tomographic images that havehigher resistivity contrasts than those obtained using stan-dard back-projection methods Furthermore filtering of thesensitivity matrix with the correlation filter proposed andtested above reduces smoothness in the final tomographicrepresentation

The values chosen for the parameters of the filtered Jaco-bian damped LSQR imaging (a damping parameter value 120582 asymp

003 in the first matrix inversion and a correction parameter120594 asymp 5 in the filtering procedure) worked sufficiently wellwith both synthetic and field data In all those cases where

sharp-boundary models were sufficiently representative (ietunnels voids archaeological remains etc) the procedurehere presented seemed to be efficient enough to give reliableimages of the subsoil

Further simulations on noised data (not presented in thispaper) showed that back-projected images are not particu-larly influenced by noise In fact they tend to highlight onlythe main structures while masking small anomalies that areprobably caused by noise

In conclusion the quickness of the technique togetherwith its almost total independence from choice of parametersand from data noise suggests that proposed procedurecan be a useful as well as a fast technique of approxi-mate image reconstruction It can therefore be carried outdirectly in the field for a first and fast preliminary resultFurthermore these could be used as a startingmodel instead

International Journal of Geophysics 9

of the homogenous model or the pseudosection to constrainthe inversion procedure

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D Patella ldquoIntroduction to ground surface self-potentialtomographyrdquo Geophysical Prospecting vol 45 no 4 pp 653ndash681 1997

[2] P Mauriello and D Patella ldquoResistivity anomaly imaging byprobability tomographyrdquo Geophysical Prospecting vol 47 no 3pp 411ndash429 1999

[3] P Cosentino D Luzio RMartorana and L Terranova ldquoTomo-graphic techniques for pseudo-section representationrdquo in Pro-ceedings of the 1st Meeting of Environmental and EngineeringGeophysical Society pp 485ndash488 Turin Italy 1995

[4] P Cosentino and D Luzio ldquoTomographic pseudo-inversion ofresistivity profilesrdquo Annali di Geofisica vol 40 no 5 pp 1127ndash1144 1997

[5] P Cosentino D Luzio and R Martorana ldquoTomographic resis-tivity 3D mapping filter coefficients and depth correctionrdquo inProceedings of the 4thMeeting of Environmental and EngineeringGeophysical Society pp 279ndash282 European Section BarcelonaSpain 1998

[6] A Roy andAApparao ldquoDepth of investigation in direct currentmethodsrdquo Geophysics vol 36 no 5 pp 943ndash959 1971

[7] D B Geselowitz ldquoAn application of electrocardiographic leadtheory to impedance plethysmographyrdquo IEEE Transactions onBiomedical Engineering vol 18 no 1 pp 38ndash41 1971

[8] D C Barber andA D Seagar ldquoFast reconstruction of resistanceimagesrdquo Clinical Physics and Physiological Measurement vol 8supplement A pp 47ndash54 1987

[9] M Noel and B Xu ldquoArchaeological investigation by electricalresistivity tomography a preliminary studyrdquo Geophysical Jour-nal International vol 107 no 1 pp 95ndash102 1991

[10] C C Barber B H Brown and I L Freeston ldquoImaging spatialdistributions of resistivity using applied potential tomographyrdquoElectronics Letters vol 19 no 22 pp 933ndash935 1983

[11] D C Barber andBH Brown ldquoErrors in reconstruction of resis-tivity images using a linear reconstruction techniquerdquo ClinicalPhysics and Physiological Measurement vol 9 supplement App 101ndash104 1988

[12] D C Barber ldquoImage reconstruction in applied potentialtomographymdashelectrical impedance tomographyrdquo InternalReport Department of Medical Physics and ClinicalEngineering University of Sheffield 1990

[13] C J Kotre ldquoA sensitivity coefficient method for the reconstruc-tion of electrical impedance tomogramsrdquo Clinical Physics andPhysiological Measurement vol 10 no 3 pp 275ndash281 1989

[14] C J Kotre ldquoEIT image reconstruction using sensitivityweighted filtered back-projectionrdquo Physiological Measurementvol 15 supplement 2 pp A125ndashA136 1994

[15] H Shima and T Sakayama ldquoResistivity tomography anapproach to 2-D resistivity inverse problemsrdquo in Proceedingsof the 57th Annual International Meeting Society of ExplorationGeophysicists Expanded Abstracts pp 204ndash207 1987

[16] P R McGillivray and D W Oldenburg ldquoMethods for calcu-lating Frechet derivatives and sensitivities for the non-linearinverse problem a comparative studyrdquo Geophysical Prospectingvol 38 no 5 pp 499ndash524 1990

[17] M H Loke and R D Barker ldquoLeast-squares deconvolution ofapparent resistivity pseudosectionsrdquo Geophysics vol 60 no 6pp 1682ndash1690 1995

[18] H Shima ldquo2-D and 3-D resistivity image reconstruction usingcrosshole datardquo Geophysics vol 57 no 10 pp 1270ndash1281 1992

[19] W Menke Geophysical Data Analysis Discrete Inverse TheoryAcademic Press New York NY USA 1989

[20] Y L Yaoguo Li and D W Oldenburg ldquoApproximate inversemappings in DC resistivity problemsrdquo Geophysical JournalInternational vol 109 no 2 pp 343ndash362 1992

[21] H Dehghani D C Barber and I Basarab-Horwath ldquoIncor-porating a priori anatomical information into image recon-struction in electrical impedance tomographyrdquo PhysiologicalMeasurement vol 20 no 1 pp 87ndash102 1999

[22] P Capizzi P L Cosentino G Fiandaca R Martorana PMessina and S Vassallo ldquoGeophysical investigations at theHimera archaeological site northern Sicilyrdquo Near Surface Geo-physics vol 5 no 6 pp 417ndash426 2007

[23] P Capizzi P L Cosentino G Fiandaca R Martorana and PMessina ldquo2D GPR and geoelectrical modelling tests on man-made tunnels and cavitiesrdquo in Proceedings of the 11th EuropeanMeeting of Environmental and Engineering Geophysics B036Near Surface Palermo Italy 2005

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

4 International Journal of Geophysics

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

10 15 20 25 30 35

N(120588a)

N(120588)

120588amin 120588min120588amax120588max(Ωm)

Figure 3 Pattern of the normalizing119873(120588119890) function applied to a setof apparent resistivity values and to the corresponding set of first-step resistivity values

0010203040506070809

1

0 01 02 03 04 05 06 07 08 09 1High correlation Low correlation

120594 = 50120594 = 20

120594 = 10 120594 = 8

120594 = 5

120594 = 3

120594 = 2

120594 = 1

120594 = 05

120594 = 01

|N(120588) minus N(120588a )|

Φ(120588a120588)

Figure 4 Pattern of filtering function Φ at different values ofparameter 120594

diagonal matrix of the same size as [BTB] In this way thesquare matrix [BTB] is regularized to obtain an approximatesolution

For a nonzero value of 120582 an inverse can be calculatedalthough its condition number and hence the stability of theinversion depend on the value of damping factor 120582 for largevalues the image obtained can result as being too smooth andblurred however if 120582 is too small inversion can produce verynoisy images

Figure 2 shows the results of the one-step damped least-square inversion of synthetic data calculated for a modelhaving two square bodies with resistivity equal to 1000Ωmburied at different depths in a homogeneous medium of100Ωm resistivity Synthetic tests showed that for 120582 le

001 the back-projected images were generally noised andfurthermore artifacts are present due to the instability of theprocess As 120582 increases noise attenuates while the resistivitygradient decreases Therefore if damping is too high (120582 ge

01) the image becomes too smooth and blurred All thesynthetic tests carried out with 2D data suggested that a goodcompromise for 2D inversions is to choose 120582 asymp 003

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

minus2

minus4

minus6

minus8

(a)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

minus2

minus4

minus6

minus8

(b)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

minus2

minus4

minus6

minus8

60 80 100 120 140 160 180 200 220(Ωm)

(c)

Figure 5 Results of filtered Jacobian damped LSQR imagingobtained by varying correction parameter 120594 (a) 120594 = 05 (b) 120594 = 5and (c) 120594 = 50 The model is the same as that in Figure 2

33 Recalculation of the Sensitivity Matrix Using a Corre-lation Filter (Gradient Enhancing) The subsequent step ofthe imaging technique proposed is a recalculation of thesensitivity matrix B This is substituted by a matrix B1015840 inwhich each term is calculated by applying a correlation filter

1198611015840

119894119895= 119861119894119895 sdot Φ [120588119886119895 120588119895] (10)

The aim of filtering is to attenuate term 119861119894119895 linking the119894th voxel and the 119895th resistivity datum when the first-stepresistivity value of the 119894th voxel and the apparent resistivityvalue of the 119895th datum show a low correlation

In order to correctly estimate a correlation value betweendata sets of different kinds both sets of experimental data(apparent resistivities and first-step resistivities) are previ-ously normalized using the following normalizing function

119873(120588119890) = 2(ln 120588119890 minus ln 120588119890min

ln 120588119890max minus ln 120588119890min) minus 1 (11)

where 120588119890 is the datum (it can be 120588119886 or 120588) and 120588119890min and 120588119890maxare respectively the minimum and the maximum values

Figure 3 shows the pattern of the normalizing function119873(120588119890) applied to a set of data measures and to the first-step

International Journal of Geophysics 5

15 20 25 30 35 40 45

x (m)z

(m)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

(a)

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

(b)

Figure 6 Results of filtered Jacobian dampedLSQR imaging obtained by varying the depth of an anomalous square body (a)A resistive squarebody (1000Ωm) in a homogeneous medium (100Ωm) and (b) a conductive square body (10Ωm) in a homogenous medium (100Ωm)

resistivity values In this way 119873(120588119890) ranges from minus1 (for aminimum resistivity) to 1 (for a maximum)

The filtering function Φ(120588119886 120588) is then defined as follows

Φ(120588119886 120588) = 119890minus120594(12)|119873(120588) minus119873(120588

119886)| (12)

where 120594 is a correction parameter that controls the grade ofattenuation of terms 119861119894119895

In this way Φ(120588119886 120588) varies from 119890minus120594 (if the correlation

between 120588119886 and 120588 is the lowest) to 1 (if the correlation is thehighest)

Figure 4 shows the pattern of the filtering function fordifferent values of parameter 120594The lower the correlation thelower is the value of Φ(120588119886 120588) (the attenuation being higher)Furthermore the higher the value of 120594 the higher is thegradient of attenuation

34 Inversion of the Filtered Matrix B1015840 Finally each sensitiv-ity coefficient is recalculated by means of (10) and using thedamped least-squares inversion now considering the filteredmatrix B1015840 instead of B

120588119899= 1205880 + [B1015840TB + 120582119865maxI]

minus1

B1015840T (120588a minus 1205880) (13)

In Figure 5 the influence of varying correction parameter120594 on the back-projection is shown The sharpness of thenew tomographic image depends on the value of correction

parameter 120594 generally if 120594 le 1 the image obtained isgenerally too smooth As 120594 increases the anomalous bodiesbecome more contrasted However when 120594 is greater than10 images become noised and the anomalies break down inseveral parts

All the synthetic tests carried out with 2D data suggestedthat a good compromise for 2D inversions is to choose 120594 asymp 5

In spite of the long presentation the four steps are in factvery quick to carry out when using an automatic procedurewith a simple notebook

4 Results of Some Tests on Synthetic Models

The procedure proposed was tested on synthetic dataobtained by simulating pseudosections of different arrayscarried out on several simple 2D discrete models All thesynthetic tests stressed that the estimated shapes depths andresistivity contrasts of the anomalous bodies depend on thekind of array used Results seem to suggest that the bestestimation is obtained by using the Wenner-Schlumbergerarray Hereafter only the results obtained using this latterarray will be discussed

For each model the minimum electrode distance wasfixed at 1m and apparent resistivity measures were calculatedconsidering that order 119899 varied between 1 and 10 and that thepotential electrode distance MN was equal to 1 2 and 3m

6 International Journal of Geophysics

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

120588 = 2Ωm

120588 = 10Ωm

120588 = 20Ωm

120588 = 50Ωm

120588 = 80Ωm

120588 = 120Ωm

120588 = 200Ωm

120588 = 500Ωm

120588 = 1000Ωm

120588 = 5000Ωm

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

Figure 7 Results of filtered Jacobian damped LSQR imaging obtained by varying the resistivity of an anomalous square body buried in ahomogeneous medium (100Ωm) from 2Ωm to 5000Ωm

Several tests were carried out by changing the dimen-sions the position and the depth of the targets and by varyingthe values of the above defined parameters

The results obtained by varying the depth (from 1 to 3m)of a square target (3m times 3m) are shown in Figure 6 In ahomogeneous medium (120588 = 100Ωm) a resistive (1000ΩmFigure 6(a)) or conductive (10Ωm Figure 6(b)) squaredprism is placed under the profile at varying depths Theresolution and the contrast of the obtained image obviouslydecrease with depth As a consequence the anomalous bodyis still recognizable until a depth of about 25m

Figure 7 shows the tomographic images obtained startingfrom square-sized targets inwhich the resistivity of the targets

varies from 2Ωm to 5000Ωm In cases of very low resistivitythe tomographic shape does not fit the real shape Thecorrelation between the tomographic images and the modelsincreases with the resistivity of the target Specifically thedifference between the real top of the target and the estimatedone decreases

Finally the results of a more complex model are shownApparent resistivity measures were simulated starting from amodel consisting of four prisms of different shapes and resis-tivities buried in a homogeneous medium Figure 8 showsa comparison between back-projection using transposedmatrix B (Figure 8(a)) the image obtained by the techniquehere proposed using a damped least-squares solution of

International Journal of Geophysics 7

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(a)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(b)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(c)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

(d)

Figure 8 Back-projection fast imaging and inversions on datasimulated starting from amodel with four prisms of different shapesand resistivities (resp 1000Ωm the resistive ones and 10Ωm theconductive ones) buried in a homogeneous medium (100Ωm) Acomparison ismade between the back-projection obtained using thetransposed of matrix B (a) the image obtained by a damped least-squares solution of the filtered sensitivity matrix (b) the standardleast-squares constrain inversion (c) and robust data constraininversion (d) The color scales are the same

the filtered sensitivity matrix (Figure 8(b)) and two inver-sions carried out using the RES2DINV software respectivelywith a standard least-squares constrain (Figure 8(c)) andwith a robust data constrain algorithm (Figure 8(d)) Resultsof back-projections are strongly smoothed and dependenton the lateral position of the anomalous body in respectof the section Furthermore the resistivity contrast is verylow if compared to the real one Instead the damped least-squares solution of the filtered sensitivity matrix allowsa less smoothed and more accurate representation of thetargets which show higher resistivity contrasts and morecorrect shapes especially if referred to the resistive targets

The resistivity range showed is considerablywider than that ofthe back-projection and it is near the range of values obtainedin the inversions Nonuniqueness involved in standard least-squares constrain procedure implies that invertedmodels canpresent artifacts linked to the choice of inversion parametersThe image obtained by the damped least-squares solution ofthe filtered sensitivity matrix is instead less influenced bythe choice of parameters and does not produce significantartifacts

5 Test on Experimental Measures

The reliability of the proposed method was tested in severalarchaeological and environmental casesThe results of two ofthese are discussed below

Figure 9 shows a test on a set of geoelectrical measurescarried out on the plane of Himera [22] to detect buriedarcheological structures A 2D dipole-dipole resistivity sur-vey was carried out using 64 electrodes spaced 05m apartand with order 119899 from 1 to 9

ERT results showed clear resistive localized anomalieswhich are connected with wall-like relicsThis was confirmedby an archeological excavation near the profile in which thestructure of a building in line with geoelectrical anomalieswas located In fact the survey direction was perpendicularto that of the buried archaeological structures Furthermorethe low background resistivity values shown by the inversionwere interpreted as representing river deposits having differ-ent moisture characteristics

The comparison between the fast imaging and the robustinversion shows that the structures detected by the fastimaging technique have very similar shapes to those of theinversion

The second case regards an area on the outskirts ofMarsala (Western Sicily) where many sandstone quarries arepresent [23] some of which are abandoned In this area themain outcropping formation is the Calcarenite di Marsalawhich has been exploited for a long time as building stone

A geophysical model of the subsoil was designed usingdetailed geological information and the geometrical shapesof some galleries that were physically investigated Thisallowed us to compare synthetic and experimental dataIn the survey here presented the filtered Jacobian dampedLSQR model shows three resistive anomalies correspondingto three buried tunnels one of which was actually inspectedIn Figure 10 the grey lines represent the positions and theshapes of the galleries The fast imaging model (Figure 10(a))shows three resistive anomalies in correspondence with thegalleries even though it shows a lower resistivity contrast andsmoother boundaries compared with the inversion model(Figure 10(b))

6 Conclusions

An in-depth discussion on this topic involves taking intoconsideration not only the type of synthetic andor real(sharp or smooth boundary) model to be used but alsothe equivalence problem which is always relevant However

8 International Journal of Geophysics

21

3 4

A998400A

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

201000

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1 2 34

(m)

(Ωm)

A998400A

(b)

1000

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

1 2 3 4

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

(m) A998400A

(Ωm)

(c)

Figure 9 Results of a dipole-dipole survey carried out on the plane of Himera to detect buried archeological structures (a) Map of thearchaeological excavation (the black arrow indicates the position of the survey) (b) Filtered Jacobian damped LSQR imaging (c) Standardleast-squares constrain inversion The black numbers indicate some resistive localized anomalies which are well related to wall-like relics(red numbers)

0 5 10 15 20 25 30 35 40 45 50

10

5

0

x (m)

z(m

)

1500 1750 2000 2250 2500 2750 3000(Ωm)

(a)

0 5 10 15 20 25 30 35 40 45 50

10

5

0

x (m)

z(m

)

1500 1750 2000 2250 2500 2750 3000(Ωm)

(b)

Figure 10 Results of the geoelectrical survey carried out on the test site of Marsala (Italy) (a) filtered Jacobian damped LSQR imaging (b)standard least-squares constrain inversion The superimposed black lines represent the real shapes of the tunnels

the simulations and field data here presented stress thatthe filtered Jacobian damped LSQR imaging can be a validtool when looking for a fast approach to the tomographicrepresentation of geoelectrical data

The modification of the back-projection equation pro-posed above indeed leads to tomographic images that havehigher resistivity contrasts than those obtained using stan-dard back-projection methods Furthermore filtering of thesensitivity matrix with the correlation filter proposed andtested above reduces smoothness in the final tomographicrepresentation

The values chosen for the parameters of the filtered Jaco-bian damped LSQR imaging (a damping parameter value 120582 asymp

003 in the first matrix inversion and a correction parameter120594 asymp 5 in the filtering procedure) worked sufficiently wellwith both synthetic and field data In all those cases where

sharp-boundary models were sufficiently representative (ietunnels voids archaeological remains etc) the procedurehere presented seemed to be efficient enough to give reliableimages of the subsoil

Further simulations on noised data (not presented in thispaper) showed that back-projected images are not particu-larly influenced by noise In fact they tend to highlight onlythe main structures while masking small anomalies that areprobably caused by noise

In conclusion the quickness of the technique togetherwith its almost total independence from choice of parametersand from data noise suggests that proposed procedurecan be a useful as well as a fast technique of approxi-mate image reconstruction It can therefore be carried outdirectly in the field for a first and fast preliminary resultFurthermore these could be used as a startingmodel instead

International Journal of Geophysics 9

of the homogenous model or the pseudosection to constrainthe inversion procedure

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D Patella ldquoIntroduction to ground surface self-potentialtomographyrdquo Geophysical Prospecting vol 45 no 4 pp 653ndash681 1997

[2] P Mauriello and D Patella ldquoResistivity anomaly imaging byprobability tomographyrdquo Geophysical Prospecting vol 47 no 3pp 411ndash429 1999

[3] P Cosentino D Luzio RMartorana and L Terranova ldquoTomo-graphic techniques for pseudo-section representationrdquo in Pro-ceedings of the 1st Meeting of Environmental and EngineeringGeophysical Society pp 485ndash488 Turin Italy 1995

[4] P Cosentino and D Luzio ldquoTomographic pseudo-inversion ofresistivity profilesrdquo Annali di Geofisica vol 40 no 5 pp 1127ndash1144 1997

[5] P Cosentino D Luzio and R Martorana ldquoTomographic resis-tivity 3D mapping filter coefficients and depth correctionrdquo inProceedings of the 4thMeeting of Environmental and EngineeringGeophysical Society pp 279ndash282 European Section BarcelonaSpain 1998

[6] A Roy andAApparao ldquoDepth of investigation in direct currentmethodsrdquo Geophysics vol 36 no 5 pp 943ndash959 1971

[7] D B Geselowitz ldquoAn application of electrocardiographic leadtheory to impedance plethysmographyrdquo IEEE Transactions onBiomedical Engineering vol 18 no 1 pp 38ndash41 1971

[8] D C Barber andA D Seagar ldquoFast reconstruction of resistanceimagesrdquo Clinical Physics and Physiological Measurement vol 8supplement A pp 47ndash54 1987

[9] M Noel and B Xu ldquoArchaeological investigation by electricalresistivity tomography a preliminary studyrdquo Geophysical Jour-nal International vol 107 no 1 pp 95ndash102 1991

[10] C C Barber B H Brown and I L Freeston ldquoImaging spatialdistributions of resistivity using applied potential tomographyrdquoElectronics Letters vol 19 no 22 pp 933ndash935 1983

[11] D C Barber andBH Brown ldquoErrors in reconstruction of resis-tivity images using a linear reconstruction techniquerdquo ClinicalPhysics and Physiological Measurement vol 9 supplement App 101ndash104 1988

[12] D C Barber ldquoImage reconstruction in applied potentialtomographymdashelectrical impedance tomographyrdquo InternalReport Department of Medical Physics and ClinicalEngineering University of Sheffield 1990

[13] C J Kotre ldquoA sensitivity coefficient method for the reconstruc-tion of electrical impedance tomogramsrdquo Clinical Physics andPhysiological Measurement vol 10 no 3 pp 275ndash281 1989

[14] C J Kotre ldquoEIT image reconstruction using sensitivityweighted filtered back-projectionrdquo Physiological Measurementvol 15 supplement 2 pp A125ndashA136 1994

[15] H Shima and T Sakayama ldquoResistivity tomography anapproach to 2-D resistivity inverse problemsrdquo in Proceedingsof the 57th Annual International Meeting Society of ExplorationGeophysicists Expanded Abstracts pp 204ndash207 1987

[16] P R McGillivray and D W Oldenburg ldquoMethods for calcu-lating Frechet derivatives and sensitivities for the non-linearinverse problem a comparative studyrdquo Geophysical Prospectingvol 38 no 5 pp 499ndash524 1990

[17] M H Loke and R D Barker ldquoLeast-squares deconvolution ofapparent resistivity pseudosectionsrdquo Geophysics vol 60 no 6pp 1682ndash1690 1995

[18] H Shima ldquo2-D and 3-D resistivity image reconstruction usingcrosshole datardquo Geophysics vol 57 no 10 pp 1270ndash1281 1992

[19] W Menke Geophysical Data Analysis Discrete Inverse TheoryAcademic Press New York NY USA 1989

[20] Y L Yaoguo Li and D W Oldenburg ldquoApproximate inversemappings in DC resistivity problemsrdquo Geophysical JournalInternational vol 109 no 2 pp 343ndash362 1992

[21] H Dehghani D C Barber and I Basarab-Horwath ldquoIncor-porating a priori anatomical information into image recon-struction in electrical impedance tomographyrdquo PhysiologicalMeasurement vol 20 no 1 pp 87ndash102 1999

[22] P Capizzi P L Cosentino G Fiandaca R Martorana PMessina and S Vassallo ldquoGeophysical investigations at theHimera archaeological site northern Sicilyrdquo Near Surface Geo-physics vol 5 no 6 pp 417ndash426 2007

[23] P Capizzi P L Cosentino G Fiandaca R Martorana and PMessina ldquo2D GPR and geoelectrical modelling tests on man-made tunnels and cavitiesrdquo in Proceedings of the 11th EuropeanMeeting of Environmental and Engineering Geophysics B036Near Surface Palermo Italy 2005

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

International Journal of Geophysics 5

15 20 25 30 35 40 45

x (m)z

(m)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

(a)

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45

x (m)

z(m

)

0

minus2

minus4

minus6

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

(b)

Figure 6 Results of filtered Jacobian dampedLSQR imaging obtained by varying the depth of an anomalous square body (a)A resistive squarebody (1000Ωm) in a homogeneous medium (100Ωm) and (b) a conductive square body (10Ωm) in a homogenous medium (100Ωm)

resistivity values In this way 119873(120588119890) ranges from minus1 (for aminimum resistivity) to 1 (for a maximum)

The filtering function Φ(120588119886 120588) is then defined as follows

Φ(120588119886 120588) = 119890minus120594(12)|119873(120588) minus119873(120588

119886)| (12)

where 120594 is a correction parameter that controls the grade ofattenuation of terms 119861119894119895

In this way Φ(120588119886 120588) varies from 119890minus120594 (if the correlation

between 120588119886 and 120588 is the lowest) to 1 (if the correlation is thehighest)

Figure 4 shows the pattern of the filtering function fordifferent values of parameter 120594The lower the correlation thelower is the value of Φ(120588119886 120588) (the attenuation being higher)Furthermore the higher the value of 120594 the higher is thegradient of attenuation

34 Inversion of the Filtered Matrix B1015840 Finally each sensitiv-ity coefficient is recalculated by means of (10) and using thedamped least-squares inversion now considering the filteredmatrix B1015840 instead of B

120588119899= 1205880 + [B1015840TB + 120582119865maxI]

minus1

B1015840T (120588a minus 1205880) (13)

In Figure 5 the influence of varying correction parameter120594 on the back-projection is shown The sharpness of thenew tomographic image depends on the value of correction

parameter 120594 generally if 120594 le 1 the image obtained isgenerally too smooth As 120594 increases the anomalous bodiesbecome more contrasted However when 120594 is greater than10 images become noised and the anomalies break down inseveral parts

All the synthetic tests carried out with 2D data suggestedthat a good compromise for 2D inversions is to choose 120594 asymp 5

In spite of the long presentation the four steps are in factvery quick to carry out when using an automatic procedurewith a simple notebook

4 Results of Some Tests on Synthetic Models

The procedure proposed was tested on synthetic dataobtained by simulating pseudosections of different arrayscarried out on several simple 2D discrete models All thesynthetic tests stressed that the estimated shapes depths andresistivity contrasts of the anomalous bodies depend on thekind of array used Results seem to suggest that the bestestimation is obtained by using the Wenner-Schlumbergerarray Hereafter only the results obtained using this latterarray will be discussed

For each model the minimum electrode distance wasfixed at 1m and apparent resistivity measures were calculatedconsidering that order 119899 varied between 1 and 10 and that thepotential electrode distance MN was equal to 1 2 and 3m

6 International Journal of Geophysics

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

120588 = 2Ωm

120588 = 10Ωm

120588 = 20Ωm

120588 = 50Ωm

120588 = 80Ωm

120588 = 120Ωm

120588 = 200Ωm

120588 = 500Ωm

120588 = 1000Ωm

120588 = 5000Ωm

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

Figure 7 Results of filtered Jacobian damped LSQR imaging obtained by varying the resistivity of an anomalous square body buried in ahomogeneous medium (100Ωm) from 2Ωm to 5000Ωm

Several tests were carried out by changing the dimen-sions the position and the depth of the targets and by varyingthe values of the above defined parameters

The results obtained by varying the depth (from 1 to 3m)of a square target (3m times 3m) are shown in Figure 6 In ahomogeneous medium (120588 = 100Ωm) a resistive (1000ΩmFigure 6(a)) or conductive (10Ωm Figure 6(b)) squaredprism is placed under the profile at varying depths Theresolution and the contrast of the obtained image obviouslydecrease with depth As a consequence the anomalous bodyis still recognizable until a depth of about 25m

Figure 7 shows the tomographic images obtained startingfrom square-sized targets inwhich the resistivity of the targets

varies from 2Ωm to 5000Ωm In cases of very low resistivitythe tomographic shape does not fit the real shape Thecorrelation between the tomographic images and the modelsincreases with the resistivity of the target Specifically thedifference between the real top of the target and the estimatedone decreases

Finally the results of a more complex model are shownApparent resistivity measures were simulated starting from amodel consisting of four prisms of different shapes and resis-tivities buried in a homogeneous medium Figure 8 showsa comparison between back-projection using transposedmatrix B (Figure 8(a)) the image obtained by the techniquehere proposed using a damped least-squares solution of

International Journal of Geophysics 7

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(a)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(b)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(c)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

(d)

Figure 8 Back-projection fast imaging and inversions on datasimulated starting from amodel with four prisms of different shapesand resistivities (resp 1000Ωm the resistive ones and 10Ωm theconductive ones) buried in a homogeneous medium (100Ωm) Acomparison ismade between the back-projection obtained using thetransposed of matrix B (a) the image obtained by a damped least-squares solution of the filtered sensitivity matrix (b) the standardleast-squares constrain inversion (c) and robust data constraininversion (d) The color scales are the same

the filtered sensitivity matrix (Figure 8(b)) and two inver-sions carried out using the RES2DINV software respectivelywith a standard least-squares constrain (Figure 8(c)) andwith a robust data constrain algorithm (Figure 8(d)) Resultsof back-projections are strongly smoothed and dependenton the lateral position of the anomalous body in respectof the section Furthermore the resistivity contrast is verylow if compared to the real one Instead the damped least-squares solution of the filtered sensitivity matrix allowsa less smoothed and more accurate representation of thetargets which show higher resistivity contrasts and morecorrect shapes especially if referred to the resistive targets

The resistivity range showed is considerablywider than that ofthe back-projection and it is near the range of values obtainedin the inversions Nonuniqueness involved in standard least-squares constrain procedure implies that invertedmodels canpresent artifacts linked to the choice of inversion parametersThe image obtained by the damped least-squares solution ofthe filtered sensitivity matrix is instead less influenced bythe choice of parameters and does not produce significantartifacts

5 Test on Experimental Measures

The reliability of the proposed method was tested in severalarchaeological and environmental casesThe results of two ofthese are discussed below

Figure 9 shows a test on a set of geoelectrical measurescarried out on the plane of Himera [22] to detect buriedarcheological structures A 2D dipole-dipole resistivity sur-vey was carried out using 64 electrodes spaced 05m apartand with order 119899 from 1 to 9

ERT results showed clear resistive localized anomalieswhich are connected with wall-like relicsThis was confirmedby an archeological excavation near the profile in which thestructure of a building in line with geoelectrical anomalieswas located In fact the survey direction was perpendicularto that of the buried archaeological structures Furthermorethe low background resistivity values shown by the inversionwere interpreted as representing river deposits having differ-ent moisture characteristics

The comparison between the fast imaging and the robustinversion shows that the structures detected by the fastimaging technique have very similar shapes to those of theinversion

The second case regards an area on the outskirts ofMarsala (Western Sicily) where many sandstone quarries arepresent [23] some of which are abandoned In this area themain outcropping formation is the Calcarenite di Marsalawhich has been exploited for a long time as building stone

A geophysical model of the subsoil was designed usingdetailed geological information and the geometrical shapesof some galleries that were physically investigated Thisallowed us to compare synthetic and experimental dataIn the survey here presented the filtered Jacobian dampedLSQR model shows three resistive anomalies correspondingto three buried tunnels one of which was actually inspectedIn Figure 10 the grey lines represent the positions and theshapes of the galleries The fast imaging model (Figure 10(a))shows three resistive anomalies in correspondence with thegalleries even though it shows a lower resistivity contrast andsmoother boundaries compared with the inversion model(Figure 10(b))

6 Conclusions

An in-depth discussion on this topic involves taking intoconsideration not only the type of synthetic andor real(sharp or smooth boundary) model to be used but alsothe equivalence problem which is always relevant However

8 International Journal of Geophysics

21

3 4

A998400A

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

201000

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1 2 34

(m)

(Ωm)

A998400A

(b)

1000

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

1 2 3 4

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

(m) A998400A

(Ωm)

(c)

Figure 9 Results of a dipole-dipole survey carried out on the plane of Himera to detect buried archeological structures (a) Map of thearchaeological excavation (the black arrow indicates the position of the survey) (b) Filtered Jacobian damped LSQR imaging (c) Standardleast-squares constrain inversion The black numbers indicate some resistive localized anomalies which are well related to wall-like relics(red numbers)

0 5 10 15 20 25 30 35 40 45 50

10

5

0

x (m)

z(m

)

1500 1750 2000 2250 2500 2750 3000(Ωm)

(a)

0 5 10 15 20 25 30 35 40 45 50

10

5

0

x (m)

z(m

)

1500 1750 2000 2250 2500 2750 3000(Ωm)

(b)

Figure 10 Results of the geoelectrical survey carried out on the test site of Marsala (Italy) (a) filtered Jacobian damped LSQR imaging (b)standard least-squares constrain inversion The superimposed black lines represent the real shapes of the tunnels

the simulations and field data here presented stress thatthe filtered Jacobian damped LSQR imaging can be a validtool when looking for a fast approach to the tomographicrepresentation of geoelectrical data

The modification of the back-projection equation pro-posed above indeed leads to tomographic images that havehigher resistivity contrasts than those obtained using stan-dard back-projection methods Furthermore filtering of thesensitivity matrix with the correlation filter proposed andtested above reduces smoothness in the final tomographicrepresentation

The values chosen for the parameters of the filtered Jaco-bian damped LSQR imaging (a damping parameter value 120582 asymp

003 in the first matrix inversion and a correction parameter120594 asymp 5 in the filtering procedure) worked sufficiently wellwith both synthetic and field data In all those cases where

sharp-boundary models were sufficiently representative (ietunnels voids archaeological remains etc) the procedurehere presented seemed to be efficient enough to give reliableimages of the subsoil

Further simulations on noised data (not presented in thispaper) showed that back-projected images are not particu-larly influenced by noise In fact they tend to highlight onlythe main structures while masking small anomalies that areprobably caused by noise

In conclusion the quickness of the technique togetherwith its almost total independence from choice of parametersand from data noise suggests that proposed procedurecan be a useful as well as a fast technique of approxi-mate image reconstruction It can therefore be carried outdirectly in the field for a first and fast preliminary resultFurthermore these could be used as a startingmodel instead

International Journal of Geophysics 9

of the homogenous model or the pseudosection to constrainthe inversion procedure

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D Patella ldquoIntroduction to ground surface self-potentialtomographyrdquo Geophysical Prospecting vol 45 no 4 pp 653ndash681 1997

[2] P Mauriello and D Patella ldquoResistivity anomaly imaging byprobability tomographyrdquo Geophysical Prospecting vol 47 no 3pp 411ndash429 1999

[3] P Cosentino D Luzio RMartorana and L Terranova ldquoTomo-graphic techniques for pseudo-section representationrdquo in Pro-ceedings of the 1st Meeting of Environmental and EngineeringGeophysical Society pp 485ndash488 Turin Italy 1995

[4] P Cosentino and D Luzio ldquoTomographic pseudo-inversion ofresistivity profilesrdquo Annali di Geofisica vol 40 no 5 pp 1127ndash1144 1997

[5] P Cosentino D Luzio and R Martorana ldquoTomographic resis-tivity 3D mapping filter coefficients and depth correctionrdquo inProceedings of the 4thMeeting of Environmental and EngineeringGeophysical Society pp 279ndash282 European Section BarcelonaSpain 1998

[6] A Roy andAApparao ldquoDepth of investigation in direct currentmethodsrdquo Geophysics vol 36 no 5 pp 943ndash959 1971

[7] D B Geselowitz ldquoAn application of electrocardiographic leadtheory to impedance plethysmographyrdquo IEEE Transactions onBiomedical Engineering vol 18 no 1 pp 38ndash41 1971

[8] D C Barber andA D Seagar ldquoFast reconstruction of resistanceimagesrdquo Clinical Physics and Physiological Measurement vol 8supplement A pp 47ndash54 1987

[9] M Noel and B Xu ldquoArchaeological investigation by electricalresistivity tomography a preliminary studyrdquo Geophysical Jour-nal International vol 107 no 1 pp 95ndash102 1991

[10] C C Barber B H Brown and I L Freeston ldquoImaging spatialdistributions of resistivity using applied potential tomographyrdquoElectronics Letters vol 19 no 22 pp 933ndash935 1983

[11] D C Barber andBH Brown ldquoErrors in reconstruction of resis-tivity images using a linear reconstruction techniquerdquo ClinicalPhysics and Physiological Measurement vol 9 supplement App 101ndash104 1988

[12] D C Barber ldquoImage reconstruction in applied potentialtomographymdashelectrical impedance tomographyrdquo InternalReport Department of Medical Physics and ClinicalEngineering University of Sheffield 1990

[13] C J Kotre ldquoA sensitivity coefficient method for the reconstruc-tion of electrical impedance tomogramsrdquo Clinical Physics andPhysiological Measurement vol 10 no 3 pp 275ndash281 1989

[14] C J Kotre ldquoEIT image reconstruction using sensitivityweighted filtered back-projectionrdquo Physiological Measurementvol 15 supplement 2 pp A125ndashA136 1994

[15] H Shima and T Sakayama ldquoResistivity tomography anapproach to 2-D resistivity inverse problemsrdquo in Proceedingsof the 57th Annual International Meeting Society of ExplorationGeophysicists Expanded Abstracts pp 204ndash207 1987

[16] P R McGillivray and D W Oldenburg ldquoMethods for calcu-lating Frechet derivatives and sensitivities for the non-linearinverse problem a comparative studyrdquo Geophysical Prospectingvol 38 no 5 pp 499ndash524 1990

[17] M H Loke and R D Barker ldquoLeast-squares deconvolution ofapparent resistivity pseudosectionsrdquo Geophysics vol 60 no 6pp 1682ndash1690 1995

[18] H Shima ldquo2-D and 3-D resistivity image reconstruction usingcrosshole datardquo Geophysics vol 57 no 10 pp 1270ndash1281 1992

[19] W Menke Geophysical Data Analysis Discrete Inverse TheoryAcademic Press New York NY USA 1989

[20] Y L Yaoguo Li and D W Oldenburg ldquoApproximate inversemappings in DC resistivity problemsrdquo Geophysical JournalInternational vol 109 no 2 pp 343ndash362 1992

[21] H Dehghani D C Barber and I Basarab-Horwath ldquoIncor-porating a priori anatomical information into image recon-struction in electrical impedance tomographyrdquo PhysiologicalMeasurement vol 20 no 1 pp 87ndash102 1999

[22] P Capizzi P L Cosentino G Fiandaca R Martorana PMessina and S Vassallo ldquoGeophysical investigations at theHimera archaeological site northern Sicilyrdquo Near Surface Geo-physics vol 5 no 6 pp 417ndash426 2007

[23] P Capizzi P L Cosentino G Fiandaca R Martorana and PMessina ldquo2D GPR and geoelectrical modelling tests on man-made tunnels and cavitiesrdquo in Proceedings of the 11th EuropeanMeeting of Environmental and Engineering Geophysics B036Near Surface Palermo Italy 2005

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

6 International Journal of Geophysics

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

15 20 25 30 35 40 45x (m)

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

z(m

)

0

minus2

minus4

minus6

120588 = 2Ωm

120588 = 10Ωm

120588 = 20Ωm

120588 = 50Ωm

120588 = 80Ωm

120588 = 120Ωm

120588 = 200Ωm

120588 = 500Ωm

120588 = 1000Ωm

120588 = 5000Ωm

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

Figure 7 Results of filtered Jacobian damped LSQR imaging obtained by varying the resistivity of an anomalous square body buried in ahomogeneous medium (100Ωm) from 2Ωm to 5000Ωm

Several tests were carried out by changing the dimen-sions the position and the depth of the targets and by varyingthe values of the above defined parameters

The results obtained by varying the depth (from 1 to 3m)of a square target (3m times 3m) are shown in Figure 6 In ahomogeneous medium (120588 = 100Ωm) a resistive (1000ΩmFigure 6(a)) or conductive (10Ωm Figure 6(b)) squaredprism is placed under the profile at varying depths Theresolution and the contrast of the obtained image obviouslydecrease with depth As a consequence the anomalous bodyis still recognizable until a depth of about 25m

Figure 7 shows the tomographic images obtained startingfrom square-sized targets inwhich the resistivity of the targets

varies from 2Ωm to 5000Ωm In cases of very low resistivitythe tomographic shape does not fit the real shape Thecorrelation between the tomographic images and the modelsincreases with the resistivity of the target Specifically thedifference between the real top of the target and the estimatedone decreases

Finally the results of a more complex model are shownApparent resistivity measures were simulated starting from amodel consisting of four prisms of different shapes and resis-tivities buried in a homogeneous medium Figure 8 showsa comparison between back-projection using transposedmatrix B (Figure 8(a)) the image obtained by the techniquehere proposed using a damped least-squares solution of

International Journal of Geophysics 7

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(a)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(b)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(c)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

(d)

Figure 8 Back-projection fast imaging and inversions on datasimulated starting from amodel with four prisms of different shapesand resistivities (resp 1000Ωm the resistive ones and 10Ωm theconductive ones) buried in a homogeneous medium (100Ωm) Acomparison ismade between the back-projection obtained using thetransposed of matrix B (a) the image obtained by a damped least-squares solution of the filtered sensitivity matrix (b) the standardleast-squares constrain inversion (c) and robust data constraininversion (d) The color scales are the same

the filtered sensitivity matrix (Figure 8(b)) and two inver-sions carried out using the RES2DINV software respectivelywith a standard least-squares constrain (Figure 8(c)) andwith a robust data constrain algorithm (Figure 8(d)) Resultsof back-projections are strongly smoothed and dependenton the lateral position of the anomalous body in respectof the section Furthermore the resistivity contrast is verylow if compared to the real one Instead the damped least-squares solution of the filtered sensitivity matrix allowsa less smoothed and more accurate representation of thetargets which show higher resistivity contrasts and morecorrect shapes especially if referred to the resistive targets

The resistivity range showed is considerablywider than that ofthe back-projection and it is near the range of values obtainedin the inversions Nonuniqueness involved in standard least-squares constrain procedure implies that invertedmodels canpresent artifacts linked to the choice of inversion parametersThe image obtained by the damped least-squares solution ofthe filtered sensitivity matrix is instead less influenced bythe choice of parameters and does not produce significantartifacts

5 Test on Experimental Measures

The reliability of the proposed method was tested in severalarchaeological and environmental casesThe results of two ofthese are discussed below

Figure 9 shows a test on a set of geoelectrical measurescarried out on the plane of Himera [22] to detect buriedarcheological structures A 2D dipole-dipole resistivity sur-vey was carried out using 64 electrodes spaced 05m apartand with order 119899 from 1 to 9

ERT results showed clear resistive localized anomalieswhich are connected with wall-like relicsThis was confirmedby an archeological excavation near the profile in which thestructure of a building in line with geoelectrical anomalieswas located In fact the survey direction was perpendicularto that of the buried archaeological structures Furthermorethe low background resistivity values shown by the inversionwere interpreted as representing river deposits having differ-ent moisture characteristics

The comparison between the fast imaging and the robustinversion shows that the structures detected by the fastimaging technique have very similar shapes to those of theinversion

The second case regards an area on the outskirts ofMarsala (Western Sicily) where many sandstone quarries arepresent [23] some of which are abandoned In this area themain outcropping formation is the Calcarenite di Marsalawhich has been exploited for a long time as building stone

A geophysical model of the subsoil was designed usingdetailed geological information and the geometrical shapesof some galleries that were physically investigated Thisallowed us to compare synthetic and experimental dataIn the survey here presented the filtered Jacobian dampedLSQR model shows three resistive anomalies correspondingto three buried tunnels one of which was actually inspectedIn Figure 10 the grey lines represent the positions and theshapes of the galleries The fast imaging model (Figure 10(a))shows three resistive anomalies in correspondence with thegalleries even though it shows a lower resistivity contrast andsmoother boundaries compared with the inversion model(Figure 10(b))

6 Conclusions

An in-depth discussion on this topic involves taking intoconsideration not only the type of synthetic andor real(sharp or smooth boundary) model to be used but alsothe equivalence problem which is always relevant However

8 International Journal of Geophysics

21

3 4

A998400A

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

201000

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1 2 34

(m)

(Ωm)

A998400A

(b)

1000

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

1 2 3 4

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

(m) A998400A

(Ωm)

(c)

Figure 9 Results of a dipole-dipole survey carried out on the plane of Himera to detect buried archeological structures (a) Map of thearchaeological excavation (the black arrow indicates the position of the survey) (b) Filtered Jacobian damped LSQR imaging (c) Standardleast-squares constrain inversion The black numbers indicate some resistive localized anomalies which are well related to wall-like relics(red numbers)

0 5 10 15 20 25 30 35 40 45 50

10

5

0

x (m)

z(m

)

1500 1750 2000 2250 2500 2750 3000(Ωm)

(a)

0 5 10 15 20 25 30 35 40 45 50

10

5

0

x (m)

z(m

)

1500 1750 2000 2250 2500 2750 3000(Ωm)

(b)

Figure 10 Results of the geoelectrical survey carried out on the test site of Marsala (Italy) (a) filtered Jacobian damped LSQR imaging (b)standard least-squares constrain inversion The superimposed black lines represent the real shapes of the tunnels

the simulations and field data here presented stress thatthe filtered Jacobian damped LSQR imaging can be a validtool when looking for a fast approach to the tomographicrepresentation of geoelectrical data

The modification of the back-projection equation pro-posed above indeed leads to tomographic images that havehigher resistivity contrasts than those obtained using stan-dard back-projection methods Furthermore filtering of thesensitivity matrix with the correlation filter proposed andtested above reduces smoothness in the final tomographicrepresentation

The values chosen for the parameters of the filtered Jaco-bian damped LSQR imaging (a damping parameter value 120582 asymp

003 in the first matrix inversion and a correction parameter120594 asymp 5 in the filtering procedure) worked sufficiently wellwith both synthetic and field data In all those cases where

sharp-boundary models were sufficiently representative (ietunnels voids archaeological remains etc) the procedurehere presented seemed to be efficient enough to give reliableimages of the subsoil

Further simulations on noised data (not presented in thispaper) showed that back-projected images are not particu-larly influenced by noise In fact they tend to highlight onlythe main structures while masking small anomalies that areprobably caused by noise

In conclusion the quickness of the technique togetherwith its almost total independence from choice of parametersand from data noise suggests that proposed procedurecan be a useful as well as a fast technique of approxi-mate image reconstruction It can therefore be carried outdirectly in the field for a first and fast preliminary resultFurthermore these could be used as a startingmodel instead

International Journal of Geophysics 9

of the homogenous model or the pseudosection to constrainthe inversion procedure

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D Patella ldquoIntroduction to ground surface self-potentialtomographyrdquo Geophysical Prospecting vol 45 no 4 pp 653ndash681 1997

[2] P Mauriello and D Patella ldquoResistivity anomaly imaging byprobability tomographyrdquo Geophysical Prospecting vol 47 no 3pp 411ndash429 1999

[3] P Cosentino D Luzio RMartorana and L Terranova ldquoTomo-graphic techniques for pseudo-section representationrdquo in Pro-ceedings of the 1st Meeting of Environmental and EngineeringGeophysical Society pp 485ndash488 Turin Italy 1995

[4] P Cosentino and D Luzio ldquoTomographic pseudo-inversion ofresistivity profilesrdquo Annali di Geofisica vol 40 no 5 pp 1127ndash1144 1997

[5] P Cosentino D Luzio and R Martorana ldquoTomographic resis-tivity 3D mapping filter coefficients and depth correctionrdquo inProceedings of the 4thMeeting of Environmental and EngineeringGeophysical Society pp 279ndash282 European Section BarcelonaSpain 1998

[6] A Roy andAApparao ldquoDepth of investigation in direct currentmethodsrdquo Geophysics vol 36 no 5 pp 943ndash959 1971

[7] D B Geselowitz ldquoAn application of electrocardiographic leadtheory to impedance plethysmographyrdquo IEEE Transactions onBiomedical Engineering vol 18 no 1 pp 38ndash41 1971

[8] D C Barber andA D Seagar ldquoFast reconstruction of resistanceimagesrdquo Clinical Physics and Physiological Measurement vol 8supplement A pp 47ndash54 1987

[9] M Noel and B Xu ldquoArchaeological investigation by electricalresistivity tomography a preliminary studyrdquo Geophysical Jour-nal International vol 107 no 1 pp 95ndash102 1991

[10] C C Barber B H Brown and I L Freeston ldquoImaging spatialdistributions of resistivity using applied potential tomographyrdquoElectronics Letters vol 19 no 22 pp 933ndash935 1983

[11] D C Barber andBH Brown ldquoErrors in reconstruction of resis-tivity images using a linear reconstruction techniquerdquo ClinicalPhysics and Physiological Measurement vol 9 supplement App 101ndash104 1988

[12] D C Barber ldquoImage reconstruction in applied potentialtomographymdashelectrical impedance tomographyrdquo InternalReport Department of Medical Physics and ClinicalEngineering University of Sheffield 1990

[13] C J Kotre ldquoA sensitivity coefficient method for the reconstruc-tion of electrical impedance tomogramsrdquo Clinical Physics andPhysiological Measurement vol 10 no 3 pp 275ndash281 1989

[14] C J Kotre ldquoEIT image reconstruction using sensitivityweighted filtered back-projectionrdquo Physiological Measurementvol 15 supplement 2 pp A125ndashA136 1994

[15] H Shima and T Sakayama ldquoResistivity tomography anapproach to 2-D resistivity inverse problemsrdquo in Proceedingsof the 57th Annual International Meeting Society of ExplorationGeophysicists Expanded Abstracts pp 204ndash207 1987

[16] P R McGillivray and D W Oldenburg ldquoMethods for calcu-lating Frechet derivatives and sensitivities for the non-linearinverse problem a comparative studyrdquo Geophysical Prospectingvol 38 no 5 pp 499ndash524 1990

[17] M H Loke and R D Barker ldquoLeast-squares deconvolution ofapparent resistivity pseudosectionsrdquo Geophysics vol 60 no 6pp 1682ndash1690 1995

[18] H Shima ldquo2-D and 3-D resistivity image reconstruction usingcrosshole datardquo Geophysics vol 57 no 10 pp 1270ndash1281 1992

[19] W Menke Geophysical Data Analysis Discrete Inverse TheoryAcademic Press New York NY USA 1989

[20] Y L Yaoguo Li and D W Oldenburg ldquoApproximate inversemappings in DC resistivity problemsrdquo Geophysical JournalInternational vol 109 no 2 pp 343ndash362 1992

[21] H Dehghani D C Barber and I Basarab-Horwath ldquoIncor-porating a priori anatomical information into image recon-struction in electrical impedance tomographyrdquo PhysiologicalMeasurement vol 20 no 1 pp 87ndash102 1999

[22] P Capizzi P L Cosentino G Fiandaca R Martorana PMessina and S Vassallo ldquoGeophysical investigations at theHimera archaeological site northern Sicilyrdquo Near Surface Geo-physics vol 5 no 6 pp 417ndash426 2007

[23] P Capizzi P L Cosentino G Fiandaca R Martorana and PMessina ldquo2D GPR and geoelectrical modelling tests on man-made tunnels and cavitiesrdquo in Proceedings of the 11th EuropeanMeeting of Environmental and Engineering Geophysics B036Near Surface Palermo Italy 2005

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

International Journal of Geophysics 7

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(a)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(b)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

(c)

0 5 10 15 20 25 30 35

x (m)

z(m

)

0

2

4

6

20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

(Ωm)

(d)

Figure 8 Back-projection fast imaging and inversions on datasimulated starting from amodel with four prisms of different shapesand resistivities (resp 1000Ωm the resistive ones and 10Ωm theconductive ones) buried in a homogeneous medium (100Ωm) Acomparison ismade between the back-projection obtained using thetransposed of matrix B (a) the image obtained by a damped least-squares solution of the filtered sensitivity matrix (b) the standardleast-squares constrain inversion (c) and robust data constraininversion (d) The color scales are the same

the filtered sensitivity matrix (Figure 8(b)) and two inver-sions carried out using the RES2DINV software respectivelywith a standard least-squares constrain (Figure 8(c)) andwith a robust data constrain algorithm (Figure 8(d)) Resultsof back-projections are strongly smoothed and dependenton the lateral position of the anomalous body in respectof the section Furthermore the resistivity contrast is verylow if compared to the real one Instead the damped least-squares solution of the filtered sensitivity matrix allowsa less smoothed and more accurate representation of thetargets which show higher resistivity contrasts and morecorrect shapes especially if referred to the resistive targets

The resistivity range showed is considerablywider than that ofthe back-projection and it is near the range of values obtainedin the inversions Nonuniqueness involved in standard least-squares constrain procedure implies that invertedmodels canpresent artifacts linked to the choice of inversion parametersThe image obtained by the damped least-squares solution ofthe filtered sensitivity matrix is instead less influenced bythe choice of parameters and does not produce significantartifacts

5 Test on Experimental Measures

The reliability of the proposed method was tested in severalarchaeological and environmental casesThe results of two ofthese are discussed below

Figure 9 shows a test on a set of geoelectrical measurescarried out on the plane of Himera [22] to detect buriedarcheological structures A 2D dipole-dipole resistivity sur-vey was carried out using 64 electrodes spaced 05m apartand with order 119899 from 1 to 9

ERT results showed clear resistive localized anomalieswhich are connected with wall-like relicsThis was confirmedby an archeological excavation near the profile in which thestructure of a building in line with geoelectrical anomalieswas located In fact the survey direction was perpendicularto that of the buried archaeological structures Furthermorethe low background resistivity values shown by the inversionwere interpreted as representing river deposits having differ-ent moisture characteristics

The comparison between the fast imaging and the robustinversion shows that the structures detected by the fastimaging technique have very similar shapes to those of theinversion

The second case regards an area on the outskirts ofMarsala (Western Sicily) where many sandstone quarries arepresent [23] some of which are abandoned In this area themain outcropping formation is the Calcarenite di Marsalawhich has been exploited for a long time as building stone

A geophysical model of the subsoil was designed usingdetailed geological information and the geometrical shapesof some galleries that were physically investigated Thisallowed us to compare synthetic and experimental dataIn the survey here presented the filtered Jacobian dampedLSQR model shows three resistive anomalies correspondingto three buried tunnels one of which was actually inspectedIn Figure 10 the grey lines represent the positions and theshapes of the galleries The fast imaging model (Figure 10(a))shows three resistive anomalies in correspondence with thegalleries even though it shows a lower resistivity contrast andsmoother boundaries compared with the inversion model(Figure 10(b))

6 Conclusions

An in-depth discussion on this topic involves taking intoconsideration not only the type of synthetic andor real(sharp or smooth boundary) model to be used but alsothe equivalence problem which is always relevant However

8 International Journal of Geophysics

21

3 4

A998400A

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

201000

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1 2 34

(m)

(Ωm)

A998400A

(b)

1000

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

1 2 3 4

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

(m) A998400A

(Ωm)

(c)

Figure 9 Results of a dipole-dipole survey carried out on the plane of Himera to detect buried archeological structures (a) Map of thearchaeological excavation (the black arrow indicates the position of the survey) (b) Filtered Jacobian damped LSQR imaging (c) Standardleast-squares constrain inversion The black numbers indicate some resistive localized anomalies which are well related to wall-like relics(red numbers)

0 5 10 15 20 25 30 35 40 45 50

10

5

0

x (m)

z(m

)

1500 1750 2000 2250 2500 2750 3000(Ωm)

(a)

0 5 10 15 20 25 30 35 40 45 50

10

5

0

x (m)

z(m

)

1500 1750 2000 2250 2500 2750 3000(Ωm)

(b)

Figure 10 Results of the geoelectrical survey carried out on the test site of Marsala (Italy) (a) filtered Jacobian damped LSQR imaging (b)standard least-squares constrain inversion The superimposed black lines represent the real shapes of the tunnels

the simulations and field data here presented stress thatthe filtered Jacobian damped LSQR imaging can be a validtool when looking for a fast approach to the tomographicrepresentation of geoelectrical data

The modification of the back-projection equation pro-posed above indeed leads to tomographic images that havehigher resistivity contrasts than those obtained using stan-dard back-projection methods Furthermore filtering of thesensitivity matrix with the correlation filter proposed andtested above reduces smoothness in the final tomographicrepresentation

The values chosen for the parameters of the filtered Jaco-bian damped LSQR imaging (a damping parameter value 120582 asymp

003 in the first matrix inversion and a correction parameter120594 asymp 5 in the filtering procedure) worked sufficiently wellwith both synthetic and field data In all those cases where

sharp-boundary models were sufficiently representative (ietunnels voids archaeological remains etc) the procedurehere presented seemed to be efficient enough to give reliableimages of the subsoil

Further simulations on noised data (not presented in thispaper) showed that back-projected images are not particu-larly influenced by noise In fact they tend to highlight onlythe main structures while masking small anomalies that areprobably caused by noise

In conclusion the quickness of the technique togetherwith its almost total independence from choice of parametersand from data noise suggests that proposed procedurecan be a useful as well as a fast technique of approxi-mate image reconstruction It can therefore be carried outdirectly in the field for a first and fast preliminary resultFurthermore these could be used as a startingmodel instead

International Journal of Geophysics 9

of the homogenous model or the pseudosection to constrainthe inversion procedure

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D Patella ldquoIntroduction to ground surface self-potentialtomographyrdquo Geophysical Prospecting vol 45 no 4 pp 653ndash681 1997

[2] P Mauriello and D Patella ldquoResistivity anomaly imaging byprobability tomographyrdquo Geophysical Prospecting vol 47 no 3pp 411ndash429 1999

[3] P Cosentino D Luzio RMartorana and L Terranova ldquoTomo-graphic techniques for pseudo-section representationrdquo in Pro-ceedings of the 1st Meeting of Environmental and EngineeringGeophysical Society pp 485ndash488 Turin Italy 1995

[4] P Cosentino and D Luzio ldquoTomographic pseudo-inversion ofresistivity profilesrdquo Annali di Geofisica vol 40 no 5 pp 1127ndash1144 1997

[5] P Cosentino D Luzio and R Martorana ldquoTomographic resis-tivity 3D mapping filter coefficients and depth correctionrdquo inProceedings of the 4thMeeting of Environmental and EngineeringGeophysical Society pp 279ndash282 European Section BarcelonaSpain 1998

[6] A Roy andAApparao ldquoDepth of investigation in direct currentmethodsrdquo Geophysics vol 36 no 5 pp 943ndash959 1971

[7] D B Geselowitz ldquoAn application of electrocardiographic leadtheory to impedance plethysmographyrdquo IEEE Transactions onBiomedical Engineering vol 18 no 1 pp 38ndash41 1971

[8] D C Barber andA D Seagar ldquoFast reconstruction of resistanceimagesrdquo Clinical Physics and Physiological Measurement vol 8supplement A pp 47ndash54 1987

[9] M Noel and B Xu ldquoArchaeological investigation by electricalresistivity tomography a preliminary studyrdquo Geophysical Jour-nal International vol 107 no 1 pp 95ndash102 1991

[10] C C Barber B H Brown and I L Freeston ldquoImaging spatialdistributions of resistivity using applied potential tomographyrdquoElectronics Letters vol 19 no 22 pp 933ndash935 1983

[11] D C Barber andBH Brown ldquoErrors in reconstruction of resis-tivity images using a linear reconstruction techniquerdquo ClinicalPhysics and Physiological Measurement vol 9 supplement App 101ndash104 1988

[12] D C Barber ldquoImage reconstruction in applied potentialtomographymdashelectrical impedance tomographyrdquo InternalReport Department of Medical Physics and ClinicalEngineering University of Sheffield 1990

[13] C J Kotre ldquoA sensitivity coefficient method for the reconstruc-tion of electrical impedance tomogramsrdquo Clinical Physics andPhysiological Measurement vol 10 no 3 pp 275ndash281 1989

[14] C J Kotre ldquoEIT image reconstruction using sensitivityweighted filtered back-projectionrdquo Physiological Measurementvol 15 supplement 2 pp A125ndashA136 1994

[15] H Shima and T Sakayama ldquoResistivity tomography anapproach to 2-D resistivity inverse problemsrdquo in Proceedingsof the 57th Annual International Meeting Society of ExplorationGeophysicists Expanded Abstracts pp 204ndash207 1987

[16] P R McGillivray and D W Oldenburg ldquoMethods for calcu-lating Frechet derivatives and sensitivities for the non-linearinverse problem a comparative studyrdquo Geophysical Prospectingvol 38 no 5 pp 499ndash524 1990

[17] M H Loke and R D Barker ldquoLeast-squares deconvolution ofapparent resistivity pseudosectionsrdquo Geophysics vol 60 no 6pp 1682ndash1690 1995

[18] H Shima ldquo2-D and 3-D resistivity image reconstruction usingcrosshole datardquo Geophysics vol 57 no 10 pp 1270ndash1281 1992

[19] W Menke Geophysical Data Analysis Discrete Inverse TheoryAcademic Press New York NY USA 1989

[20] Y L Yaoguo Li and D W Oldenburg ldquoApproximate inversemappings in DC resistivity problemsrdquo Geophysical JournalInternational vol 109 no 2 pp 343ndash362 1992

[21] H Dehghani D C Barber and I Basarab-Horwath ldquoIncor-porating a priori anatomical information into image recon-struction in electrical impedance tomographyrdquo PhysiologicalMeasurement vol 20 no 1 pp 87ndash102 1999

[22] P Capizzi P L Cosentino G Fiandaca R Martorana PMessina and S Vassallo ldquoGeophysical investigations at theHimera archaeological site northern Sicilyrdquo Near Surface Geo-physics vol 5 no 6 pp 417ndash426 2007

[23] P Capizzi P L Cosentino G Fiandaca R Martorana and PMessina ldquo2D GPR and geoelectrical modelling tests on man-made tunnels and cavitiesrdquo in Proceedings of the 11th EuropeanMeeting of Environmental and Engineering Geophysics B036Near Surface Palermo Italy 2005

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

8 International Journal of Geophysics

21

3 4

A998400A

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

201000

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1 2 34

(m)

(Ωm)

A998400A

(b)

1000

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

1 2 3 4

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

(m) A998400A

(Ωm)

(c)

Figure 9 Results of a dipole-dipole survey carried out on the plane of Himera to detect buried archeological structures (a) Map of thearchaeological excavation (the black arrow indicates the position of the survey) (b) Filtered Jacobian damped LSQR imaging (c) Standardleast-squares constrain inversion The black numbers indicate some resistive localized anomalies which are well related to wall-like relics(red numbers)

0 5 10 15 20 25 30 35 40 45 50

10

5

0

x (m)

z(m

)

1500 1750 2000 2250 2500 2750 3000(Ωm)

(a)

0 5 10 15 20 25 30 35 40 45 50

10

5

0

x (m)

z(m

)

1500 1750 2000 2250 2500 2750 3000(Ωm)

(b)

Figure 10 Results of the geoelectrical survey carried out on the test site of Marsala (Italy) (a) filtered Jacobian damped LSQR imaging (b)standard least-squares constrain inversion The superimposed black lines represent the real shapes of the tunnels

the simulations and field data here presented stress thatthe filtered Jacobian damped LSQR imaging can be a validtool when looking for a fast approach to the tomographicrepresentation of geoelectrical data

The modification of the back-projection equation pro-posed above indeed leads to tomographic images that havehigher resistivity contrasts than those obtained using stan-dard back-projection methods Furthermore filtering of thesensitivity matrix with the correlation filter proposed andtested above reduces smoothness in the final tomographicrepresentation

The values chosen for the parameters of the filtered Jaco-bian damped LSQR imaging (a damping parameter value 120582 asymp

003 in the first matrix inversion and a correction parameter120594 asymp 5 in the filtering procedure) worked sufficiently wellwith both synthetic and field data In all those cases where

sharp-boundary models were sufficiently representative (ietunnels voids archaeological remains etc) the procedurehere presented seemed to be efficient enough to give reliableimages of the subsoil

Further simulations on noised data (not presented in thispaper) showed that back-projected images are not particu-larly influenced by noise In fact they tend to highlight onlythe main structures while masking small anomalies that areprobably caused by noise

In conclusion the quickness of the technique togetherwith its almost total independence from choice of parametersand from data noise suggests that proposed procedurecan be a useful as well as a fast technique of approxi-mate image reconstruction It can therefore be carried outdirectly in the field for a first and fast preliminary resultFurthermore these could be used as a startingmodel instead

International Journal of Geophysics 9

of the homogenous model or the pseudosection to constrainthe inversion procedure

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D Patella ldquoIntroduction to ground surface self-potentialtomographyrdquo Geophysical Prospecting vol 45 no 4 pp 653ndash681 1997

[2] P Mauriello and D Patella ldquoResistivity anomaly imaging byprobability tomographyrdquo Geophysical Prospecting vol 47 no 3pp 411ndash429 1999

[3] P Cosentino D Luzio RMartorana and L Terranova ldquoTomo-graphic techniques for pseudo-section representationrdquo in Pro-ceedings of the 1st Meeting of Environmental and EngineeringGeophysical Society pp 485ndash488 Turin Italy 1995

[4] P Cosentino and D Luzio ldquoTomographic pseudo-inversion ofresistivity profilesrdquo Annali di Geofisica vol 40 no 5 pp 1127ndash1144 1997

[5] P Cosentino D Luzio and R Martorana ldquoTomographic resis-tivity 3D mapping filter coefficients and depth correctionrdquo inProceedings of the 4thMeeting of Environmental and EngineeringGeophysical Society pp 279ndash282 European Section BarcelonaSpain 1998

[6] A Roy andAApparao ldquoDepth of investigation in direct currentmethodsrdquo Geophysics vol 36 no 5 pp 943ndash959 1971

[7] D B Geselowitz ldquoAn application of electrocardiographic leadtheory to impedance plethysmographyrdquo IEEE Transactions onBiomedical Engineering vol 18 no 1 pp 38ndash41 1971

[8] D C Barber andA D Seagar ldquoFast reconstruction of resistanceimagesrdquo Clinical Physics and Physiological Measurement vol 8supplement A pp 47ndash54 1987

[9] M Noel and B Xu ldquoArchaeological investigation by electricalresistivity tomography a preliminary studyrdquo Geophysical Jour-nal International vol 107 no 1 pp 95ndash102 1991

[10] C C Barber B H Brown and I L Freeston ldquoImaging spatialdistributions of resistivity using applied potential tomographyrdquoElectronics Letters vol 19 no 22 pp 933ndash935 1983

[11] D C Barber andBH Brown ldquoErrors in reconstruction of resis-tivity images using a linear reconstruction techniquerdquo ClinicalPhysics and Physiological Measurement vol 9 supplement App 101ndash104 1988

[12] D C Barber ldquoImage reconstruction in applied potentialtomographymdashelectrical impedance tomographyrdquo InternalReport Department of Medical Physics and ClinicalEngineering University of Sheffield 1990

[13] C J Kotre ldquoA sensitivity coefficient method for the reconstruc-tion of electrical impedance tomogramsrdquo Clinical Physics andPhysiological Measurement vol 10 no 3 pp 275ndash281 1989

[14] C J Kotre ldquoEIT image reconstruction using sensitivityweighted filtered back-projectionrdquo Physiological Measurementvol 15 supplement 2 pp A125ndashA136 1994

[15] H Shima and T Sakayama ldquoResistivity tomography anapproach to 2-D resistivity inverse problemsrdquo in Proceedingsof the 57th Annual International Meeting Society of ExplorationGeophysicists Expanded Abstracts pp 204ndash207 1987

[16] P R McGillivray and D W Oldenburg ldquoMethods for calcu-lating Frechet derivatives and sensitivities for the non-linearinverse problem a comparative studyrdquo Geophysical Prospectingvol 38 no 5 pp 499ndash524 1990

[17] M H Loke and R D Barker ldquoLeast-squares deconvolution ofapparent resistivity pseudosectionsrdquo Geophysics vol 60 no 6pp 1682ndash1690 1995

[18] H Shima ldquo2-D and 3-D resistivity image reconstruction usingcrosshole datardquo Geophysics vol 57 no 10 pp 1270ndash1281 1992

[19] W Menke Geophysical Data Analysis Discrete Inverse TheoryAcademic Press New York NY USA 1989

[20] Y L Yaoguo Li and D W Oldenburg ldquoApproximate inversemappings in DC resistivity problemsrdquo Geophysical JournalInternational vol 109 no 2 pp 343ndash362 1992

[21] H Dehghani D C Barber and I Basarab-Horwath ldquoIncor-porating a priori anatomical information into image recon-struction in electrical impedance tomographyrdquo PhysiologicalMeasurement vol 20 no 1 pp 87ndash102 1999

[22] P Capizzi P L Cosentino G Fiandaca R Martorana PMessina and S Vassallo ldquoGeophysical investigations at theHimera archaeological site northern Sicilyrdquo Near Surface Geo-physics vol 5 no 6 pp 417ndash426 2007

[23] P Capizzi P L Cosentino G Fiandaca R Martorana and PMessina ldquo2D GPR and geoelectrical modelling tests on man-made tunnels and cavitiesrdquo in Proceedings of the 11th EuropeanMeeting of Environmental and Engineering Geophysics B036Near Surface Palermo Italy 2005

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

International Journal of Geophysics 9

of the homogenous model or the pseudosection to constrainthe inversion procedure

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D Patella ldquoIntroduction to ground surface self-potentialtomographyrdquo Geophysical Prospecting vol 45 no 4 pp 653ndash681 1997

[2] P Mauriello and D Patella ldquoResistivity anomaly imaging byprobability tomographyrdquo Geophysical Prospecting vol 47 no 3pp 411ndash429 1999

[3] P Cosentino D Luzio RMartorana and L Terranova ldquoTomo-graphic techniques for pseudo-section representationrdquo in Pro-ceedings of the 1st Meeting of Environmental and EngineeringGeophysical Society pp 485ndash488 Turin Italy 1995

[4] P Cosentino and D Luzio ldquoTomographic pseudo-inversion ofresistivity profilesrdquo Annali di Geofisica vol 40 no 5 pp 1127ndash1144 1997

[5] P Cosentino D Luzio and R Martorana ldquoTomographic resis-tivity 3D mapping filter coefficients and depth correctionrdquo inProceedings of the 4thMeeting of Environmental and EngineeringGeophysical Society pp 279ndash282 European Section BarcelonaSpain 1998

[6] A Roy andAApparao ldquoDepth of investigation in direct currentmethodsrdquo Geophysics vol 36 no 5 pp 943ndash959 1971

[7] D B Geselowitz ldquoAn application of electrocardiographic leadtheory to impedance plethysmographyrdquo IEEE Transactions onBiomedical Engineering vol 18 no 1 pp 38ndash41 1971

[8] D C Barber andA D Seagar ldquoFast reconstruction of resistanceimagesrdquo Clinical Physics and Physiological Measurement vol 8supplement A pp 47ndash54 1987

[9] M Noel and B Xu ldquoArchaeological investigation by electricalresistivity tomography a preliminary studyrdquo Geophysical Jour-nal International vol 107 no 1 pp 95ndash102 1991

[10] C C Barber B H Brown and I L Freeston ldquoImaging spatialdistributions of resistivity using applied potential tomographyrdquoElectronics Letters vol 19 no 22 pp 933ndash935 1983

[11] D C Barber andBH Brown ldquoErrors in reconstruction of resis-tivity images using a linear reconstruction techniquerdquo ClinicalPhysics and Physiological Measurement vol 9 supplement App 101ndash104 1988

[12] D C Barber ldquoImage reconstruction in applied potentialtomographymdashelectrical impedance tomographyrdquo InternalReport Department of Medical Physics and ClinicalEngineering University of Sheffield 1990

[13] C J Kotre ldquoA sensitivity coefficient method for the reconstruc-tion of electrical impedance tomogramsrdquo Clinical Physics andPhysiological Measurement vol 10 no 3 pp 275ndash281 1989

[14] C J Kotre ldquoEIT image reconstruction using sensitivityweighted filtered back-projectionrdquo Physiological Measurementvol 15 supplement 2 pp A125ndashA136 1994

[15] H Shima and T Sakayama ldquoResistivity tomography anapproach to 2-D resistivity inverse problemsrdquo in Proceedingsof the 57th Annual International Meeting Society of ExplorationGeophysicists Expanded Abstracts pp 204ndash207 1987

[16] P R McGillivray and D W Oldenburg ldquoMethods for calcu-lating Frechet derivatives and sensitivities for the non-linearinverse problem a comparative studyrdquo Geophysical Prospectingvol 38 no 5 pp 499ndash524 1990

[17] M H Loke and R D Barker ldquoLeast-squares deconvolution ofapparent resistivity pseudosectionsrdquo Geophysics vol 60 no 6pp 1682ndash1690 1995

[18] H Shima ldquo2-D and 3-D resistivity image reconstruction usingcrosshole datardquo Geophysics vol 57 no 10 pp 1270ndash1281 1992

[19] W Menke Geophysical Data Analysis Discrete Inverse TheoryAcademic Press New York NY USA 1989

[20] Y L Yaoguo Li and D W Oldenburg ldquoApproximate inversemappings in DC resistivity problemsrdquo Geophysical JournalInternational vol 109 no 2 pp 343ndash362 1992

[21] H Dehghani D C Barber and I Basarab-Horwath ldquoIncor-porating a priori anatomical information into image recon-struction in electrical impedance tomographyrdquo PhysiologicalMeasurement vol 20 no 1 pp 87ndash102 1999

[22] P Capizzi P L Cosentino G Fiandaca R Martorana PMessina and S Vassallo ldquoGeophysical investigations at theHimera archaeological site northern Sicilyrdquo Near Surface Geo-physics vol 5 no 6 pp 417ndash426 2007

[23] P Capizzi P L Cosentino G Fiandaca R Martorana and PMessina ldquo2D GPR and geoelectrical modelling tests on man-made tunnels and cavitiesrdquo in Proceedings of the 11th EuropeanMeeting of Environmental and Engineering Geophysics B036Near Surface Palermo Italy 2005

Submit your manuscripts athttpwwwhindawicom

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ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in