Resistivity anomaly imaging by probability tomography, Paolo Mauriello and Domenico Patella

Resistivity anomaly imaging by probabilitytomography1

Paolo Mauriello2 and Domenico Patella3

Abstract

Probability tomography is a new concept reflecting the inherently uncertain nature ofany geophysical interpretation. The rationale of the new procedure is based on the factthat a measurable anomalous field, representing the response of a buried feature to aphysical stimulation, can be approximated by a set of partial anomaly sourcecontributions. These may be given a multiplicity of configurations to generatecumulative responses, which are all compatible with the observed data within theaccuracy of measurement. The purpose of the new imaging procedure is the design ofan occurrence probability space of elementary anomaly sources, located anywhereinside an explored underground volume. In geoelectrics, the decomposition is madewithin a regular resistivity lattice, using the Frechet derivatives of the electric potentialweighted by resistivity difference coefficients. The typical tomography is a diffuseimage of the resistivity difference probability pattern, that is quite different from theusual modelled geometry derived from standard inversion.

Introduction

In a recent paper, Mauriello, Monna and Patella (1998) extended to geoelectricmeasurements the principles of probability tomography, previously proposed byPatella (1997) for the self-potential (SP) method. This extension involved the chargeoccurrence probability concept, and the geoelectric tomography in effect consisted ofan image reconstruction of the most probable location of electrical charges induced bythe primary source over buried resistivity discontinuities. Numerous tests performedon synthetic examples and near-surface field data have demonstrated the efficiency ofthe tomography algorithm and the physical reliability of charge occurrence probabilityimaging in geoelectrics.

In this paper, we deal again with geoelectric probability tomography, consideringnow the resistivity parameter. With this new formulation we propose a patternrecognition method to investigate the most probable distribution of underground

q 1999 European Association of Geoscientists & Engineers 411

Geophysical Prospecting, 1999, 47, 411–429

1 Received March 1998, revision accepted December 1998.2 Institute of Technologies Applied to Cultural Heritage, National Research Council, Rome, Italy.3 Department of Physical Sciences, University ‘‘Federico II’’, Naples, Italy. E-mail: domenico.patella@

na.infn.it

resistivity anomalies. The present contribution thus complements the previousapproach by Mauriello et al. (1998). For simplicity, we limit the analysis to the 2Dgeoelectric pseudosection technique.

Resistivity probability tomography

The resistivity anomaly occurrence probability function

We consider a set of apparent resistivity data ra(,, n) (, ¼ 1, 2 . . , L; n ¼ 1, 2 . . , N),measured by any electrode device (pole–pole, pole–dipole, dipole–dipole, etc.) along astraight-line profile located on the free surface of an inhomogeneous, isotropicresistivity structure. Using the standard rules for pseudosection tracing, we assign thera(,, n) values to the nodes of a vertical 2D grid across the profile. At each node , is theposition along the x-axis, defining the profile, and n is the pseudodepth along thevertical z-axis, positive downwards (see Fig. 1).

We assume the whole portion of ground contributing to all of the measured ra(,, n)data to be composed of Q elementary cells with a sufficiently small volume DV, eachidentified by a true resistivity rq (q ¼ 1, 2 . . , Q). Expanding ra(,, n) in a Taylor series,we obtain

Drað,; nÞ ¼ rað,; nÞ ¹ ra;0ð,; nÞ

¼XQ

q¼1

∂ra;0ð,; nÞ

∂rqDrq þ

X(higher order derivatives); ð1Þ

where Dra(,, n) represents the difference of the measured apparent resistivity ra(,, n)from an apparent resistivity ra,0(,, n), computed at the same (,, n) node using areference model indicated by mod0. Drq is the difference between the actual resistivityin the qth cell and the resistivity in the same cell obtained using mod0.

Adopting the same scheme that was used to develop the electric charge occurrence

412 P. Mauriello and D. Patella

q 1999 European Association of Geoscientists & Engineers, Geophysical Prospecting, 47, 411–429

Figure 1. The dipole–dipole pseudosection profiling method.

probability tomography (Patella 1997; Mauriello et al. 1998), we now introduce apower function W, related to the apparent anomaly data function Dra(,, n) as follows:

W ¼XL

,¼1

XNn¼1

½Drað,; nÞÿ2: ð2Þ

Using the expansion (1), we extract from W the main contribution W 0, referred to asthe first-order derivative, given by

W 0 ¼XL

,¼1

XNn¼1

Drað,; nÞXQ

q¼1

∂ra;0ð,; nÞ

∂rqDrq; ð3Þ

which, rearranging the sums and putting

Iqð,; nÞ ¼ ∂ra;0ð,; nÞ=∂rq; ð4Þ

becomes

W 0 ¼XQ

q¼1

Drq

XL

, ¼1

XNn¼1

Drað,; nÞIqð,; nÞ: ð5Þ

Applying Schwarz’s inequality to a generic qth double sum in (5), we obtain

XL

,¼1

XNn¼1

Drað,; nÞIqð,; nÞ

" #2

#XL

, ¼1

XNn¼1

½Drað,; nÞÿ2·XL

,¼1

XNn¼1

½Iqð,; nÞÿ2: ð6Þ

Finally, dividing the square root of the left-hand term of (6) by the square root of thecorresponding right-hand term, we introduce the function

hq ¼ Cq

XL

,¼1

XNn¼1

Drað,; nÞIqð,; nÞ; ð7Þ

where

Cq ¼XL

,¼1

XNn¼1

½Drað,; nÞÿ2·XL

,¼1

XNn¼1

½Iqð,; nÞÿ2

" #¹1=2

: ð8Þ

It is easy to prove that the function hq satisfies the condition

¹1 # hq # þ1: ð9Þ

Each hq value is heuristically interpreted as the probability that a resistivity anomalylocated in the qth cell, deviating from mod0, is responsible for the whole set of measuredapparent resistivities, within the first-order expansion. Positive and negative values ofhq result from increments and decrements of resistivity in the qth cell with respect tomod0, respectively. We refer to hq as the resistivity anomaly occurrence probability(RAOP) function.

The RAOP function can be computed easily provided that the Jacobian matrix termIq(,, n) is assigned an explicit form, completely independent of grid resistivities. The

Resistivity anomaly imaging 413


only possibility of obtaining such a type of Iq(,, n) function is to assume mod0 tobe a homogeneous, isotropic half-space. In this case Iq(,, n) can be determinedanalytically, using the Frechet derivative of the electrical potential f, introducedby Loke and Barker (1995) following the theory developed by Park and Van(1991).

The resistivity probability tomography imaging

Using the RAOP function, the probability tomography imaging consists of a scanningprocedure operated by the test function Iq(,, n) on the field data set Dra(,, n), alongthe vertical section through the measuring profile.

Ideally, the procedure consists of moving a resistivity anomaly element of unitstrength through the cells of the lattice in order to recognize where resistivity deviationsfrom mod0 are located in a probabilistic sense. In each position of the scanning element,i.e. for each value of q, we calculate, by means of (7), the relative hq value, which isattributed to the centre of the cell where the scanning element is temporarily located. Aresistivity probability tomography image can finally be drawn by contouring or colourranging the whole set of computed hq values.

Of course, the most general approach is 3D, but the simplified 2D data acquisition isthe most frequently used procedure. Obviously, the 2D approach lacks off-profileresolution and the significance of the RAOP function decreases rapidly outside theprofile section.

The scanning function

For simplicity, we limit our analysis to the 2D pseudosection profiling technique,performed using a dipole–dipole electrode configuration (see Fig. 1). As stated above,the straight-line profile is assumed to be the x-axis of a plane rectangular coordinatesystem, where the vertical z-axis is positive downwards. The origin can be placedanywhere along the profile, e.g. coincident with the first current electrode position (seeFig. 1). Moreover, the dipole amplitude a is equal, in current practice, to the advancingstep along the profile.

The dipole–dipole apparent resistivity rDDa (,, n) is defined as

rDDa ð,; nÞ ¼

K DD

I,Dfð,; nÞ; ð10Þ

where (see Fig. 1) I, is the intensity of the primary current injected into the groundthrough the current electrodes A and B in the ,th and (, – 1)th positions, respectively,f is the electrical potential function and KDD is the dipole–dipole geometrical factor,computed by (Hanneson 1990) as

K DD ¼ panðn þ 1Þðn þ 2Þ: ð11Þ



The potential difference Df(,, n) is expanded as

Dfð,; nÞ ¼ fð,; n þ , Þ ¹ fð, ¹ 1; n þ ,Þ ¹ fð,; n þ , þ 1Þ þ fð, ¹ 1; n þ , þ 1Þ:

ð12Þ

Using the definitions (4), (10) and (12), the dipolar scanning function IDDq (,, n) can

be written in extended form as

IDDq ð,; nÞ ¼

K DD

I,

∂∂rq

½fð,; n þ ,Þ ¹ fð, ¹ 1; n þ , Þ

¹ fð,; n þ , þ 1Þ þ fð, ¹ 1; n þ , þ 1Þÿ: ð13Þ

The four Frechet derivatives are taken from Loke and Barker (1995) as follows:

∂fð,; n þ ,Þ

∂rq¼

I, DV4p2

×½xq ¹ ,aÿ½xq ¹ ðn þ ,Þaÿ þ y2

q þ z2q

f½xq ¹ ,aÿ2 þ y2q þ z2

qg3=2f½xq ¹ ðn þ , Þaÿ2 þ y2

q þ z2qg

3=2 ;

ð14Þ

∂fð, ¹ 1; n þ ,Þ

∂rq¼

I, DV4p2

×½xq ¹ ð, ¹ 1Þaÿ½xq ¹ ðn þ , Þaÿ þ y2

q þ z2q

f½xq ¹ð, ¹ 1Þaÿ2 þy2q þz2

qg3=2f½xq ¹ðn þ , Þaÿ2 þ y2

q þ z2qg

3=2 ;

ð15Þ

∂fð,; n þ , þ 1Þ

∂rq¼

I, DV4p2

×½xq ¹ ,aÿ½xq ¹ ðn þ , þ 1Þaÿ þ y2

q þ z2q

f½xq ¹ ,aÿ2 þ y2q þ z2

qg3=2f½xq ¹ ðn þ , þ 1Þaÿ2 þ y2

q þ z2qg

3=2 ;

ð16Þ

∂fð,¹1; nþ,þ1Þ

∂rq¼

I, DV4p2

×½xq ¹ ð, ¹ 1Þaÿ½xq ¹ ðn þ , þ 1Þaÿ þ y2

q þ z2q

f½xq ¹ð,¹1Þaÿ2 þy2q þz2

qg3=2f½xq ¹ðnþ,þ1Þaÿ2 þy2

q þz2qg

3=2 ;

ð17Þ

where xq, yq, zq are the coordinates of the barycentre of the cubic element with volumeDV and resistivity rq.



Discussion

The reference model

Even though the scanning function Iq(,, n) is independent of the resistivity of thereference homogeneous half-space, we still need to assign a value to this resistivity inorder to compute the data function Dra(,, n). A very reliable uniform resistivity can beeither the background true resistivity, if known, or simply the average apparentresistivity.

In this context, the resistivity anomaly concept has a purely relative meaning, since it,in effect, represents a departure from the selected reference resistivity. Therefore, theRAOP tomography is a ‘mod0-dependent’ method. None the less, we expect to find, inprinciple, a general consistency among all of the images deriving from different,plausible choices of mod0. These images would actually represent different, butequivalent, ways of looking at the same geoelectric structure. This aspect will beclarified below, during the presentation of a synthetic example.

The first-order contribution

The use of only the first-order contribution W 0 to the total power W, a function of theapparent resistivity anomaly function Dra(,, n), deserves further explanation for theversatility and potentiality of this new method to be fully appreciated.

Basically, the theoretical foundations of the probability tomography (Patella 1997)do not allow, in resistivity anomaly imaging, more than one derivative order of thera,0(,, n) function to be used simultaneously. If the Taylor series (1) of ra(,, n) hadbeen truncated at a derivative order higher than the first, it would have been impossiblefor the unknown resistivity departure coefficients Drq to disappear from the expressionof the hq function. The automatic cancellation of the unknown Drq multipliers is themost relevant characteristic of resistivity probability tomography imaging and is thereason why this new imaging method requires no firm guess about the resistivitydeparture coefficients Drq to be made in advance.

Of course, we are aware that any influence of one resistivity deviation over another iscompletely neglected in a first-order tomography and that a rather smooth image islikely to be the final result. In further work, we shall develop, separately, the power termW 00 related to the second-order derivatives. We will investigate the relevant informationwhich W 00 adds to the W 0 tomography and how, in a W 00 tomography, structuralinformation can be distinguished from high wavenumber noise.

Probability tomography versus inversion

From the conceptual point of view, a big difference exists between any of the currentresistivity inversion methods and our new probability tomography imaging.

Resistivity inversion is basically a deterministic approach, because ideally its strategyis to retrieve the true resistivity structure from a measured apparent resistivity data set.



However, in practice, a large number of equivalent solutions can be derived because ofdata inaccuracy and noise contamination. A priori information is essential for thechoice of the base model (Oldenburg, McGillivray and Ellis 1993). The a prioriinformation is also expected to reduce the drawbacks of non-uniqueness.

The tomography imaging described here is basically a linearized probabilisticapproach because its aim is to obtain the ‘occurrence probability’ of a resistivityanomaly anywhere in the volume under investigation. As demonstrated previously, thealgorithm does not require constraints on the unknown parameters. Moreover, anyhypothetical resistivity model, matching a measured apparent resistivity data set, ispotentially included, to a first-order approximation, within the probability tomographyimage corresponding to the given set. In our strategy, the available a priori informationis of no direct methodological value. It can eventually be used in a following phase tohelp interpret a geoelectric physical tomography in geological terms, if necessary.

Applications

Synthetic examples

In order to test the resolution power of the resistivity probability tomography, we firstdeal with the response of a synthetic model.

The model consists of three prismatic blocks having resistivities of 5, 10 and 500 Qm,buried in a uniform half-space of resistivity 100 Qm. Figure 2 shows the plan and cross-section of the three-prism model. Initially, we analyse the response of each prismseparately, and then the response of the combined three-prism model. The segmentAA0, indicated in Fig. 2, is the straight-line profile, across which the dipole–dipolepseudosection simulation was performed, using a dipolar spread and a sampling step,each of 5 m. A set of 200 apparent resistivity values were contoured to draw each of thesynthetic pseudosections shown in Fig. 3. Random noise (5%) affects every simulation.

The results from the resistivity probability tomographic imaging are shown in Fig. 4.The 100 Qm background resistivity was taken as the uniform resistivity of the referencehomogeneous half-space. The inverted V-shaped perturbing effects, typical of thistechnique, completely vanish with this tomographic filtering.

The first three tomographic sections in Fig. 4 show the three prisms analysedseparately. The tomographic images for these three simple cases are self-evident. Awell-contoured RAOP nucleus of congruent algebraic sign is obtained correspondingto the actual position of each block. Considering now the combined three-prism model,the following features can be seen in the RAOP tomography in Fig. 4d: (i) an intensenegative nucleus to the left, corresponding closely to the 5 Qm conductive body (Fig.4a); (ii) a central positive nucleus, easily ascribable to the 500 Qm resistive prism (Fig.4c); and (iii) a weak negative nucleus to the right, corresponding closely with thelocation of the 10 Qm conductive prism (Fig. 4b). In terms of resolution, this lastfeature is probably the most interesting result. Indeed, on the right-hand side ofthe original pseudosection (Fig. 3d), where the 10 Qm prism is located, the only





experimental evidence is a diffuse, weak apparent resistivity halo that can hardly beascribed to a buried feature.

We now consider the effects due to a change of the reference half-space uniformresistivity. As stated above, besides the background true resistivity, the averageapparent resistivity can also be used as a reliable reference resistivity. Of course, this isthe most obvious choice for the analysis of actual field data, when there is no indicationof which value should be attributed to the background true resistivity. In principle, wecould also take any apparent resistivity value as a reference half-space resistivity. Weanalyse all of these possibilities in order to verify to what extent an apparent resistivitydifference function Dra(,, n) can still be significant in this new probability tomographicmethod. Outside the interval of the measured apparent resistivity values, any otherreference resistivity would be an unrealistic assumption.

Figure 5 shows a sequence of RAOP tomographies, resulting from 13 differentreference values, selected every 10 Qm in the full apparent resistivity range 20–130 Qm,including the average apparent resistivity of 103.5 Qm. The previously discussedtomography, using the background resistivity of 100 Qm, is shown again in Fig. 5i. We

Figure 2. A synthetic three-prism resistivity model: (a) plan view, (b) cross-sectional view.



Figure 3. Dipole–dipole apparent resistivity pseudosections for (a) the prism with 5 Qmresistivity, (b) the prism with 10 Qm resistivity, (c) the prism with 500 Qm resistivity and (d) thecombined three-prism model. For location and size of the prisms, refer to Fig. 2.



Figure 4. Tomography images of the resistivity anomaly occurrence probability for (a) theprism with 5 Qm resistivity, (b) the prism with 10 Qm resistivity, (c) the prism with 500 Qmresistivity and (d) the combined three-prism model. For location and size of the prisms, referto Fig. 2.

observe that the RAOP tomography pattern of Fig. 5i is roughly the same as thatobtained using the average apparent resistivity (Fig. 5j), owing to the very smalldifference existing between the two resistivity values.

The RAOP tomography changes significantly if we consider the calculated



Figure 5. Tomography images of the resistivity anomaly occurrence probability for the three-prism model of Fig. 2, using as reference resistivity: (a) the minimum apparent resistivity 20 Qm,(b) 30 Qm, (c) 40 Qm, (d) 50 Qm, (e) 60 Qm, (f) 70 Qm, (g) 80 Qm, (h) 90 Qm, (i) thebackground true resistivity 100 Qm, (j) the average apparent resistivity 103.5 Qm, (k) 110 Qm, (l)120 Qm, and (m) the maximum apparent resistivity 130 Qm.

minimum and maximum apparent resistivities of 20 Qm and 130 Qm, respectively. Ascan be seen in Fig. 5a, in the first case the 10 Qm prism is the least resolved bodybecause of the vanishing resistivity contrast with the reference resistivity. The infinitelyextended background volume of resistivity 100 Qm becomes a positive resistivityanomaly that dominates the whole section. The appearance of the central, positiveRAOP nucleus demonstrates that the prism of resistivity 500 Qm is the best resolvedbody. The use of the maximum apparent resistivity of 130 Qm leads to almost a reverseconfiguration (Fig. 5m). The infinitely extended background body of resistivity100 Qm now becomes a negative resistivity anomaly that again dominates the wholesection. Nevertheless, two well-contoured, more negative, nuclei appear to originatefrom the two smaller prisms having the lowest true resistivities. Moreover, the existenceof the central resistive prism can be inferred from the visible distortion of the negativeisolines on both sides of the prism.

All the other tomographies provide a discrete spectrum of intermediate patterns. Weobserve a gradual transformation from one to the other extreme pattern, passingthrough the more resolved tomographies, corresponding to the true backgroundresistivity and the average apparent resistivity. Intuitively, we may state that the bestresolution derives from all those reference values that induce the largest density ofvanishing values of the hq function. This is usually true when the choice is thebackground resistivity of a large extended body, and is always true when the choice isthe average apparent resistivity.

In conclusion, we are now able to confirm the statement made previously about theexpected general equivalence of the various tomographies which can be processedusing different plausible resistivity values for the reference half-space. The imagesshown in Fig. 5 demonstrate that the physical information deriving from the RAOPtomographies has a basically invariant structure, despite the diversity of the images,obtained by changing the reference resistivity. The resolution can, however, bedifferent, because it depends on the amount of contrast between the referenceresistivity and the resistivity of a target body. The analysis made so far ultimatelyindicates that, within the limits of first-order tomography, the average apparentresistivity is the reference value leading to the most balanced resolution of all theexisting resistivity anomalies.

Field examples

We consider two field examples. The first example is an application to archaeology andthe second is an application to volcanology.

Archaeological applicationWe consider the same application dealt with in our previous paper (Mauriello et al.1998). This was the study of the response due to a hypogeal dromos-chamber tomblocated in the Sabine Necropolis at Colle del Forno, along the Tiberine Valley 30 kmnorth of Rome. Two zero-offset parallel straight-line profiles were planned there,





Figure 6. Archaeological application: (a) and (b) apparent resistivity pseudosections; (c) and (d)resistivity probability tomographies.

crossing almost perpendicularly an elongated morphological feature on the surface,very probably caused by the presence of a tomb. The two profiles were assumed tocross the entrance corridor (dromos) and the main body (chamber) of a tomb,respectively.

Figures 6a and b show the corresponding pseudosections, each obtained with a set of152 apparent resistivities measured with a constant dipole spacing of 0.5 m. The fielddata are taken from Cammarano et al. (1998). The first pseudosection (Fig. 6a) ischaracterized by a pronounced inverted V-shaped low-resistivity anomaly, while in thesecond pseudosection (Fig. 6b) a resistivity high appears to dominate the surveyedarea. A less well-defined inverted V-shaped effect and a resistivity low on the left-handside of the profile also characterize the second pseudosection.

Figures 6c and d show the probability tomographies across the two profiles. Auniform half-space with a background resistivity of 24 Qm has been assumed asmod0. This figure is known to represent the true resistivity of the dominatinggeological formation (lithoid tuff), hosting the Sabine Necropolis. In particular, thetomography of Fig. 6c, which corresponds to the pseudosection of Fig. 6a, ischaracterized by a well-contoured negative nucleus centred at about 1.2 m depth.Thus the probability of occurrence of a resistivity decrease below 24 Qm is veryhigh. Accounting for the position, shape, extension and sign of the nucleus, theinterpretation is that we may have detected the suspected dromos, provided that weassume its interior to be totally filled with conductive loose sediments. Actually, thisis a situation which has frequently been met during the exploration of many othertombs in the Sabine district. Accordingly, the tomography of Fig. 6d, whichcorresponds to the pseudosection of Fig. 6b, is characterized by an equally well-contoured positive nucleus appearing in the depth range from 1 to 2 m belowground level. Thus the probability of occurrence of a resistivity increase above24 Qm is very high. The larger vertical and horizontal extensions of the nucleuswould now suggest the existence of an empty cavity representing the originalchamber. Given also that the two inversely signed nuclei occupy the same positionalong the two parallel profiles, the probability that we may have detected a uniquewell-preserved dromos-chamber system is very high.

Finally, to justify the RAOP negative nucleus on the left-hand side of the tomographyof Fig. 6d, we assume that a second deeper chamber tomb with collapsed materialinside may have been detected. Since no evidence of the entrance corridor appears inthe tomography of Fig. 6c, the interpretation is that the dromos of this new suspectedtomb is probably located on the opposite side, i.e. along the opposite slope of theoblong hill, below which the whole necropolis was excavated.

Volcanological applicationWe consider now an application of the dipole–dipole geoelectric technique to the studyof the shallower plumbing system of La Fossa volcano on the island of Vulcano in theAeolian archipelago, Southern Italy.



The island of Vulcano was characterized in the past by intense explosive activity. Todate, the observed phenomena include the notable increase of temperature andemission rate of La Fossa crater fumaroles, indicating an increase in the flux of hot deepmagmatic gases (Barberi et al. 1991). In order to locate the shallow fracture systemthrough which the hot gases migrate upwards, several geoelectric profiles wereacquired at the base of La Fossa cone. We show the results obtained along one of theseprofiles, located as in Fig. 7, where a cyclic apparent resistivity time variation wasmeasured during approximately four years of observations, from 1992 to 1996. Duringthis period the chosen profile was measured 14 times at irregular sampling intervals,ranging from 1 to 10 months. Figure 8 shows the complete set of pseudosections,redrawn after Di Maio et al. (1997).



Figure 7. Volcanological application: the Vulcano island survey area.



In Fig. 8, an alternate sequence of apparent resistivity decrease and increase phases isclearly evident, especially in the central sector of the profile. In this sector, unusualvariations in the apparent resistivity were recorded at some points, of up to five ordersof magnitude, from values as low as 10 Qm to values as high as 105 Qm. To show theresistivity variations more clearly, each pseudosection is drawn with its own colourscale, which is not unique for the whole set, because the range of apparent resistivityvariation differs from one plot to another.

The observed apparent resistivity changes have led to the conclusion that a three-step cyclic mechanism, say ‘hot magmatic gas uprising/water-to-vapour transforma-tion/inland sea water recall’, would probably occur in this zone of intense secondaryvolcanic activity (Di Maio et al. 1997).

In order to improve the probability tomography images, a mod0 corresponding to theaverage apparent resistivity has been adopted, case by case. Figure 9 shows thecomplete set of tomographies corresponding to the pseudosections of Fig. 8. The mainevidence is the very neat migration dynamics of the RAOP high, which wouldcorrespond to the variable position of a gas-vapour-rich bubble during its ascenttowards the free surface, according to the above volcanological hypothesis. Moreover,the RAOP low, repeatedly occurring at the right-hand side of the profile, probablyindicates a sea-water recall inland, triggered by the pressure drop within the pores, leftempty behind the migrating bubble.

Conclusion

We have addressed the problem of geoelectric probability tomography by consideringthe resistivity parameter. Our purpose was to provide a simple tool for imagereconstruction of the most probable location of resistivity anomalies underground, inthe most objective way. The important aspect of the analysis developed above is thatthe resistivity signatures are considered only from a probabilistic viewpoint. This isquite a new concept in geophysics, which conforms to the inherently uncertain natureof the geophysical interpretation process.

To this end, it is worthwhile pointing out that the probability concept, introducedhere, is not the direct consequence of statistics performed on a set of repeatedmeasurements, representing the different responses of a simulated buried system in thepresence of varying sources of error. It is much more: it is the consequence of theintrinsic non-uniqueness of the geophysical solution. Thus the statistical basis consistsof many models providing, within the accuracy of measurement, equivalent responsesthat can in no way be distinguished from one another.



Figure 8. Volcanological application: apparent resistivity pseudosections, measured in (a) June1992, (b) April 1993, (c) September 1993, (d) November 1993, (e) December 1993, (f) April1994, (g) June 1994, (h) July 1994, (i) December 1994, (j) January 1995, (k) February 1995, (l)May 1995, (m) October 1995, (n) May 1996.

428P.M

aurielloand

D.P

atella

q1999

European

Association

ofG

eoscientists&

Engineers,G

eophysicalProspecting,47,411

–429 Figure 9. Volcanological application: resistivity probability tomographies. For the sequence of the tomosections from (a) to (n) refer to Fig. 8.

References

Barberi F., Neri G., Valenza M. and Villari L. 1991. 1987–1990 unrest at Vulcano. ActaVulcanologica 1, 95–106.

Cammarano F., Mauriello P., Patella D., Piro S., Rosso F. and Versino L. 1998. Integration ofhigh resolution geophysical methods. Detection of shallow depth bodies of archaeologicalinterest. Annali di Geofisica 41, 359–368.

Di Maio R., Mauriello P., Patella D., Petrillo Z., Piscitelli S., Siniscalchi A. and Veneruso M.1997. Self-potential, geoelectric and magnetotelluric studies in Italian active volcanic areas.Annali di Geofisica 40, 519–537.

Hanneson J.E. 1990. A model for interpreting IP/resistivity data from areas of steep dip and thinoverburden. In: Induced Polarization, Applications and Case Histories (eds J.P. Fink, E.O.McAlister, B.K. Stenberg, S.H. Ward and W.G. Wieduwilt). Series Investigation in Geophysics4, 128–149. SEG, Tulsa.

Loke M.H. and Barker R.D. 1995. Least-squares deconvolution of apparent resistivitypseudosections. Geophysics 60, 1682–1690.

Mauriello P., Monna D. and Patella D. 1998. 3D geoelectric tomography and archaeologicalapplications. Geophysical Prospecting 46, 543–570.

Oldenburg D.W., McGillivray P.R. and Ellis R.G. 1993. Generalized subspace methods forlarge-scale inverse problems. Geophysical Journal International 114, 12–20.

Park S.K. and Van G.P. 1991. Inversion of pole–pole data for 3D resistivity structure beneatharrays of electrodes. Geophysics 56, 951–960.

Patella D. 1997. Introduction to ground surface self-potential tomography. GeophysicalProspecting 45, 653–681.



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Resistivity anomaly imaging by probability tomography, Paolo Mauriello and Domenico Patella