Application of the 3D Magnetotelluric Inversion Code in a Geologically Complex Area

Geophysical Prospecting, 2010, 58, 1177–1192 doi: 10.1111/j.1365-2478.2010.00896.x

Application of the 3D magnetotelluric inversion code in a geologicallycomplex area

Qibin Xiao1∗, Xinping Cai2, Xingwang Xu2, Guanghe Liang2 and Baolin Zhang2

1Institute of Geology, China Earthquake Administration, Beijing 100029, China, and 2Institute of Geology and Geophysics, ChineseAcademy of Sciences, Beijing 100029, China

Received December 2008, revision accepted April 2010

ABSTRACTThe WSINV3DMT code makes the implementation of 3D inversion of magnetotel-luric data feasible using a single PC. Audio-magnetotelluric data were collected alongtwo profiles in a Cu-Ni mining area in Xinjiang, China, where the apparent resistiv-ity and phase curves, the phase tensors and the magnetic induction vectors indicate acomplex 3D conductivity structure. 3D inversions were carried out to reveal the elec-trical structure of the area. The final 3D model is selected from the inversion resultsusing different initial Lagrange values and steps. The relatively low root-mean-square(rms) misfit and model norm indicate a reliable electrical model. The final modelincludes four types of low resistivity areas, the first ones coincide with the knownlocation of an orebody and further forward modelling indicates that they are not infull connectivity to form a low resistivity zone. The second ones are not controlledby magnetotelluric sites and embody little information of the observed data, they areconsidered as tedious structures. The third one is near to the regional Kangguer faultand should be treated carefully considering the effect of the fault. The last ones areisolated and existing at a limited level as the first ones, they should be paid moreattention to.

Key words: 3D inversion, Forward modelling, Geologically complex area, Magne-totellurics.

INTRODUCTION

In the last ten or more years, the 2D inversion techniques havereplaced one-dimensional inversion and become the main-stream in magnetotelluric (MT) data interpretation. Com-mon inversion codes are, for instance, the Occam method(Wannamaker, Stodt and Rijo 1986, 1987; Constable, Parkerand Constable 1987; deGroot-Hedlin and Constable 1990,2004), the reduced basis Occam inversion (Siripunvarapornand Egbert 2000, 2007), the inversion method based on anBayesian information criterion (Uchida 1993), the non-linearconjugate gradients (Rodi and Mackie 2001) and the rapid

∗E-mail: [email protected]

relaxation inversion (Smith and Booker 1991). 2D inversionmethods made the application fields of magnetotellurics ex-pand rapidly. On the other hand, 2D inversion methods en-counter increasing challenges in geologically complex regions.The typical problems that increase the uncertainty of the in-version results are the static shift of the apparent resistiv-ity curves and the distortion of the impedance tensor, bothcaused by local inhomogeneous bodies at shallow level, aswell as the determination of an appropriate 2D strike directionand hence the right selection of polarization modes. Thoughthere are some special discussions on the veracity of 2D inver-sion (Berdichevsky, Dmitriev and Pozdnjakova 1998; Ogawa2002; Ledo et al. 2002; Ledo 2005) and different tools, such asdecomposition of impedance tensor, static shift removing anddetermination of the regional electrical strike direction, have

C© 2010 European Association of Geoscientists & Engineers 1177

1178 Qibin Xiao et al.

been proposed (Bahr 1988, 1991; Jones 1988; Groom andBailey 1989; deGroot-Hedlin 1991; Ogawa and Uchida 1996;Ogawa 1999; McNeice and Jones 2001). They are based onsome simplifications of the true structure, for example, mostmethods of decomposition of the impedance tensor are basedon the assumption that the nature or dimensionality of theregional conductivity structure is 2D. In order to increase theveracity and stability of magnetotelluric data interpretationfurther, the 3D inversion has become more common in MTdata interpretation, a fine 3D model can even compensate forthe static shift and distortion caused by shallow inhomoge-neous bodies. A number of 3D inversion codes have been de-veloped recently (Avdeev 2005), e.g., the conjugate gradientsmethod (Mackie and Madden 1993), the non-linear conjugategradients method (Newmann and Alumbaugh 2000; Mackie,Rodi and Watts 2001) and the 3D inversion technology basedon the Gauss-Newton algorithm (Sasaki 2001; Farquharsonet al. 2002; Avdeev and Avdeeva 2006; Han et al. 2008).Though all these three-dimensional inversion methods havebeen validated with synthetic data, the 3D inverse problem isfar from being solved. Most 3D inversion routines can onlybe applied on a high-end workstation or parallel machine. Inaddition, there have been few discussions on the stability andreliability of practical application (Mackie et al. 2001; Hanet al. 2008; Farquharson and Craven 2009).

Siripunvaraporn and Egbert (2000) applied the data-spacemethod to solve the 2D magnetotelluric (MT) inversion prob-lem for the first time and developed the conversion of Occaminversion based on model-space to data-space, which greatlyincreases the computational speed of inversion. Recently,they applied the data-space method to 3D MT inversion(Siripunvaraporn et al. 2005a; Siripunvaraporn, Egbert andUyeshima 2005b). With great decreasing of computationalconsumption, it is possible to implement 3D MT inversion ona single PC. In this article we apply the 3D MT inversion codeWSINV3DMT introduced by Siripunvaraporn et al. (2005a)to a set of MT data obtained in the Tulargen Cu-Ni miningarea, Xinjiang. The 3D inversion using WSINV3DMT wasstable, converged rapidly and achieved a good data fit, sug-gesting a reliable electrical model. The final 3D conductivitystructure was tested with forward modelling.

THEORETICAL BA C K GR OUN D

In the forward subroutine of WSINV3DMT, Siripunvara-porn, Egbert and Lenbury (2002) adopted the popular stag-gered grid finite difference method and used the second-orderMaxwell’s equation as equation (2) to solve the electric field,

then used the first-order Maxwell’s equation as equation (1)to solve the magnetic field.

∇ × E = iωμH, (1)

∇ × ∇ × E = iωμσ E. (2)

In the above equations, μ is the air magnetic permeability, ωis the angular frequency, σ is the conductivity, E is the electricfield and H is the magnetic field.

The inversion subroutine of WSINV3DMT is based on theOccam inversion. The objective function ψ(m,λ) has the fol-lowing form:

ψ(m, λ) = (m − m0)TC−1m (m − m0)

+ λ−1{(d − F [m])TC−1

d (d − F [m])}. (3)

Here m is the resistivity model, M is the number of modelparameters, m0 the prior model, Cm the model covariancematrix that defines the resistivity variation of magnitude andsmoothness relative to the prior model, d the observed data,N the number of observed data, F[m] the model response, Cd

the data covariance matrix and λ the Lagrange multiplier.The traditional iterative approximate solutions of equation

(3) are as follows:

mk+1(λ) = αk+1 J Tk C−1

d Xk + m0. (4)

Figure 1 Geology and layout of geophysical exploration work in theTulargen Cu-Ni mining area: 1. Quaternary system; 2. Carboniferousstratum; 3. volcanic rock of Devonian system; 4. granite of Hercynianperiod; 5. granite-prophyrite of Hercynian period; 6. survey line andnumber; 7. MT site and number; 8. known ultrabasic ore-bearingrock mass; 9. fault zone.

C© 2010 European Association of Geoscientists & Engineers, Geophysical Prospecting, 58, 1177–1192

Application of a 3D magnetotelluric inversion code 1179

Here k is the iteration number, Jk = (∂F/∂m)k is an N × M

sensitivity matrix calculated at mk, Xk = d − F [mk] + Jk(mk −m0), αk+1 = [λC−1

m + �mk ]−1, �m

k = J Tk C−1

d Jk is the M × M

‘model-space cross-product’ matrix.The key point of the inversion subroutine of WSINV3DMT

is implementing a series of matrix transforms to equation (4)and to obtain a new iterative expression:

mk+1(λ) = CmJ Tk βk+1 Xk + m0. (5)

Here βk+1 = [λCd + �nk]−1, �n

k = JkCmJ Tk is the N × N

‘data-space cross-product’ matrix.The main difference between equations (4) and (5) is that

the dimension of the system of equations to be solved changesgreatly, the number of equations decreases from M × M toN × N. In many practical cases, N will be much less thanM, hence, this transformation to data space results in a greatsaving on computational costs of both memory and centralprocessing unit (CPU) time (Siripunvaraporn et al. 2005a).

In 3D magnetotelluric finite difference approximations, ei-ther the electric fields or the magnetic fields can be solved first,the former is referred to as FDE, while the latter is referredto as FDH. Mackie, Smith and Madden (1994) used FDHfor 3D MT modelling, while Smith (1996) and Alumbaughet al. (1996) used FDE. Siripunvaraporn et al. (2002) pointedout that the solutions obtained by FDE are less sensitive togrid resolution than those obtained by FDH and comparedthe 3D numerical solutions with the analytic solutions of ahalf-space model and a 1D layered model under different gridresolutions.

Siripunvaraporn et al. (2005a,b) inverted synthetic data setsboth along a single profile and on a plane with WSINV3DMT,obtaining reasonable results. Miensopust, Martı and Jones(2007) also tested the inversion codes using different gridsand data sets from simple synthetic models in order to un-derstand how different parameters and mesh sizing affectthe resulting models. While Heise et al. (2008) obtained the

Figure 2 XY and YX apparent resistivity (ρa) and phase (ϕ) curves of magnetotelluric sites in the Tulargen Cu-Ni mining area. Solid circles: XYcomponent; empty circles: YX component. The phase values are adjusted to the first quadrant. The 5-channel sites are 1, 5, 6, 9, 11, 14, 16, 19.



resistivity structure of the Rotokawa geothermal system,Ingham et al. (2009) studied the deep resistivity struc-ture of the Mount Ruapehu volcano in New Zealand withWSINV3DMT.

F IELD DATA INV E R SI ON

The Tulargen mining area lies 200 km to the east of Hami,Xinjiang, China. The main strata in the mining area arevolcanic-sedimentary rocks of Carboniferous age and volcanicclastic rocks of the Wutongwo group (San et al. 2007). At thesouth side and middle-east section of the mining area, there is alarge range of Proterozoic deep metamorphic rock covered un-comfortably by the Carboniferous volcanic-sedimentary rock.At the northern side of the mining area, namely, north of theKangguer fault, the welded volcanic-agglomerate includingschist-bearing and gneiss-bearing breccias of Devonian systemoutcrop. Besides, the granite (porphyry) and basic-ultrabasic

complex of the Hercynian period are well developed in themining area. The Tulargen Cu-Ni deposit is of whole-rockmineralization and ultrabasic rock-type. The geological mapof the mining area (Fig. 1) shows that the known ore-bearingmagmatic body extends in the northeast-east direction, about700 m in length and 50–70 m in width (Fig. 1). A local drillinghole displays that the ore-bearing magmatic body dips southsteeply and extends more than 150 m in depth (San et al.2007).

In 2003, we carried out an audio-magnetotelluric work inthe Tulargen mining area along two profiles AA′ and BB′

shown in Fig. 1. There are 19 magnetotelluric sites in total;the general site space is from 100–300 m with locally densifiedsite distribution. The field data were obtained with GMS06MT measuring systems by Metronix. In the field work, weused two standard five-channel systems (which record bothelectric and magnetic fields) and some two-channel systems

Figure 3 XX and YY apparent resistivity (ρa) and phase (ϕ) curves of magnetotelluric sites in the Tulargen Cu-Ni mining area. Solid circles:XX component; empty circles: YY component. The phase values are adjusted to the first quadrant.



(which only record local electric fields) working together. Thedetailed layout of the five-channel MT system followed thegeneral convention: Hx in south-north direction, Hy in east-west direction, Hz to the ground surface, Ex in south-northdirection and Ey in east-west direction. The layout of the elec-tric channels of the two-channel systems is the same as thoseof the five-channel systems. Both the two-channel systems andfive-channel systems were recording synchronously controlledby GPS antennas, so that the two-channel systems can sharethe magnetic fields recorded by the five-channel systems. Afterprocessing, we obtained the impedance tensors from which we

calculated apparent resistivities and phase data in a frequencyrange of 0.3734–8000 Hz, which corresponds to a depth rangethat allows detecting the unknown shallow orebodies.

Figure 2 shows the XY and YX apparent resistivity andphase curves of the 19 MT sites in the Tulargen Cu-Ni miningarea. Although there exist few outliers at some frequenciesat a few sites because of disturbance (for example, the highfrequency of sites 1 and 3), the general shape of the curves issmooth and can be used for inversion. The amplitudes of theXY apparent resistivity are relatively unstable, for example,the XY apparent resistivity curves of sites 3, 21, 9, 11 and

Figure 4 Phase tensor skew angles (β) at f = 3318.56 Hz, 765.68 Hz, 176.66 Hz, 40.76 Hz. The skew angle β is defined by the direction of themain axis of the phase tensor ellipse (the red solid line) and the direction of the strike axis (or its normal, showed as the blue solid line).



16 are lower than the others, which indicates the conductivitycontrasts existing around these sites. At sites 7, 8, 10, 18and 19, the XY and YX apparent resistivity curves departfrom each other, while the phase curves are the same at highfrequencies, which may be caused by a static shift becauseof near-surface inhomogenities under the MT sites. Figure 3shows the XX and YY apparent resistivity and phase curvesof the 19 MT sites, with many more outliers and the curvesmore scattered than those of XY and YX. The amplitudes ofXX and YY apparent resistivity at most sites except sites 21,9 and 11 are greater than 10 �m, which indicate the survey

coordinate system is deviating from regional 2D electrical axes(if these exist).

Data dimensionality analysis

Phase tensor (Caldwell, Bibby and Brown 2004) is a usefulmethod to assess the dimensionality of the data and is espe-cially meaningful in complicated 3D situations. It is indepen-dent of distortion and can be presented as an ellipse usingthe maximum tensor value (Φmax), the minimum tensor value(Φmin) and the skew angle (β). As shown in Fig. 4, we present

Figure 5 Phase tensor ellipses superimposed by the magnetic induction vectors of five-channel MT sites at f = 3318.56 Hz, 765.68 Hz, 176.66 Hz,40.76 Hz. The red arrows show the imaginary part of the magnetic induction vectors, while the blue arrows show the real part of the magneticinduction vectors.



the phase tensor ellipses together with their main axes andskew angles at four different frequencies. The main axes ofphase tensor ellipses at high frequencies (as f = 3318.56 Hz,765.68 Hz) are more unstable than those at relatively low fre-quency (as f = 40.76 Hz), the skew angles of sites 2, 3, 5, 21,6 are more than 3˚ at frequencies 3318.56 Hz and 176.66 Hz.In general, the conductivity structure under sites 2, 3, 5, 21, 6close to 3D, the conductivity structure of sites 17 and 19 arealso complex at f = 3318.56 Hz.

Magnetic induction vectors are also indicators for the geo-electric strike and dimensionality of the region (Parkinson1959; Schmucker 1970; Siemon 1997). The real parts ofthe induction vectors are orthogonal to the geoelectric strike(Padilha et al. 2006). Their magnitudes can imply the inho-mogeneity of buried media. We obtained induction vectors ateach of the five-channel MT sites in the mining area, as shownin Fig. 5, both the directions and magnitudes of the vectorschange greatly from high frequency to low frequency. For ex-ample, at f = 3318.56 Hz, the real vectors (as at sites 11, 9, 6,5, 1, 19) imply a nearly EW regional strike, then the arrowsrotate counter-clockwise at f = 765.68 and 176.66 Hz andat f = 40.76 Hz, they imply a northwest-southeast regionalstrike (as at sites 5, 6, 14, 16, 19). The variety in the di-

rections of the induction vectors at different frequencies mayindicate complex geoelectric structures underground.

3D initial model description

In the 3D MT inversion code WSINV3DMT, the model direc-tions are defined as follows: x in the NS direction with northpositive; y in the EW direction with east positive and z positivedownwards. In the plane view, the centre point of the modelis the origin of the model’s coordinate system, the distancesfrom the model boundaries to the origin are equal. We con-structed the 3D initial model of the Tulargen Cu-Ni miningarea as a homogeneous half-space of 100 �m. The horizon-tal grid and vertical layers of the core section are shown inFig. 6, the number of grids from south to north is 35, fromwest to east 35 and the number of vertical layers is 30 (with-out air layers), so the total number of model cells is M =35 × 35 × 30 = 36750.

Input data description and 3D inversion

In the 3D MT inversion code WSINV3DMT, the basic el-ements forming input data are real and imaginary parts of

Figure 6 Plane grids (left) of the core section in the 3D initial model and vertical grids (right) from surface down (the solid points in the planegrids displaying MT survey sites).



impedance tensor (Z), we can either use the sub-diagonaldata (Zxy.real, Zxy.imag, Zyx.real, Zyx.imag) or the fullimpedance tensor (Zxx.real, Zxx.imag, Zxy.real, Zxy.imag,Zyx.real, Zyx.imag, Zyy.real, Zyy.imag). As shown in Figs 2and 3, the errors existing in the observed data are verylarge at some frequencies and these large errors will notonly make a very small rms (root-mean-square, rms =√∑

((Obs d − Rsp d)/err d)2/N, where Obs_d are the ob-served data, Rsp_d are the model responses, err d are theerrors of observed data and N is the total number of observeddata) at the beginning of the 3D inversion but also producemodels with little change of the initial model. According tothese reasons, we set the error scale of the observed impedancetensor as 5% to ensure the model responses fit well with the

observed data. The outliers in the observed data are excludedby changing their error scales to as large as 999 times 5%.

The total number of data N is determined by the numberof sites, frequency number and number of impedance ten-sor elements. In the Tulargen Cu-Ni mining area, we usedall of the 19 MT sites, selected 18 frequencies in the range0.3734–8000 Hz and adopted all the eight impedance ten-sor elements. Hence, the total number of data was N =19 × 18 × 8 = 2736.

After constructing the initial model and the input data, weshould confirm that the 3D inversion can be carried out in ourPC. For the 3D MT inversion code WSINV3DMT, the RAMcost is about 1.2 × (8N2 + 8NM), in the Tulargen Cu-Ni min-ing area, it needs 989.1 Mb RAM to run the 3D MT inversion.

Figure 7 Plots of model norm (upper), rms (middle) and λ (bottom) for each iteration of the 3D MT inversion.



In fact, the 3D inversion is feasible on a PC configured with 1GB RAM.

The WSINV3DMT inherits the basic idea of Occam, ineach iteration of WSINV3DMT inversion, the first stage triesto bring the data misfit to the target level, once the misfitreaches the desired level, the next stage begins by keepingthe misfit at the desired level, varying Lagrange multiplierλ to seek the model of the smallest norm. In applying theWSINV3DMT inversion the default values were 5, 0.1, 0.10.1 for the spatial smoothing parameters (τ and δx, δy, δz) anddifferent Lagrange multipliers (initial λ = 2.0, 5.0, 10.0 with1.0 and 0.5 step respectively) were used to find a reasonablemodel. It cost about 6 hours for one iteration on an Inter-core Quad Processer (2.83 GHz) PC. Figure 7 displays theinversion parameters of the 3D inversion in the Tulargen Cu-Ni mining area, which shows that small steps for λ makes thechange of rms and model norm gentle. As the rms misfit is

inconsistent with the corresponding model norm, a small rmsmisfit may produce a rough model, so we selected the thirdmodel produced with an initial λ = 5.0 and 0.5 step from the3D inversions results. The rms for the selected model is 2.266and the model norm is 1.62 × 104, the low rms indicates thatthe model can reflect the information contained in observeddata to a great extent.

Results and discussion

Figure 8 shows the 3D model response curves of the XY andYX components together with the corresponding observeddata. All the XY phase curves fit well with the correspondingobserved data, as well as the YX phase curves, except sites 21and 6. Generally, the XY component of apparent resistivityresponse curves fit better with the observed data than the YXcomponent of apparent resistivity. The possible static shifts in

Figure 8 Comparison of the 3D model response and observed data. The solid circles show observed apparent resistivity and phase data of XY,the empty circles show the observed YX, the solid lines show the 3D responses of XY, the dash lines show the 3D responses of YX.



the observed apparent resistivity data of sites 7, 8, 10, 18, and19 are compensated to some extent, which indicates that theinitial model is fine at shallow level to incorporate near-surfacestructure in the inversion (Sasaki 2004). Figure 9 shows the 3Dmodel response curves of XX and YY components togetherwith the corresponding observed data, though most of themodel response curves shift or part from the observed data,the response curves are smooth and following up the shapesof the observed data to some extent.

With the selected 3D model, a series of plane slices of re-sistivity in the Tulargen Cu-Ni mining area were obtained.Figure 10 shows the resistivity slices at different depths, thelow resistivity areas (with logarithm value less than 1.5) areisolated at shallow level. At depth from 20–40 m, the low resis-tivity areas below sites 21, 9, 11 and 16 appear (Fig. 10b) andthe isolated low resistivity areas extend vertically (Fig. 10c–e).

The characteristic is consistent with the relatively low appar-ent resistivity of these sites in Fig. 2. The low resistivity areasbelow sites 21 and 16 are not connected to form an anoma-lous zone as the known ore-bearing magmatic body in Fig. 1,though the low resistivity area below site 16 offsets a little to-ward site 21 at depth 140–220 m (Fig. 10f), they are extendingvertically as a whole and in isolated shape at depth less than220 m. At the depth of 220–320 m, the low resistivity areasbelow sites 9, 21, 16 begin to fade, while the low resistivityarea below site 3 appears and extends towards site 2 and site16 (Fig. 10g). There exist low resistivity areas away from MTsites, such as the area south-west of site 1 (Fig. 10d–i), thearea north of site 19 (Fig. 10g–i) and the area east of site 15(Fig. 10f–h). The low resistivity area north of site 11 is stableand clear, it shifts towards south-east and enlarges at depth.At the depth of 520–620 m (Fig. 10j), the low resistivity areas

Figure 9 Comparison of the 3D model response and observed data. The solid circles show observed apparent resistivity and phase data of XX,the empty circles show the observed YY, the solid lines show the 3D responses of XX, the dash lines show the 3D responses of YY.



Figure 10 The resistivity slices at different depth in the Tulargen Cu-Ni mining area. The crosses show the locations of MT sites.

begin to fade. At depths greater than 820 m (Fig. 10l), all thelow resistivity anomalies vanish.

Figure 11 shows the 3D Iso-surface (called as Iso-0) of re-sistivity value 1.5 (logarithmic value), the image gives the out-line of the low resistivity areas, just as analysed from theplane slices. The large low resistivity centres are located inthe northern part of the mining area, the low resistivity areasbelow sites 21 and 16 are not connected to form a zone asshown in Fig. 1. The low resistivity areas marked as A, B andC are not controlled by MT sites. As the distance between thetwo MT profiles is about 500 m, which is greater than thedistances between MT sites, we first made a modified modelof Iso-0 (called Iso-1) with the low resistivity areas below sites

21 and 16 being connected and calculated the responses. Thetotal rms for Iso-1 is 2.525. We made another modified modelof Iso-0 (called Iso-2) by replacing the values of the low re-sistivity areas as A, B and C in Iso-0 with their surroundingresistivity. The total rms for Iso-2 is 2.286. Figure 12 showsthe 3D Iso-surface of Iso-1 and the comparison of model re-sponses and observed data, it shows that the connected lowresistivity zone has little influence on sites 15 and 16 but hascertain influence on sites 21 and 6, which coincides with therms of each site in Fig. 13. It indicates that the known ore-bearing magmatic body is not a fully connected low resistivityzone. In Fig. 14, the calculated XY and YX apparent resistiv-ity and phase curves of Iso-2 can fit well with the observed



Figure 11 3D Iso-surface of resistivity at value 1.5 in logarithm inthe Tulargen Cu-Ni mining area. Solid points show the MT sites, thedashed ellipses enclose the low resistivity areas not controlled by MTsites.

data as those of Iso-0, the calculated XX and YY apparent re-sistivity and phase curves change slightly from the responsesof Iso-0, the detail rms of each site in Fig. 13 shows that onlythe rms of the sub-diagonal elements of site 19 and the rmsof the diagonal elements of site 1 have a small increase. Itseems that the low resistivity areas A, B and C are tediousstructures.

CONCLUSIONS

We applied the 3D MT inversion code WSINV3DMT in theTulargen Cu-Ni mining area on a single PC machine. Whenapplying WSINV3DMT to observed data, large errors in thedata will result in a small starting rms and therefore the modelswill only change slightly compared to the initial model. Settingthe error of the impedance tensor to 5% resulted in a betterfitting of the observed data.

The inversions started with a 100 �m half-space model anddefault values were used for the spatial smoothing parameters,the rms misfit can reach a minimum with several iterations.To ensure a reasonable model, we compared the model norm,fitting RMS versus Lagrange multiplier λ with different initialλ and steps based on the same half-space model. In this appli-cation, we selected a model with a relatively small rms and amodel norm as the final model.

The Kangguer fault is the boundary between the strata ofDevonian and the strata of Carboniferous. In the resistivityslices, it is also displayed as an electrical boundary. The strataof Devonian show relative low resistivity, while the strata ofCarboniferous show relative high resistivity. The low resistiv-ity areas in the electrical model can be divided into four types:the low resistivity areas below sites 21 and 16 consistent withthe known ore-bearing magmatic body but they are isolated atdepth less than 220 m, further forward modelling shows thatthey are not in full connectivity so as to form a low resistivityzone. The low resistivity areas marked as A, B and C in Fig. 11may be considered as tedious structures because they embodylittle information of the observed data from the results of for-ward modelling. The low resistivity area north-east of site 11is very large but it should be treated carefully considering theeffect of the regional Kangguer fault to the north of site 9. Thelow resistivity areas below sites 3 and 9 are isolated and existonly at a limited level, they are comparable with the low re-sistivity areas below sites 21 and 16 and should be paid moreattention to.

In our application, the WSINV3DMT program fits the ob-served data of XY and YX components very well and followsup the shapes of XX and YY components to a great extent. Onthe one hand, it seems to be a good choice in geological com-plex regions where the 2D MT inversion methods are limited;on the other hand, there is a trade-off between data fittingand model norm, sometimes, sensitivity tests are needed todetermine the final 3D model.

ACKNOWLEDGEMENTS

This research has been supported by the Director Foundationof the Institute of Geology, China Earthquake Administration(Grant No. DF-IGCEA-0608–2–16) and the National Natu-ral Science Foundation of China (Grant Nos 40974042 and40534023). Mr Siripunvaraporn and Mr Egbert are acknowl-edged for providing their MT inversion programs for both 2Dand 3D. We also thank the anonymous reviewers and editorsfor their comments that led to significant improvements inthis paper. Finally, we are grateful for the help provided by704 Party, Xinjiang Bureau of Nonferrous Metals GeologicalExploration.

REFERENCES

Alumbaugh D.L., Newman G.A., Prevost L. and Shadid J.N. 1996.Three-dimensional wideband electromagnetic modeling on mas-sively parallel computers. Radio Science 31, 1–23.



Figure 12 The modified 3D model of Iso-0 (called as Iso-1) and the comparison of the 3D model response and observed data. The Iso-surfaceof resistivity is at value 1.5 in logarithm, the solid points in Iso-surface show the MT sites, the dashed ellipse encloses the added low resistivityarea in Iso-1.

Avdeev D.B. 2005. Three-dimensional electromagnetic modeling andinversion from theory to application. Surveys in Geophysics 26,767–799.

Avdeev D.B. and Avdeeva A.D. 2006. A rigorous three-dimensionalmagnetotelluric inversion. Progress in Electromagnetics Research62, 41–48.

Bahr K. 1988. Interpretation of the magnetotelluric impedance tensor,regional induction and local distortion. Journal of Geophysics 62,119–127.

Bahr K. 1991. Geological noise in magnetotelluric data: a classifica-tion of distortion types. Physics of the Earth and Planetary Interiors66, 24–38.

Berdichevsky M.N., Dmitriev V.I. and Pozdnjakova E.E. 1998. Ontwo-dimensional interpretation of magnetotelluric soundings. Geo-physical Journal International 133, 585–606.

Caldwell T.G., Bibby H.M. and Brown C. 2004. The magnetotel-luric phase tensor. Geophysical Journal International 158, 457–469.



Figure 13 The rms of each site for Iso-0, Iso-1 and Iso-2. rms_diagmeans the rms of the diagonal elements of impedance tensors,the rms_sub_diag means the rms of the sub-diagonal elements ofimpedance tensors, the rms_full means the rms of all elements ofimpedance tenors. The solid diamonds show the rms of Iso-0, theupper triangles show the rms of Iso-1, the lower triangles show therms of Iso-2.

Constable S.C., Parker R.L. and Constable C.G. 1987. Occam’s in-version – A practical algorithm for generating smooth models fromelectromagnetic sounding data. Geophysics 52, 289–300.

Farquharson C.G. and Craven J.A. 2009. Three-dimensional inver-sion of magnetotelluric data for mineral exploration: An examplefrom the McArthur River uranium deposit, Saskatchewan, Canada.Journal of Applied Geophysics 68, 450–458.

Farquharson C.G., Oldenburg D.W., Haber E. and Shekhtman R.2002. An algorithm for the three-dimensional inversion of mag-netotelluric data. 72nd SEG meeting, Salt Lake City, Utah, USA,Expanded Abstracts, 649–652.

Groom R.W. and Bailey R.C. 1989. Decomposition of magne-totelluric impedance tensors in the presence of local three-dimensional galvanic distortion. Journal of Geophysical Research94, 1913–1925.

deGroot-Hedlin C. 1991. Removal of static shift in two dimensionsby regularized inversion. Geophysics 56, 2102–2106.

deGroot-Hedlin C. and Constable S.C. 1990. Occams’s inversion togenerate smooth, two-dimensional models from magnetotelluricdata. Geophysics 55, 1613–1624.

deGroot-Hedlin C. and Constable S.C. 2004. Inversion of magne-totelluric data for 2D structure with sharp resistivity contrasts.Geophysics 69, 78–86.

Han N., Nam M.J., Kim H.J., Lee T.J., Song Y. and Suh J.H. 2008.Efficient three-dimensional inversion of magnetotelluric data usingapproximate sensitivities. Geophysical Journal International 175,477–485.

Heise W., Caldwell T.G., Bibby H.M. and Bannister S.C. 2008. Three-dimensional modelling of magnetotelluric data from the Rotokawageothermal field, Taupo Volcanic Zone, New Zealand. Geophysi-cal Journal International 173, 740–750.

Ingham M.R., Bibby H.M., Heise W., Jones K.A., Cairns P., DravitzkiS. et al. 2009. A magnetotelluric study of Mount Ruapehu volcano,New Zealand. Geophysical Journal International 179, 887–904.

Jones A.G. 1988. Static shift of magnetotelluric data and its removalin a sedimentary basin environment. Geophysics 53, 967–978.

Ledo J. 2005. 2-D versus 3-D magnetotelluric data interpretation.Surveys in Geophysics 26, 511–543.

Ledo J., Queralt P., Marti A. and Jones A.G. 2002. Two-dimensionalinterpretation of three-dimensional magnetotelluric data: An exam-ple of limitations and resolution. Geophysical Journal International150, 127–139.

Mackie R.L. and Madden T.R. 1993. Three-dimensional magnetotel-luric inversion using conjugate gradients. Geophysical Journal In-ternational 115, 215–229.

Mackie R.L., Rodi W. and Watts M.D. 2001. 3-D magnetotelluricinversion for resource exploration. 71st SEG meeting, San Antonio,Texas, USA, Expanded Abstracts, 1501–1504.

Mackie R.L., Smith J.T. and Madden T.R. 1994. Three-dimensionalelectromagnetic modeling using finite difference equations: Themagnetotelluric example. Radio Science 29, 923–935.

McNeice G.W. and Jones A.G. 2001. Multisite, Multifrequencytensor decomposition of magnetotelluric data. Geophysics 66,158–173.

Miensopust M., Martı A. and Jones A.G. 2007. Inversion of syntheticdata using WSINV3DMT code. 4th International Symposium onThree-Dimensional Electromagnetics, 27–30 September, Freiberg,Germany, 27–30.

Newman G.A. and Alumbaugh D.L. 2000. Three dimensional mag-netotelluric inversion using non-linear conjugate gradients. Geo-physical Journal International 140, 410–424.

Ogawa Y. 1999. Constrained inversion of COPROD-2S2 datasetusing model roughness and static shift. Earth Planets Space 51,1145–1151.

Ogawa Y. 2002. On two-dimensional modeling of magnetotelluricfield data. Surveys in Geophysics 23, 251–272.

Ogawa Y. and Uchida T. 1996. A two-dimensional magnetotelluricinversion assuming Gaussian static shift. Geophysical Journal In-ternational 126, 69–76.

Padilha A.L., Vitorello I., Padua M.B. and Bologna M.S. 2006.Lithospheric and sublithospheric anisotropy beneath central-southeastern Brazil constrained by long period magnetotelluricdata. Physics of the Earth and Planetary Interiors 158, 190–209.

Parkinson W. 1959. Directions of rapid geomagnetic variations. Geo-physical Journal Of the Royal Astronomical Society 2, 1–14.

Rodi W. and Mackie R.L. 2001. Nonlinear conjugate gradients algo-rithm for 2-D magnetotelluric inversion. Geophysics 66, 174–187.

San J.Z., Hui W.D., Qin K.Z., Sun H., Xu X.W., Liang G.H. et al.2007. Geological characteristics of Tulargen magmatic Cu-Ni-Codeposit in eastern Xinjiang and its exploration direction. MineralDeposits 26, 307–316.

Sasaki Y. 2001. Full 3-D inversion of electromagnetic data on PC.Journal of Applied Geophysics 46, 45–54.



Figure 14 The modified 3D model of Iso-0 (called Iso-2) and the comparison of the 3D model response and observed data. The Iso-surface ofresistivity is at value 1.5 in logarithm, the solid points in the Iso-surface show the MT sites.

Sasaki Y. 2004. Three-dimensional inversion of static-shifted magne-totelluric data. Earth, Planets and Space 56, 239–248.

Schmucker U. 1970. Anomalies of geomagnetic variations in thesouthwestern United States. Bulletin of the Scripps Institution ofOceanography 13, 1–165.

Siemon B. 1997. An interpretation technique for superimposed in-duction anomalies. Geophysical Journal International 130, 73–88.

Siripunvaraporn W. and Egbert G. 2000. An efficient data-subspaceinversion method for 2-D magnetotelluric data. Geophysics 65,791–803.

Siripunvaraporn W. and Egbert G. 2007. Data space conjugate gra-dient inversion for 2-D magnetotelluric data. Geophysical JournalInternational 170, 986–994.

Siripunvaraporn W., Egbert G. and Lenbury Y. 2002. Numer-ical accuracy of magnetotelluric modeling: A comparison of



finite difference approximation. Earth, Planets and Space 54, 721–725.

Siripunvaraporn W., Egbert G., Lenbury Y. and Uyeshima M. 2005a.Three-dimensional magnetotelluric inversion, data space method.Physics of the Earth and Planetary Interiors 150, 3–14.

Siripunvaraporn W., Egbert G. and Uyeshima M. 2005b. Interpre-tation of 2-D Magnetotelluric Profile Data with 3-D Inversion,Synthetic Examples. Geophysical Journal International 160, 804–814.

Smith J.T. 1996. Conservative modeling of 3-D electromagnetic fields.Part II: Biconjugate gradient solution and an accelerator. Geo-physics 61, 1319–1324.

Smith J.T. and Booker J.R. 1991. Rapid inversion of two- and three-dimensional magnetotelluric data. Journal of Geophysical Research96, 3905–3922.

Uchida T. 1993. Smooth 2-D inversion for magnetotelluric data basedon statistical criterion ABIC. Journal of Geomagnetics and Geo-electrics 45, 841–858.

Wannamaker P.E., Stodt J.A. and Rijo L. 1986. Two-dimensionaltopographic responses in magnetotellurics modeled using finite el-ements. Geophysics 51, 2131–2144.

Wannamaker P.E., Stodt J.A. and Rijo L. 1987. A stable finite-elementsolution for two-dimensional magnetotelluric modeling. Geophys-ical Journal of the Royal Astronomical Society 88, 277–296.


Documents

Application of the 3D Magnetotelluric Inversion Code in a Geologically Complex Area