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Role of 1D MT inversion in a 3D geothermal fieldDhananjay Kumar*, and G. Michael Hoversten, Chevron Energy Technology Company, Gregg Nordquist,

Chevron Geothermal and Power Operations, William Cumming, Cumming Geoscience

Summary

An extensive magnetotelluric (MT) survey comprised of 85sites has been acquired over the Darajat geothermal field in

Indonesia to map the geothermal reservoir and theoverlying clay cap. The rouged topography and thegeometry of the margin of the clay cap makes the resistivitystructure 3D at reservoir depth. Although 3D MT inversionis now commonly used in geothermal interpretations 1D

and 2D MT inversions are still effective tools for a varietyof tasks such as quality assurance. Lower dimensionalinversion can also play two critical roles in determining andassessing the resistivity model derived by 3D inversion: 1)

by providing a good starting model to reduce the

computational cost of the 3D inversion, and 2) by providinga computationally feasible path to stochastic inversion of

the data that provides realistic parameters standarddeviations for use in assessing reliability of the resistivitymodel. Using a spatially constrained 1D stochastic

inversion of the MT data, we investigate the common claimthat 1D inversion can provide a pseudo 3D model whichclosely matches the 3D inversion for the overburden andclay cap layers. The discrepancy between the pseudo 3D

and true 3D inverse models increases with depth, howeverthe presence of the core resistive feature of the field is stillindicated at approximately the same depth as found in thetrue 3D model. Analysis of the 1D model parameter

probability density functions shows that layer thicknessesare better determined than layer resistivities.

Introduction

The magnetotelluric (MT) method has been widely used toresolve resistivity patterns in geothermal reservoirs,

because MT method can resolve the low resistivity, low

permeability hydrothermal smectite clay cap that acts as thetrap over high temperature geothermal reservoirs in bothsedimentary and igneous environments (Ussher et al.,

2000). The temperature related transition from smectite tomore resistive and more brittle illite and chloride is closelycorrelated with the top of permeable geothermal reservoirs.

Geothermal MT success case histories have sometimesfocused on mapping the base of the low resistivity smectiteclay cap using 1D layered inversion (Anderson et al.,2000). Although 3D MT inversion has been increasinglyemphasized in geothermal MT exploration (Cumming, et

al., 2000; Uchida and Sasaki, 2006; Arnason et al., 2010)and is now in-house application at Chevron, it is stillrelatively expensive and 1D inversion remains the mostcommon imaging methods used for quality assurance and

uncertainty testing (Cumming and Mackie, 2010).

Figure 1: Darajat geothermal field is located in the West

Java province of Indonesia, about 150km southeast of

Jakarta (figure modified from Hadi et al., 2005).

A total of 85 MT sites, with usable 5-component MT data

from 0.001 to 120 Hz, were acquired during surveys in1997 and 2004 over the Darajat geothermal field inIndonesia (Figure 1) to derive an electrical resistivity model

of the geothermal reservoir. The low resistivity patternimaged by earlier MT inversions matched the smectite-illiteclay transition determined from wells and conformed to thereservoir isotherms reasonably well. However, ambiguity

was particularly evident on the margins of the reservoir fortargeting makeup wells. Because of the geothermal powerfacilities, data quality is compromised in some areas, but itis unclear to what extent this affects the reliability of the

MT inversions.

It is well known and widely appreciated that the inversionof MT data is non-unique, like most geophysical imaging

methods. The reliability of an MT inversions resolution ofearth properties depends not only on the noise level in theMT data and the accuracy of the MT forward responsecalculation for a particular earth model, but also on the

criteria used to choose a single final model from the manynon-unique possibilities. Currently the computationally

practical 3D inversion algorithms fall into the category of

gradient based algorithms subject to regularization

constraints designed to weight the inversion towards morerealistic models. As is the case with the 3D inversion used

in this paper (Commer and Newman, 2008), thesetechniques find a single model which fits the observed data.If estimates of model parameter resolution are needed (e.g.how well is the thickness of the clay cap resolved) they

cannot be accurately derived from deterministic inversion

1EG Denver 2 1 Annual Meeting 2 1 SEG

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1D MT inversion in a 3D geothermal field

using model covariance matrix for two reasons: 1) a highdegree of parameter correlation is induced by regularizationof pixilated models, and 2) no formal theory exists to

account for the off diagonal cross-correlation coefficientsof the matrix. Even when the number of parameters can be

reduced thereby reducing the parameter correlationstandard deviations derived from the diagonal of the

correlation matrix significantly underestimate the trueparameter variance as measured by the model parameterprobability density function (pdf) (Trainer and Hoversten,2009).

Of the methods commonly used to characterize modeluncertainties, stochastic inversion is arguably the mostgeneral, but it is currently not feasible in 3D. As a cost-

effective alternative, we demonstrate that 1D stochasticinversion can provide significant information about modeluncertainty and can provide a good starting point for 3Dinversion. We show that while statistical moments such as

the median and mode of the parameter pdfs can be used to

generate a single model, they are not guaranteed to providea model that best fits the data. This can be accomplished

by a gradient based inverse starting from the modelconstructed from mode values of the parameter pdfs.

MT inversion

Because the on-diagonal elements of the MT impedancewere less reliable only the off-diagonal elements of theimpedance (Zxyand Zyx

) are used in the 3D inversion. The

inversion model included the detailed topography model;and therefore no static corrections were applied. Of themany MT parameters that can be used for 1D inversion, wechose the determinant of impedance (Berdichevskiy and

Dmitriev, 1976) because many investigators have foundthat it works well in geothermal setting and requires nointerpreter input (Anderson et al, 2000; Arnason et al.,2010).

We have developed a stochastic Markov Chain MonteCarlo (MCMC) inverse algorithm (Gilks et al., 1996) and adeterministic least squares 1D MT inverse algorithm which

invert all available MT soundings simultaneously subject tolateral and vertical smoothing of the 1D model parameters.

The stochastic MCMC algorithm without lateral smoothingis described in Trainor and Hoversten (2009). The lateralsmoothing approach was demonstrated by Viezzoli et al.,2008 for airborne EM data, where the set of data locations

are triangulated to generate a list of nearest neighbors for

each site. The lateral smoothing between sites is scaled bythe inverse distance to the neighbors. Vertical smoothing oflayer resistivity and thickness can be done if a large number

of layers are specified. In this work we test the propertiesof the algorithm using only 4 layers to represent the majorelements of the model.

The lateral smoothing using nearest neighbor sites asconstrain in the 1D stochastic MCMC algorithms is addedas prior which modifies the likelihood function as:

= errBxEf C

2

1exp)|( (1)

with

( )

= = == = =

+

=

N

l

lNN

m

NP

n

mn

lmijk

c

ijkijkN

i j

nfreq

k p

pp

d

xMeerr

1

)(

1 1 ln

ln

2

1

2

1 1

1

The likelihood function describes the posterior probability

of candidate model xCgiven the observed data. Embeddedin this exponential function (equation 1) is the misfit

between the observed data e and the calculated data M,

each at frequency k scaled by the data errors . Thus, the

total number of data is the product of the number offrequencies (nfreq) and number of sites (N) multiplied bytwo for the real and imaginary parts. NN(l) is the number

of nearest neighbors to the lth

site and NP is the number ofparameters, p, in the 1D models, and d is the distance

between two sites. is the Lagrange multiplier controllingthe tradeoff between data fit and model smoothness.

The model update, mi+1, at the (i+1)th iteration for the

regularized least square inversion (LSQ) can be expressedas (Newman and Alumbaugh, 1997):

[ ] dDGWWGGm TTTi 1

1

+ += , (2)

with DAG= , and )( ii Amddd += , where m is the

model parameter vector, Dis the data-weighting matrix, Ais the model sensitivity matrix (the Jacobian), is the

model smoothing trade-off parameter, W is the

regularization matrix, and the superscript T denotestranspose of a matrix. The data-weighting matrix is theinverse of the data standard deviations. The spatial model

smoothing is applied as in the stochastic inversion via W.

Results

Figure 2 shows a depth slice through a 3D conductivitymodel at 0 m elevation (mASL) (~ 1800 m below thesurface) from 3D inversion using the code of Commer and

Newman (2008). The 3D inversion was started from a 0.1S/m half space below topography. The figure showscontour of the top of the Andesite intrusion as mapped from

boreholes. The resistivity structure and the top Andesite are

well correlated, and are also consistent with gravity data(Rajeki et al., 2010). The 3D resistivity structure impliesthat the Andesite may still be present at 0 mASL to thenorth where contours from wells do not match the 3D

model. The ambiguity may be related to variation in rockproperties or to uncertainty in the resistivity model.Because a thorough assessment of model uncertainty using


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a 3D MT inversion algorithm is a computationallyimpractical task, it was hoped that the resolution of thisfeature could be tested using a 1D stochastic approach.

7 98 00 0 7 99 00 0 8 00 00 0 8 01 00 0 8 02 00 0 8 03 00 0 8 04 00 0

Easting (m)

9199000

9200000

9201000

9202000

9203000

9204000

9205000

Northing(m)

S/m

Figure 2. Depth slice of conductivity from 3D MT inversion(blue color shows resistive body) at 0 (mASL) elevation

through Darajat Geothermal field. East-west black line is

location of cross section shown in Figure 5. Major faults

and the top of Andesite elevation contours are also posted.

The unit of conductivity is Siemens per meter (S/m).

The stochastic MCMC inversion provides complete pdfsof layer parameters from which we must choose one of themoments of the distribution (mean, mode or median) if a

single value is desired. The mode of the distributionrepresents the most likely value so we use that to constructmodel resistivities and thicknesses. These models are nothowever guaranteed to provide the best fit to the observed

data in a least squares sense. For that we use the modes

from the MCMC to create starting models for the LSQinversion. Figure 3 presents examples of a bad and a gooddata fits for 1D constrained inversion, and Figure 4 shows

example of pdfs at site 35. We have observed that the LSQinversion performs much better using starting modelsgenerated from the MCMC.

By comparing the 1D inversion with the 3D inversion(Figure 5) we find a reasonably good agreement formapping of the overburden and conductive clay cap (layers

1 and 2: b, c and d). Below the conductive layer the matchwith the 3D model is generally poor. Generally the bestdetermined parameter from the 1D MCMC as indicated bythe standard deviation from the pdfs (Figure 4) is the

resistivity of the clay cap. Clay cap from 1D inversion is

thicker than 3D inverted model that indicate a need to usemore layers in 1D inversion. Based on the uncertaintyanalysis of 1D stochastic MCMC inverted models the layer

thicknesses seem to be better determined than layerresistivities, however this is different from conventionalwisdom (Simpson and Bahr, 2005).

(a)Site: DJ-35

(b)

(c) (d)

Site: DJ-35

Site: DJ-25Site: DJ-25Phase(degrees)

Ph

ase(degrees)

10

90

90

10

100

100

10

10

App.R

esistivity(ohm-m)

App.

Resistivity(ohm-m)

0.1 100.1 10

Frequency (Hz)Frequency (Hz)

10.001 0.001

Figure 3: Data mismatch. Comparing 1D inverted model

synthetics with field data from two MT sites: site DJ-35

where 1D MCMC provides good data fitting (a and b) and

site DJ-25 where 1D MCMC provides poor data fitting (c

and d). Synthetic based on 1D LSQ is shown by red circlepoints and synthetics based on 1D MCMC (using mode of

model pdf) is shown in blue + mark. 1D field data are

shown by the black X points and errors in data are shown

by black dashed lines.

1 h1

2 h2

3 h34

4-layer

model

1

2

3

4

h1

h2

h3

frequency

frequ

ency

frequency

frequency

frequency

frequency

frequen

cy

dev

Figure 4: Parameter pdfs after 1D MCMC constrained

inversion for a 4 layer 1D model at Site 35. The upper 4

are layer resistivities and the lower 3 are layer thicknesses.

The statistical measures are also marked.


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X (m)798500 803500

Z(m)

-

1000

1000

Z(m)

Z(m)

Z(m)

(a)

(b)

(c)

(d)

3D Inversion

1D MCMC unconstrained

1D MCMC constrained

1D LSQ constrained

Red: from (b)

White: from (c)

Black: from (d)

35 34 33 420b

-

1000

1000

-

1000

1000

site

Figure 5: West to East cross-section at easting 9202500

through 3D inversion (a), 1D MCMC unconstrained

inversion (b), 1D MCMC constrained inversion (c), and 1D

LSQ constrained inversion (d). The layer interfaces from 4-

layer 1D inversions are shown on the 3D inverted model

(a). Note that 1D MCMC unconstrained inverted model is

also shown for comparison with constrained inversions.Model parameters from 1D MCMC shown here is mode of

pdfs, and the mode of pdfs from (c) was used as starting

model for LSQ constrained inversion (d). Top and base of

reservoir is marked on the 1D inverted models (b, c and d).

Discussions and Conclusions

In geothermal exploration a high quality MT data set can be

used to resolve the depths to and the geometry of the clay-cap overlying the geothermal reservoir. Beneath the

conductive clay cap the resolution worsens, and details ofthe resistivity structure at reservoir depths are uncertain.

When integrated with other geologic and geochemical datathe geometry of the clay cap as defined with a detailedinversion of the MT data provides important constraints onthe location and size of the reservoir. By implementing a

1-D stochastic inversion we aim to better understand andquantify the uncertainties of the resistivity structure of theshallow high resistivity overburden and the clay cap. Thisshould help to provide meaningful constraints for the

shallow structure in the 3-D modeling and may in turnimprove confidence in deeper features at reservoir depths.

Testing of the MCMC inversion shows that the mode ofmodel parameter pdfs from the 1D stochastic MCMC

inversion provides a pseudo 3D resistivity model that is ingeneral matches with the 3D inverse model. The accuracy

of match between 1D and 3D derived models is best for thelayer above the clay cap and the clay cap and thendecreases with depth. The advantages of 1D MCMCinversion are, 1) speed, and 2) uncertainties in model

parameters. An important next step will be to developwork flows that can use the information obtained fromthese uncertainties to provide starting model for 3Dinversion. The mode of the model parameter pdfs

generally provides a good match to data, but if a singlebest-fitting model is desired LSQ provides this when thestarting model is constructed from the mode of the pdfsafter 1D MCMC inversion.

The uncertainty analysis based on these tests of 1Dstochastic MCMC inversion of Darajat data indicates thatthe resistivity of the clay cap is best resolved and in general

layer thicknesses are better resolved than layer resistivities;these conclusions require further verification. In future onecan 1) work on better understanding of the effects of noise

in data and the effects on inverted models, 2) use controlledsource electromagnetic data (e.g., time domain EM) toconstrain relatively resistive geothermal reservoir, 3) make

use of seismic data (e.g., micro earthquake data) tocorrelate seismic velocity and resistivity models to

constrain subsurface model, 4) make weighting () forspatial constrain in 1D MCMC as variable, and 5) try 2D

MCMC.

Acknowledgements

We thank Chevron ETC and Chevron Geothermal andPower for permission to publish.


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EDITED REFERENCES

Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2010SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata foreach paper will achieve a high degree of linking to cited sources that appear on the Web.

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