Inversion of pole‐pole data for 3-D resistivity structure beneath arrays of electrodes

Park, Stephen K.; Van, Gregory P.

doi:10.1190/1.1443128

Cited by 188 publications

(132 citation statements)

References 15 publications

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“…We have run many inversions with different deep resistivity structures in the a priori model each time, and we are always able to resolve the same features. The average resistivity in each layer shown in Figure 9 is comparable to that obtained by Park and Van (1991). However, our results more clearly show the lateral and vertical variations that are important for studying leakage monitoring data collected afterwards.…”

Section: Analysis Of Field Datasupporting

confidence: 68%

“…Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/ of water was used as a comparison for the measurements taken afterwards and to determine the resistivity structure of the test area. Park and Van (1991) applied a 3-D inversion algorithm to image the background resistivity structure. However, as a result of the limitation in the algorithm, they could invert only a small number of model parameters (7 x 7 x 5).…”

Section: Analysis Of Field Datamentioning

confidence: 99%

“…Petrick et al (1981) outlined a 3-D alphacenter method that involves solving for image sources representing conductivity distributions and applying a leastsquares algorithm for the inversion. Park and Van (1991) developed a 3-D inversion procedure using maximum likelihood inverse theory and Dey and Morrison's (1979) finitedifference forward modeling code. However, their inversions were limited to small models because standard matrix inversion techniques were used to solve the maximum likelihood inverse equations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

3‐D resistivity forward modeling and inversion using conjugate gradients

Zhang¹,

Mackie²,

Madden³

1994

SEG Technical Program Expanded Abstracts 1994

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We have developed rapid 3-D do resistivity forward modeling and inversion algorithms that use conjugate gradient relaxation techniques. In the forward network modeling calculation, an incomplete Cholesky decomposition for preconditioning and sparse matrix routines combine to produce a fast and efficient algorithm (approximately 2 minutes CPU time on a Sun SPARCstation 2 for 50 x 50 x 20 blocks). The side and bottom boundary conditions are scaled impedance conditions that take into account the local current flow at the boundaries as a result of any configuration of current sources.For the inversion, conjugate gradient relaxation is used to solve the maximum likelihood inverse equations. Since conjugate gradient techniques only require the results of the sensitivity matrix A or its transpose A T multiplying a vector, we are able to bypass the actual computation of the sensitivity matrix and the inversion of ATA, thus greatly decreasing the time needed to do 3-D inversions.We demonstrate 3-D resistivity tomographic imaging using pole-pole resistivity data collected during an experiment for a leakage monitoring system near evaporation ponds at the Mojave Generating Station in Laughlin, Nevada.

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Section: Analysis Of Field Datasupporting

confidence: 68%

Section: Analysis Of Field Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

3‐D resistivity forward modeling and inversion using conjugate gradients

Zhang¹,

Mackie²,

Madden³

1994

SEG Technical Program Expanded Abstracts 1994

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“…This means that application of standard 2D techniques on embankment dams with measurement layouts along the crest of the dam cannot be used without cau-tion because of the obvious 3D effects from the dam geometry. It is possible to use 3D inversion techniques ͑Park and Van, 1991;Sasaki, 1994;Zhang et al, 1995;Loke and Barker, 1996͒. However, they still may not be convenient for repeated measurements, mainly because of limitations in computational resources and because data sets are 2D if only measured along the crest.…”

Section: Introductionmentioning

confidence: 99%

2.5D resistivity modeling of embankment dams to assess influence from geometry and material properties

2006

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Repeated resistivity measurement is a potentially powerful method for monitoring development of internal erosion and anomalous seepage in earth embankment dams. This study is part of a project to improve current longterm monitoring routines and data interpretation and increasing the understanding when interpreting existing data. This is accomplished by modeling various occurrences typical of embankment structures using properties from two rockfill embankment dams with central till cores in the north of Sweden. The study evaluates the influence from 3D effects created by specific dam geometry and effects of water level fluctuations in the reservoir. Moreover, a comparison between different layout locations is carried out, and detectability of internal erosion scenarios is estimated through modeling of simulated damage situations. Software was especially developed to model apparent resistivity for geometries and material distributions for embankment dams. The model shows that the 3D effect from the embankment geometry is clearly significant when measuring along dam crests. For dams constructed with a conductive core of fine-grained soil and high-resistive rockfill, the effect becomes greatly enhanced. Also, water level fluctuations have a clear effect on apparent resistivities. Only small differences were found between the investigated arrays. A layout along the top of the crest is optimal for monitoring on existing dams, where intrusive investigations are normally avoided, because it is important to pass the current through the conductive core, which is often the main target of investigation. The investigation technique has proven beneficial for improving monitoring routines and increasing the understanding of results from the ongoing monitoring programs. Although the technique and software are developed for dam modeling, it could be used for estimation of 3D influence on any elongated structure with a 2D cross section.

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“…plemented, and applied to different array configurations (Queralt et al, 1991;Park and Van, 1991;Oldenburg et al, 1993;Oldenburg and Li, 1994;Zhang et al, 1995;Spitzer, 1995;Loke and Barker, 1996a, b). At present, the usual practice to map shallow structures is to perform a survey along a profile assumed to be perpendicular to a suspected strike axis, with electrodes deployed along this direction, and in many cases using multielectrode arrays.…”

Section: Introductionmentioning

confidence: 99%

Geoelectrical modeling of shallow structures using parallel and perpendicular arrays

2014

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In this article we analyze the sensitivity of a geoelectrical modeling technique to image 2D shallow structures. Firstly, we extend a previously developed 2D method based on Rayleigh-Fourier expansions, in order to allow arbitrary locations for the electrodes and also 3D earth models. This method is an alternative to finite element and finite difference techniques and is especially suitable to model multilayered structures, with smooth irregular boundaries. Then, for simple 2D models we build up two synthetic pseudosections, one for electrode deployments parallel to a profile perpendicular to the strike, and other for deployments perpendicular to it. We analyze the advantages in using both pseudosections to model these structures. We also compare geoelectric results with the corresponding audiomagnetotelluric transverse electric and transverse magnetic responses. Finally, we perform a geoelectrical survey to image a shallow buried structure and show the goodness of the model fit obtained considering both pseudosections. For the examples studied here, we conclude that considering both pseudosections leads to a more accurate description of the structures. When a 2D anomaly is present, its effect on the perpendicular component is more focused, both in width and depth, than in the parallel component. Hence the perpendicular component helps to constrain the localization of the inhomogeneity. In addition, we find similarities between the geoelectric parallel and perpendicular responses and the corresponding audiomagnetotelluric transverse magnetic and transverse electric results, respectively. When inverting audiomagnetotelluric data using 2D codes, better resolution in the electrical imaging is obtained when both modes are considered; then it is expected that 2D imaging of geoelectric data including both arrays should lead to an optimization of the inversion process. Even more, if results of these inversions could be used in correlation with AMT results, it is clear that this kind of joint inversion should contribute to remove uncertainties allowing an improvement in the description of the actual structures.

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Inversion of pole‐pole data for 3-D resistivity structure beneath arrays of electrodes

Cited by 188 publications

References 15 publications

3‐D resistivity forward modeling and inversion using conjugate gradients

3‐D resistivity forward modeling and inversion using conjugate gradients

2.5D resistivity modeling of embankment dams to assess influence from geometry and material properties

Geoelectrical modeling of shallow structures using parallel and perpendicular arrays

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