• The Journal of Engineering Geology
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• v.14 no.1
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• pp.21-28
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• 2004

Three-dimensional (3-D) resistivity inversion including a topographic effect can be considered theoretically to be the technique of acquiring the most accurate image in the interpretation of resistivity data, because it includes characteristic image that the actual subsurface structure is 3-D. In this study, a finite-element method was used as the numerical method in modeling, and the efficiency of Jacobian calculation has been maximized with sensitivity analysis for the destination block in inversion process. Also, during the iterative inversion, the resolution of inversion can be improved with the method of selecting the optimal value of Lagrange multiplier yielding minimum RMS(root mean square) error in the parabolic equation. In this paper, we present synthetic examples to compare the difference between the case which has the toprographic effect and the other case which has not the effect in the inversion process.

• 한국지구물리탐사학회:학술대회논문집
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• 2008.10a
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• pp.47-50
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• 2008

Streamer resistivity surveys in shallow marine environments were carried out to analyze sediment characteristics at the bottom of reservoir. Because the resistivity values of reservoir water are very low and those of sediment are relatively high, apparent resistivity values increase with depth. And it is necessary to eliminate the apparent resistivity data decreased highly when the number of separation increases. According to the repeated data processing, we proposed the resistivity ratio of upper-to-lower layer is $0.6{\sim}0.8$ because the RMS error of inversion leads to the minimum in these range. As a result of the inversion for two- and three-layer model, the inversion including water depth is proved to be more effective than conventional method.

• Journal of the Korean earth science society
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• v.23 no.1
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• pp.15-29
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• 2002

Bayesian inversion for gravity and resistivity data was performed to investigate the cavity structure appearing as a lava tunnel in Cheju Island, Korea. Dipole-dipole DC resistivity data were proposed for a prior information of gravity data and we applied the geostatistical techniques such as kriging and simulation algorithms to provide a prior model information and covariance matrix in data domain. The inverted resistivity section gave the indicator variogram modeling for each threshold and it provided spatial uncertainty to give a prior PDF by sequential indicator simulations. We also presented a more objective way to make data covariance matrix that reflects the state of the achieved field data by geostatistical technique, cross-validation. Then Gaussian approximation was adopted for the inference of characteristics of the marginal distributions of model parameters and Broyden update for simple calculation of sensitivity matrix and SVD was applied. Generally cavity investigation by geophysical exploration is difficult and success is hard to be achieved. However, this exotic multiple interpretations showed remarkable improvement and stability for interpretation when compared to data-fit alone results, and suggested the possibility of diverse application for Bayesian inversion in geophysical inverse problem.

• Geomechanics and Engineering
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• v.35 no.2
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• pp.109-119
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• 2023

Ground subsidence in urban areas due to excessive development and degraded underground facilities is a serious problem. Geophysical surveys have been conducted to estimate the distribution and scale of cavities and subsidence. In this study, electrical resistivity tomography (ERT) was performed near an area of road subsidence in an urban area. The subsidence arose due to groundwater leakage that carried soil into a neighboring excavation site. The ERT survey line was located between the main subsidence area and an excavation site. Because ERT data are affected by rapid topographic changes and surrounding structures, the influence of the excavation site on the data was analyzed through field-scale numerical modeling. The effect of an excavation should be considered when interpreting ERT data because it can lead to wrong anomalous results. A method for performing 2D inversion after correcting resistivity data for the effect of the excavation site was proposed. This method was initially tested using a field-scale numerical model that included the excavation site and subsurface anomaly, which was a loosened zone, and was then applied to field data. In addition, ERT data were interpreted using an existing in-house 3D algorithm, which considered the effect of excavation sites. The inversion results demonstrated that conductive anomalies in the loosened zone were greater compared to the inversion that did not consider the effects of excavation.

• Geophysics and Geophysical Exploration
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• v.6 no.4
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• pp.199-206
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• 2003

Characteristics of the static shift are discussed by comparing the three-dimensional MT inversion with/without static shift parameterization. The galvanic distortion by small-scale shallow feature often leads severe distortion in inverted resistivity structures. The new inversion algorithm is applied to four numerical data sets contaminated by different amount of static shift. In real field data interpretations, we generally do not have any a-priori information about how much the data contains the static shift. In this study, we developed an algorithm for finding both Lagrangian multiplier for smoothness and the trade-off parameter for static shift, simultaneously in 3-D MT inversion. Applications of this inversion routine for the numerical data sets showed quite reasonable estimation of static shift parameters without any a-priori information. The inversion scheme is successfully applied to all the four data sets, even when the static shift does not obey the Gaussian distribution. Allowing the static shift parameters have non-zero degree of freedom to the inversion, we could get more accurate block resistivities as well as static shifts in the data. When inversion does not consider the static shift as inversion parameters (conventional MT inversion), the block resistivities on the surface are modified considerably to match possible static shift. The inhomogeneous blocks on the surface can generate the static shift at low frequencies. By those mechanisms, the conventional 3-D MT inversion can reconstruct the resistivity structures to some extent in the deeper parts even when moderate static shifts are in the data. As frequency increased, however, the galvanic distortion is not frequency independent any more, and thus the conventional inversion failed to fit the apparent resistivity and phase, especially when strong static shift is added. Even in such case, however, reasonable estimation of block resistivity as well as static shift parameters were obtained by 3-D MT inversion with static shift parameterization.

• Geophysics and Geophysical Exploration
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• v.11 no.4
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• pp.326-334
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• 2008

The resistivity method has been used to image the electrical properties of the subsurface. Especially, this method has become suitable for monitoring since data could be rapidly and automatically acquired. In this study, we developed a time-lapse inversion algorithm for the interpretation of resistivity monitoring data. The developed inversion algorithm imposes a big penalty on the model parameter with small change, while a minimal penalty on the model parameter with large change compared to the reference model. Through the numerical experiments, we can ensure that the time-lapse inversion result shows more accurate and focused image where model parameters have changed. Also, applying the timelapse inversion method to the leakage detection of an embankment dam, we can confirm that there are three major leakage zones, but they have not changed over time.

• Geophysics and Geophysical Exploration
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• v.10 no.4
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• pp.314-321
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• 2007

Recently, multi-dimensional joint inversion of geophysical data based on fundamentally different physical properties is being actively studied. Joint inversion can provide a way to obtaining much more accurate image of the subsurface structure. Through the joint inversion, furthermore, it is possible to directly estimate non-geophysical material properties from geophysical measurements. In this study, we developed a new algorithm for jointly inverting dc resistivity and seismic traveltime data based on the multiple constraints: (1) structural similarity based on cross-gradient, (2) correlation between two different material properties, and (3) a priori information on the material property distribution. Through the numerical experiments of surface dc resistivity and seismic refraction surveys, the performance of the proposed algorithm was demonstrated and the effects of different regularizations were analyzed. In particular, we showed that the hidden layer problem in the seismic refraction method due to an inter-bedded low velocity layer can be solved by the joint inversion when appropriate constraints are applied.

• Geophysics and Geophysical Exploration
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• v.24 no.4
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• pp.171-179
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• 2021

We outline a process for estimating Cole-Cole parameters from time-domain induced polarization (IP) data. The IP transients are all inverted to 2D Cole-Cole earth models that include resistivity, chargeability, relaxation time, and the frequency exponent. Our inversion algorithm consists of two stages. We first convert the measured voltage decay curves into time series of current-on time apparent resistivity to circumvent the negative chargeability problem. As a first step, a 4D inversion recovers the resistivity model at each time channel that increases monotonically with time. The desired intrinsic Cole-Cole parameters are then recovered by inverting the resistivity time series of each inversion block. In the second step, the Cole-Cole parameters can be estimated readily by setting the initial model close to the true value through a grid search method. Finally, through inversion procedures applied to synthetic data sets, we demonstrate that our algorithm can image the Cole-Cole earth models effectively.

• Geophysics and Geophysical Exploration
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• v.10 no.2
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• pp.138-146
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• 2007

This paper describes 2.5D induced polarization (IP) modeling and inversion algorithms using complex resistivity. The complex resistivity method has merits for acquiring more valuable information about hydraulic parameters and pore fluid than the conventional IP methods. The IP modeling and inversion algorithms are developed by allowing complex arithmetic in existing DC modeling and inversion algorithms. The IP modeling and inversion algorithms use a 2.5D DC finite-element algorithm and a damped least-squares method with smoothness constraints, respectively. The accuracy of the IP modeling algorithm is verified by comparing its responses of two synthetic models with two different approaches: linear filtering for a three-layer model and an integral equation method for a 3D model. Results from these methods are well matched to each other. The inversion algorithm is validated by a synthetic example which has two anomalous bodies, one is more conductive but non-polarizable than the background, and the other is polarizable but has the same resistivity as the background. From the inverted section, we can cleary identify each anomalous body with different locations. Furthermore, in order to verify its efficiency to the real filed example, we apply the inversion algorithm to another three-layer model which includes phase anomaly in the second layer.

• Geophysics and Geophysical Exploration
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• v.18 no.1
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• pp.9-13
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• 2015

All the resistivity data contain various kinds of noise. The major sources of noise in DC resistivity measurement are high contact resistance, measurement errors, and sporadic background noise. Thus, it is required to measure data noise to accurately interpret resistivity data. Reciprocal measurements can provide a measure of data precision and noise. In this study, we proposed a data-weighting method from reciprocity measurement. Furthermore, a data-weighting method using both the reciprocity error and data-misfit in the inversion process was studied. Applying the data-weighting method to the inversion of 3D resistivity data, it was confirmed that local anomalies are slightly suppressed in the final inversion results.