• Geophysics and Geophysical Exploration
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• v.16 no.3
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• pp.131-138
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• 2013

We developed a method for inverting magnetic data to image 2D susceptibility models. The major difficulty in the inversion of the potential data is the nonuniqueness. Furthermore, generally the number of inversion blocks are greater than the number of the magnetic data available, and thus the magnetic inversion leads to under-determined problem, which aggravates the nonuniqueness. When the magnetic data were inverted by the general least-squares method, the anomalous susceptibility would be concentrated near the surface in the inverted section. To overcome this nonuniqueness problem, we propose a new resolution model constraint that is calculated from the parameter resolution. The model constraint imposes large penalty on the model parameter with good resolution, on the other hand small penalty on the model parameter with poor resolution. Thus, the deep-seated model parameter, generally having poor resolution, can be effectively resolved. The developed inversion algorithm is applied to the inversion of the synthetic data for typical models of magnetic anomalies and is tested on real airborne data obtained at the Okcheon belt of Korea.

• Journal of the Korean Geotechnical Society
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• v.21 no.4
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• pp.145-154
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• 2005

Love wave and Rayleigh wave are the major elastic waves belonging to the category of the surface wave. Those waves are used to determine the ground stiffness profile using their dispersion characteristics. The fact that Love wave is not contaminated by P-wave makes Love wave superior to Rayleigh wave and other body waves. Therefore, the information that Love wave carries is more distinct and clearer than that of others. Based on theoretical research, the joint inversion analysis that uses the dispersion information of both Love and Rayleigh wave was proposed. This analysis consists of the forward modeling using transfer matrix, the sensitivity matrix for evaluating the ground system and DLSS (Damped Least Square Solution) as an inversion technique. The technique of joint inversion uses the dispersion characteristics of Love wave and Rayleigh wave simultaneously making the sensitivity matrix. The sensitivity matrix was used for inversion analysis repeatedly to find the approximate ground stiffness profile. The purpose of the joint inversion analysis is to improve accuracy and convergency of inversion results by utilizing that frequency contribution of each wave is different.

• Geophysics and Geophysical Exploration
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• v.10 no.1
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• pp.50-59
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• 2007

The advent of towed geo-electrical array surveying on water and land has resulted in datasets of magnitude approaching that of airborne electromagnetic surveying and most suited to 1D inversion. Robustness and complete automation is essential if processing and reliable interpretation of such data is to be viable. Sharp boundaries such as river beds and the top of saline aquifers must be resolved so use of smoothness constraints must be minimised. Suitable inversion algorithms must intelligently handle low signal-to-noise ratio data if conductive basement, that attenuates signal, is not to be misrepresented. A noise-level aware inversion algorithm that operates with one elastic thickness layer per electrode configuration has been coded. The noise-level aware inversion identifies if conductive basement has attenuated signal levels so that they are below noise level, and models conductive basement where appropriate. Layers in the initial models are distributed to span the effective depths of each of the geo-electric array quadrupoles. The algorithm works optimally on data collected using geo-electric arrays with an approximately exponential distribution of quadrupole effective depths. Inversion of data from arrays with linear electrodes, used to reduce contact resistance, and capacitive-line antennae is plausible. This paper demonstrates the effectiveness of the algorithm using theoretical examples and an example from a salt interception scheme on the Murray River, Australia.

• Journal of the Korean Geophysical Society
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• v.3 no.3
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• pp.161-174
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• 2000

Bayesian inversion is a stable approach to infer the subsurface structure with the limited data from geophysical explorations. In geophysical inverse process, due to the finite and discrete characteristics of field data and modeling process, some uncertainties are inherent and therefore probabilistic approach to the geophysical inversion is required. Bayesian framework provides theoretical base for the confidency and uncertainty analysis for the inference. However, most of the Bayesian inversion require the integration process of high dimension, so massive calculations like a Monte Carlo integration is demanded to solve it. This method, though, seemed suitable to apply to the geophysical problems which have the characteristics of highly non-linearity, we are faced to meet the promptness and convenience in field process. In this study, by the Gaussian approximation for the observed data and a priori information, fast Bayesian inversion scheme is developed and applied to the model problem with electric well logging and dipole-dipole resistivity data. Each covariance matrices are induced by geostatistical method and optimization technique resulted in maximum a posteriori information. Especially a priori information is evaluated by the cross-validation technique. And the uncertainty analysis was performed to interpret the resistivity structure by simulation of a posteriori covariance matrix.

• Geophysics and Geophysical Exploration
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• v.7 no.3
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• pp.207-212
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• 2004

This article reviews recent developments in three-dimensional (3-D) magntotelluric (MT) imaging. The inversion of MT data is fundamentally ill-posed, and therefore the resultant solution is non-unique. A regularizing scheme must be involved to reduce the non-uniqueness while retaining certain a priori information in the solution. The standard approach to nonlinear inversion in geophysis has been the Gauss-Newton method, which solves a sequence of linearized inverse problems. When running to convergence, the algorithm minimizes an objective function over the space of models and in the sense produces an optimal solution of the inverse problem. The general usefulness of iterative, linearized inversion algorithms, however is greatly limited in 3-D MT applications by the requirement of computing the Jacobian(partial derivative, sensitivity) matrix of the forward problem. The difficulty may be relaxed using conjugate gradients(CG) methods. A linear CG technique is used to solve each step of Gauss-Newton iterations incompletely, while the method of nonlinear CG is applied directly to the minimization of the objective function. These CG techniques replace computation of jacobian matrix and solution of a large linear system with computations equivalent to only three forward problems per inversion iteration. Consequently, the algorithms are efficient in computational speed and memory requirement, making 3-D inversion feasible.

• 한국지구물리탐사학회:학술대회논문집
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• 2008.10a
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• pp.51-56
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• 2008

The waveform inversion for isotropic media has ever been studied since the 1980s, but there has been few studies for anisotropic media. We present a seismic waveform inversion algorithm for 2-D heterogeneous transversely isotropic structures. A cell-based finite difference algorithm for anisotropic media in time domain is adopted. The steepest descent during the non-linear iterative inversion approach is obtained by backpropagating residual errors using a reverse time migration technique. For scaling the gradient of a misfit function, we use the pseudo Hessian matrix which is assumed to neglect the zero-lag auto-correlation terms of impulse responses in the approximate Hessian matrix of the Gauss-Newton method. We demonstrate the use of these waveform inversion algorithm by applying them to a two layer model and the anisotropic Marmousi model data. With numerical examples, we show that it's difficult to converge to the true model when we assumed that anisotropic media are isotropic. Therefore, it is expected that our waveform inversion algorithm for anisotropic media is adequate to interpret real seismic exploration data.

• Journal of the Korean Geophysical Society
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• v.2 no.2
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• pp.135-142
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• 1999

Interpretations of 3-component magnetic logging data obtained for a reinforced bar as a model of the line of the magnetic dipoles are conducted using a least squared inversion technique. The length of the bar is 1.12 m, sampling interval is 0.05 m, the distance between the bar and the borehole is 0.3 m, and the top of the bar is fixed at 0 m of depth. The bar is set to be approximately vertical. Magnetic anomalies smoothed with FFT are used as input data for the inversion. For the interpretation of magnetic logging data the depth to the top, the length, the magnetic moment per unit length, the direction of the magnetization (declination and inclination), and the bearing and plunge of the line of magnetic dipoles are left as unknown parameters. The comparison of the results obtained from the individual inversion of the horizontal component or the vertical component of the magnetic anomalies, and those from the simultaneous inversion of horizontal and vertical component of the magnetic anomalies shows that there exist some disagreements between each inversion result. The depth to the bottom of the bar, which is actually 1.12 m, is estimated as 1.18 m, and the inclination of the magnetization is estimated as -76°by simultaneous inversion. The negative value of the inclination indicates that the strength of the remnant magnetization is much greater than that of the induced magnetization, so that the direction of the resultant magnetization points to the top of the bar.

• Geophysics and Geophysical Exploration
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• v.4 no.2
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• pp.25-33
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• 2001

Loop-loop electromagnetic (EM) survey in frequency domain has been carried out in order to provide basic solution to geotechnical applications. Source and receiver configuration may be horizontal co-planar (HCP) and/or vertical co-planar (VCP). Three quadrature components of mutual impedance ratio for each configuration are used to construct the subsurface image. For the purpose of obtaining the model response and validating the reasonable performance of the inversion, we obtained each responses of two-layered and three-layered earth models and two-dimensional (2-D) isolated anomalous body. The response of 2-D isolated anomalous body has been calculated using extended Born approximation for the solution of 2.5-D integral equation describing EM scattering problem. As a result of the least-squares inversion with variable Lagrangian multiplier, we could construct more resolvable image from HCP data than VCP data. Furthermore, joint inversion of HCP and VCP data made better stability and resolution of the inversion. Resistivity values, however, did not exactly match the true ones. Loop-loop EM field data was obtained with EM34-3XL system manufactured by Geonics Ltd. (Canada). Electrical resistivity survey was conducted on the same line for the comparison in advance. Since the constructed image from loop-loop EM data by 2-D inversion algorithm showed almost similar resistivity distribution to that from electrical resistivity one, we expect the developed 2.5-D loop-loop EM inversion program can be applied for the reconnaissance site survey.

• Geophysics and Geophysical Exploration
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• v.9 no.4
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• pp.299-303
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• 2006

Geologic noise, especially located at shallow depth, can be a great obstacle in the interpretation of geophysical data. Thus, it is important to suppress geologic noise in order to accurately detect major anomalous bodies in the survey area. In the inversion of geophysical data, model parameters at shallow depth, which have small size and low contrast of physical property, can be regarded as one of geologic noise. The least-squares method with smoothness constraint has been widely used in the inversion of geophysical data. The method imposes a big penalty on the large model parameter, while a small penalty on the small model parameter. Therefore, it is not easy to suppress small anomalous boies. In this study, we developed a new inversion scheme which can effectively suppress geologic noise by imposing a big penalty on the slowly varying model parameter and a small penalty on the largely varying model parameter. We call the method MTE (main-target emphasizing) inversion. Applying the method to the inversion of 2.5D small loop EM data, we can ensure that it is effective in suppressing small anomalous boies and emphasizing major anomalous bodies in the survey area.

• Geophysics and Geophysical Exploration
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• v.10 no.4
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• pp.229-240
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• 2007

In this study, seismic anisotropic tomography algorithm was developed for imaging the seismic velocity anisotropy of the subsurface. This algorithm includes several inversion schemes in order to make the inversion process stable and robust. First of all, the set of the inversion parameters is limited to one slowness, two ratios of slowness and one direction of the anisotropy symmetric axis. The ranges of the inversion parameters are localized by the pseudobeta transform to obtain the reasonable inversion results and the inversion constraints are controlled efficiently by ACB(Active Constraint Balancing) method. Especially, the inversion using the Fresnel volume is applied to the anisotropic tomography and it can make the anisotropic tomography more stable than ray tomography as it widens the propagation angle coverage. The algorithm of anisotropic tomography is verified through the numerical experiments. And, it is applied to the real field data measured at limestone region and the results are discussed with the drill log and geological survey data. The anisotropic tomography algorithm will be able to provide the useful tool to evaluate and understand the geological structure of the subsurface more reasonably with the anisotropic characteristics.