• Geophysics and Geophysical Exploration
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• v.14 no.1
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• pp.7-17
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• 2011

We have developed an inversion code for three-dimensional (3D) resistivity tomography including the anisotropy effect. The algorithm is based on the finite element approximations for the forward modelling and Active Constraint Balancing method is adopted to enhance the resolving power of the smoothness constraint least-squares inversion. Using numerical experiments, we have shown that anisotropic inversion is viable to get an accurate image of the subsurface when the subsurface shows strong electrical anisotropy. Moreover, anisotropy can be used as additional information in the interpretation of subsurface. This algorithm was also applied to the field dataset acquired in the abandoned old mine area, where a high-rise apartment block has been built up over a mining tunnel. The main purpose of the investigation was to evaluate the safety analysis of the building due to old mining activities. Strong electrical anisotropy has been observed and it was proven to be caused by geological setting of the site. To handle the anisotropy problem, field data were inverted by a 3D anisotropic tomography algorithm and we could obtain 3D subsurface images, which matches well with geology mapping observations. The inversion results have been used to provide the subsurface model for the safety analysis in rock engineering and we could assure the residents that the apartment has no problem in its safety after the completion of investigation works.

• Geophysics and Geophysical Exploration
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• v.22 no.1
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• pp.1-11
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• 2019

Well logging technologies are used to measure the physical properties of reservoirs through boreholes. These technologies have been utilized to understand reservoir characteristics, such as porosity, fluid saturation, etc., using equations based on rock physics models. The analysis of well logs is performed by selecting a reliable rock physics model adequate for reservoir conditions or characteristics, comparing the results using the Archie's equation or simandoux method, and determining the most feasible reservoir properties. In this study, we developed a joint inversion algorithm to estimate physical properties in shaly sandstone reservoirs based on the pre-existing algorithm for sandstone reservoirs. For this purpose, we proposed a rock physics model with respect to shale volume, constructed the Jacobian matrix, and performed the sensitivity analysis for understanding the relationship between well-logging data and rock properties. The joint inversion algorithm was implemented by adopting the least-squares method using probabilistic approach. The developed algorithm was applied to the well-logging data obtained from the Colony gas sandstone reservoir. The results were compared with the simandox method and the joint inversion algorithms of sand stone reservoirs.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.5B
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• pp.830-841
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• 2000

We extend the sue of the method of least square to develop a recursive algorithm for the design of adaptive transversal filters such that, given the least-square estimate of this vector of the filter at iteration n-1, we may compute the updated estimate of this vector at iteration a upon the arrival of new data. We begin the development of the RLS algorithm by reviewing some basic relations that pertain to the method of least squares. Then, by exploiting a relation in matrix algebra known as the matrix inversion lemma, we develop the RLS algorithm. An important feature of the RLS algorithm is that it utilizes information contained in the input data, extending back to the instant of time when the algorithm is initiated. In this paper, we propose new tap weight updated RLS algorithm in adaptive transversal filter with data-recycling buffer structure. We prove that convergence speed of learning curve of RLS algorithm with data-recycling buffer is faster than it of exiting RL algorithm to mean square error versus iteration number. Also the resulting rate of convergence is typically an order of magnitude faster than the simple LMS algorithm. We show that the number of desired sample is portion to increase to converge the specified value from the three dimension simulation result of mean square error according to the degree of channel amplitude distortion and data-recycle buffer number. This improvement of convergence character in performance, is achieved at the (B+1)times of convergence speed of mean square error increase in data recycle buffer number with new proposed RLS algorithm.

• Geophysics and Geophysical Exploration
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• v.1 no.3
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• pp.155-160
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• 1998

EM tomography technique has been developed. The algorithm used the extended Born approximations for forward modeling and reconstructed a conductivity image by a smoothness constraint least squares inversion method. Observed data, the vertical components of secondary magnetic fields, were simulated with the 3-D integral equation code. The results showed that the location of anomalous body could be imaged very well, but conductivity of the body was lower than real one and the vertical resolution was much higher than the horizontal resolution.

• Geophysics and Geophysical Exploration
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• v.7 no.1
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• pp.7-13
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• 2004

In this paper, we demonstrate that Common Mid-Point (CMP) cross-correlation gathers of multi-channel and multi-shot surface waves give accurate phase-velocity curves, and enable us to reconstruct two-dimensional (2D) velocity structures with high resolution. Data acquisition for CMP cross-correlation analysis is similar to acquisition for a 2D seismic reflection survey. Data processing seems similar to Common Depth-Point (CDP) analysis of 2D seismic reflection survey data, but differs in that the cross-correlation of the original waveform is calculated before making CMP gathers. Data processing in CMP cross-correlation analysis consists of the following four steps: First, cross-correlations are calculated for every pair of traces in each shot gather. Second, correlation traces having a common mid-point are gathered, and those traces that have equal spacing are stacked in the time domain. The resultant cross-correlation gathers resemble shot gathers and are referred to as CMP cross-correlation gathers. Third, a multi-channel analysis is applied to the CMP cross-correlation gathers for calculating phase velocities of surface waves. Finally, a 2D S-wave velocity profile is reconstructed through non-linear least squares inversion. Analyses of waveform data from numerical modelling and field observations indicate that the new method could greatly improve the accuracy and resolution of subsurface S-velocity structure, compared with conventional surface-wave methods.

• 한국지구물리탐사학회:학술대회논문집
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• 2006.06a
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• pp.117-122
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• 2006

In the geophysical monitoring to understand the change of subsurface material properties with time, the time-invariant static subsurface model is commonly adopted to reconstruct a time-lapse image. This assumption of static model, however, can be invalid particularly when fluid migrates very quickly in highly permeable medium in the brine injection experiment. In such case, the resultant subsurface images may be severely distorted. In order to alleviate this problem, we develop a new least-squares inversion algorithm under the assumption that the subsurface model will change continuously in time. Instead of sampling a time-space model into numerous space models with a regular time interval, a few reference models in space domain at different times pre-selected are used to describe the subsurface structure continuously changing in time; the material property at a certain space coordinate are assumed to change linearly in time. Consequently, finding a space-time model can be simplified into obtaining several reference space models. In order to stabilize iterative inversion and to calculate meaningful subsurface images varying with time, the regularization along time axis is introduced assuming that the subsurface model will not change significantly during the data acquisition. The performance of the proposed algorithm is demonstrated by the numerical experiments using the synthetic data of crosshole dc resistivity tomography.

• Geophysics and Geophysical Exploration
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• v.5 no.4
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• pp.236-249
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• 2002

We have extended the three-dimensional (3-D) resistivity imaging algorithm to cover the 3-D resistivity tomography problem, where resistivity data are acquired using electrodes installed in several boreholes as well as at the earth surface. The imaging algorithm consists of the 3-D finite element forward modeling and least-squares inversion scheme, where the ACB (Active Constraint Balancing) is adopted to enhance the resolving power of the inversion. Sensitivity analysis with numerical verifications shows that 3-D resistivity tomography is a very appealing method and can be used to get 3-D attitude of subsurface structures with very high-resolution. Moreover, we could accurately handle the topography effect, which could cause artifacts in the resistivity tomography. In the application of 3-D resistivity tomography to the real field data set acquired at the quarry mine, we could derive a very reasonable and accurate image of the subsurface.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.4
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• pp.213-221
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• 2013

This paper introduces a mesh continuation scheme for a one-dimensional inverse medium problem to reconstruct the spatial distribution of elastic wave velocities in heterogeneous semi-infinite solid domains. To formulate the inverse problem, perfectly-matched-layers(PMLs) are introduced as wave-absorbing boundaries that surround the finite computational domain truncated from the originally semi-infinite extent. To tackle the inverse problem in the PML-truncated domain, a partial-differential-equations(PDE)-constrained optimization approach is utilized, where a least-squares misfit between calculated and measured surface responses is minimized under the constraint of PML-endowed wave equations. The optimization problem iteratively solves for the unknown wave velocities with their updates calculated by Fletcher-Reeves conjugate gradient algorithms. The optimization is performed using a mesh continuation scheme through which the wave velocity profile is reconstructed in successively denser mesh conditions. Numerical results showed the robust performance of the mesh continuation scheme in reconstructing target wave velocity profile in a layered heterogeneous solid domain.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.4
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• pp.691-698
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• 2003

We extend the sue of the method of least square to develop a recursive algorithm for the design of adaptive transversal filters such that, given the least-square estimate of this vector of the filter at iteration n-l, we may compute the updated estimate of this vector at iteration n upon the arrival of new data. We begin the development of the RLS algorithm by reviewing some basic relations that pertain to the method of least squares. Then, by exploiting a relation in matrix algebra known as the matrix inversion lemma, we develop the RLS algorithm. An important feature of the RLS algorithm is that it utilizes information contained in the input data, extending back to the instant of time when the algorithm is initiated. In this paper, we propose new tap weight updated RLS algorithm in adaptive transversal filter with data-recycling buffer structure. We prove that convergence speed of learning curve of RLS algorithm with data-recycling buffer is faster than it of exiting RLS algorithm to mean square error versus iteration number. Also the resulting rate of convergence is typically an order of magnitude faster than the simple LMS algorithm. We show that the number of desired sample is portion to increase to converge the specified value from the three dimension simulation result of mean square error according to the degree of channel amplitude distortion and data-recycle buffer number. This improvement of convergence character in performance, is achieved at the B times of convergence speed of mean square error increase in data recycle buffer number with new proposed RLS algorithm.

• Geophysics and Geophysical Exploration
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• v.8 no.1
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• pp.18-25
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• 2005

We derive refraction statics for seismic data recorded in a hard rock terrain, in which there are large and rapid variations in the depth of weathering. The statics corrections range from less than 10 ms to more than 70 ms, often over distances as short as 12 receiver intervals. This study is another demonstration of the importance in obtaining accurate initial refraction models of the weathering in hard rock terrains in which automatic residual statics may fail. We show that the statics values computed with a simple model of the weathering using the Generalized Reciprocal Method (GRM) and the Refraction Convolution Section (RCS) are comparable in accuracy to those computed with a more complex model of the weathering, using least-mean-squares inversion with the conjugate gradient algorithm (Taner et al., 1998). The differences in statics values between the GRM model and that of Taner et al. (1998) systematically vary from an average of 2ms to 4ms over a distance of 8.8 km. The differences between these two refraction models and the final statics model, which includes the automatic residual values, are generally less than 5 ms. The residuals for the GRM model are frequently less than those for the model of Taner et al. (1998). The RCS statics are picked approximately 10 ms later, but their relative accuracy is comparable to that of the GRM statics. The residual statics values show a general correlation with the refraction statics values, and they can be reduced in magnitude by using a lower average seismic velocity in the weathering. These results suggest that inaccurate average seismic velocities in the weathered layer may often be a source of short-wavelength statics, rather than any shortcomings with the inversion algorithms in determining averaged delay times from the traveltimes.