• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.185-190
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• 2007

In this study, we developed the 2.5D EM modeling and inversion algorithm for cross-hole source and receiver geometry. Considering the cross-hole environment, we use a VMD (vertical magnetic dipole) as a source and vertical magnetic fields as a measuring data. Developed inversion algorithm is tested for the isolated block model which has a conductive and a resistivity anomaly respectively. For the conductive anomaly, its size and resistivity are inverted well on the inversion results, while for the resistive anomaly, the location of anomalous block is shown on the inverted section, but its values are far from the exact value. Furthermore, artificial conductive anomalies are shown around the resistive anomalous zone. If we consider the inversion artifact shown in the test inversion of restive block, it is almost impossible to image the resistive zone. However, the main target of EM tomography in the engineering problem is conductive target such as fault zone, and contaminated zone etc., EM tomography algorithm can be used for detecting the anomalous zone.

• Geophysics and Geophysical Exploration
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• v.26 no.4
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• pp.268-274
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• 2023

Finite source inversion is performed with a Green's function matrix and geodetic coseismic displacement. Conventionally, the Green's function matrix is constructed using the Okada model (Okada, 1985). However, for more realistic earthquake simulations, recent research has widely adopted the physics-based model, which can consider various material properties such as elasticity, viscoelasticity, and elastoplasticity. We used the physics-based software PyLith, which is suitable for earthquake modeling. However, the PyLith does not provide a mesh generator, which makes it difficult to perform finite source inversions that require numerous subfaults and observation points within the model. Therefore, in this study, we developed CPInterface (COMSOL-PyLith Interface) to improve the convenience of finite source inversion by combining the processes of creating a numerical model including sub-faults and observation points, simulating earthquake modeling, and constructing a Green's function matrix. CPInterface combines the grid generator of COMSOL with PyLith to generate the Green's function matrix automatically. CPInterface controls model and fault information with simple parameters. In addition, elastic subsurface anomalies and GPS observations can be placed flexibly in the model. CPInterface is expected to enhance the accessibility of physics-based finite source inversions by automatically generating the Green's function matrix.

• 한국지구물리탐사학회:학술대회논문집
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• 2003.11a
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• pp.459-463
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• 2003

Waveform inversion requires extracting a reliable low frequency content of seismic data for estimating of the low wave number velocity model. The low frequency content of the seismic data is usually discarded or neglected because of the band-limited response of the source and the receivers. In this study, however small the spectral of the low frequency seismic data is, we assume that it is possible to extract a reliable phase information of the low frequency from the seismic data and use it in waveform inversion. To this end, we exploit the frequency domain finite element modeling and source-receiver reciprocity to calculate the $Frech\`{e}t$ derivative of the phase of the seismic data with respect to the earth model parameter such as velocity, and then apply a damped least squares method to invert the phase of the seismic data. Through numerical example, we will attempt to demonstrate the feasibility of our method in estimating the correct velocity model for prestack depth migration.

• Geophysics and Geophysical Exploration
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• v.19 no.3
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• pp.136-144
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• 2016

Since seismic inversion is based on the wave equation, it is important to calculate the solution of wave equation exactly. In particular, full waveform inversion would produce reliable results only when the forward modeling is accurately performed because it uses full waveform. When we use finite-difference or finite-element method to solve the wave equation, the convergence of numerical scheme should be guaranteed. Although the general proof of convergence is provided theoretically, the consistency and stability of numerical schemes should be verified for practical applications. The implementation of source function is the most crucial factor for the consistency of modeling schemes. While we have to use the sinc function normalized by grid spacing to correctly describe the Dirac delta function in the finite-difference method, we can simply use the value of basis function, regardless of grid spacing, to implement the Dirac delta function in the finite-element method. If we use frequency-domain wave equation, we need to use a conservative criterion to determine both sampling interval and maximum frequency for the source wavelet generation. In addition, the source wavelet should be attenuated before applying it for modeling in order to make it obey damped wave equation in case of using complex angular frequency. With these conditions satisfied, we can develop reliable inversion algorithms.

• Proceedings of the KSEEG Conference
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• 2002.04a
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• pp.167-169
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• 2002

The extended Born, or localized nonlinear approximation of integral equation (IE) solution has been applied to inverting single-hole electromagnetic (EM) data using a cylindrically symmetric model. The extended Born approximation is less accurate than a full solution but much superior to the simple Born approximation. When applied to the cylindrically symmetric model with a vertical magnetic dipole source, however, the accuracy of the extended Born approximation is greatly improved because the electric field is scalar and continuous everywhere. One of the most important steps in the inversion is the selection of a proper regularization parameter for stability. Occam's inversion (Constable et al., 1987) is an excellent method for obtaining a stable inverse solution. It is extremely slow when combined with a differential equation method because many forward simulations are needed but suitable for the extended Born solution because the Green's functions, the most time consuming part in IE methods, are repeatedly re-usable throughout the inversion. In addition, the If formulation also readily contains a sensitivity matrix, which can be revised at each iteration at little expense. The inversion algorithm developed in this study is quite stable and fast even if the optimum regularization parameter Is sought at each iteration step. Tn this paper we show inversion results using synthetic data obtained from a finite-element method and field data as well.

• Geophysics and Geophysical Exploration
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• v.2 no.1
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• pp.43-53
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• 1999

Numerical modeling and inversion for electromagnetic exploration methods are essential to understand behaviour of electromagnetic fields in complex subsurface. In this study, a finite element method was adopted as a numerical scheme for the 2.5-dimensional forward problem. And a finite element equation considering linear conductivity variation was proposed, when 2.5-dimensional differential equation to couple eletric and magnetic field was implemented. Model parameters were investigated for near-field with large source effects and far-field with responses dominantly by homogeneous half-space. Numerical responses by this study were compared with analytic solutions in homogeneous half-space. Blocky inversion model was modified to be applied to the forward calculation in this study and it was also adopted in the inversion algorithm. Resolution for isolated bodies were investigated to confirm possibility and limitation of inversion for electromagnetic exploration data.

• The Bulletin of The Korean Astronomical Society
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• v.45 no.1
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• pp.44.4-45
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• 2020

The solar chromosphere can be observed well through strong absorption lines. We infer the physical parameters of chromospheric plasmas from these lines using a multilayer spectral inversion. This is a new technique of spectral inversion. We assume that the atmosphere consists of a finite number of layers. In each layer the absorption profile is constant and the source function is allowed to vary with optical depth. Specifically, we consider a three-layer model of radiative transfer where the lowest layer is identified with the photosphere and the two upper layers are identified with the chromosphere. This three-layer model is fully specified by 13 parameters. Four parameters can be fixed to prescribed values, and one parameter can be determined from the analysis of a satellite photospheric line. The remaining eight parameters are determined from a constrained least-squares fitting. We applied the multilayer spectral inversion to the spectral data of the Hα and the Ca II 854.21 nm lines taken in a quiet region by the Fast Imaging Solar Spectrograph (FISS) of the Goode Solar Telescope (GST). We find that our model successfully fits most of the observed profiles and produces regular maps of the model parameters. We conclude that our multilayer inversion is useful to infer chromospheric plasma parameters on the Sun.

• Geophysics and Geophysical Exploration
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• v.11 no.1
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• pp.68-77
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• 2008

We have developed an inversion algorithm for loop-loop electromagnetic (EM) data, based on the localised non-linear or extended Born approximation to the solution of the 2.5D integral equation describing an EM scattering problem. Source and receiver configuration may be horizontal co-planar (HCP) or vertical co-planar (VCP). Both multi-frequency and multi-separation data can be incorporated. Our inversion code runs on a PC platform without heavy computational load. For the sake of stable and high-resolution performance of the inversion, we implemented an algorithm determining an optimum spatially varying Lagrangian multiplier as a function of sensitivity distribution, through parameter resolution matrix and Backus-Gilbert spread function analysis. Considering that the different source-receiver orientation characteristics cause inconsistent sensitivities to the resistivity structure in simultaneous inversion of HCP and VCP data, which affects the stability and resolution of the inversion result, we adapted a weighting scheme based on the variances of misfits between the measured and calculated datasets. The accuracy of the modelling code that we have developed has been proven over the frequency, conductivity, and geometric ranges typically used in a loop-loop EM system through comparison with 2.5D finite-element modelling results. We first applied the inversion to synthetic data, from a model with resistive as well as conductive inhomogeneities embedded in a homogeneous half-space, to validate its performance. Applying the inversion to field data and comparing the result with that of dc resistivity data, we conclude that the newly developed algorithm provides a reasonable image of the subsurface.

• Smart Structures and Systems
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• v.21 no.2
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• pp.163-170
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• 2018

The dynamic response of a finite length thermo-piezoelectric rod with variable material properties is investigated in the context of the fractional order theory of thermoelasticity. The rod is subjected to a moving heat source and fixed at both ends. The governing equations are formulated and then solved by means of Laplace transform together with its numerical inversion. The results of the non-dimensional temperature, displacement and stress in the rod are obtained and illustrated graphically. Meanwhile, the effects of the fractional order parameter, the velocity of heat source and the variable material properties on the variations of the considered variables are presented, and the results show that they significantly influence the variations of the considered variables.

• Geophysics and Geophysical Exploration
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• v.19 no.1
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• pp.45-50
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• 2016

Generally, a point source has been routinely used in the electrical resistivity measurements because of easy installation. If steel-cased wells are used as long electrodes, we can expect the better depth of investigation. However, the resistivity data with long electrodes can not be processed with a conventional inversion algorithm because a long electrode produces the different primary potential distribution compared with the point source. In this study, we proposed a new technique to process the electrical resistivity data with long electrodes by replacing the long electrode with a sequence of point electrodes. Comparing the potentials obtained from the technique with the analytic/numerical solution, we ensure that the proposed technique can be used for the numerical resistivity modeling based on the finite difference or finite element method.