The Experts below are selected from a list of 1434 Experts worldwide ranked by ideXlab platform
Changsoo Shin - One of the best experts on this subject based on the ideXlab platform.
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Laplace Domain Full Waveform Inversion Using Single Damping Constant
77th EAGE Conference and Exhibition 2015, 2015Co-Authors: Y Park, Jungkyun Shin, S. Jeon, H. Jin, Changsoo ShinAbstract:We suggest a new method for the Laplace domain full waveform inversion (FWI) which use single damping constant. This method makes the Laplace domain FWI more efficient, because the proposed method uses only one damping constant during inversion process. To scale the gradient Direction properly, we use simple depth window function to Steepest Descent Direction. We demonstrate that the algorithm is working by numerical test using synthetic data set.
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A time-domain waveform inversion using filtering techniques
SEG Technical Program Expanded Abstracts 2010, 2010Co-Authors: Minkyung Son, Youngseo Kim, Changsoo ShinAbstract:If local minima are present in a calculation of an objective function, it is difficult to identify subsurface information. Therefore, it is essential to exploit new technique to reduce the number of local minima in seismic inversions. To make the Steepest Descent Direction head toward the global minimum, we propose using a full waveform inversion with filtering techniques. During the inversion process, we allocated a time window that includes the time corresponding to the highest amplitude of each observed trace. In the calculation of the objective function using an 2 L norm , data contained by the
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Comparison of scaling methods for waveform inversion
Geophysical Prospecting, 2009Co-Authors: Ugeun Jang, Dong-joo Min, Changsoo ShinAbstract:Waveform inversion can lead to faint images for later times due to geometrical spreading. The proper scaling of the Steepest-Descent Direction can enhance faint images in waveform inversion results. We compare the effects of different scaling techniques in waveform inversion algorithms using the Steepest-Descent method. For the scaling method we use the diagonal of the pseudo-Hessian matrix, which can be applied in two different ways. One is to scale the Steepest-Descent Direction at each frequency independently. The other is to scale the Steepest-Descent Direction summed over the entire frequency band. The first method equalizes the Steepest-Descent Directions at different frequencies and minimizes the effects of the band-limited source spectrum in waveform inversion. In the second method, since the Steepest-Descent Direction summed over the entire frequency band is divided by the diagonal of the pseudo-Hessian matrix summed over the entire frequency band, the band-limited property of the source wavelet spectrum still remains in the scaled Steepest-Descent Directions. The two scaling methods were applied to both standard and logarithmic waveform inversion. For standard waveform inversion, the method that scales the Steepest-Descent Direction at every frequency step gives better results than the second method. On the other hand, logarithmic waveform inversion is not sensitive to the scaling method, because taking the logarithm of wavefields automatically means that results for the Steepest-Descent Direction at each frequency are commensurate with each other. If once the Steepest-Descent Directions are equalized by taking the logarithm of wavefields in logarithmic waveform inversion, the additional equalizing effects by the scaling method are not as great as in conventional waveform inversion.
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Magnetotelluric inversion via reverse time migration algorithm of seismic data
Journal of Computational Physics, 2007Co-Authors: Changsoo ShinAbstract:We propose a new algorithm for two-dimensional magnetotelluric (MT) inversion. Our algorithm is an MT inversion based on the Steepest Descent method, borrowed from the backpropagation technique of seismic inversion or reverse time migration, introduced in the middle 1980s by Lailly and Tarantola. The Steepest Descent Direction can be calculated efficiently by using the symmetry of numerical Green's function derived from a mixed finite element method proposed by Nedelec for Maxwell's equation, without calculating the Jacobian matrix explicitly. We construct three different objective functions by taking the logarithm of the complex apparent resistivity as introduced in the recent waveform inversion algorithm by Shin and Min. These objective functions can be naturally separated into amplitude inversion, phase inversion and simultaneous inversion. We demonstrate our algorithm by showing three inversion results for synthetic data.
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Efficient electric resistivity inversion using adjoint state of mixed finite-element method for Poisson's equation
Journal of Computational Physics, 2006Co-Authors: Sukjoon Pyun, Changsoo ShinAbstract:We propose an electric resistivity inversion method that is similar to the reverse time migration technique applied to seismic data. For calculating model responses and inversion, we use the mixed finite-element method with the standard P"1-P"0 pair for triangular decompositions, which makes it possible to compute both the electric potential and the electric field vector economically. In order to apply the adjoint state of the Poisson equation in the resistivity inverse problem, we introduce an apparent electric field defined as the dot product between the computed electric field vector and a weighting factor and then defining a virtual source to compute the partial derivative of the electric field vector. We exploit the adjoint state (the symmetry of Green's function) of matrix equations derived from solving the Poisson equation by the mixed finite-element method, for the calculation of the Steepest Descent Direction of our objective function. By computing the Steepest Descent Direction by a dot product of backpropagated residual and virtual source, we can avoid the cumbersome and expensive process of computing the Jacobian matrix directly. We calibrate our algorithm on a synthetic of a buried conductive block and obtain an image that is compatible with the limits of the resistivity method.
George A. Mcmechan - One of the best experts on this subject based on the ideXlab platform.
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2‐D full‐wavefield inversion for wide‐aperture, elastic, seismic data
Geophysical Journal International, 1992Co-Authors: Robert Sun, George A. McmechanAbstract:SUMMARY Full-wavefield inversion of two-component (elastic), wide-aperture, seismic data from surface sources and receivers simultaneously provides 2-D estimates of both P and SV velocity distributions. The algorithm operates on common-source gathers; it involves cross-correlation of propagating source and residual wavefields to define the Steepest Descent Direction used to update the velocities at each point in a 2-D finite-difference grid. The solution is stable even in the presence of random noise and when the input traces are unequally spaced. Examples include a stack of flat layers and a folded and faulted structure.
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Full-wavefield inversion of wide-aperture SH and Love wave data
Geophysical Journal International, 1991Co-Authors: Robert Sun, George A. McmechanAbstract:SUMMARY Reverse-time linearized inversion is implemented for synthetic wide-aperture SH and Love wave data, including multiple reflections, to estimate the S-wave velocity in a two-dimensionally inhomogeneous medium. Complete wide-aperture wavefields, in which triplications, pre- and post-critical reflections, and surface waves (Love waves) are present, can be imaged by reverse-time inversion to estimate the SH velocity distribution. The algorithm operates on common-source gathers and involves cross-correlation of the source and recorded wavefields to define the Steepest Descent Direction to update the velocity at each point on a finite-difference grid. Effects of noise can be reduced by stacking information from different sources.
Dong-joo Min - One of the best experts on this subject based on the ideXlab platform.
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Comparison of scaling methods for waveform inversion
Geophysical Prospecting, 2009Co-Authors: Ugeun Jang, Dong-joo Min, Changsoo ShinAbstract:Waveform inversion can lead to faint images for later times due to geometrical spreading. The proper scaling of the Steepest-Descent Direction can enhance faint images in waveform inversion results. We compare the effects of different scaling techniques in waveform inversion algorithms using the Steepest-Descent method. For the scaling method we use the diagonal of the pseudo-Hessian matrix, which can be applied in two different ways. One is to scale the Steepest-Descent Direction at each frequency independently. The other is to scale the Steepest-Descent Direction summed over the entire frequency band. The first method equalizes the Steepest-Descent Directions at different frequencies and minimizes the effects of the band-limited source spectrum in waveform inversion. In the second method, since the Steepest-Descent Direction summed over the entire frequency band is divided by the diagonal of the pseudo-Hessian matrix summed over the entire frequency band, the band-limited property of the source wavelet spectrum still remains in the scaled Steepest-Descent Directions. The two scaling methods were applied to both standard and logarithmic waveform inversion. For standard waveform inversion, the method that scales the Steepest-Descent Direction at every frequency step gives better results than the second method. On the other hand, logarithmic waveform inversion is not sensitive to the scaling method, because taking the logarithm of wavefields automatically means that results for the Steepest-Descent Direction at each frequency are commensurate with each other. If once the Steepest-Descent Directions are equalized by taking the logarithm of wavefields in logarithmic waveform inversion, the additional equalizing effects by the scaling method are not as great as in conventional waveform inversion.
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Efficient calculation of the Steepest Descent Direction for source-independent seismic waveform inversion: An amplitude approach
Journal of Computational Physics, 2005Co-Authors: Yunseok Choi, Changsoo Shin, Dong-joo MinAbstract:In seismic waveform inversion, if we have no information on source signature, we need to invert seismic data and source signature either simultaneously or successively. In order to avoid the iterative update of the source signature in waveform inversion based on classical, local optimization techniques, we propose two source-independent objective functions using amplitude spectra of Fourier-transformed wavefields. One is constructed by normalizing the amplitude spectra of observed data and modeled data with respect to the respective reference amplitudes. The other is achieved by cross-multiplying the amplitude spectra of observed data and modeled data with the respective reference amplitudes. In the computation of the Steepest Descent Direction, we circumvent explicitly computing the Jacobian by employing a matrix formalism of the wave equation in the frequency domain. Through numerical examples for the Marmousi model, we demonstrate that our inversion algorithms can reproduce the subsurface velocity structure without estimating source signature.
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efficient calculation of Steepest Descent Direction for source independent waveform inversion using normalized wavefield by convolution
Seg Technical Program Expanded Abstracts, 2004Co-Authors: Soonhong Cheong, Changsoo Shin, Dong-joo Min, Sukjoon Pyun, Sangyong SuhAbstract:Summary In conventional waveform inversion, geophysicists usually invert a velocity model as well as a source signature simultaneously. For a source-independent waveform inversion, we define a new objective function by multiplying both observed data and forward modeled data by the respective reference wavefields on the cross. For computation of the Steepest Descent of the new objective function, we exploit a matrix formalism originated from the symmetry of Green’s function of wave equation. In this case, we calculate the Steepest Descent without explicitly computing the Jacobian matrix. Numerical structure of our algorithm resembles that of prestack reverse-time migration and waveform inversion.
Hataeyoung - One of the best experts on this subject based on the ideXlab platform.
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Efficient calculation of the Steepest Descent Direction for source-independent seismic waveform inversion
Journal of Computational Physics, 2005Co-Authors: Choiyunseok, Shinchangsoo, Mindong-joo, HataeyoungAbstract:In seismic waveform inversion, if we have no information on source signature, we need to invert seismic data and source signature either simultaneously or successively. In order to avoid the iterat...
Yixun Shi - One of the best experts on this subject based on the ideXlab platform.
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Modified Quasi-Newton Methods for Solving Systems of Linear Equations
International Journal of Contemporary Mathematical Sciences, 2007Co-Authors: Yixun ShiAbstract:Quasi-Newton methods for unconstrained optimization problems are considered for solving a system of linear equations Ax = b where A ∈ R n×n , Rank(A )= n, b ∈ R n , and x ∈ R n is the vector of unknowns. This problem can be converted into an equivalent quadratic optimization problem. Based on the observation that if H ≈ (A T A) −1 = A −1 (A T ) −1 then ¯ x = HA T b can be taken as an approximate solution of the problem, we propose a modification to the Quasi-Newton method. The modified algorithm incorporates the above observation. Global convergence is ensured by adding the Steepest Descent Direction into the combination. Numerical experiments are also reported.
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A projected‐Steepest‐Descent potential‐reduction algorithm for convex programming problems
Numerical Linear Algebra with Applications, 2004Co-Authors: Yixun ShiAbstract:A recent work of Shi (Numer. Linear Algebra Appl. 2002; 9: 195–203) proposed a hybrid algorithm which combines a primal-dual potential reduction algorithm with the use of the Steepest Descent Direction of the potential function. The complexity of the potential reduction algorithm remains valid but the overall computational cost can be reduced. In this paper, we make efforts to further reduce the computational costs. We notice that in order to obtain the Steepest Descent Direction of the potential function, the Hessian matrix of second order partial derivatives of the objective function needs to be computed. To avoid this, we in this paper propose another hybrid algorithm which uses a projected Steepest Descent Direction of the objective function instead of the Steepest Descent Direction of the potential function. The complexity of the original potential reduction algorithm still remains valid but the overall computational cost is further reduced. Our numerical experiments are also reported. Copyright © 2004 John Wiley & Sons, Ltd.
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On the projected Descent Direction methods for solving convex programming problems
Neural Parallel & Scientific Computations archive, 2003Co-Authors: Yixun ShiAbstract:A recent paper [14] has considered the possibility of combining interior point strategy with Steepest Descent method when solving convex programming problems, in such a way that the convergence property of the interior point method remains valid but many iterations do not request the solution of a system of equations. Motivated by this general idea, the paper [14] proposed a hybrid algorithm which combines a primal-dual potential reduction algorithm with the use of the Steepest Descent Direction of the potential function. The O(√n|ln e|) complexity of the potential reduction algorithm remains valid but the overall computational cost can be reduced. In this paper, we discuss the relation between this method and general projected Descent Direction methods, and compare it with a projected Steepest Descent Direction method for solving complex programming problems.
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A combination of potential reduction steps and Steepest Descent steps for solving convex programming problems
Numerical Linear Algebra with Applications, 2002Co-Authors: Yixun ShiAbstract:This paper studies the possibility of combining interior point strategy with a Steepest Descent method when solving convex programming problems, in such a way that the convergence property of the interior point method remains valid but many iterations do not request the solution of a system of equations. Motivated by this general idea, we propose a hybrid algorithm which combines a primal–dual potential reduction algorithm with the use of the Steepest Descent Direction of the potential function. The complexity of the potential reduction algorithm remains valid but the overall computational cost can be reduced. Our numerical experiments are also reported. Copyright © 2002 John Wiley & Sons, Ltd.
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Globally Convergent Algorithms for Unconstrained Optimization
Computational Optimization and Applications, 2000Co-Authors: Yixun ShiAbstract:A new globalization strategy for solving an unconstrained minimization problem is proposed based on the idea of combining Newton's Direction and the Steepest Descent Direction WITHIN each iteration. Global convergence is guaranteed with an arbitrary initial point. The search Direction in each iteration is chosen to be as close to the Newton's Direction as possible and could be the Newton's Direction itself. Asymptotically the Newton step will be taken in each iteration and thus the local convergence is quadratic. Numerical experiments are also reported. Possible combination of a Quasi-Newton Direction with the Steepest Descent Direction is also considered in our numerical experiments. The differences between the proposed strategy and a few other strategies are also discussed.