• 한국지구물리탐사학회:학술대회논문집
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• 2006.06a
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• pp.131-135
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• 2006

A seismic waveform inversion for prestack seismic data based on the Gauss-Newton method is presented. The Gauss-Newton method for seismic waveform inversion was proposed in the 80s but has rarely been studied. Extensive computational and memory requirements have been principal difficulties. To overcome this, we used different sizes of grids in the inversion stage from those of grids in the wave propagation simulation, temporal windowing of the simulation and approximation of virtual sources for calculating partial derivatives, and implemented this algorithm on parallel supercomputers. We show that the Gauss-Newton method has high resolving power and convergence rate, and demonstrate potential applications to real seismic data.

• Geophysics and Geophysical Exploration
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• v.22 no.4
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• pp.202-209
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• 2019

In this study, an acoustic full-waveform inversion using Adam optimizer was proposed. The steepest descent method, which is commonly used for the optimization of seismic waveform inversion, is fast and easy to apply, but the inverse problem does not converge correctly. Various optimization methods suggested as alternative solutions require large calculation time though they were much more accurate than the steepest descent method. The Adam optimizer is widely used in deep learning for the optimization of learning model. It is considered as one of the most effective optimization method for diverse models. Thus, we proposed seismic full-waveform inversion algorithm using the Adam optimizer for fast and accurate convergence. To prove the performance of the suggested inversion algorithm, we compared the updated P-wave velocity model obtained using the Adam optimizer with the inversion results from the steepest descent method. As a result, we confirmed that the proposed algorithm can provide fast error convergence and precise inversion results.

• Geophysics and Geophysical Exploration
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• v.14 no.3
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• pp.214-219
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• 2011

We perform the frequency-domain waveform inversion based on the residual-selection strategy. In the residual-selection strategy, we classify time-domain residual wavefields into several groups according to the order of absolute amplitudes. Because the residual wavefields are normalized after regularization of the gradient directions within each group, the residual-selection strategy plays a role in enhancing the small-amplitude wavefields, which contributes to improving the deep parts of inverted subsurface images. After classifying residuals in the time domain, they are transformed to the frequency domain. Waveform inversion is performed in the frequency domain using the back-propagation technique which has been popularly used in reverse-time migration. The residual-selection strategy is applied to the SEG/EAGE salt and IFP Marmousi models. Numerical results show that the residual-selection strategy yields better results than the conventional frequency-domain waveform inversion.

• Geophysics and Geophysical Exploration
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• v.5 no.1
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• pp.33-45
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• 2002

It was necessary to devise new techniques to overcome and enhance the resolution limits of traveltime tomography. Waveform inversion has been one of the methods for giving very high resolution result. High resolution image could be acquired because waveform inversion used not only phase but amplitude. But waveform inversion was much time consuming Job because forward and backward modeling was needed at each iteration step. Velocity-stress method was used for effective modeling. Resolution limits of imaging methods such as travel time inversion, acoustic and elastic waveform inversion were investigated with numerical models. it was investigated that Resolution limit of waveform inversion was similar tn resolution limit of migration derived by Schuster. Horizontal resolution limit could be improved with increased coverage by adding VSP data in cross hole that had insufficient coverage. Also, waveform inversion was applied to realistic models to evaluate applicability and using initial guess of travel time tomograms to reduce non-linearity of waveform inversion showed that the better reconstructed image could be acquired.

• 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.

• Geophysics and Geophysical Exploration
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• v.11 no.3
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• pp.177-183
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• 2008

The sub-salt imaging technique becomes more crucial to detect the hydro-carbonates in petroleum exploration as the target reservoirs get deeper. However, the weak reflections from the sub-salt structures prevent us from obtaining high fidelity sub-salt image. As an effort to overcome this difficulty, we applied the waveform inversion by implementing multi-grid technique to the sub-salt imaging. Through the comparison between the conventional waveform inversion using fixed grid and the multi-grid technique, we confirmed that the waveform inversion using multi-grid technique has advantages over the conventional fixed grid waveform inversion. We showed that the multi-grid technique can complement he velocity estimation result of the waveform inversion for imaging the sub-salt structures, of which velocity model cannot be obtained correctly by the conventional fixed grid waveform inversion.

• Geophysics and Geophysical Exploration
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• v.23 no.1
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• pp.38-49
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• 2020

Full-waveform inversion (FWI) is an optimization process of fitting observed and modeled data to reconstruct high-resolution subsurface physical models. In acoustic FWI (AFWI), pressure data acquired using a marine streamer has mainly been used to reconstruct the subsurface P-wave velocity models. With recent advances in marine seismic-acquisition techniques, acquiring multi-component data in marine environments have become increasingly common. Thus, AFWI strategies must be developed to effectively use marine multi-component data. Herein, we proposed an AFWI strategy using horizontal and vertical particle-acceleration data. By analyzing the modeled acoustic data and conducting sensitivity kernel analysis, we first investigated the characteristics of each data component using AFWI. Common-shot gathers show that direct, diving, and reflection waves appearing in the pressure data are separated in each component of the particle-acceleration data. Sensitivity kernel analyses show that the horizontal particle-acceleration wavefields typically contribute to the recovery of the long-wavelength structures in the shallow part of the model, and the vertical particle-acceleration wavefields are generally required to reconstruct long- and short-wavelength structures in the deep parts and over the whole area of a given model. Finally, we present a sequential-inversion strategy for using the particle-acceleration wavefields. We believe that this approach can be used to reconstruct a reasonable P-wave velocity model, even when the pressure data is not available.

• Geophysics and Geophysical Exploration
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• v.22 no.2
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• pp.49-55
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• 2019

In this study, we presented a reference-shot subset method for stable convergence of full waveform inversion using a cyclic-shot subsampling technique. Full waveform inversion needs repetitive modeling of wave propagation and thus its calculation time increases as the number of sources increases. In order to reduce the computation time, we can use a cyclic-shot subsampling method; however, it makes the cost function oscillate in the early stage of the inversion and causes a problem in applying the convergence criteria. We introduced a method in which the cost function is calculated using a fixed reference-shot subset while updating the model parameters using the cyclic-shot subsampling method. Through the examples of full waveform inversion using the Marmousi velocity model, we confirmed that the convergence of cost function becomes stable even under the cyclic-shot subsampling method if using a reference-shot subset.

• Geophysics and Geophysical Exploration
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• v.14 no.3
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• pp.220-226
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• 2011

In the elastic wave equations, both horizontal and vertical displacements are defined. Since we can measure both the horizontal and vertical displacements in field acquisition, these displacements compose a displacement vector. In this study, we propose a frequency-domain elastic waveform inversion technique taking advantage of the magnitudes of displacement vectors to define objective function. When we apply this displacement-vector objective function to the frequency-domain waveform inversion, the inversion process naturally incorporates the back-propagation algorithm. Through the inversion examples with the Marmousi model and the SEG/EAGE salt model, we could note that the RMS error of the solution obtained by our algorithm decreased more stably than that of the conventional method. Particularly, the density of the Marmousi model and the low-velocity sub-salt zone of the SEG/EAGE salt model were successfully recovered. Since the gradient direction obtained from the proposed objective function is numerically unstable, we need additional study to stabilize the gradient direction. In order to perform the waveform inversion using the displacementvector objective function, it is necessary to acquire multi-component data. Hence, more rigorous study should be continued for the multi-component land acquisition or OBC (Ocean Bottom Cable) multi-component survey.

• Geophysics and Geophysical Exploration
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• v.20 no.4
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• pp.199-206
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• 2017

Field data obtained from marine exploration are influenced by various environmental factors such as wind, waves, tidal current and flow velocity of a background medium. Most environmental factors except for the flow velocity are properly corrected in the data processing stage. In this study, the wave equation modeling considering flow velocity is used to generate observation data, and numerical experiments using the observation data were conducted to analyze the effect of flow velocity on waveform inversion. The numerical examples include the results with unrealistic flow velocities. In addition, an algorithm is suggested to numerically extract flow velocity for waveform inversion. The proposed algorithm was applied to the modified Marmousi2 model to obtain the results depending on the flow velocity. The effect of flow velocity on updated physical properties was verified by comparing the inversion results without considering flow velocity and those obtained from the proposed algorithm.