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Ho Seuk Bae Sukjoon Pyun Wookeen Chung Seung‐Goo Kang Changsoo Shin 《Geophysical Prospecting》2012,60(3):413-432
We developed a frequency‐domain acoustic‐elastic coupled waveform inversion based on the Gauss‐Newton conjugate gradient method. Despite the use of a high‐performance computer system and a state‐of‐the‐art parallel computation algorithm, it remained computationally prohibitive to calculate the approximate Hessian explicitly for a large‐scale inverse problem. Therefore, we adopted the conjugate gradient least‐squares algorithm, which is frequently used for geophysical inverse problems, to implement the Gauss‐Newton method so that the approximate Hessian is calculated implicitly. Thus, there was no need to store the Hessian matrix. By simultaneously back‐propagating multi‐components consisting of the pressure and displacements, we could efficiently extract information on the subsurface structures. To verify our algorithm, we applied it to synthetic data sets generated from the Marmousi‐2 model and the modified SEG/EAGE salt model. We also extended our algorithm to the ocean‐bottom cable environment and verified it using ocean‐bottom cable data generated from the Marmousi‐2 model. With the assumption of a hard seafloor, we recovered both the P‐wave velocity of complicated subsurface structures as well as the S‐wave velocity. Although the inversion of the S‐wave velocity is not feasible for the high Poisson's ratios used to simulate a soft seafloor, several strategies exist to treat this problem. Our example using multi‐component data showed some promise in mitigating the soft seafloor effect. However, this issue still remains open. 相似文献
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Elastic waves, such as Rayleigh and mode‐converted waves, together with amplitude versus offset variations, serve as noise in full waveform inversion using the acoustic approximation. Heavy preprocessing must be applied to remove elastic effects to invert land or marine data using the acoustic inversion method in the time or frequency domains. Full waveform inversion using the elastic wave equation should be one alternative; however, multi‐parameter inversion is expensive and sensitive to the starting velocity model. We implement full acoustic waveform inversion of synthetic land and marine data in the Laplace domain with minimum preprocessing (i.e., muting) to remove elastic effects. The damping in the Laplace transform can be thought of as an automatic time windowing. Numerical examples show that Laplace‐domain acoustic inversion can yield correct smooth velocity models even with the noise originating from elastic waves. This offers the opportunity to develop an accurate smooth starting model for subsequent inversion in the frequency domain. 相似文献
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This is the first in a series of three papers focused on using variants of a logarithmic objective function approach to full waveform inversion. In this article, we investigate waveform inversion using full logarithmic principles and compare the results with the conventional least squares approach. We demonstrate theoretically that logarithmic inversion is computational similar to the conventional method in the sense that it uses exactly the same back‐propagation technology as used in least‐squares inversion. In the sense that it produces better results for each of three numerical examples, we conclude that logarithmic inversion is also more robust. We argue that a major reason for the inherent robustness is the fact that the logarithmic approach produces a natural scaling of the amplitude of the residual wavefield by the amplitude of the modelled wavefield that tends to stabilize the computations and consequently improve the final result. We claim that any superiority of the logarithmic inversion is based on the fact that it tends to be tomographic in the early stage of the inversion and more dependent on amplitude differences in the latter stages. 相似文献
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In the second paper of this three part series, we studied the case of conventional and logarithmic phase‐only approaches to full‐waveform inversion. Here, we concentrate on deriving amplitude‐only approaches for both conventional‐ and logarithmic‐based methods. We define two amplitude‐only objective functions by simply assuming that the phase of the modelled wavefield is equal to that of the observed wavefield. We do this for both the conventional least‐squares approach and the logarithmic approach of Shin and Min. We show that these functions can be optimized using the same reverse‐time propagation algorithm of the full conventional methodology. Although the residuals in this case are not really residual wavefields, they can both be considered and utilized in that sense. In contrast to the case for our phase‐only algorithms, we show through numerical tests that the conventional amplitude‐only inversion is better than the logarithmic method. 相似文献
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Comparison of waveform inversion, part 2: phase approach 总被引：1，自引：0，他引：1
In this paper, we take advantage of the natural separation into amplitude and phase of a logarithmic‐based approach to full‐wavefield inversion and concentrate on deriving purely kinematic approaches for both conventional and logarithmic‐based methods. We compare the resulting algorithms theoretically and empirically. To maintain consistency between this and the previous paper in this series, we continue with the same symbolism and notation and apply our new algorithms to the same three data sets. We show that both of these new techniques, although different in implementation style, share the same computational methodology. We also show that reverse‐time back‐propagation of the residuals for our new kinematic methods continues to be the basis for calculation of the steepest‐descent vector. We conclude that the logarithmic phase‐based method is more practical than its conventionally based counterpart, but, in spite of the fact that the conventional algorithm appears unstable, differences are not great. 相似文献
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In this paper we propose a 3D acoustic full waveform inversion algorithm in the Laplace domain. The partial differential equation for the 3D acoustic wave equation in the Laplace domain is reformulated as a linear system of algebraic equations using the finite element method and the resulting linear system is solved by a preconditioned conjugate gradient method. The numerical solutions obtained by our modelling algorithm are verified through a comparison with the corresponding analytical solutions and the appropriate dispersion analysis. In the Laplace‐domain waveform inversion, the logarithm of the Laplace transformed wavefields mainly contains long‐wavelength information about the underlying velocity model. As a result, the algorithm smoothes a small‐scale structure but roughly identifies large‐scale features within a certain depth determined by the range of offsets and Laplace damping constants employed. Our algorithm thus provides a useful complementary process to time‐ or frequency‐domain waveform inversion, which cannot recover a large‐scale structure when low‐frequency signals are weak or absent. The algorithm is demonstrated on a synthetic example: the SEG/EAGE 3D salt‐dome model. The numerical test is limited to a Laplace‐domain synthetic data set for the inversion. In order to verify the usefulness of the inverted velocity model, we perform the 3D reverse time migration. The migration results show that our inversion results can be used as an initial model for the subsequent high‐resolution waveform inversion. Further studies are needed to perform the inversion using time‐domain synthetic data with noise or real data, thereby investigating robustness to noise. 相似文献
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This paper presents a mathematical model which computes the hydrodynamic characteristics of a curtainwall–pile breakwater (CPB) using circular piles, by modifying the model developed for rectangular piles by Suh et al. [2006. Hydrodynamic characteristics of pile-supported vertical wall breakwaters. Journal of Waterway, Port, Coastal and Ocean Engineering 132(2), 83–96]. To examine the validity of the model, laboratory experiments have been conducted for CPB with various values of draft of curtain wall, spacing between piles, and wave height and period. Comparisons between measurement and prediction show that the mathematical model adequately reproduces most of the important features of the experimental results. The mathematical model based on linear wave theory tends to over-predict the reflection coefficient as the wave height increases. As the draft of the curtain wall increases and the porosity between piles decreases, the reflection and transmission coefficient increases and decreases, respectively, as expected. As the relative water depth increases, however, the effect of porosity disappears because the wave motion is minimal in the lower part of a water column for short waves. 相似文献
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Convergence criteria are provided for truncating the evanescent eigenmode series in the Green's function for vertical, axisymmetric bodies of revolution. To numerically compute the strength of the source distribution for both the exciting and restoring forces, separate criteria are required for the off-diagonal and for the diagonal elements in the matrix of coefficients for the source strengths. The Black-Fenton algorithms for wave-induced exciting forces on vertical axisymmetric bodies of revolution are extended to include the wave-induced restoring forces. The Gauss-Seidel matrix version method recommended by Fenton is compared with the Gauss elimination method and is found to be non-converging for near deep water wave conditions. Comparison between theory and measured data for the dynamic response of a discus buoy demonstrates the convergence criteria over a range of dimensionless frequencies in relatively deep water wave conditions. 相似文献
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