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Full waveform inversion algorithms are widely used in the construction of subsurface velocity models. In the following study, we propose a Laplace–Fourier-domain waveform inversion algorithm that uses both Laplace-domain and Fourier-domain wavefields to achieve the reconstruction of subsurface velocity models. Although research on the Laplace–Fourier-domain waveform inversion has been published recently that study is limited to fluid media. Because the geophysical targets of marine seismic exploration are usually located within solid media, waveform inversion that is approximated to acoustic media is limited to the treatment of properly identified submarine geophysical features. In this study, we propose a full waveform inversion algorithm for isotropic fluid–solid media with irregular submarine topography comparable to a real marine environment. From the fluid–solid system, we obtained P and S wave velocity models from the pressure data alone. We also suggested strategies for choosing complex frequency bands constructed of frequencies and Laplace coefficients to improve the resolution of the restored velocity structures. For verification, we applied our Laplace–Fourier-domain waveform inversion for fluid–solid media to synthetic data that were reconstructed for fluid–solid media. Through this inversion test, we successfully restored reasonable velocity structures. Furthermore, we successfully extended our algorithm to a field data set. 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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Myung Hoon Kim Yunseok Choi Young Ho Cha Changsoo Shin 《Pure and Applied Geophysics》2009,166(12):1967-1985
In order to correctly interpret marine exploration data, which contain many elastic signals such as S waves, surface waves and converted waves, we have developed both a frequency-domain modeling algorithm for acoustic-elastic coupled media with an irregular interface, and the corresponding waveform inversion algorithm. By applying the continuity condition between acoustic (fluid) and elastic (solid) media, wave propagation can be properly simulated throughout the coupled domain. The arbitrary interface is represented by tessellating square and triangular finite elements. Although the resulting complex impedance matrix generated by finite element methods for the acoustic-elastic coupled wave equation is asymmetric, we can exploit the usual back-propagation algorithm used in the frequency domain through modern sparse matrix technology. By running numerical experiments on a synthetic model, we demonstrate that our inversion algorithm can successfully recover P- and S-wave velocity and density models from marine exploration data (pressure data only). 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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Comparison of Frequency-Selection Strategies for 2D Frequency-Domain Acoustic Waveform Inversion 总被引：1，自引：0，他引：1
Youngseo Kim Hobum Cho Dong-Joo Min Changsoo Shin 《Pure and Applied Geophysics》2011,168(10):1715-1727
Several frequency-selection strategies have been used to obtain global minimum solutions in waveform inversion. One strategy,
called the discretization method, is to discretize frequencies with a large sampling interval to minimize redundancy in wavenumber
information. Another method, the grouping method, groups frequencies with redundancy in wavenumber information. The grouping
method can be carried out in two ways. With the first method, the minimum frequency is fixed and the maximum frequency is
gradually extended upward (i.e., the overlap-grouping method). Under the second method, frequencies are not overlapped across
the groups and waveform inversion proceeds from lower to higher frequency groups (i.e., the individual-grouping method). In
this study, we compare these three frequency-selection strategies using both synthetic and real data examples based on logarithmic
waveform inversion. Numerical examples for synthetic and real field data demonstrate that the three frequency-selection methods
provide solutions closer to the global minimum compared to solutions resulting from simultaneously performed waveform inversion,
and that the individual-grouping method yields slightly better resolution for the velocity models than the other methods,
particularly for the deeper part. These results may imply that using either too small or too large data sets at every stage
slightly deteriorates inversion results, and that grouping data in appropriately sized aggregations improves inversion results. 相似文献
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通过在频率域双程波动方程模拟算法中加入一个复数频率（实部表示频率,虚部表示衰减因子）压制地震波初至走时之后的能量,从而把初至走时及其振幅的计算问题转换为单一频率波场中最大能量走时和振幅的拾取问题,然后利用单一频率域波场的相位项和振幅项分别计算初至走时及其振幅.本文还提出利用参数分析方法求取最优的复数频率,并给出数值计算例子,将本方法的计算结果与有限差分程函方程初至走时和最大能量走时振幅进行比较,结果表明,该方法具有适应于任意复杂介质和多炮多接收点走时和振幅的计算. 相似文献
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While most research has mainly focused on the volume change, flow, and shear strength of unsaturated earth materials, investigations of tensile strength of unsaturated earth materials especially granular materials have not received much attention except for cemented and clayey materials. Thus, direct tension experiments were carried out to quantify the actual magnitude of tensile strength induced by water in moist granular soil at especially low water contents (w<4%). The magnitudes of the measured tensile strength are significantly different from zero. A simple experimental tensile strength model is proposed. Practicing engineers can use this model for approximate estimation of the tensile strength of unsaturated granular soils without experiments and for precise design or analysis of most engineered facilities relying on the unsaturated granular soils in the vadose zone. The experimental data are also compared with a theoretical model developed for monosized spheres at low water contents, and its application for a real granular earth material having a variety of particles is discussed. The nonlinear behavior of the tensile strength for moist granular soil is appropriately simulated with a model. 相似文献
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A fully three‐dimensional finite‐element algorithm has been developed for simulating controlled‐source electromagnetic surveys. To exploit the advantages of geometric flexibility, frequency‐domain Maxwell's equations of the secondary electric field were discretised using edge‐based finite elements while the primary field was calculated analytically for a horizontally layered‐earth model. The resulting system of equations for the secondary field was solved using a parallel version of direct solvers. The accuracy of the algorithm was successfully verified by comparisons with integral‐equations and iterative solutions, and the applicability to models containing large conductivity contrasts was verified against published data. The advantages of geometry‐conforming meshes have been demonstrated by comparing different mesh systems to simulate an inclined sheet model. A comparison of the performance between direct and iterative solvers demonstrated the superior efficiency of direct solvers, particularly for multisource problems. 相似文献