Progress in research on transmission loss compensation for one-way wave equations in mixed domains
Exploration geophysicist Claerbout proposed the one-way wave equation and applied it to seismic migration imaging in 1985. This method is widely used in seismic migration due to its advantages such as high calculation efficiency and high calculation accuracy under complex media conditions. The one-way wave equation is obtained by approximately splitting the two-way wave equation along the main propagation direction of the seismic wave (usually defined as the depth direction). Therefore, when using the one-way wave equation to calculate the wave field, there will be a large amplitude error. The amplitude error mainly includes geometric diffusion, Q attenuation, and transmission loss. The first two errors are better corrected, and the transmission loss problem is limited by the traditional one-way wave equation solution and has not been solved well.
Sun Weijia, a postdoctoral fellow in the Department of Seismology, Laboratory of Deep Earth Structures and Processes, Institute of Geology and Geophysics, Chinese Academy of Sciences, and researcher Fu Liyun, a co-supervisor, conducted relevant research on the theoretical issues of single-pass wave equation transmission loss compensation. They first divided the underground medium into a series of thin plates (as shown in Figure 1); then established the boundary integral equations at the upper and lower boundaries, and solved the equations to obtain the solution of the one-way wave equation that compensated for transmission losses. The traditional method usually divides the underground medium into a series of thin slices, that is, the seismic wave field at the depth z has no transmission relationship with the seismic wave field at the upper and lower layers, and this method divides the underground medium into a series of thin plates, that is, the seismic wave at the depth z The field considers the transmission effect of the seismic wave field at the upper and lower boundaries, which is the key to successfully solve the theoretical problem of one-way wave equation transmission loss compensation. Figure 2 compares the transmission coefficients calculated by the traditional one-way wave equation, the method in this study, and the full-wave finite difference method, where the transmission coefficient is defined as the amplitude ratio (A2 / A1) above and below the interface. It is found by comparison that the transmission coefficient calculated by the method in this study is very consistent with the transmission coefficient calculated by the full-wave finite difference method.
The research results were recently published in the internationally renowned geophysics journal Geophysics (Sun et al. Compensation for transmission losses based on one-way propagators in the mixed domain. Geophysics. 2012, 77 (3): 65-72).
Figure 1: Schematic diagram of non-uniform media divided into thin plates. And Γ2 are the upper and lower boundaries of the thin plate, and the two sides of the thin plate extend to infinity.
Figure 2: Two-layer fault model a) and transmission coefficient b) calculated by different methods. The thin solid line represents the transmission coefficient calculated by the traditional one-way wave equation, the thick solid line represents the transmission coefficient calculated by the method in this paper, and the dotted line represents the transmission coefficient calculated by the full-wave finite difference method.
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