Summary
Seismic exploration in the conditions of complex surface topography in western China is a world-wide problem. A complex surface and weathering zone has a great influence on the results of seismic processing. The traditional rectangular grid finite difference method is difficult to adapt to the fluctuation of surface topography, but the difference method based on triangular grid can be used directly for forward modeling on models with complex top surfaces and migration without statics preprocessing. In this paper, we propose a layered irregular grid finite difference method, and apply it in acoustic wave finite difference prestack reverse-time migration. Tests on model data verify that the method introduced here can achieve perfect results in application.
Introduction
Complex near-surface problems are often accompanied by intense fluctuation, steep dip angle and the big change of speed, which affect the quality of image at near surface seriously. At present, there are two main types to treat irregular surface: the first one is to correct the surface wave field through the static correction methods, and the second one is to finish the depth migration imaging of irregular surface directly. But it’s difficult to calculate the static correction values in areas with complex structures, and it’s also difficult for static correction to eliminate distortion on seismic wave field caused by irregular topography. So it is the direct depth migration imaging at irregular surface that becomes the focus of our research.
The traditional finite difference algorithm is implemented based on rectangular grid, so the curved interface or irregular surface can be only replaced by a series of ladderlike line, which may cause the false dispersion error in the process of numerical calculation. In recent years, scholars made a lot of researches, aiming at the shortcomings of the rectangular grid. Some scholars applied the elastic wave equation under the rectangular grid in the curved coordinate system, and transformed the irregular interface regional into the regular with an auxiliary coordinate system (Tessmer, 1992; Heshtolm, 1994; Nielsen, 1994; et al.). Fornberg and Komatitsch realized the pseudo-spectral method forward modeling under the body-fitted grid. Chu and Wang (2005) applied the triangular grid into the seismic forward modeling. Then it’s easy to adapt to the irregular surface. But generating grid requires a great deal of computation. Xiaodong Sun (2011) applied the method of irregular topography into the prestack reverse-time migration.
