Elastic wave modelling and reverse-time migration by a staggered-grid finite-difference method

Zaiming Jiang

ABSTRACT

Four aspects of reverse-time migration are discussed. They are wave modelling, computational boundaries, reverse-time migration algorithms, and computational resources.

Wave modelling is a part of reverse-time migration. Finite-difference methods based on staggered-grid schemes are studied to model wave phenomena in elastic media. Modelled wave cases include 1D P-wave, 2D SH-wave, 2D P-SV wave and 3D-wave cases, and analyzed wave phenomena and seismic problems include wave velocity, wavelength, geometrical spreading, seismic resolution, surface boundary, seismic reflection, transmission, and diffraction, different situations of head waves, guided waves, Rayleigh waves, rigid boundaries, and so on. It is found that the modelling results are usually faithful to the real world and are consistent with seismic theories.

The computational boundary problem has been a persistent topic in the literature of wave modelling. After examining two of the most popular solutions to the problem, absorbing boundary conditions, and a nonreflecting boundary condition, a method of combining these two solutions is proposed. The proposed method results in fewer boundary reflections with little computational cost.

Reverse-time migration is the heart of the dissertation. There are three special features of the method studied in the dissertation. One feature is the finite-difference method employed. People have practiced wave modelling on both non-staggered and staggered grids, but they rarely use staggered-grid schemes in reverse-time migration despite the known advantages the staggered-grid schemes. This dissertation applies a staggered-grid scheme to reverse-time migration. The second feature about the migration method is a new method of imaging conditions for elastic reverse-time migration, which is referred to as 'source energy normalized imaging conditions'. The third feature is the reverse-time migration workflow for multicomponent seismic data processing. It is unique in some way. For example, ground roll suppression is not a necessary part in the workflow.

High demands of computational resources pose challenges and are a drawback for finite-difference depth migration methods. On this topic, the dissertation briefly discusses parallel computing and the problem of disk space.

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