Isotropic angle-domain elastic reverse-time migration

Wavefield imaging

Seismic imaging is based on numerical solutions to wave equations, which can be classified into ray-based (integral) solutions and wavefield-based (differential) solutions. Kirchhoff migration is a typical ray-based imaging procedure which is computationally efficient but often fails in areas of complex geology, such as sub-salt, because the wavefield is severely distorted by lateral velocity variations leading to complex multipathing. Wavefield imaging works better for complex geology, but is more expensive than Kirchhoff migration. Depending on computational time constraints and available resources, different levels of approximation are applied to accelerate imaging, i.e. one-way vs. two-way, acoustic vs. elastic, isotropic vs. anisotropic, etc.

Despite the complexity of various types of wavefield migration algorithms, any wavefield imaging method can be separated into two parts: wavefield reconstruction followed by the application of an imaging condition. For prestack depth migration, source and receiver wavefields have to be reconstructed at all locations in the subsurface. The wavefield reconstruction can be carried out using extrapolation in either depth or time , and with different modeling approaches, such as finite-differences (Dablain, 1986; Alford et al., 1974), finite-elements (Bolt and Smith, 1976), or spectral methods (Dai and Cheadle, 1996; Seriani et al., 1992; Seriani and Priolo, 1991) . After reconstructing wavefields with the recorded data as boundary conditions into the subsurface, an imaging condition must be applied at all locations in the subsurface in order to obtain a seismic image. The simplest types of imaging conditions are based on cross-correlation or deconvolution of the reconstructed wavefields (Claerbout, 1971). These imaging conditions can be implemented in the time or frequency domain depending on the domain in which wavefields have been reconstructed. Here, we concentrate on reverse-time migration with wavefield reconstruction and imaging condition implemented in the time domain.

Isotropic angle-domain elastic reverse-time migration