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Introduction

Wave equation migration for elastic data usually consists of two steps. The first step is wavefield reconstruction in the subsurface from data recorded at the surface. The second step is the application of an imaging condition which extracts reflectivity information from the reconstructed wavefields.

The elastic wave equation migration for multicomponent data can be implemented in two ways. The first approach is to separate recorded elastic data into compressional and transverse (P and S) modes and use the separated data for acoustic wave equation migration separately. This acoustic imaging approach to elastic waves is more frequently used, but it is fundamentally based on the assumption that P and S data can be successfully separated on the surface, which is not always true (Zhe and Greenhalgh, 1997; Etgen, 1988). The second approach is to not separate P and S modes on the surface, but to extrapolate the entire elastic wavefield at once, and then separate wave modes prior to applying an imaging condition. The reconstruction of elastic wavefields can be implemented using various techniques, including reconstruction by time reversal (RTM) (Chang and McMechan, 1994,1986) or by Kirchhoff integral techniques (Hokstad, 2000).

The imaging condition applied to the reconstructed vector wavefields directly determines the quality of the images. Conventional crosscorrelation imaging condition does not separate the wave modes and crosscorrelates the Cartesian components of the elastic. In general, the various wave modes (P and S) are mixed on all wavefield components and cause crosstalk and image artifacts. Yan and Sava (2009) suggest using imaging conditions based on elastic potentials, which require crosscorrelation of separated modes. Potential-based imaging condition creates images that have clear physical meaning, in contrast with images obtained with Cartesian wavefield components, thus justifying the need for wave mode separation.

As the need for anisotropic imaging increases, more processing and migration are performed based on anisotropic acoustic one-way wave equations (Alkhalifah, 1998; Fowler et al., 2010; Shan, 2006; Shan and Biondi, 2005; Alkhalifah, 2000; Fletcher et al., 2009). However, much less research has been done on anisotropic elastic migration based on two-way wave equations. Elastic Kirchhoff migration (Hokstad, 2000) obtains pure-mode and converted mode images by downward continuation of elastic vector wavefields with a visco-elastic wave equation. The wavefield separation is effectively done with elastic Kirchhoff integration, which handles both P and S waves. However, Kirchhoff migration does not perform well in areas of complex geology where ray theory breaks down (Gray et al., 2001), thus requiring migration with more accurate methods, such as reverse time migration.

One of the complexities that impedes elastic wave equation anisotropic migration is the difficulty to separate anisotropic wavefields into different wave modes after reconstructing the elastic wavefields. However, the proper separation of anisotropic wave modes is as important for anisotropic elastic migration as is the separation of isotropic wave modes for isotropic elastic migration. The main difference between anisotropic and isotropic wavefield separation is that Helmholtz decomposition is only suitable for the separation of isotropic wavefields and is inadequate for anisotropic wavefields.

In this chapter, I show how to construct wavefield separators for VTI (vertical transverse isotropy) media applicable to models with spatially varying parameters. I apply these operators to anisotropic elastic wavefields and show that they successfully separate anisotropic wave modes, even for extremely anisotropic media.

The main application of this technique is in the development of elastic reverse time migration. In this case, complete wavefields containing both P and S wave modes are reconstructed from recorded data. The reconstructed wavefields are separated in pure wave modes prior to the application of a conventional crosscorrelation imaging condition. I limit the scope of this chapter only to the wave-mode separation procedure in highly heterogeneous media, although the ultimate goal of this procedure is to aid elastic RTM.


next up previous [pdf]

Next: Separation method Up: Yan and Sava: VTI Previous: Yan and Sava: VTI

2013-08-29