Summary

It is important to apply certain intrinsic properties (e.g., the wave propagation directions and particle motion information) in reconstructed wavefields in order to solve the image problems exhibited in elastic reverse time migration (RTM). This paper presents a procedure to decompose the source and receiver wavefields into local plane waves as well as to separate them into pure P and S modes. We generate the partial PP and PS images by crosscorrelation of these plane waves along different directions, and then formulate an imaging condition as a product of an angle-domain operator and the partial images. The new angle-domain imaging condition substantially reduces the artifacts in the PP image and produces the PS image with correct polarizations. However, the imaging procedure involves intensive computations. A numerical algorithm, which can greatly reduce the calculation, is proposed to improve the efficiency.

Introduction

Elastic RTM has advantages over acoustic RTM for migrating multi-component data because it more accurately characterizes the physical process of wave propagation in the subsurface. Elastic RTM reconstructs the source wavefields forward in time and receiver wavefields backward in time by finite difference method (Baysal et al., 1983; McMechan, 1983; Whitmore, 1983). It then applies an imaging condition to extract reflectivity information out of the reconstructed wavefields. The elastic imaging condition is more complex than acoustic imaging condition because both source and receiver wavefields are vector fields and each component is composed of P and S modes. Yan and Sava (2008) extensively reviewed various conventional elastic imaging conditions, including imaging with vector displacements and imaging with scalar and vector potentials. They suggested separating the wavefield into P and S mode using Helmholtz decomposition and formulated an extended imaging condition for angledomain imaging. The existing elastic RTM imaging conditions often inherits the drawbacks of acoustic imaging condition, creating strong artifacts in migrated image. The artifacts are resulted from spurious cross-correlation of head waves, diving waves and backscattered waves at the imaging step (Yoon et al., 2004). These events are particularly serious where high velocity contrasts or high velocity gradient exist. Recently, several methods have been proposed to eliminate the artifacts in acoustic RTM scenario. Fletcher et al. (2005) suppressed the image artifacts by introducing a directional damping term to the non-reflecting wave equation. Mulder and Plessix (2004) applied a low-cut filter in wavenumber domain to attenuate the artifacts. Guitton et al. (2006) removed the artifacts with more advanced post-imaging filters, e.g., Laplacian filter, derivative filter and least square filter. Yoon et al. (2004) suggested putting a weighting function to the imaging condition according to the reflection angle, which is calculated from Poynting vectors of source and receiver waves. Xie and Wu (2006) decomposed the full wavefields into their one-way components along horizontal and vertical directions by Rayleigh integral and applied the imaging condition to the appropriate combinations of the wave components. Liu et al. (2007) tested the vertical wave imaging condition, but they used Fourier transform to get one-way component.

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