Quasi-Elastic Least-Squares Reverse-Time Migration of PS Reflections

Conventional analysis of amplitude variation with offset for elastic PS reflections is based on analytical reflection coefficients in a layered medium, and wave-equation based PS migration is mainly used to produce a structural image. To overcome this problem, we develop a least-squares reverse-Time migration method for elastic PS reflections based on a quasi-elastic-wave equation. The quasi-elastic-wave equation can accurately model PS reflections with elastic amplitude under the first-order Born approximation. Our least-squares reverse-Time migration method inverts for perturbations of the S-wave velocity/impedance and density by minimizing the L2 norm of the difference between recorded and predicted PS reflections modeled using a quasi-elastic-wave equation. We refer to our new method as quasi-elastic least-squares reverse-Time migration of PS reflections. Numerical tests on synthetic and field data show that our method can properly handle the amplitudes of elastic PS reflections and provides an accurate estimate of the perturbations of S-wave velocity/impedance and density. Extending the method to the 3D case is not straightforward, which might require incorporating certain PS data processing techniques into inversion.