Three‐dimensional, prestack, plane wave migration of teleseismic P‐to‐S converted phases: 1. Theory

Abstract

We present the theoretical foundations for a prestack migration technique to image teleseismic P‐to‐S converted phases. The method builds on teleseismic P wave deconvolution, pseudostation stacking [Neal and Pavlis, 1999] and on the idea of using a plane wave decomposition for imaging as introduced by Treitel et al. [1982]. Deconvolution operators are constructed by pseudostation stacking of the array aligned to the incident P wave arrival times to produce a space‐variable deconvolution operator. The resulting data are then muted to remove the deconvolved direct P wave pulse and pseudostation stacked over a grid of feasible slowness vectors. The pseudostation stack interpolates the wave field onto a regular grid along Earth's surface producing a series (one per slowness vector) of uniformly sampled three‐dimensional data cubes (two space variables and time). The plane wave components can be propagated downward using a form of approximate ray tracing with a three‐dimensional Earth model. This yields a series of distorted cubes topologically equivalent to the original uniformly sampled data cubes. These data volumes are summed as a weighted stack with the weights derived from an integration formula for inverse scattering based on the generalized Radon transform. This allows an image of the subsurface to be constructed on an event by event basis beneath the array. We apply this technique to data from the Lodore array that was deployed in northwestern Colorado. The results suggest the presence of a major lithospheric‐scale discontinuity defined by a south dipping boundary.