Extended images in action

Image gathers as a function of subsurface offset are an important tool for migration-velocity and amplitude-versus-angle analysis in areas of complex geology. Traditionally, these gathers are thought of as multidimensional correlations of the source and receiver wavefields. The bottleneck in computing the gathers lies in the fact that one needs to store and compute these wavefields and in correlating the wavefields to obtain the desired image gathers. Therefore, the image gathers are typically only computed for a limited number of subsurface points and for a limited range of subsurface offsets. In this presentation, we offer a new perspective on such gathers by organizing the extended image as a function of all subsurface offsets for all subsurface points in a matrix whose (i,j) entry captures the interaction between gridpoints i and j. Of course, it is infeasible to form and store this matrix. Instead, we propose an efficient algorithm to glean information from the image volume via the action of matrix-vector products with this matrix. We illustrate how this can be used to (i) form conventional image gathers and construct objective functions for automated MVA and (ii) calculate true two-way wave-equation angle gathers that allow us to carry out linearized angle-versus-offset inversion with geologic-dip correction. This is joint work with Tristan van Leeuwen and Rajiv Kumar.