Microlocal Analysis of Borehole Seismic Data

Abstract: Borehole seismic data is obtained by receivers located in a well, with sources located on the surface, or in another well. We study approximate reconstruction of the soundspeed using linearized filtered backprojection for three types of data sets. The sources may form a dense array on the surface, or be located along a line on the surface (walk-away geometry) or in another borehole (crosswell). We show that for the dense array, reconstruction is feasible, with no artifacts in the absence of caustics in the background ray geometry, and mild artifacts in the presence of fold caustics in a sense that we define. In contrast, the walk-away and crosswell data sets both give rise to strong, non removable artifacts.