Interferometry by deconvolution: Part 2 — Theory for elastic waves and application to drill-bit seismic imaging

Deconvolution interferometry successfully recovers the impulse response between two receivers without the need for an independent estimate of the source function. Here we extend the method of interferometry by deconvolution to multicomponent data in elastic media. As in the acoustic case, elastic deconvolution interferometry retrieves only causal scattered waves that propagate between two receivers as if one acts as a pseudosource of the point-force type. Interferometry by deconvolution in elastic media also generates artifacts because of a clamped-point boundary condition imposed by the deconvolution process. In seismic-while-drilling (SWD) practice, the goal is to determine the subsurface impulse response from drill-bit noise records. Most SWD technologies rely on pilot sensors and/or models to predict the drill-bit source function, whose imprint is then removed from the data. Interferometry by deconvolution is of most use to SWD applications in which pilot records are absent or provide unreliable estimates of bit excitation. With a numerical SWD subsalt example, we show that deconvolution interferometry provides an image of the subsurface that cannot be obtained by correlations without an estimate of the source autocorrelation. Finally, we test the use of deconvolution interferometry in processing SWD field data acquired at the San Andreas Fault Observatory at Depth (SAFOD). Because no pilot records were available for these data, deconvolution outperforms correlation in obtaining an interferometric image of the San Andreas fault zone at depth.