Imaging Conditions for Time-reverse Acoustics

The time reverse modeling (TRM) algorithm is almost identical to making shot illumination maps in shot-profile migration by extracting the zero lag of an autocorrelated wave field after successive extrapolation steps. Time reverse modeling is designed to locate sources within a model domain by producing energy intensity images after propagating reversed data traces into the interior of the domain with wave-equation extrapolators. This is closely related to illumination maps because both procedures require extrapolation of a seismic wave field into the model domain, but differ by utilizing slightly variant imaging conditions. The imaging condition for TRM is conventionally the maximum amplitude value extracted from the time axis after propagation. This assumes that the energy recorded at each receiver will constructively interfere in the model domain at the (x-z) location of the source to produce a maximum. The autocorrelation imaging condition for an illumination map solves the same kinematic imaging problem but differs from TRM by a square-root.