Interferometric modeling of wave propagation in inhomogeneous elastic media using time reversal and reciprocity

Time reversal of arbitrary, elastodynamic wavefields in partially open media can be achieved by measuring the wavefield on a surface surrounding the medium and applying the time reverse of those measurements as a boundary condition. We use a representation theorem to derive an expression for the time-reversed wavefield at arbitrary points in the interior. When this expression is used to compute, in a second point, the time-reversed wavefield originating from a point source, the time-reversed Green’s function between the two points is observed. By invoking reciprocity, we obtain an expression that is suitable for modeling of wave propagation through the medium. From this we develop an efficient and flexible two-stage modeling scheme. In the initial phase, the model is illuminated systematically from a surface surrounding the medium using a sequence of conventional forward-modeling runs. Full waveforms are stored for as many points in the interior as possible. In the second phase, Green’s functions between arbitrary points in the volume can be computed by crosscorrelation and summation of data computed in the initial phase. We illustrate the method with a simple acoustic example and then apply it to a complex region of the elastic Pluto model. It is particularly efficient when Green’s functions are desired between a large number of points, but where there are few common source or receiver points. The method relies on interference of multiply scattered waves, but it is stable. We show that encoding the boundary sources using pseudonoise sequences and exciting them simultaneously, akin to daylight imaging, is inefficient and in all explored cases leads to relatively high-noise levels.