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Velocities

In the theory developed above, there is an allowance for differing source and receiver wavefield velocities (vs and vg). This occurs with different wavefield scattering modes. Figure [*] illustrates the primary elastic scattering modes arising in teleseismic imaging for an incident planar P-wave source. In the forward-scattering scenario, two modes arise when the incident wavefront refracts/converts from a given scattering point. The same incident P-wavefront also reflects/converts downward from the free-surface and then reflects/converts upward from the same scattering point. Accordingly, backscattering gives rise to four in-plane scattering modes (plus one out-of-plane SV to SH scattering mode; see Table 1).

 
Modes
Figure 4
Diagram of primary scattering elastic scenarios in teleseismic imaging. Incident P-wavefront directly refracts/converts from a scattering point, but also may reflect/convert downward from the free-surface and then reflect/convert upward from the scattering point. Legs spent as P- and S-waves are drawn in black and light gray, respectively
Modes
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To represent the difference in propagation direction of source wavefronts in the forward- and backscattering scenarios, a negative velocity is used. That is, for forward- and backscattering, velocities of opposite and like sign are used, respectively. This is the equivalent of choosing to take the complex conjugate of both the source and receiver wavefields in the forward-scattering scenario Claerbout (1971). Table 1 in the Appendix A gives the velocities used for all six primary elastic scattering modes.


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Stanford Exploration Project
7/8/2003