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![]() | Passive seismic imaging applied to synthetic data | ![]() |
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The proof of this conjecture for a one dimensional earth is given as a
problem set in Claerbout (1976).
The outline of the derivation that follows uses
the transform approach developed there, where
is the unit
delay operator
.
Consider a plane-layered Earth model with the reflection seismology
geometry shown in Figure 1. If the system is lossless then the energy
flux through the top layer has to be equal to the
flux through the half-space below. Therefore,
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(1) |
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(2) |
8-7
Figure 1. Reflection seismology geometry - Claerbout (1979). |
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Comparing the reflection seismology geometry with the
earthquake seismology geometry shown in Figure 2 gives
by reciprocity. Therefore
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(3) |
This theorem can be extended to a two dimensional plane-layered Earth by considering slant stacks (Claerbout, 1985).
8-8
Figure 2. Earthquake seismology geometry - from Claerbout (1979). All the waves (1, ![]() ![]() |
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![]() | Passive seismic imaging applied to synthetic data | ![]() |
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