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| A numerical tour of wave propagation | |
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Up: Full waveform inversion (FWI)
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Recall that the basic acoustic wave equation can be specified as
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(91) |
where
.
The Green's function
is defined by
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(92) |
Thus the integral representation of the solution can be given by
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(93) |
where
denotes the convolution operator.
A perturbation
will produce a field
defined by
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(94) |
Note that
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(95) |
Eq. (94) subtracts Eq. (91), yielding
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(96) |
Using the Born approximation, Eq. (96) becomes
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(97) |
Again, based on integral representation, we obtain
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(98) |
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|
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| A numerical tour of wave propagation | |
|
Next: Gradient computation
Up: Full waveform inversion (FWI)
Previous: Conjugate gradient (CG) implementation
2021-08-31