An Inversion Method for Elastic Wave Fields
, by Robert W. Clayton
The inversion of two-demensional elastic displacement fields can be
handled in a very similar manner to the way the acoustic problem is
handled. The Born approximation of the Lippman-Schwinger equation
yields a simple relationship in the Fourier-transform domain between
the observed horizontal and vertical displacement fields, and the
scattering potential. Basically, the observaticons are a liner
combination of the scattering potential evaluated along four different
shells. The four shells may be interpreted P to P, P to S, S to P, and
S to S scattering.
If the source is either purely compressional or purely shear, then one
experiment will suffice to invert the forward equation. If the source
is a (known) mixture of P and S components, then twon experiments with
different combinations of P and S components are necessary for the
inversion.
STANFORD