### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 5aPA7. A new generalized k-space (GkS) method for transient elastodynamic
scattering problems.

**Qing-Huo Liu
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*Schlumberger-Doll Res., Old Quarry Rd., Ridgefield, CT 06877
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A conventional approach to simulating transient elastic wave propagation
in inhomogeneous media has been the finite-difference (FD) method. However, the
FD method requires a large number of grids in order to obtain accurate results.
This is because in conventional FD schemes, second-order (sometimes
higher-order) differences are used to approximate the spatial derivatives. In
this work, a new generalized k-space (GkS) method is described for
elastodynamic scattering problems. From its integral representation in
spatial-frequency (r-f ) domain, a local equation is derived for the
displacement field in spectral-frequency (k-f ) domain. This equation becomes a
time-convolution equation in spectral-time (k-t) domain. Using two temporal
propagators, compressional and shear, this time-convolution equation can be
converted into two time-stepping equations, which become much easier to solve.
Hence, at each time step, the solution is first obtained in the k-t domain, and
then transformed to the r-t domain by using spatial FFT. Since the GkS method
uses the Fourier transform to represent the spatial derivatives, it is much
more accurate than the FD method. Numerical examples show that the GkS method
with only four grids per wavelength can achieve the same accuracy as the FD
method with 16 grids per wavelength.