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

## 1pAO10. A structure function constraint for stable least-squares inversion
of reflection data.

**Kenneth E. Gilbert
**

**
Timothy J. Kulbago
**

**
P. Jason White
**

**
**
*Appl. Res. Lab. and the Graduate Prog. in Acoust., Penn State Univ., P.O.
Box 30, State College, PA 16804
*

*
*
High-frequency seismic profiles often indicate that the near-surface
sediments in shallow water are layered on scales larger than about 0.5 m but
not on smaller scales. Consequently, for a meaningful least-squares inversion
of reflection data using a horizontally stratified sediment model, the
wavelengths in the insonifying wave should be long enough to ``average out''
the small-scale sediment structure. With such a finite wavelength inversion,
the sediment model must include some resolution constraints in order to yield a
stable inversion. A common approach, for example, is to consider a stack of
homogeneous layers where each layer is thicker than, say, a quarter of a
wavelength. An alternative constraint method based on a structure function or,
equivalently, an autocorrelation function, is presented. It is shown that with
a structure function constraint, a stable inversion is obtained even if the
layered structure approaches a continuous profile. Without the constraint, the
inversion becomes meaningless as a continuum is approached. [Work supported by
NRL and ONR.]