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.]