Kenneth E. Gilbert
Timothy J. Kulbago
Appl. Res. Lab. and the Graduate Program in Acoust., Penn State Univ., P.O. Box 30, State College, PA 16804
A simple analytic expression is derived for the impulse response of a continuously stratified sediment. The expression, which neglects multiple scattering, allows a straightforward calculation of both the forward and inverse problem, but more importantly, it clearly establishes the ``Bragg condition'' as a fundamental limitation on the inversion of acoustic data dominated by single scattering. (For normal incidence backscatter, the Bragg condition states that an acoustic probe signal of wavelength (lambda) senses or ``filters out'' only the Fourier component of the impedance profile having wavelength (lambda)/2, i.e., (lambda)[sub medium]=(lambda)[sub acoustic]/2.) The validity of the analytic expression is demonstrated by comparing it with exact numerical calculations for both the forward and inverse problem. In particular, it is shown that to obtain trends in impedance that occur over meters, requires a probe signal with wavelengths of approximately twice the desired trend distance. Many high-frequency inversions reported in the literature show trends with wavelengths that are orders of magnitude larger than any wavelength in the probe signal. Consequently, it is worthwhile to ask whether the long wavelength trends, which cannot be acoustically sensed by the short wavelength probe signals, are physically meaningful, or whether they are artifacts of arbitrary underlying assumptions in the signal processing method. [Work supported by NRL and ONR.]