### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 4aUW9. The Bragg condition limitation on inversion of normal incidence
reflection data.

**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.]