2 July 1999

Applied Physics Laboratory

University of Washington

Seattle, Washington 98105

(206) 543-1359, -6785 (fax), drj@apl.washington.edu

(206) 543-1290, -6785 (fax), djtang@apl.washington.edu

The purpose of this work is to adapt existing scattering models to simulations of SAX99 acoustic measurements. These simulations are to be used in designing the APL-UW acoustic instrumentation and will also be used for data analysis. Initial work is based on a fluid sediment model and perturbation theory. If the results of SAX99 indicate that these assumptions are too restrictive, the simulations will be generalized subject to the limitations of currently available scattering models.

A 3-D Monte Carlo simulation capability has been developed for acoustic penetration due to scattering by the rough water–sediment interface. Small-roughness perturbation theory has been combined with a high-frequency propagation approximation to provide complex time series for the output of buried hydrophones with sources placed in the water column. The regime of validity of the perturbation approximation has been determined in 2-D exact calculations by Eric Thorsos, and the high-frequency propagation approximation has been checked by comparison with exact 3-D calculations. Simulations using parameters relevant to SAX99 and also to past measurements by Chotiros [1] fall within the validity regimes of both approximations.

The Monte-Carlo method improves upon the formally averaged method [2] and has been shown [3] to compare favorably with previous experimental results, given reasonable assumptions regarding roughness statistics. During FY98–99 these simulations were used to support the design of the penetration experiment. Initial efforts were also undertaken in designing algorithms for data analysis.

Simulations for array design were constrained by consideration of the mechanics of hydrophone insertion and unwanted scattering by hydrophones. The result of this effort was an array consisting of five vertical subarrays in a triangular pattern. Monte Carlo simulations showed that changes as small as 15° in transmitter azimuth (relative to the array) were sufficient to cause decorrelation of hydrophone outputs when isotropic roughness spectra were used. This result was used in developing a strategy for placement of the movable source, based on averaging over azimuth at constant range to obtain statistical ensembles. Monte Carlo simulations were also used to model errors in planned acoustic surveys of buried hydrophone positions and in estimating interference levels due to unwanted scattering by the cofferdam to be used in hydrophone insertion.

Simulations were conducted in FY98–99 to assess the ability of various processing schemes to discriminate between two penetration mechanisms: refraction of a slow Biot wave and roughness scattering. Both coherent and incoherent processing methods were examined using the adaptive normalization method employed by Chotiros [1] and a non-adaptive method. The non-adaptive, coherent method provided the best discrimination between penetration mechanisms. Further simulation work is needed to assess other candidate processing methods. In addition, the simulation capability will be used to study above-critical-angle geometries relevant to detection and classification of buried targets.

The purpose of this work is two-fold. One is to model the enhanced penetration due to the presence of volume inhomogeneities; the other is to model the scattered field when both the source and receiver are in the sediment.

In all our simulations, the sediment is modeled as an effective fluid that is characterized by its mean sound speed and mean density, the first-order statistics of the sound speed and density (their spectra and cross spectrum), and a frequency-dependent attenuation coefficient. All these environmental parameters are expected to be measured in the SAX99 experiment.

In FY98 a Monte Carlo simulation capability was developed and is currently being refined. This approach can account for three-dimensional volume inhomogeneities in simulations of acoustic penetration of sediments. The simulations have shown that sediment volume inhomogeneities can scatter sound from the region of the evanescent wave associated with a flat seafloor to regions deeper in the sediment at intensity levels of interest to penetration. It was also shown that the cross spectrum of sound speed and density has an important effect on the level of the penetrating field caused by scattering from volume inhomogeneities. This result motivates our effort to measure this cross spectrum. However, when realistic seafloor roughness is present, we expect rough surface scattering to dominate the penetrating field. Following SAX99, we will use this capability extensively in data/model comparisons of penetration measurements, including above-critical-angle geometries for spatial coherence studies.

Since we anticipate volume scattering will be much weaker than rough surface scattering, we are developing a simulation capability that will enable us to model the scattered field when both source and receiver are in the sediment. Such measurements are planned for the SAX99 experiment by NRL and APL-UW. By comparing the results of this simulation technique with SAX99 data, we will be able to understand if perturbation theory is adequate to model volume scattering in the 10–50 kHz range. If such comparisons are favorable, we will also use the modeling capability to separate intrinsic attenuation from scattering loss. On the other hand, an unfavorable model/data comparison will suggest modifications of our model.

[1] N.P. Chotiros, "Biot
model of sound propagation in water-saturated sediments," *J. Acoust.
Soc. Am., 97*, 199–214 (1995).

[2] E.I. Thorsos, D.R. Jackson,
J.E. Moe, and K.L Williams, "Modeling of subcritical penetration into sediments
due to interface roughness," in *High Frequency Acoustics in Shallow
Water*, edited by N. G. Pace et al. (NATO SACLANT Undersea Research Centre,
La Spezia, Italy, 1997), pp. 563–569.

[3] E.I. Thorsos, D.R. Jackson,
and K.L. Williams, "Modeling of subcritical penetration into sediments
due to interface roughness," submitted to *J. Acoust. Soc. Am.*

[4] D. Tang, "Small scale
volumetric inhomogeneities of shallow water sediments: Measurements and discussion,"
in *High Frequency Acoustics in Shallow Water*, edited by N. G. Pace et
al. (NATO SACLANT Undersea Research Centre, La Spezia, Italy, 1997), pp. 539–546.

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