Eric I. Thorsos

The validity of the perturbation approximation for rough surface scattering using a Gaussian roughness spectrum

The validity of the perturbation approximation for rough surface scattering is examined (1) by comparison with exact results obtained by solving an integral equation and (2) through comparison of low‐order perturbation predictions with higher‐order predictions. The pressure release boundary condition is assumed, and the field quantity calculated is the bistatic scattering cross section. A Gaussian roughness spectrum is used, and the surfaces have height variations in only one direction. It is found, in general, that the condition kh≪1 (k is the acoustic wavenumber, h is the rms surface height) is insufficient to guarantee the accuracy of first‐order (or higher‐order) perturbation theory. When the surface correlation length l becomes too large or too small with h held fixed, higher‐order perturbation terms can make larger contributions to the scattering cross section than lower‐order terms. An explanation for this result is given. The regions of validity for low‐order perturbation theory are also given. Th...

An overview of SAX99: acoustic measurements

A high-frequency acoustic experiment was performed at a site 2 km from shore on the Florida Panhandle near Fort Walton Beach in water of 18-19 m depth. The goal of the experiment was, for high-frequency acoustic fields (mostly In the 10-300-kHz range), to quantify backscattering from the seafloor sediment, penetration into the sediment, and propagation within the sediment. In addition, spheres and other objects were used to gather data on acoustic detection of buried objects. The high-frequency acoustic interaction with the medium sand sediment was investigated at grazing angles both above and below the critical angle of about 30/spl deg/. Detailed characterizations of the upper seafloor physical properties were made to aid in quantifying the acoustic interaction with the seafloor. Biological processes within the seabed and the water column were also investigated with the goal of understanding their impact on acoustic properties. This paper summarizes the topics that motivated the experiment, outlines the scope of the measurements done, and presents preliminary acoustics results.

An investigation of the small slope approximation for scattering from rough surfaces. Part I. Theory

Thorsos, E.I., and S.L. Broschat, An investigation of the small slope approximation for scattering from rough surfaces: Part I: Theory, J. Acoust. Soc. Am., Vol. 97, No. 4, 2082-2093, Apr. 1995. http://dx.doi.org/10.1121/1.412001.

An investigation of the small slope approximation for scattering from rough surfaces: Part II: Numerical studies

Broschat, S.L., and E.I. Thorsos, An investigation of the small slope approximation for scattering from rough surfaces: Part II: Numerical studies, J. Acoust. Soc. Am., Vol. 101, No. 5, 2615-2625, May 1997. http://dx.doi.org/10.1121/1.418502.

Studies of scattering theory using numerical methods

Abstract Numerical simulations, using both exact and approximate methods, are used to study rough surface scattering in both the smd and large roughness regimes. This study is limited lo scattcring lrom rough one-dimensional surfaces that obey the Dirichlet boundary condition and have a Gaussian roughness spectrum. For surfdces with small roughness (kh≪1, where k is the radiation wavenumber and h is the root-mean-square (RMS) Surface height), perturbation theory is known to be valid. However, it is shown numerically that when kh≪1 and kl≳6 (where I is the surface correlation length) the Kirchhoffapprorimation is valid except at low grazing angles, and one must sum the first three orders of perturbation theory obtain the correct result. For kh≪1 and kl≅1, first-order perturbation theory is accurate. In this region, the accuracy of the first two terms of the iterative series solution of the exact integral equation is examined; the first term a1 this series is the Kirchhoff approximation, It is shown numeric...

Acoustic scattering from a solid aluminum cylinder in contact with a sand sediment: Measurements, modeling, and interpretation

Understanding acoustic scattering from objects placed on the interface between two media requires incorporation of scattering off the interface. Here, this class of problems is studied in the particular context of a 61 cm long, 30.5 cm diameter solid aluminum cylinder placed on a flattened sand interface. Experimental results are presented for the monostatic scattering from this cylinder for azimuthal scattering angles from 0 degrees to 90 degrees and frequencies from 1 to 30 kHz. In addition, synthetic aperture sonar (SAS) processing is carried out. Next, details seen within these experimental results are explained using insight derived from physical acoustics. Subsequently, target strength results are compared to finite-element (FE) calculations. The simplest calculation assumes that the source and receiver are at infinity and uses the FE result for the cylinder in free space along with image cylinders for approximating the target/interface interaction. Then the effect of finite geometries and inclusion of a more complete Greens function for the target/interface interaction is examined. These first two calculations use the axial symmetry of the cylinder in carrying out the analysis. Finally, the results from a three dimensional FE analysis are presented and compared to both the experiment and the axially symmetric calculations.

Terahertz scattering from granular material

Terahertz (THz) imaging is emerging as a potentially powerful method of detecting explosive devices, even in the presence of occluding materials. However, the characteristic spectral signatures of pure explosive materials may be altered or obscured by electromagnetic scattering caused by their granular nature. This paper presents THz transmission measurements of granular systems representative of explosives and presents results from dense media theory that accurately explain the observed scattering response.

High-frequency subcritical acoustic penetration into a sandy sediment

During the sediment acoustics experiment, SAX99, a hydrophone array was deployed in sandy sediment near Fort Walton Beach, Florida, in a water depth of 18 m. Acoustic methods were used to determine array element positions with an accuracy of about 0.5 cm, permitting coherent beamforming at frequencies in the range 11-50 kHz. Comparing data and simulations, it has been concluded that the primary cause of subcritical acoustic penetration was diffraction by sand ripples that were dominant at this site. These ripples had a wavelength of approximately 50 cm and RMS relief of about 1 cm. The level and angular dependence of the sound field in the sediment agree within experimental uncertainties with predictions made using small-roughness perturbation theory.

Fine-scale volume heterogeneity measurements in sand

As part of the effort to characterize the acoustic environment during the high frequency sediment acoustics experiment (SAX99), fine-scale variability of sediment density was measured by an in situ technique and by core analysis. The in situ measurement was accomplished by a newly developed instrument that measures sediment conductivity. The conductivity measurements were conducted on a three-dimensional (3-D) grid, hence providing a set of data suited for assessing sediment spatial variability. A 3-D sediment porosity matrix is obtained from the conductivity data through an empirical relationship (Archies Law). From the porosity matrix, sediment bulk density is estimated from known average grain density. A number of cores were taken at the SAX99 site, and density variations were measured using laboratory techniques. The power spectra were estimated from both techniques and were found to be appropriately fit by a power-law. The exponents of the horizontal one-dimensional (1-D) power-law spectra have a depth-dependence and range from 1.72 to 2.41. The vertical 1-D spectra have the same form, but with an exponent of 2.2. It was found that most of the density variability is within the top 5 mm of the sediment, which suggests that sediment volume variability will not have major impact on acoustic scattering when the sound frequency is below 100 kHz. At higher frequencies, however, sediment volume variability is likely to play an important role in sound scattering.

Application of the operator expansion method to scattering from one‐dimensional moderately rough Dirichlet random surfaces

A new method for computing wave scattering from rough surfaces, called the operator expansion (OE) method, has been proposed by D. M. Milder [J. Acoust. Soc. Am. 89(2), 529–541 (1991)]. In this paper, the OE method is examined in its application to acoustic scattering from one‐dimensional randomly rough surfaces with Gaussian and Pierson–Moskowitz roughness spectra satisfying the pressure release (Dirichlet) boundary condition. The operator expansion solution, which is expressed in a systematic series, is found to converge rapidly and monotonically for moderately rough surfaces, that is, for surfaces whose slope‐height roughness parameter khs, given by the product of acoustic wave number k, rms surface height h, and rms surface slope s, is less than about 0.25. Through comparison with a numerically exact integral equation solution, the OE method is found to be accurate over a wide range of incident and scattering angles. The method is currently used in a Monte Carlo computation of the scattering cross sec...