Acoustic Scattering from a Poro-Elastic Sediment

Transcription

1 Acoustic Scattering from a Poro-Elastic Sediment Marcia J. Isakson 1, Nicholas P. Chotiros 1 1 Applied Research Laboratories, The University of Texas, Burnet Rd., Austin, TX {misakson,chotiros}@arlut.utexas.edu

2 Acoustic Scattering from a Poro-Elastic Sediment Marcia J. Isakson 1, Nicholas P. Chotiros 1 1 Applied Research Laboratories, The University of Texas, Burnet Rd., Austin, TX {misakson,chotiros}@arlut.utexas.edu In order to determine the specular component of scattering of a spherical wave from ocean sediment, three main effects must be considered: spherical wave effects, the reflection coefficient from the sediment, and scattering. In this study, reflection data from a sandy bottom over a frequency range from 5 to 80 khz is compared to specular scattering models based on visco-elastic and poro-elastic representations of the sediment. The data were taken as part of the Experimental Validation of Acoustics modeling techniques (EVA) sea test conducted in Biodola Bay, Isola d Elba in October of Measurements of both the sediment parameters and the interface roughness were conducted as part of the test. At the lowest frequencies, scattering effects were found to be negligible allowing a thorough analysis of the reflection coefficient. Scattering effects were prevalent at the higher frequencies. They were modeled using a Kirchhoff approximation to the Helmholtz/Kirchhoff integral coupled with a visco-elastic and poro-elastic reflection coefficient. The data were consistent with a poro-elastic representation of the sediment. [Work supported by the Office of Naval Research, Ocean Acoustics Program.] 1 Introduction Both passive and active sonar operation in littoral waters rely on accurate predictions of acoustic loss at the boundaries. This work concentrates on the loss at the sediment/water interface by comparing high quality measurements over a large frequency range with high fidelity models. Generally, there are two contributors to loss at the waveguide boundary, the reflection coefficient which quantifies the amount of reflected and transmitted energy due to the impedance contrast and scattering from roughness at the interface. In this study, the loss is also affected by spherical waves at the interface due to ray displacement. 2 The EVA Experiment The experiment was conducted in October 2006 off the coast of Isola d Elba, Italy in Biodola Bay from the platform, R/V Leonardo as part of the Experimental Validation of Acoustic modeling techniques (EVA) experiment. The sediment at the site was a medium sand devoid of sea grass with no apparent ripple structure. This site was well characterized both at this experiment and at a previous experiment, the Generic Oceanographic Array Technologies (GOATS) experiment in [1, 2] Therefore, accurate measurements of the water and sediment sound speeds and attenuations were available. Measurements of the bottom loss were obtained by hanging four receivers and a source from the platform. The receivers were placed so that the entire angle range from 7-77 degrees was covered. The source was lifted relative to the receivers to cover the angle range. The source transmitted a frequency modulated pulse between 5 and 80 khz. The chirp was customized to the transfer function of the experimental system to reduce the dynamic range. The entire experiment was also conducted in deeper waters to calibrate the beam pattern of the system. Details of the chirp and calibration experiment can be found in reference [3]. The data were corrected for the beam pattern, match filtered and band pass filtered. The bottom loss was computed using two methods. The peak response was calculated as the ratio of the maximum of the reflected path of the matched filter response to that of the direct path. The energy response was calculated as the ratio of the area under the reflected path response of the matched filtered signal to that of the direct path. The peaks were integrated to a level of 6 db down from the maximum level. This data analysis procedure is described more thoroughly in references [4] and [5] Additionally, measurements of the local microtopography were taken by the ROV mounted laser profiling system (ROV- LPS) from the Applied Research Laboratories at The University of Texas. A description of this system can be found in Reference [6]. A sample of the measured microtopography is shown in Fig. 1. The interface roughness was found to be isotropic and follow a von Karman type power spectrum. 3 Modeling Figure 1: Transmission Loss. Three effects were considered the bulk reflection coefficient, scattering from the sediment/water interface and spherical

3 wave effects. Each are described below. 3.1 Reflection Coefficient The reflection coefficient describes the amount of energy reflected from an flat interface due to the impedance contrast on the boundary. Historically, the reflection coefficient for a sandy sediment has been based on the fluid model. However, since shear waves have been measured in sands, an elastic model will be considered here [7]. The elastic reflection coefficient is based on five parameters, the complex compressional wave speeds for the fluid and the sediment, the complex shear wave speed of the sediment, and the densities of the fluid and the sediment. All of these except shear wave speed were measured on site and given in reference [8]. There has been considerable evidence that the elastic model is inadequate to describe acoustic propagation in sands including direct evidence that the reflection is not well described by this model [4, 9, 10]. Specifically, adjustments must be made in the sound speed and density of the sediment to account for dispersion and additional losses due to poro-elastic effects. Therefore, a poro-elastic reflection coefficient based on the Biot model [11, 12] formulated by Stoll [13] is used to calculate the reflection coefficient. The thirteen input parameters are given in reference [8]. It is important to note that the Biot model predicts a large dispersion in the frequency range of interest. 3.2 Interface Scattering Interface scattering significantly affects bottom loss measurements especially at higher acoustic frequencies. In this experiment, scattering was computed from 2D realizations of the surface derived from the measured power spectrum from the laser line measurements. One thousand realizations of the surface were calculated and the acoustic scattering from the surface was determined using the reflection coefficient calculated from either the elastic or poro-elastic model. The scattering was calculated using the Helmholtz- Kirchhoff integral simplified by the Kirchhoff approximation which is most accurate near specular [14]. Details of this process can be found in reference [8]. A common way to calculate the effects of scattering in the specular direction is to assume that the power spectrum of the interface roughness is Gaussian. Then the scattering can be described with an analytic expression: where χ is given by: R coh (θ i ) = R(θ i )e χ2 (1) χ = kh(sinθ i + sinθ s ) (2) Here, R coh is the coherent part of the reflection after scattering, R is the flat surface reflection coefficient, θ i is the incident angle, k is the acoustic wavenumber, h is the RMS height of the surface and θ s is the scattered angle. This expression is also evaluated based on the measured RMS height of the surface and compared with the data. 3.3 Spherical wave effects For the lower frequencies of this experiment, spherical wave effects can significantly alter the measured bottom loss. Spherical wave effects occur when a flat interface is close to a spherical source relative to an acoustic wavelengths. The spherical wave front near the source can be described as a superposition of complex plane waves. When a spherical wavefront encounters a flat interface, ray displacement occurs as the evanescent plane waves interact with the surface. This can be computed by integrating the reflection over the sum of both the real and imaginary plane waves comprising the spherical wavefront. This process, plane wave decomposition or PWD, is derived in reference [15]. The effect on bottom loss is a decrease in the apparent critical angle and an interference structure sub-critically. All bottom loss curves presented in this paper are integrated over the plane wave decomposition of the spherical wave. However, this effect is primarily noticed in frequencies below 8 khz for this geometry. 4 Results 4.1 Reflection Coefficient As noted in the above section, interface scattering is primarily a higher frequency effect for this interface while spherical wave effects are prevalent primarily for the lower frequency range in this experimental geometry. One of the primary issues to be addressed with this experiment is the correct representation of the reflection coefficient of the sediment. In other words, is an elastic model sufficient to describe the reflection from the sediment or is a poro-elastic model necessary? The lower frequency data has been shown to have very little effects from interface scattering. (See both reference [8] and Fig. 3.) Therefore, these data are ideal to compare the basic models of the reflection coefficient. Also, it is shown that the energy response is more robust to the effects of scattering. In Fig. 2, the energy response of the data from a frequency band centered at 14 khz is compared to a flat interface reflection coefficient calculated using PWD based on the elastic model and one based on the poro-elastic model. The data clearly are overestimated by the elastic model while the poro-elastic model is consistent with the data. It should be noted that the poro-elastic model employed predicts a compressional wave speed at this frequency that is almost 5% below what was measured. However, the measurement of the compressional sound speed was made at 200 khz. Therefore, this model predicts a steep dispersion.

4 Figure 2: The energy response of bottom loss of a frequency band centered at 14 khz compared to an elastic model with PWD based on measured parameters and a PWD poro-elastic model. Figure 3: The measured peak and energy responses at for a band of frequencies centered at 8 khz compared with the scattering models based on the poro-elastic reflection coefficient. 4.2 Interface Scattering Shown in Fig. 3 and Fig. 4 are the peak and energy responses of the data compared with models of the scattering based on the PWD poro-elastic reflection coefficient and the Kirchhoff scattering model from 1000 realizations based on the measured power spectrum or the Gaussian surface assumption. Note that the scattering has little effect at the lower frequencies for this interface. The scattering models predict only a slight variation from the flat interface. Additionally, the energy and peak responses are nearly identical. The energy response is expected to be more robust with respect to scattering effects since energy which has a slight path length difference due to scattering would still be captured in the response. However, at this frequency the effects of scattering are small. However, consider the effects of scattering in Fig. 4. In this case, the models predict a large contribution to bottom loss due to scattering. Also, note that the peak and energy response of the data are significantly different. The peak response is much more influenced by scattering while the energy response captures much of the slightly scattered energy. The energy values are consistent with the flat interface response suggesting that the flat surface reflection coefficient can be probed by considering an energy response. The peak response is consistent with the Kirchhoff approximation based on the realizations from the measured power spectrum. However, the bottom loss based on scattering from the Gaussian surface using the analytic expression in Equation (1) is inconsistent with the data. Figure 4: The measured peak and energy responses at for a band of frequencies centered at 45 khz compared with the scattering models based on the poro-elastic reflection coefficient. 5 Conclusions Bottom loss data was taken at the Experimental Validation of Acoustic modeling techniques (EVA) in Biodola Bay off the coast of Isola d Elba in October of An angle range of 7-77 degrees grazing and a frequency range of 5-80 khz were probed. The data were calculated as both a peak response, a ratio of the peak of the matched filtered

5 response of the reflected and direct path and an energy response, a ratio of the integrated energy of the reflected and direct paths. The microtopography was found to be isotropic and followed a von Karman type power spectrum. The data were compared with models of the bottom loss which included the flat interface reflection coefficient, interface scattering based both on realizations from the measured power spectrum and an assumption of Gaussian roughness and plane wave decomposition to account for spherical wave effects. Scattering effects were found to be significant only in the higher end of the frequency range while spherical wave effects were significant at the lower end for this geometry. The data were inconsistent with an elastic representation of the sediment. The energy response was found to have a much smaller influence from scattering effects and were consistent with the flat interface bottom loss at the frequency range shown. The peak response were highly influenced by scattering and were consistent with a poro-elastic reflection coefficient modified by scattering model based on a Kirchhoff approximation of scattering from 1000 surface interface realizations. The data were inconsistent with a Gaussian representation of the interface. References [1] A. Maguer, W.L.J. Fox, H. Schmidt, E. Pouliquen, and E. Bovio. Mechanisms for subcritical penetraion into a sandy bottom: Experimental and modeling results. Journal of the Acoustical Society of America, 107: , [2] A. Tesei, Maguer A., W.L.J. Fox, R. Lim, and H. Schmidt. Measurements and modeling of acoustic scattering from partially and completely buried spherical shells. Journal of the Acoustical Society of America, 112: , [3] M.J. Isakson, N.P. Chotiros, J.N. Piper, and M. Zampolli. Measurements of the bottom loss magnitude and phase from 5 to 50 khz and 10 to 77 degrees grazing at the experimental validation of acoustic modeling techniques (EVA) sea test. In Proceedings of the OCEANS 2007 MTS/IEEE VANCOUVER Conference and Exhibition, [4] H.J. Camin and M.J. Isakson. A comparison of spherical wave sediment reflection coefficient measurements to elastic and poro-elastic models. Journal of the Acoustical Society of America, 120: , [5] M.J. Isakson, N.P. Chotiros, H.J. Camin, and J.N. Piper. Reflection coefficient measurements in a complex environment at the Sedimant Acoustics experiment 2004, (SAX04). IEEE Journal of Oceanic Engineering, Submitted, [6] N.P. Chotiros, M.J. Isakson, J.N. Piper, and M. Zampolli. Seafloor roughness measurement from a ROV. In Proc. International Symposium on Underwater Technology 2007, April, Tokyo, Japan, pages 52 57, [7] B. Luke. In situ measurement of stiffness profiles in the seafloor using the spectral-analysis-of-waves SASW method. Technical Report under ARL:UT Independent Research and Development Program, Austin, TX, [8] M.J. Isakson, N.P. Chotiros, R.A. Yarbrough, and J. N. Piper. Quantifying the effects of roughness scattering on reflection coefficient measurements. Journal of the Acoustical Society of America, In Review, [9] A.D. Worley. The impact of experimental error and sediment models on reflection coefficient invesion, Masters thesis. PhD thesis, University of Texas at Austin, [10] K.L. Williams, S.G. Kargl, E.I. Thorsos, and D.J. Tang. Synthetic aperture sonar SAS imaging and acoustic scattering strength measurements during SAX04 Sediment Acoustics experiment : Experimental results and associated modeling. In Boundary influences in high frequency, shallow water acoustics, University of Bath, Bath, UK, pages , Bath, England, Sept University of Bath Press. [11] M.A. Biot. Theory of propagation of elastic waves in a fluid saturated porous solid I. Low frequency range. Journal of the Acoustical Society of America, 28: , [12] M.A. Biot. Theory of propagation of elastic waves in a fluid saturated porous solid II. Higher frequency range. Journal of the Acoustical Society of America, 28: , [13] R.D. Stoll. Sediment Acoustics, Lecture Notes in Earth Science. Springer Verlag, [14] J.A. Ogilvy. Theory of Wave Scattering from Random Rough Surfaces. IOP Publishing Ltd., [15] L.M. Brekhovskikh. Waves in Layered Media. Academic Press, New York, 1980.

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