Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-10T05:33:24.319Z Has data issue: false hasContentIssue false
  • English
  • Français

Simulation of Propagating Acoustic Wavefronts with Random Sound Speed

Published online by Cambridge University Press:  03 June 2015

Sheri L. Martinelli
Sheri L. Martinelli*
Affiliation:
Undersea Warfare Weapons, Vehicles, and Defensive Systems Department, Naval Undersea Warfare Center, Newport, Rhode Island 02841, USA
*
*Corresponding author.Email:sherimartinelli@alumni.brown.edu
Get access

Abstract

A method for simulating acoustic wavefronts propagating under random sound speed conditions is presented. The approach applies a level set method to solve the Eikonal equation of high frequency acoustics for surfaces of constant phase, instead of tracing rays. The Lagrangian nature often makes full-field ray solutions difficult to reconstruct. The level set method captures multiple-valued solutions on a fixed grid. It is straightforward to represent other sources of uncertainty in the input data using this model, which has an advantage over Monte Carlo approaches in that it yields an expression for the solution as a function of random variables.

Keywords

60H3565M7065C20Level set methodwavefront methodshigh-frequency acoustic propagationstochastic collocation
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 4 , October 2014 , pp. 1081 - 1101
Copyright
Copyright © Global Science Press Limited 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Jensen, F., Kuperman, W., Porter, M., and Schmidt, H., Computational Ocean Acoustics. Modern Acoustics and Signal Processing, New York: Springer, second ed., 2011.Google Scholar
[2]Roux, P., Cornuelle, B., Kuperman, W., and Hodgkiss, W., The structure of raylike arrivals in a shallow-water waveguide, J. Acoust. nauoc. Amer., vol. 124, pp. 3430–39,2008.Google Scholar
[3]Singer, A., Nelson, J., and Kozat, S., Signal processing for underwater acoustic communications, Communications Magazine, IEEE, vol. 47, pp. 90 –96, January 2009.Google Scholar
[4]Martinelli, S., An application of the level set method to underwater acoustic propagation, Commun. Comput. Phys., vol. 12, no. 5, pp. 1359–1391,2012.Google Scholar
[5]Osher, S. and Sethian, J., Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. nauhys., vol. 79, pp. 12–49,1988.Google Scholar
[6]Osher, S., Cheng, L.-T., Kang, M., Shim, H., and Tsai, Y.-H., Geometric optics in a phase-space-based level set and Eulerian framework, J. Comput. Phys., vol. 179, pp. 622–648,2002.Google Scholar
[7]Godin, O., Restless rays, steady wave fronts, J. Acoust. Soc. Amer., vol. 122, pp. 3353–3363, 2007.Google Scholar
[8]Martinelli, S., A Level-Sets-Based Wavefront Propagation Method for Underwater Acoustics. PhD thesis, Brown University, May 2012.Google Scholar
[9]Xiu, D. and Hesthaven, J., High-order collocation methods for differential equations with random inputs, SIAM J. Sci. Comput., vol. 27, pp. 1118–1139,2005.Google Scholar
[10]Chauviere, C., Hesthaven, J., and Lurati, L., Computational modeling of uncertainty in time-domain electromagnetics, SIAM J. Sci. Comput., vol. 28, pp. 751–775,2006.Google Scholar
[11]Nobile, F., Tempone, R., and Webster, C., A sparse grid stochastic collocation method for partial differential equations with random input data, SIAM J. Numer. Anal., vol. 46, pp. 23092345, 2008.Google Scholar
[12]Preston, J., Tasdizen, T., Terry, C., Cheung, A., and Kirby, R., Using the stochastic collocation method for the uncertainty quantification of drug concentration due to depot shape variability, IEEE Trans. Biomed. Eng., vol. 56, no. 3, pp. 609–620, 2009.Google Scholar
[13]Pätz, T. and Preusser, T., Segmentation of stochastic images using level set propagation with uncertain speed, J. Math. Imaging Vis., pp. 1–21,2013.Google Scholar
[14]Xiu, D., Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton, New Jersey: Princeton University Press, 2010.Google Scholar
[15]Trees, H. Van, Detection, Estimation, and Modulation Theory: Part I. New York: Wiley-Interscience, paperback ed., 2001.Google Scholar
[16]Widom, H., Asymptotic behavior of the eigenvalues of certain integral equations II, Arch. Ration. Mech. An., vol. 17, pp. 215–229,1964.Google Scholar
[17]Duda, T., Ocean sound channel ray path perturbations from internal-wave shear and strain, J. Acoust. Soc. Amer., vol. 118, pp. 2899–2903,2005.Google Scholar
[18]Colosi, J., Geometric sound propagation through an inhomogeneous and moving ocean: Scattering by small scale internal wave currents, J. Acoust. Soc. Amer., vol. 119, pp. 705708, 2006.CrossRefGoogle Scholar
[19]Martinelli, S., Numerical boundary conditions for specular reflection in a level-sets-based wavefront propagation method, Commun. Comput. Phys., vol. 14, no. 2, pp. 509–536,2013.Google Scholar
[20]Finette, S., A stochastic response surface formulation of acoustic propagation through an uncertain ocean waveguide environment, J. Acoust. Soc. Amer., vol. 126, pp. 2242–2247, 2009.Google Scholar
[21]Boyd, J., Chebyshev and Fourier Spectral Methods. New York: Dover, second ed., 2001.Google Scholar
[22]Smolyak, S., Quadrature and interpolation formulas for tensor products of certain classes of functions, Soviet Math. Dokl., vol. 4, pp. 240–243,1963.Google Scholar
[23]Gerstner, T. and Griebel, M., Numerical integration using sparse grids, Numerical Algorithms, vol. 18, pp. 209–232,1998.Google Scholar
[24]Novak, E. and Ritter, K., Simple cubature formulas with high polynomial exactness, Constr. Approx., vol. 15, pp. 499–522,1999.Google Scholar
[25]Shen, J. and Wang, L.-L., Some recent advances on spectral methods for unbounded domains, Commun. Comput. Phys., vol. 5, pp. 195–241,2009.Google Scholar
[26]Jin, S., Liu, H., Osher, S., and Tsai, Y.-H., Computing multivalued physical observables for the semiclassical limit of the Schrodinger equation, J. Comput. Phys., vol. 205, pp. 222–241,2005.Google Scholar
[27]Jin, S., Liu, H., Osher, S., and Tsai, R., Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems, J. Comput. Phys., vol. 210, pp. 497518, 2005.Google Scholar
[28]Liu, H., Osher, S., and Tsai, R., Multi-valued solution and level set methods in computational high frequency wave propagation, Communications in Computational Physics, vol. 1, no. 5, pp. 765–804, 2006.Google Scholar
[29]Azaïs, J.-M., León, J., and Wschebor, M., Some applications of Rice formulas to waves, ArXiv e-prints, Oct. 2009, 0910.0763v1.Google Scholar
[30]Azaïs, J.-M., Leon, J., and Wschebor, M., Rice formulae and Gaussian waves, Bernoulli, vol. 17, no. 1,pp. 170–193,2011.Google Scholar
[31]Newhall, A., Duda, T., et al., Acoustic and oceanographic observations and configuration information for the WHOI moorings from the SW06 experiment, Tech. Rept. WHOI-2007-04, Woods Hole Oceanographic Institute, May 2007.Google Scholar