An axisymmetric time-domain spectral-element method for full-wave simulations: Application to ocean acoustics

The numerical simulation of acoustic waves in complex three-dimensional (3D) media is a key topic in many branches of science, from exploration geophysics to non-destructive testing and medical imaging. With the drastic increase in computing capabilities this field has dramatically grown in the last 20 years. However many 3D computations, especially at high frequency and/or long range, are still far beyond current reach and force researchers to resort to approximations, for example, by working in two dimensions (plane strain) or by using a paraxial approximation. This article presents and validates a numerical technique based on an axisymmetric formulation of a spectral finite-element method in the time domain for heterogeneous fluid-solid media. Taking advantage of axisymmetry enables the study of relevant 3D configurations at a very moderate computational cost. The axisymmetric spectral-element formulation is first introduced, and validation tests are then performed. A typical application of interest in ocean acoustics showing upslope propagation above a dipping viscoelastic ocean bottom is then presented. The method correctly models backscattered waves and explains the transmission losses discrepancies pointed out in F. B. Jensen, P. L. Nielsen, M. Zampolli, M. D. Collins, and W. L. Siegmann, Proceedings of the 8th International Conference on Theoretical and Computational Acoustics (ICTCA) (2007). Finally, a realistic application to a double seamount problem is considered.