  The numerical simulation of acoustic waves in complex 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 twenty 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 2D (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 Jensen et al. (2007). Finally, a realistic application to a
double seamount problem is considered.
