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Center for Nonlinear Studies |
A wave propagation problem is range dependent if there are horizontal variations in the environment, such as sloping boundaries and interfaces and variations of wave speeds within layers. In general, it is very difficult to solve range-dependent problems because they cannot be solved by the method of separation of variables. On domains that are huge relative to a wavelength, solving such problems may require a supercomputer. For many problems in the geosciences, such as seismology and ocean acoustics, the environment varies gradually in the horizontal directions. Such problems may often be solved very accurately and very efficiently with the parabolic equation method, which involves factoring the operator in the full wave equation to obtain a parabolic wave equation. They key to efficiency is that a parabolic wave equation accounts only for energy that propagates outward in range. The key to accuracy is that outgoing energy often dominates back-scattered energy in a gradually range-dependent environment. This talk will introduce basic concepts and discuss applications in ocean acoustics, seismology, and Arctic acoustics.