Generalization of the rotated parabolic equation to variable slopes

Abstract

The rotated parabolic equation [J. Acoust. Soc. Am. 87, 1035-1037 (1990)] is generalized to problems involving ocean-sediment interfaces of variable slope. The approach is based on approximating a variable slope in terms of a series of constant slope regions. The original rotated parabolic equation algorithm is used to march the field through each region. An interpolation-extrapolation approach is used to generate a starting field at the beginning of each region beyond the one containing the source. For the elastic case, a series of operators is applied to rotate the dependent variable vector along with the coordinate system. The variable rotated parabolic equation should provide accurate solutions to a large class of range-dependent seismo-acoustics problems. For the fluid case, the accuracy of the approach is confirmed through comparisons with reference solutions. For the elastic case, variable rotated parabolic equation solutions are compared with energy-conserving and mapping solutions.

Finite-element modeling in ocean acoustics: Where are we heading?

“…This new code, named ROTVARS [5], is expected to perform well for elastic bottoms with variable slopes, as long as backscattering is negligible (the usual PE one-way approximation).…”

Experimental testing of the variable rotated elastic parabolic equation

“…Data comparisons were made using the variable rotated elastic parabolic equation. 11,12 The solution uses an improved formulation of elasticity, 2 has been benchmarked against other elastic parabolic equations, 11 and is currently viewed to be the most accurate elastic parabolic equation implementation. The solution is implemented in FORTRAN 77 and runs on any modern computer without special hardware considerations.…”

“…In order to handle sloping interfaces accurately, the variable rotated parabolic equation is used. [10][11][12] As with the earlier experiment with PVC slabs, it is necessary to account for shear waves when making model comparisons. 3 We were able to achieve good agreement by accurately inverting for geometric parameters (such as source depth and bathymetry), within the bounds of experimental uncertainty.…”

Parabolic equation solution of seismo-acoustics problems involving variations in bathymetry and sediment thickness

“…7 An improved rotated parabolic equation solution accurately handles fluid-solid interfaces of variable slope. 8 In this paper, we combine these approaches to obtain parabolic equation solutions of problems involving sloping ocean bottoms and varying sediment thickness. We demonstrate the accuracy of the approach by making comparisons with finiteelement solutions.…”