Computation of the acoustical wave-fronts in a phase space

Abstract

The computation of acoustical wave-fronts in 2-D and 3-D coordinate space can be performed by the computation of rays and approximation of the fronts between the rays by some interpolation formula. The amount of neccessary rays increases with distance and rapidly exhausts memory and performance of the computer. It happens due to the extremely sophisticated and unsmooth nature of the ray picture. Due to the fact that trajectories of a dynamic system do not intersect in phase space, appropriate rays and fronts surface in phase space is smooth and can be easily approximated by a smaller number of rays, and this number increases very slow with distance. This number can be reduced by involving equations in variations, which generate tangent vectors to this surface. Formally, dimension of phase space is a doubled dimension of coordinate space. Using some properties of ray equations, the dimension of the phase space in the 2-D coordinate case can be reduced from 4-D to 3-D and in 3-D coordinate case from 6-D to 5-D. This approach opens new ways of fast global and local estimates of sound field and for inverse problems in underwater acoustics. This report produces a set of numerical and analytical examples.