The plane wave refraction on convex and concave obtuse angles in geometric acoustics approximation
A.N. Kremlev
Research Institute of Applied Informatics and Mathematical Geophysics, 14 A. Nevskogo ul., Kaliningrad, 236041
Keywords: уравнение эйконала, уравнение ГамильтонаЯкоби, лучевой параметр, преломление на выпуклом и вогнутом углах, время первых вступлений, аналитическое вязкое решение, головная волна, конечноразностная схема Годунова, eikonal equation, HamiltonJacobi equation, ray parameter, refraction on convex and concave obtuse angle, first arrival times, analytical viscosity solution, head wave, Godunov finite difference scheme
Abstract
The strict analytical solution to the eikonal equation for the plane wave refracted on convex and concave obtuse angles has been built. It has a shock line for the ray vector field and the first arrival times at the convex angle and a rarefaction cone with diffracted waves at the concave angle. This cone corresponds to the Keller diffraction cone in the geometric diffraction theory. The comparison of the first arrival times, the HamiltonJacoby equation times for downward waves and the conservation ray parameter equation times was made. It is shown that these times are equal only for precritical incident angles and are different for subcritical angles. It is shown that the most energetic wave arrival times, which have dominant practical importance, are equal to the times calculated for the conservation ray parameter equation. The numerical algorithm proposed for these times calculation may be used for arbitrary velocity models.
