Analysis on Lamb's Problem

Abstract

We implement the master relationship, Laplace-Fourier path, and determinant of a surface wave together to form a LY algorithm and apply this algorithm to solve the Lamb's problem completely. We obtain an explicit solution formula for the Lamb's problem in the space-time variable. The solution formula is given in terms of the fundamental solutions of the d'Alembert wave equations in 3-D and 2-D by the Kirchhoff's formula and Hadamard's formula . Complicated 2D-3D coupling wave structures on the surface present in the surface wave solution formula. This shows that the wave structures given in the paper are much richer than the Rayleigh wave discussed in the original articles. Further computation and estimates of the solution formula would also be discussed in this article and then gain results consistent with the theory in seismology.