Generalized Closed-Form Solutions for \(\mathcal{L}\mathcal{P}_1\)

In contrast to the 2D Lamb’s problem, where Green’s function solutions that can be directly expressed in closed form in the time domain (Chapters 2 and 3), Green’s function solutions and their spatial derivatives for 3D Lamb’s problem can only be represented in integral form in the time domain (Chapter 4). For the \(\mathcal{L}\mathcal{P}_2\) , due to fewer integrals involved and the lack of need for complex additional numerical operations, the Green’s function computation can be conveniently performed using numerical integration.