标题： Lamb问题的精确闭式解（III）：源和接收器位于地下的情况 显示英文标题

标题： Exact closed-form solutions for Lamb's problem (III): The case for buried source and receiver

摘要： 本文中，我们推导了均匀弹性半空间内部由于具有Heaviside阶跃函数时间历史的埋藏点力所引起的精确闭式解位移。 这被称为均匀半空间中弹性波方程的张量格林函数，也是经典三维Lamb问题的一个自然推广，在此之前，已有解仅限于源或接收器或两者都位于自由表面的情况。 从Johnson的复积分解出发，我们遵循Feng和Zhang提出的相似步骤，获得了初等函数以及椭圆积分形式的闭式表达。 由我们的闭式表达得到的数值结果与Johnson的结果完全一致，这验证了我们的显式公式。 显示英文摘要

摘要： In this article, we derive the exact closed-form solution for the displacement in the interior of an elastic half-space due to a buried point force with Heaviside step function time history. It is referred to as the tensor Green's function for the elastic wave equation in a uniform half-space, also a natural generalization of the classical 3-D Lamb's problem, for which previous solutions have been restricted to the cases of either the source or the receiver or both are located on the free surface. Starting from the complex integral solutions of Johnson, we follow the similar procedures presented by Feng and Zhang to obtain the closed-form expressions in terms of elementary functions as well as elliptic integrals. Numerical results obtained from our closed-form expressions agree perfectly with those of Johnson, which validates our explicit formulae conclusively.