The Green's function (GF) method, which makes use of GFs, is an important and elegant tool for solving a given boundary-value problem for the differential equation from a real engineering or physical field. Under a concentrated source, the solution of a differential equation is called a GF, which is singular at the source location, yet is very fundamental and powerful. When looking at the GFs from different physical and/or engineering fields, i.e., assigning the involved functions to real physical/engineering quantities, the GFs can be scaled and applied to large-scale problems such as those involved in Earth sciences as well as to nano-scale problems associated with quantum nanostructures. GFs are ubiquitous and everywhere: they can describe heat, water pressure, fluid flow potential, electromagnetic and gravitational potentials, and the surface tension of soap film. In the undergraduate courses Mechanics of Solids and Structural Analysis, a GF is the simple influence line or singular function. Dropping a pebble in the pond, it is the circular ripple traveling on and on. It is the wave generated by a moving ship in the opening ocean or the atom vibrating on a nanoscale sheet induced by the atomic force microscopy. In Earth science, while various GFs have been derived, a comprehensive review is missing. Thus, this article provides a relatively complete review on GFs for geophysics.

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地球物理学的格林函数：综述

使用 GF 的格林函数 (GF) 方法是解决实际工程或物理领域微分方程的给定边界值问题的重要而优雅的工具。在集中源下，微分方程的解称为 GF，它在源位置是奇异的，但非常基本和强大。当查看来自不同物理和/或工程领域的 GFs 时，即将所涉及的函数分配给实际的物理/工程量，GFs 可以缩放并应用于大规模问题，例如地球科学中涉及的问题以及与量子纳米结构相关的纳米级问题。GF 无处不在：它们可以描述热、水压、流体流动势、电磁势和重力势，和肥皂膜的表面张力。在固体力学和结构分析本科课程中，GF 是简单的影响线或奇异函数。往池塘里丢一块鹅卵石，就是一圈圈的涟漪。它是由开放海洋中移动的船舶或原子力显微镜引起的纳米级薄片上振动的原子产生的波。在地球科学中，虽然已经推导出了各种 GF，但缺少全面的审查。因此，本文对地球物理学中的 GF 进行了相对完整的回顾。它是由开放海洋中移动的船舶或原子力显微镜引起的纳米级薄片上振动的原子产生的波。在地球科学中，虽然已经推导出了各种 GF，但缺少全面的审查。因此，本文对地球物理学中的 GF 进行了相对完整的回顾。它是由开放海洋中移动的船舶或原子力显微镜引起的纳米级薄片上振动的原子产生的波。在地球科学中，虽然已经推导出了各种 GF，但缺少全面的审查。因此，本文对地球物理学中的 GF 进行了相对完整的回顾。