Snieder Roel
Center for Wave Phenomena and Department of Geophysics, Colorado School of Mines, Golden, Colorado 80401, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Oct;74(4 Pt 2):046620. doi: 10.1103/PhysRevE.74.046620. Epub 2006 Oct 27.
It is known that the Green's function for nondissipative acoustic or elastic wave propagation can be extracted by correlating noise recorded at different receivers. This property is often related to the invariance for time reversal of the acoustic or elastic wave equations. The diffusion equation is not invariant for time reversal. It is shown in this work that the Green's function of the diffusion equation can also be retrieved by correlating solutions of the diffusion equation that are excited randomly and are recorded at different locations. This property can be used to retrieve the Green's function for diffusive systems from ambient fluctuations. Potential applications include the fluid pressure in porous media, electromagnetic fields in conducting media, the diffusive transport of contaminants, and the intensity of multiply scattered waves.
众所周知，对于无耗散声波或弹性波传播而言，格林函数可通过关联不同接收器记录的噪声来提取。此特性通常与声波或弹性波方程时间反演的不变性相关。扩散方程对于时间反演并不具有不变性。本文表明，扩散方程的格林函数也可通过关联在不同位置随机激发并记录的扩散方程解来获取。这一特性可用于从环境涨落中获取扩散系统的格林函数。潜在应用包括多孔介质中的流体压力、导电介质中的电磁场、污染物的扩散输运以及多次散射波的强度。
