Retrieving the Green's function of the diffusion equation from the response to a random forcing.
Retrieving the Green's function of the diffusion equation from the response to a random forcing.
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DOI：
10.1103/physreve.74.046620
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发表时间：
2006-10
期刊：
影响因子：
--
通讯作者：
R. Snieder
中科院分区：
文献类型：
--
作者：
R. Snieder
我们知道，非耗散声波或弹性波传播的格林函数可以通过关联在不同接收器上记录的噪声来提取。这种性质通常与声波或弹性波动方程的时间反转不变性有关。对于时间反转，扩散方程不是不变的。在这项工作中表明，扩散方程的格林函数也可以通过在不同位置记录的随机激发的扩散方程的相关解来检索。该性质可用于从环境波动中检索扩散系统的格林函数。潜在的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。
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.