Green's function representations for seismic interferometry
Green's function representations for seismic interferometry
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DOI：
10.1190/1.2213955
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发表时间：
2006-08
期刊：
影响因子：
3.3
通讯作者：
K. Wapenaar;J. Fokkema
中科院分区：
文献类型：
--
作者：
K. Wapenaar;J. Fokkema
术语地震干涉测量是指通过在不同接收器位置处互相关地震观测来产生新的地震响应的原理。这个原理的第一个版本是由Claerbout（1968）推导出来的，他指出水平分层介质的反射响应可以从其透射响应的自相关性合成。对于任意三维非均匀无耗介质，根据瑞利互易定理和时间反演不变性原理，介质中任意两点之间的声波绿色函数可以用这两点上波场观测值的互相关积分来表示。积分是沿着源在一个任意形状的表面包围这些点。关于波场的扩散率没有作出任何假设。Rayleigh-Betti互易定理导致弹性动力学绿色函数的类似表示。当封闭表面的一部分是地球的自由表面时，积分只需要在封闭表面的剩余部分上计算。实际上，并非所有的源都同等重要：对重建的绿色函数的主要贡献来自静止点的源。当源发射瞬态信号时，可以应用成形滤波器来校正源子波中的差异。当源是不相关的噪声源时，表示简化为在两个点处的波场观测的直接互相关，类似于从无序介质或具有不规则边界表面的有限介质中的漫射波场检索绿色函数的方法。
The term seismic interferometry refers to the principle of generating new seismic responses by crosscorrelating seismic observations at different receiver locations. The first version of this principle was derived by Claerbout (1968), who showed that the reflection response of a horizontally layered medium can be synthesized from the autocorrelation of its transmission response. For an arbitrary 3D inhomogeneous lossless medium it follows from Rayleigh's reciprocity theorem and the principle of time-reversal invariance that the acoustic Green's function between any two points in the medium can be represented by an integral of crosscorrelations of wavefield observations at those two points. The integral is along sources on an arbitrarily shaped surface enclosing these points. No assumptions are made with respect to the diffusivity of the wavefield. The Rayleigh-Betti reciprocity theorem leads to a similar representation of the elastodynamic Green's function. When a part of the enclosing surface is the earth's free surface, the integral needs only to be evaluated over the remaining part of the closed surface. In practice, not all sources are equally important: The main contributions to the reconstructed Green's function come from sources at stationary points. When the sources emit transient signals, a shaping filter can be applied to correct for the differences in source wavelets. When the sources are uncorrelated noise sources, the representation simplifies to a direct crosscorrelation of wavefield observations at two points, similar as in methods that retrieve Green's functions from diffuse wavefields in disordered media or in finite media with an irregular bounding surface.