Marine Physical Laboratory, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0238, USA.
J Acoust Soc Am. 2011 Jun;129(6):3562-76. doi: 10.1121/1.3573989.
It is well established that the free-space Green's function can be recovered from the two-point cross-correlation function of a random noise field if the noise is white and isotropic. Ambient noise in the ocean rarely satisfies either of these conditions. However, a non-uniform spectrum could be pre-whitened by the application of a suitable filter but anisotropy cannot be so readily eliminated. To investigate the effects of vertical anisotropy, three azimuthally uniform, spatially homogeneous noise fields are analyzed, two of which are idealized, while the third is representative of ambient noise in the deep ocean. In each case, the coherence function, the cross-correlation function, and the derivative of the latter with respect to the correlation delay, are derived for vertical and horizontal alignments of the sensor pair. With vertical sensors, any step-function discontinuity in the directional density function is mapped into a delta function at an appropriate time delay in the derivative (with respect to time delay) of the cross-correlation function. No such mapping occurs with horizontal sensors. In this case, only horizontally traveling noise can generate delta functions in the derivative of the cross-correlation function, and these always appear at the retarded time on either side of the origin.
已有研究表明，如果噪声为白色且各向同性，则可以从随机噪声场的两点互相关函数中恢复自由空间格林函数。然而，海洋中的环境噪声很少满足这两个条件。但是，可以通过应用合适的滤波器预先白化非均匀谱，但各向异性却不容易消除。为了研究垂直各向异性的影响，分析了三个方位均匀、空间均匀的噪声场，其中两个是理想化的，而第三个则代表深海中的环境噪声。在每种情况下，都推导了传感器对垂直和水平对准的相干函数、互相关函数以及后者对相关延迟的导数。对于垂直传感器，方向密度函数中的任何阶跃函数不连续性都将在互相关函数的导数（相对于延迟时间）中的适当延迟处映射为δ函数。对于水平传感器则不会发生这种映射。在这种情况下，只有水平传播的噪声才能在互相关函数的导数中产生δ函数，并且这些函数总是出现在原点两侧的延迟时间处。
