高分辨率被动地震三维成像的畸变矩阵框架：在加利福尼亚圣哈辛托断层带的应用
A Distortion Matrix Framework for High-Resolution Passive Seismic 3-D Imaging: Application to the San Jacinto Fault Zone, California
摘要：
反射震波成像由于地壳中波速的波动，通常遭受分辨率和对比度的损失。在文献中，相位失真问题通常通过背景波速度模型来规避。然而，它需要介质中波速分布的先验层析成像，这通常是不可能的，特别是在深度上。在本文中，一个矩阵的震波成像的方法来检索的三维图像的底土，尽管背景波速度的粗略知识。为此，在矩阵形式下研究了地震台阵检波器之间的被动噪声互相关。更确切地说，波速波动对成像的不利影响是通过引入一种新的数学对象：失真矩阵来克服的。该算子本质上将介质内的任何虚源与从该点发射的波前由于不均匀性而经历的失真相连接。失真矩阵的时间反演分析使得能够估计传输矩阵，该传输矩阵将地面处的每个真实地震检波器和深度处的每个虚拟地震检波器联系起来。然后可以补偿地下任何点的相位失真。应用于沿圣哈辛托断层带克拉克分支记录的地震资料，示出了本方法，以提供断层的图像，直到深度为4 km，横向分辨率为80 m。引人注目的是，该分辨率几乎是由地震检波器阵列孔径施加的衍射极限的八分之一。底土的不均匀性起到散射透镜和横波波导的作用，这大大增加了阵列孔径。
英文摘要：
Reflection seismic imaging usually suffers from a loss of resolution and contrast because of the fluctuations of the wave velocities in the Earth's crust. In the literature, phase distortion issues are generally circumvented by means of a background wave velocity model. However, it requires a prior tomography of the wave velocity distribution in the medium, which is often not possible, especially in depth. In this paper, a matrix approach of seismic imaging is developed to retrieve a three-dimensional image of the subsoil, despite a rough knowledge of the background wave velocity. To do so, passive noise cross-correlations between geophones of a seismic array are investigated under a matrix formalism. More precisely, the detrimental effect of wave velocity fluctuations on imaging is overcome by introducing a novel mathematical object: The distortion matrix. This operator essentially connects any virtual source inside the medium with the distortion that a wavefront, emitted from that point, experiences due to heterogeneities. A time reversal analysis of the distortion matrix enables the estimation of the transmission matrix that links each real geophone at the surface and each virtual geophone in depth. Phase distortions can then be compensated for any point of the underground. Applied to seismic data recorded along the Clark branch of the San Jacinto fault zone, the present method is shown to provide an image of the fault until a depth of 4 km with a transverse resolution of 80 m. Strikingly, this resolution is almost one eighth below the diffraction limit imposed by the geophone array aperture. The heterogeneities of the subsoil play the role of a scattering lens and of a transverse wave guide which increase drastically the array aperture.
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