Sun Hongyu, Demanet Laurent
IEEE Trans Neural Netw Learn Syst. 2023 Jul;34(7):3385-3396. doi: 10.1109/TNNLS.2022.3172385. Epub 2023 Jul 6.
Passive seismic interferometry is a vastly generalized blind deconvolution question, where different paths through the Earth correspond to different channels called Green's functions; the sources are completely incoherent and not shared by the channels, and the question is to estimate paths (channels) that are not present in the dataset. SI, turning noise to signal, has numerous applications, from monitoring industrial activities to crustal structure investigation. No standard method of signal processing will solve SI. Instead, domain scientists resort to a simple cross-correlation operation, a.k.a. correlogram, which can retrieve the Green's function directly, but only under restrictive assumptions of ergodicity (energy equipartitioning) of the random process generating the seismic source. However, in practice, correlograms are not equal to the empirical Green's function, because these assumptions are generally far from being satisfied in realistic situations. In the framework of supervised learning, we propose to train deep neural networks (NNs) to overcome two limitations of correlation-based SI: the temporal limitation of passive recordings and the spatial limitation of the random source distribution. Deep NNs are trained to implicitly find the relationship between the empirical Green's functions and the correlograms and then used to extract the correct Green's functions from ambient noise. The input of the network is correlograms (a virtual shot gather), and the desired output is the empirical Green's function (the active shot gather). The NN can often retrieve Green's functions from 5-min passive recordings with acceptable accuracy in our synthetic example. Although an exact estimation of the source locations may not be necessary, a prior knowledge of the source directionality (through a preliminary beamforming step) is helpful when training the NN to mitigate the challenges associated with inhomogeneous source distributions (directional wave fields). In this work, all the numerical examples are based on the retrieval of P-wave reflections in the exploration scale and are conducted on synthetic data. We use a modified ResNet in our numerical experiments.
被动地震干涉测量是一个广义的盲反褶积问题，其中穿过地球的不同路径对应于称为格林函数的不同通道；震源完全不相关且各通道不共享，问题是估计数据集中不存在的路径（通道）。地震干涉测量，即将噪声转化为信号，有许多应用，从监测工业活动到地壳结构调查。没有标准的信号处理方法能解决地震干涉测量问题。相反，领域科学家采用一种简单的互相关运算，即互相关图，它可以直接检索格林函数，但前提是生成地震源的随机过程满足遍历性（能量均分）这一严格假设。然而，在实际中，互相关图并不等于经验格林函数，因为这些假设在现实情况下通常远未得到满足。在监督学习框架下，我们建议训练深度神经网络（DNN）以克服基于相关性的地震干涉测量的两个局限性：被动记录的时间局限性和随机源分布的空间局限性。训练深度神经网络以隐式地找到经验格林函数和互相关图之间的关系，然后用于从环境噪声中提取正确的格林函数。网络的输入是互相关图（虚拟炮集），期望输出是经验格林函数（有源炮集）。在我们的合成示例中，深度神经网络通常能够从5分钟的被动记录中以可接受的精度检索格林函数。虽然可能不需要精确估计震源位置，但在训练深度神经网络时，震源方向性的先验知识（通过初步波束形成步骤）有助于减轻与不均匀源分布（定向波场）相关的挑战。在这项工作中，所有数值示例均基于勘探尺度下P波反射的检索，并在合成数据上进行。我们在数值实验中使用了改进的残差网络（ResNet）。
