深度卷积神经网络与稀疏最小二乘偏移
Deep Convolutional Neural Network and Sparse Least Squares Migration
摘要：
我们将多层卷积神经网络（CNN）的前向传递转换为稀疏最小二乘迁移（LSM）问题的解决方案。CNN滤波器和特征图被示出为分别与迁移格林函数和准反射率分布类似，但不等同。这提供了在用于震波成像的算子方面的深CNN中的滤波器和特征图的物理解释。受稀疏LSM和CNN之间联系的启发，我们提出了稀疏LSM的神经网络版本。与寻找最佳反射率图像的标准LSM方法不同，神经网络LSM（NNLSM）同时找到最佳准反射率图像和准迁移格林函数。这些准迁移格林函数也被表示为CNN中的卷积滤波器，并且类似于迁移格林函数。NNLSM与标准LSM相比，其优点是计算量小，可用于去除偏移图像中的相干和非相干噪声。它的缺点是NNLSM准反射率图像只是对实际反射率分布的近似。然而，准反射率图像可以用作超分辨率属性图像，用于地质体的高分辨率描绘。
英文摘要：
We recast the forward pass of a multilayered convolutional neural network (CNN) as the solution to the problem of sparse least squares migration (LSM). The CNN filters and feature maps are shown to be analogous, but not equivalent, to the migration Green's functions and the quasi-reflectivity distribution, respectively. This provides a physical interpretation of the filters and feature maps in deep CNN in terms of the operators for seismic imaging. Motivated by the connection between sparse LSM and CNN, we propose the neural network version of sparse LSM. Unlike the standard LSM method that finds the optimal reflectivity image, neural network LSM (NNLSM) finds both the optimal quasi-reflectivity image and the quasi-migration Green's functions. These quasi-migration-Green's functions are also denoted as the convolutional filters in a CNN and are similar to migration Green's functions. The advantage of NNLSM over standard LSM is that its computational cost is significantly less and it can be used for denoising coherent and incoherent noise in migration images. Its disadvantage is that the NNLSM quasi-reflectivity image is only an approximation to the actual reflectivity distribution. However, the quasi-reflectivity image can be used as a superresolution attribute image for high-resolution delineation of geologic bodies.
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