We have 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 adopt the neural network version of sparse LSM. Unlike the standard LSM method that finds the optimal reflectivity image, neural network LSM (NNLSM) finds 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 an attribute image for high-resolution delineation of geologic bodies.

中文翻译：

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深卷积神经网络和稀疏最小二乘迁移

我们已经重铸了多层卷积神经网络（CNN）的前向通过作为稀疏最小二乘迁移（LSM）问题的解决方案。所示的CNN滤镜和特征图分别类似于迁移格林函数和准反射率分布，但并不等效。根据地震成像的运算符，这为深层CNN中的滤波器和特征图提供了物理解释。出于稀疏LSM和CNN之间的联系的激励，我们采用了稀疏LSM的神经网络版本。与找到最佳反射率图像的标准LSM方法不同，神经网络LSM（NNLSM）查找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称为CNN中的卷积滤波器，类似于迁移格林函数。与标准LSM相比，NNLSM的优势在于其计算成本显着降低，并且可用于消除迁移图像中的相干噪声和非相干噪声。它的缺点是NNLSM准反射率图像仅是实际反射率分布的近似值。但是，准反射率图像可以用作地质体高分辨率描绘的属性图像。它的缺点是NNLSM准反射率图像仅是实际反射率分布的近似值。然而，准反射率图像可以用作属性图像，用于高分辨率描绘地质体。它的缺点是NNLSM准反射率图像仅是实际反射率分布的近似值。然而，准反射率图像可以用作属性图像，用于高分辨率描绘地质体。