无监督残差网络的地震数据重构方法

野外采集的地震数据通常会存在地震道缺失的问题，对其进行重构一直是地震资料处理中的一个难题。目前使用深度学习(Deep Learning，DL)方法重构地震数据主要采用完整地震数据作为标签训练网络模型的监督学习方式，然而对实测野外数据很难获得准确的标签。对大量训练样本的依赖影响了DL方法在地震数据重构中的应用。为此，提出了一种基于残差网络的无监督DL的地震数据重构方法。该方法无需使用完整的地震数据作为训练集训练残差网络，而是以随机数据作为残差网络的输入，以含缺失地震道的地震数据作为网络的期望输出。通过对网络预测与期望输出之间的误差的反向传播，迭代优化网络参数，使网络与期望输出间的误差达到最小，获得参数最优的残差网络，并用该网络重构缺失的地震数据。在网络参数优化过程中，利用卷积的局部和平移不变性质，用卷积滤波器学习多尺度下地震数据邻域之间的相似特征，并在网络输出中呈现学习到的这些先验特征。使用所提方法重构Marmousi模型模拟地震资料和实测海洋拖缆资料中规则和不规则缺失的记录道，并与传统的快速凸集投影软阈值(FPOCS-Soft)方法的结果进行对比，结果表明，无监督残差网络方法可有效重构缺失地震道，准确性高、连续性好，精度高于FPOCS-Soft方法。

Seismic data reconstruction method based on unsupervised residual network

Seismic data collected in the field usually have the problem of missing seismic traces. Reconstructing such traces has always been a difficult problem in seismic data processing. The deep learning (DL) method currently used mainly adopts a supervised learning approach for seismic data reconstruction,that is,it needs to use complete seismic data as labels to train the network model. Nevertheless,accurate labels for measured field data are difficult to obtain,and the dependence on a large number of training samples affects the application of the depth learning method in seismic data reconstruction. Therefore,this paper proposes a seismic data reconstruction method of unsupervised deep learning based on a residual network. Instead of using complete seismic data as the training set to train the residual network,this method takes random data as the input of the residual network,with the seismic data containing the missing seismic traces as the expected output of the network. Through the back propagation of the error between the network predicted output and the expected output,the network parameters are iteratively optimized to minimize the error,obtain the residual network with the optimal parameters,and use the network to reconstruct the missing seismic data. During network parameter optimization,the local and translation invariant properties of convolution are leveraged to learn the similar features between seismic data neighborhoods at multiple scales with the convolution filter,and the learned prior features are presented in the network output. This method is used to reconstruct the regular and irregular missing traces in the seismic data simulated with the Marmousi model and the measured marine streamer data,and the results are compared with those of the traditional fast projection onto convex set-soft threshold (FPOCS-Soft) method. The comparison shows that the proposed unsupervised residual network method can effectively reconstruct missing seismic traces,offer results with high accuracy and continuity,and outperforms the FPOCS-Soft method in precision.