Seismic Data Reconstruction And Full Waveform Inversion Based On Deep Learning And Optimal Transport

In recent years,with the emergence of deep learning technology,intelligent seismic data processing and inversion imaging have become a hot research topic.Deep neural networks have great potential in seismic data processing by learning data features from samples and establishing a nonlinear mapping relationship from input to output,which can be used for batch data processing after network training.However,the network training requires a large number of labels,and the trained network in a specific situation is difficult to cope with other complex situations and lacks generalization ability.To overcome these difficulties,combining mathematical theories and models,this dissertation investigates seismic data reconstruction based on deep image denoising prior and deep recurrent inference,and full waveform inversion imaging by combining deep learning with optimal transport theory,respectively.The details are as follows.First,the seismic data reconstruction based on supervised deep learning methods requires a large number of training labels,and the trained network lacks generalization ability.To address these problems,this dissertation proposes a seismic data reconstruction method based on a deep image denoising prior.The method learns the denoising prior from natural images and embeds the trained denoising convolutional neural network as the denoising operator into the optimization algorithm of seismic data reconstruction.The method does not depend on seismic data when training the neural network,which effectively solves the problem of insufficient training labels for seismic data and achieves reconstruction results with higher signal-to-noise ratios than the traditional method in seismic data reconstruction.The method can be used for reconstruction of seismic data with arbitrary missing ratios.However,the reconstruction capability needs further improvement for data with large missing-gap and severe spectral aliasing.Then,in order to solve the problem of reconstructing seismic data with large missing-gap and severe spectral aliasing,this dissertation proposes a method for reconstructing seismic data based on deep recurrent inference.The method starts from the optimization problem of seismic data reconstruction and designs a reasonable recurrent neural network through recurrent inference mechanism to effectively learn prior knowledge from a small amount of seismic data samples.Numerical results show that this method has good generalization ability and can obtain better reconstruction results than traditional methods and deep learning methods on data with large missing-gap and severe spectral aliasing.Finally,seismic data reconstruction provides high-resolution and high signal-to-noise ratio data for full waveform inversion,but full waveform inversion suffers from strong dependence on initial guesses and high computational cost.To address the above problems,this dissertation investigates a full waveform inversion method combining deep learning and optimal transport theory.We first obtain some theoretical results of optimal transport-based full waveform inversion and propose a deep learning full waveform inversion method based on total variation regularization and Wasserstein distance.The method uses recurrent neural networks to implement full waveform inversion,then transforms seismic data into probability distributions using the proposed integrated affine transform,and finally minimizes the objective function that is formulated by Wasserstein distance and total variation regularization by automatic differentiation and a small-batch stochastic gradient algorithm.Numerical experiments show that the method is weakly dependent on the initial guess and computationally efficient compared with the traditional~2distance-based full waveform inversion.In addition,this dissertation also proposes a full waveform inversion method based on the multidimensional Wasserstein-2 distance with a fast algorithm.Numerical experiments show that the full waveform inversion based on multidimensional Wasserstein-2 distance is less dependent on the initial guesses than the full waveform inversion based on one-dimensional Wasserstein-2 distance and~2distance.