Tensor Deep Learning for Seismic Data Reconstruction
摘要
The main challenge in seismic data reconstructionSeismic data interpolation lies in accurately capturing the spatiotemporal relationshipsLatent spatial-temporal relationships between known and unknown traces, particularly in this regard to complex 3D seismic data. Many traditional tensor-based reconstructionTensor-based interpolation methods attempt to extract high-dimensional structures from the data using low-rank approximationsLow-rank approximation (LRA). However, these methods assume that the data has a simple low-rank structure, which often fails to effectively handle data with complex geological featuresComplex geological structure, thus affecting reconstruction accuracy. To address this issue, this chapter introduces a novel deep tensor autoencoder (DTAE)Deep tensor autoencoder (DTAE) model along with two variants, designed to automatically capture complex nonlinear relationships within the data through unsupervised learningData-driven, without relying on traditional low-rank assumptions. To optimize the model parameters, we propose tensor Backpropagation (TBP)Tensor backpropagation (TBP), an extension of the classical backpropagation (BP) algorithm specifically designed for tensor data. Furthermore, by leveraging the mathematical properties of the tensor-tensor productTensor-tensor product (t-product),we establish a connection between tensor autoencoders and matrix autoencodersMatrix autoencoder, which simplifies the computational process. Using this relationship, the weight parameters of the DTAEDeep tensor autoencoder (DTAE) model can be efficiently estimated by processing each data segment within the discrete cosine transform (DCT)Discrete cosine transform (DCT) space. Finally, through theoretical analysis and extensive experiments, including both synthetic and real seismic data, the effectiveness of the proposed DTAEDeep tensor autoencoder (DTAE) model in seismic data reconstruction is demonstrated.