An Unsupervised Learning Method to Suppress Seismic Internal Multiples Based on Adaptive Virtual Events and Joint Constraints of Multiple Deep Neural Networks

Abstract

In seismic data processing, the suppression of internal multiple is a challenging direction. To suppress internal multiples, we propose an unsupervised deep neural network method based on adaptive virtual events and joint constraints of multi-deep neural networks (JCMDNN). First, we use an adaptive virtual event (AVE) method to obtain predicted internal multiples by convolution and cross-correlation. The predicted internal multiples can well calibrate true internal multiples and provide good prior information. Second, we use the unsupervised deep neural network (UDNN) to map the predicted internal multiples to the estimated true internal multiples. Finally, the de-multiple results can be obtained by subtracting the estimated true internal multiples from the data containing internal multiples. Three deep neural networks (DNNs), one input data, six output data, and six pseudo-labels (PLs) are combined into the base learners and auxiliary learners of UDNN. UDNN uses the nonlinear optimization ability of DNNs to map predicted internal multiples to true internal multiples through the joint constraints of multi-DNNs. Three auxiliary learners correct outputs of the base learners to reduce the nonlinear mapping deviation of UDNN. Using joint constraints of multi-DNNs by combining all base learners and auxiliary learners is called ensemble learning. Our proposed JCMDNN method does not need true internal multiples and true primaries as the input and output data, which solves the problem of missing training datasets and has wide use ranges. The effectiveness and superiority of our proposed method to suppress internal multiples are demonstrated through two synthetic and one field data examples.