Internal Multiple Suppression Using a Physics-Constrained Deep Neural Network

Abstract

Summary Internal multiples are common in field land data and can affect migration and subsequent interpretation. They generally need to be suppressed and eliminated. We propose a physics-informed neural network (PINN) method based on the orthogonal constraint and ensemble learning to suppress internal multiples. The designed PINN includes three deep neural networks (DNNs), one input data, six output data, and six pseudo-label (PL) data. We use the adaptive virtual event (AVE) method to obtain the predicted internal multiples to calibrate the true internal multiples. The predicted internal multiples are fed into PINN as input data and mapped nonlinearly to three estimated true internal multiples. The total loss function for PINN takes characteristics of the orthogonality of primaries and internal multiples to avoid the residue of internal multiples in the de-multiple result. Also, the total loss function uses the integrated learning loss term to improve the effectiveness of multiple suppression. Three examples are given to verify the effectiveness of our proposed method in internal multiple suppression.