Enhancing multiparameter elastic full-waveform inversion with a Siamese network

Using the proper data misfit measure within full-waveform inversion (FWI) is crucial for achieving robust inversion performance. This choice is complicated by the fact that our simulations are often based on simplified assumptions of the earth admitting clean waveforms that differ from those recorded. Thus, we extend the Siamese framework for multiparameter elastic full-waveform inversion (EFWI). For this elastic implementation, we use wavelet transforms to help the network recognize the features of the data it needs to highlight for the misfit measure. Specifically, we transform seismic data into the wavelet domain using the Haar mother wavelet, with the approximation and detail components serving as inputs to the Siamese network. The Siamese network comprises two identical convolutional neural network branches with shared weights. They map the wavelet coefficients to values that can provide improved data comparison, using the Euclidean distance to measure the loss between the Siamese output branches. This proposed Siamese network is a self-supervised deep learning model, where its parameters are optimized during the EFWI iterative process. A skip connection between the Siamese network's input and output is used to ensure stability, given the random initialization of the Siamese network parameters. This design ensures that, during the initial iterations, the framework behaves similarly to conventional EFWI, preventing the introduction of noise or instability. After a few iterations, the Siamese network learns to extract significant features from its input data, leading to robust inversion performance. The integration of the Siamese network incurs only minimal additional cost compared to traditional EFWI. We tested the framework on synthetic and real data examples, demonstrating its ability to enhance the inversion performance of the conventional EFWI.