Physics-Guided Self-Supervised Learning Full Waveform Inversion with Pretraining on Simultaneous Source

Full waveform inversion (FWI) is an established precise velocity estimation tool for seismic exploration. Machine learning-based FWI could plausibly circumvent the long-standing cycle-skipping problem of traditional model-driven methods. The physics-guided self-supervised FWI is appealing in that it avoids having to make tedious efforts in terms of label generation for supervised methods. One way is to employ an inversion network to convert the seismic shot gathers into a velocity model. The objective function is to minimize the difference between the recorded seismic data and the synthetic data by solving the wave equation using the inverted velocity model. To further improve the efficiency, we propose a two-stage training strategy for the self-supervised learning FWI. The first stage is to pretrain the inversion network using a simultaneous source for a large-scale velocity model with high efficiency. The second stage is switched to modeling the separate shot gathers for an accurate measurement of the seismic data to invert the velocity model details. The inversion network is a partial convolution attention modified UNet (PCAMUNet), which combines local feature extraction with global information integration to achieve high-resolution velocity model estimation from seismic shot gathers. The time-domain 2D acoustic wave equation serves as the physical constraint in this self-supervised framework. Different loss functions are used for the two stages, that is, the waveform loss with time weighting for the first stage (simultaneous source) and the hybrid waveform with time weighting and logarithmic envelope loss for the second stage (separate source). Comparative experiments demonstrate that the proposed approach improves both inversion accuracy and efficiency on the Marmousi2 model, Overthrust model, and BP model tests. Moreover, the method exhibits excellent noise resistance and stability when low-frequency data component is missing.