Efficient Hybrid Domain Simultaneous Source Full Waveform Inversion

Full waveform inversion (FWI), recognized for its high precision, has garnered widespread application in velocity modeling. However, the computational cost of FWI continues to be a significant hurdle in its practical application. The FWI method employing multi-source simultaneous excitation, based on source-encoding, is a pivotal strategy for enhancing efficiency. However, conventional encoding methods suffer from crosstalk noise and are not adaptable to geometry where the positions of receivers are variable. To augment efficiency and ensure inversion accuracy, this paper introduces a time-frequency hybrid domain FWI algorithm that is founded on the resampled time-domain phase-sensitive detection (TD-PSD) method. This technique leverages the orthogonality of trigonometric integrals over complete periods to effectuate the decoupling of blended wavefields in the frequency domain and enables the computation of cross-correlation gradients without crosstalk. Concurrently, we propose a lossless sampling algorithm that markedly improves the efficiency of traditional TD-PSD integration calculations. Ultimately, the reliability of our proposed method is substantiated by numerical simulations on the two-dimensional (2D) overthrust model and three-dimensional (3D) field data, demonstrating that the inversion efficiency of our method is 4-6 times higher than that of traditional TD-PSD approach.