Deep Network Reparameterized Full‐Waveform Inversion From Sequential to Simultaneous Sources With Adjoint‐State Method

Full‐waveform inversion (FWI) relies on sequential‐source (SQ) workflows for high imaging precision, while simultaneous‐source (SML) encoding drastically accelerates computation but introduces irreversible wavenumber discontinuity artifacts in hybrid‐domain implementations. Existing automatic differentiation‐based deep learning (DL) FWI only supports standalone sequential‐source inversion and suffers excessive memory overhead, failing to realize crosstalk‐free multi‐source inversion. To address these limitations, we propose an adjoint‐state‐gradient coupled long short‐term memory (LSTM) reparameterized framework compatible with both SQ and SML FWIs. A dedicated LSTM regularization scheme is designed to mitigate wavenumber discontinuity induced by discrete‐frequency source encoding, combined with phase‐sensitive detection to achieve crosstalk‐free gradient calculation for multi‐source cases. Numerical tests on Marmousi II, Overthrust, and Canadian Foothills benchmark models and field seismic data demonstrate that the proposed LSTM reparameterization significantly improves inversion accuracy against conventional SQ/SML FWI. DL‐based SML FWI achieves nearly identical imaging precision to DL‐based SQ FWI while delivering over twofold computational acceleration. This unified pipeline enables flexible selection between high‐precision DL‐SQ FWI and high‐efficiency DL‐SML FWI according to field noise and computational constraints.