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The restarted L-BFGS algorithm proposed here is both stable and efficient.
This breakthrough ensures, for the first time, the applicability of advanced FWI methods to three-dimensional seismic field data.
In seismic waveform tomography, or full-waveform inversion (FWI), one effective strategy used to reduce the computational cost is shot-encoding, which encodes all shots randomly and sums them into one super shot to significantly reduce the number of wavefield simulations in the inversion.
However, this process will induce instability in the iterative inversion regardless of whether it uses a robust limited-memory BFGS (L-BFGS) algorithm.
This restarted L-BFGS algorithm balances the computational efficiency of shot-encoding, the convergence stability of the L-BFGS algorithm, and the inversion quality characteristic of random encoding in FWI.
Full-waveform inversion (FWI) is used to extract information from seismic waveforms to reconstruct a subsurface model of the Earth with complex velocities.
Therefore, the implementation of the L-BFGS algorithm is restarted at every segment.
Each segment consists of a number of iterations; the first few iterations use an invariant encoding, while the remainder use random re-coding.
The inversion algorithm used in shot-encoded FWI must be stochastic.This gradient vector is the first-order derivative of the FWI objective function with respect to the unknown model parameters, and is computed for each shot separately and is formed by cross-correlation between the incident wavefield and the adjoint wavefield.