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Full waveform inversion with random shot selection using adaptive gradient descent


Full waveform inversion (FWI) is a powerful yet computationally expensive technique that can yield subsurface models at high resolution. Randomly selected shots (mini-batches) can be used to approximate the misfit and the gradient of FWI, thereby reducing its computational cost. Here, we present a methodology to perform mini-batch FWI using the Adam algorithm, an adaptive optimization scheme based on stochastic gradient descent. It provides for stable model updates by smoothing the gradient across iterations and can also account for the curvature of the optimization landscape. We describe empirical criteria to choose the hyperparameters of the Adam algorithm and the optimal mini-batch size. The performance of the outlined scheme is illustrated on synthetic data from the Marmousi model and compared with conventional full-batch FWI. FWI with random shot selection and optimized by the Adam algorithm exhibits rapid convergence and yields superior results compared to conventional FWI implemented with the l-BFGS method.

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We would like to thank the Associate Editor Dr Arkoprovo Biswas and two anonymous reviewers for their constructive feedback.

Author information




Kuldeep formulated the research problem, wrote computer code to produce the examples and wrote the initial draft of the manuscript. Bharath Shekar provided research guidance and edited the manuscript.

Corresponding author

Correspondence to Bharath Shekar.

Additional information

Communicated by Arkoprovo Biswas




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Kuldeep, Shekar, B. Full waveform inversion with random shot selection using adaptive gradient descent. J Earth Syst Sci 130, 183 (2021).

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  • Full waveform inversion
  • random shot selection
  • optimization