Deep-learning optimization using the gradient of a custom objective function: A full-waveform inversion example study on the convolutional objective function

doi:10.1190/GEO2023-0538.1

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Deep-learning optimization using the gradient of a custom objective function: A full-waveform inversion example study on the convolutional objective function

2024-09-02

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DOI：10.1190/GEO2023-0538.1

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Abstract

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The integration of conventional high-performance full-waveform inversion (FWI) algorithms with deep-learning frameworks is an innovative and promising research direction with the potential to enhance and broaden the application prospects of this field significantly. Automatic differentiation with back- propagation techniques can derive the gradients of model parameters in an equivalent manner to that of adjoint methods; however, it requires a substantial amount of computer memory, particularly when considering the time-step layers. In addition, some excellent objective functions suitable for FWI are not available in deep-learning frameworks. In comparison, the ad- joint method, based on effective boundary storage technology, offers greater practicality for calculating the gradients of various objective functions. Therefore, this paper develops a novel approach toward FWI that integrates deep-learning optimization with high-performance gradient computation. In particular, our method inputs model parameter gradients from a custom objective function into the deep-learning framework. Herein, we use the acoustic equation with variable density as an example to demonstrate how a convolutional objective function, along with its corresponding velocity and density gradients, can be used for optimized inversion, multiscale inversion, and deep network parameterization-based multiscale inversion within the deep-learning framework. This approach provides a paradigm for deep-learning-optimized FWI, which we apply to synthetic and field data scenarios.

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