Accelerating full-waveform inversion through adaptive gradient optimization methods and dynamic simultaneous sources

SUMMARY Full-waveform inversion (FWI) is a procedure based on the minimization of a misfit (or cost) function applied to the difference between synthetic waveforms and real seismic traces that derives high-resolution velocity models. This is achieved through the iterative adjustment of the velocity model and/or some other physical parameters of the Earth’s subsurface, which generally implies large computational effort. In order to minimize this cost function, we explore the use of adaptive gradient optimization (AGO), a variant of stochastic gradient descent (SGD) methods, combining them with a dynamic simultaneous sources strategy that allow us to reduce the computational cost involved in this process. AGO methods are computationally efficient, have little memory requirements and have the capability of adapting the step length according to the optimization process’ evolution. Since a precise calibration of the step length is needed to ensure efficiency, the AGOs are well suited for this task because they are able to adapt the step length according to the optimization’s development. In this work, we propose a simple nonlinear relationship that allows an adjustment of the step length with respect to the frequencies used in the multiscale FWI, avoiding the line-search strategy’s high computational burden. Additionally, the application of this new step length rule into the AGO methods with a dynamic simultaneous sources strategy, allow us to concurrently accelerate and significantly improve the FWI’s numerical performance and results. We compare the performance and final results of seven AGO methods, using two different FWI misfit functionals (based on L1 and L2 norms) applied to estimate the final velocity models of two benchmark acoustic models: the Marmousi and the Canadian overthrust BP velocity models.