基于优化参数Adam算法的全波形反演

常规的全波形反演(FWI)计算得到的梯度往往不做优化处理, 并且每次计算模型更新量时还需要额外的波场延拓计算来获取迭代步长, 导致收敛效率和反演精度降低.本文将深度学习中的Adam算法引入到全波形反演中来, 其可在仅付出极小计算代价的前提下实现梯度的优化处理, 由梯度直接计算出模型更新量, 避免了迭代步长的计算, 且能显著提升收敛效率和反演精度; 同时针对Adam算法的默认参数优化和选取问题, 通过数值实验系统分析了不同参数的全波形反演效果, 并给出了更适合于全波形反演的优化参数.实验结果表明, 相比于默认参数的Adam算法以及L-BFGS算法的全波形反演, 基于优化参数的Adam算法其收敛速度和反演精度更高.

Full waveform inversion based on Adam algorithm with optimized parameters

For the conventional Full Waveform Inversion (FWI), the gradient is not optimized, and extra wavefield extrapolations are needed to calculate the step-length for velocity updating usually, which slows down the convergence rate and the inversion accuracy. This paper introduces Adam, a deep learning algorithm into FWI, so as to improve thse convergence efficiency and inversion accuracy with less computational cost by optimizing the gradients and providing the optimized model update value directly. Meanwhile, we systematically analyze the effect of different parameters on the FWI by lots of numerical experiments and give optimized parameters which are more suitable for FWI. Model tests demonstrate that, the FWI based on Adam algorithm with the optimized parameters has much higher convergence rate and inversion accuracy than both the FWI based on Adam algorithm with the default parameters and the FWI based on limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm.