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.

全波形反演 (FWI) 是一种强大但计算成本高的技术​​，可以生成高分辨率的地下模型。随机选择的镜头（小批量）可用于近似 FWI 的失配和梯度，从而降低其计算成本。在这里，我们提出了一种使用 Adam 算法执行小批量 FWI 的方法，这是一种基于随机梯度下降的自适应优化方案。它通过平滑迭代之间的梯度来提供稳定的模型更新，还可以考虑优化景观的曲率。我们描述了选择 Adam 算法的超参数和最佳小批量大小的经验标准。概述方案的性能在来自 Marmousi 模型的合成数据上进行了说明，并与传统的全批次 FWI 进行了比较。