Imaging Earth structure or seismic sources from seismic data involves minimizing a target misfit function, and is commonly solved through gradient-based optimization. The adjoint-state method has been developed to compute the gradient efficiently; however, its implementation can be time-consuming and difficult. We develop a general seismic inversion framework to calculate gradients using reverse-mode automatic differentiation. The central idea is that adjoint-state methods and reverse-mode automatic differentiation are mathematically equivalent. The mapping between numerical PDE simulation and deep learning allows us to build a seismic inverse modeling library, ADSeismic, based on deep learning frameworks, which supports high performance reverse-mode automatic differentiation on CPUs and GPUs. We demonstrate the performance of ADSeismic on inverse problems related to velocity model estimation, rupture imaging, earthquake location, and source time function retrieval. ADSeismic has the potential to solve a wide variety of inverse modeling applications within a unified framework.

从地震数据对地球结构或地震源进行成像涉及将目标失配函数​​最小化，通常通过基于梯度的优化来解决。已经开发了伴随状态方法来有效地计算梯度。然而，其实施可能是耗时且困难的。我们开发了一个通用的地震反演框架，以使用反向模式自动微分来计算梯度。中心思想是伴随状态方法和反向模式自动微分在数学上是等效的。PDE数值模拟与深度学习之间的映射使我们能够基于深度学习框架构建地震逆模型库ADSeismic，该库支持CPU和GPU上的高性能逆模自动微分。我们证明了ADSeismic在与速度模型估计，破裂成像，地震定位和源时间函数检索有关的反问题上的性能。ADSeismic具有在统一框架内解决各种逆向建模应用程序的潜力。