自动微分地震反演的一般方法
A General Approach to Seismic Inversion with Automatic Differentiation
摘要：
从地震数据成像地球结构或地震源涉及最小化目标失配函数，并且通常通过基于梯度的优化来解决。伴随状态方法已经被开发用于有效地计算梯度;然而，其实现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，使用反向模式自动微分计算梯度。其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价的。数值PDE模拟和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反演建模库ADSeismic，该库支持CPU和GPU上的高性能反向模式自动微分。我们展示了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相关的逆问题上的性能。ADSeismic具有在统一框架内解决各种反演建模应用的潜力。
英文摘要：
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.
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