标题： 基于射线时间的确定性和概率性偏微分方程反演的速度和震源位置的离散伴随方法 显示英文标题

标题： A discrete adjoint method for deterministic and probabilistic eikonal-equation-based inversion of traveltime for velocity and source location

摘要： 地震走时层析成像是一种流行且有用的工具，用于揭示不同尺度下的地下结构。 在本工作中，我们处理正演模型由射线方程表示的情况，并推导出一种形式来解决逆问题，其中使用离散伴随状态法高效计算梯度。 我们的方法提供了相对于速度结构和源位置的梯度，使我们能够进行一致的联合反演。 正演问题使用二阶快速行进方法求解，这提供了一种有效求解伴随问题的策略。 我们的方法允许源和接收器处于任意位置，并在源区域周围使用细化网格以减少计算走时的误差。 我们展示了如何利用离散伴随方法计算的梯度来进行确定性反演，即求解优化问题，或者用于概率（贝叶斯）方法，即获得后验概率密度函数。 我们在一组合成示例中展示了我们方法的应用，包括二维和三维情况，确定性情况下使用L-BFGS算法，概率情况下使用哈密顿蒙特卡洛算法。 显示英文摘要

摘要： Seismic traveltime tomography represents a popular and useful tool for unravelling the structure of the subsurface across the scales. In this work we address the case where the forward model is represented by the eikonal equation and derive a formalism to solve the inverse problem where gradients are calculated efficiently using the discrete adjoint state method. Our approach provides gradients with respect to both velocity structure and source locations, allowing us to perform a consistent joint inversion. The forward problem is solved using a second-order fast-marching method, which provides a strategy to efficiently solve the adjoint problem. Our approach allows for arbitrary positions of both sources and receivers and for a refined grid around the source region to reduce errors in computed traveltimes. We show how gradients computed using the discrete adjoint method can be employed to perform either deterministic inversion, i.e., solving an optimization problem, or for a probabilistic (Bayesian) approach, i.e., obtaining a posterior probability density function. We show applications of our methodology on a set of synthetic examples both in 2D and 3D using the L-BFGS algorithm for the deterministic case and the Hamiltonian Monte Carlo algorithm for the probabilistic case.