论文标题
3D异质各向异性媒体中的本征：第七部分 - 动力学，有限元实现
Eigenrays in 3D heterogeneous anisotropic media: Part VII -- Dynamics, Finite-element implementation
论文作者
论文摘要
在这一部分中，我们采用第三部分中使用的相同有限元方法，用于消失的第一个旅行时间变化（以获取固定射线），以进行第二次旅行时间变化，以计算沿固定射线的动态特性。有限的元素求解器涉及将弱公式和Galerkin方法应用于线性二阶Jacobi普通微分方程（派生在第五部分中），从而产生了用于动态射线跟踪的原始线性代数方程。在我们的公式中，线性方程式的分辨矩阵集合与针对运动学射线追踪计算的全局旅行时间Hessian相吻合，从而使动态问题的解决方案直接解决。所提出的方法是无条件稳定的（当节点之间的间隔增加时，解决方案不会爆炸），并且比常用的数值集成（例如Runge-Kutta）方法更准确，尤其是对于通过异质性各向异性模型传递的具有复杂波浪现象的固定射线。
In this part, we apply the same finite-element approach, used in Part III for the vanishing first traveltime variation (to obtain the stationary rays), for the second traveltime variation, in order to compute the dynamic characteristics along the stationary ray. The finite-element solver involves application of the weak formulation and the Galerkin method to the linear second-order Jacobi ordinary differential equation (derived in Part V), yielding an original linear algebraic equation set for dynamic ray tracing. In our formulation, the resolving matrix of the linear equation set coincides with the global traveltime Hessian computed for the kinematic ray tracing, making the solution of the dynamic problem straightforward. The proposed method is unconditionally stable (the solution does not explode when the intervals between the nodes are increased) and is more accurate than the commonly used numerical integration (e.g., Runge-Kutta) methods, in particular, for stationary rays passing through heterogeneous anisotropic models with complex wave phenomena.
