发表机构
Emerson-AspenTech; Tel Aviv University（艾默生阿斯彭科技; 特拉维夫大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出特征波理论，将特征射线方法扩展到有限频率，通过等效有效介质修正轨迹与振幅，统一射线理论与有限频率波传播。
AI 中文摘要
特征射线方法利用基于程函方程的变分公式，求解非均匀各向异性弹性介质中的两点边值射线追踪问题。在此，我们通过轨迹力学公式将该方法扩展到有限频率，其中有限频率效应由耦合相位和振幅的频率相关势表示。我们证明，有限频率传播可以通过等效有效介质在相同的变分框架内描述，既保留了原始方法的结构，又引入了对轨迹、相位、振幅、几何扩散、波前曲率和焦散行为的修正。由此产生的特征波公式仅需对射线速度及其导数进行局部修改，并在高频极限下简化为经典射线理论。涉及多路径和尖点焦散的数值示例表明，该方法能准确模拟有限频率传播效应。虽然基于射线的振幅在焦散附近变得不可靠，但相空间（马斯洛夫）处理成功地再现了有限差分波场解。这些结果确立了特征波理论作为连接非均匀各向异性介质中射线理论与有限频率波传播的统一框架。
英文摘要
The Eigenray method solves two-point boundary-value ray-tracing problems in heterogeneous anisotropic elastic media using a variational formulation based on the eikonal equation. Here, we extend the method to finite frequencies using the trajectory-mechanics formulation in which finite-frequency effects are represented by a frequency-dependent potential that couples phase and amplitude. We show that finite-frequency propagation can be described within the same variational framework through an equivalent effective medium, preserving the structure of the original method while introducing corrections to trajectories, phase, amplitudes, geometric spreading, wavefront curvature, and caustic behavior. The resulting Eigenwave formulation requires only local modifications of the ray velocity and its derivatives and reduces to classical ray theory in the high-frequency limit. Numerical examples involving multipathing and cusp caustics demonstrate accurate modeling of finite-frequency propagation effects. While ray-based amplitudes become unreliable near caustics, a phase-space (Maslov) treatment successfully reproduces finite-difference wavefield solutions. These results establish Eigenwave theory as a unified framework connecting ray theory and finite-frequency wave propagation in heterogeneous anisotropic media.
Comments72 pages and 11 figures
