Overview
This study focuses on enhancing ray tracing in dissipative anisotropic media by incorporating a modified Hamiltonian-driven shortest-path algorithm. The research addresses challenges associated with subsurface characteristics, including geologic and rheological discontinuities and directionally dependent attenuation. It evaluates the performance of different computational kernels for determining complex energy velocities and associated ray parameters such as ray velocity, ray attenuation, and ray quality factor.
Research Context
Ray tracing in dissipative anisotropic media presents difficulties due to the complex nature of the subsurface. Conventional methods, including real-ray tracing and complex energy-velocity formulations, encounter issues such as qSV cusps, wavefront triplications, and abrupt discontinuities. While recent conjugate and shortest-path extensions have been proposed to mitigate these problems, they often rely on approximate Hamiltonian formulations. These approximations are typically tested in smooth background models and often do not fully address first-arrival refraction or the coupled behavior of wave propagation and energy dissipation.
Approach
The research integrates a g*-Hamiltonian-based formulation into a shortest-path-based ray-tracing algorithm. This integration is applied to layered dissipative anisotropic media. The methodology involves computing complex energy velocities and corresponding ray quantities at a local scale. These quantities include ray velocity, ray attenuation, and ray quality factor. The study utilizes three distinct kernels for this computation:
- Original Complex Energy Velocity (OEV): Represents a conventional approach for calculating complex energy velocities.
- Conjugate Real Ray Tracing (C-RRT): An alternative method designed to address certain limitations of conventional techniques.
- g*-Hamiltonian (MEV): A modified Hamiltonian formulation integrated into the shortest-path algorithm.
The study analyzes the discrepancies and numerical behavior of these kernels. It also examines several optimization strategies to improve performance and stability.
Findings
- All three kernels (OEV, C-RRT, MEV) demonstrated agreement for qSH and qP waves.
- In qSV modeling, the OEV kernel generated pseudo-reflection or exhibited numerical instability, producing unphysical attenuation along ray paths.
- The C-RRT kernel produced significant errors, including non-physical negative attenuation in some qP and qSV traveltime values. It also resulted in strongly biased ray quality factors under the tested parameter regime.
- Among the kernels evaluated, the MEV-driven shortest-path ray tracing produced the most computationally stable first-arrival behavior.
Why This Matters
The development of more stable and accurate ray-tracing algorithms in dissipative anisotropic media is significant for understanding complex subsurface structures. Addressing issues like qSV cusps, wavefront triplications, and unphysical attenuation can lead to more reliable characterizations of geological and rheological discontinuities.