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Computation of uniform wave forms using complex rays
Dario Amodei1, Henk Keers, Don Vasco
1Department of Physics, Stanford University, Stanford, CA 94305, USA. damodei@stanford.edu
Summary
This study introduces novel numerical methods using complex rays and polynomial phase functions to solve the Helmholtz equation, enabling accurate wave propagation modeling in complex geological structures with multiple caustics.
Area of Science:
- Computational physics
- Seismology
- Applied mathematics
Background:
- The Helmholtz equation governs wave propagation, crucial in seismology and acoustics.
- Solving wave equations in heterogeneous media with caustics presents significant numerical challenges.
- Existing methods often struggle with accuracy and global solutions near caustics.
Purpose of the Study:
- To develop a robust numerical method for solving the Helmholtz equation in complex 2D velocity models.
- To achieve globally uniformly asymptotic solutions in the presence of multiple adjacent cusp caustics.
- To introduce efficient algorithms for ray tracing and phase function construction.
Main Methods:
- Numerical solution of the Helmholtz equation using complex rays and polynomial phase functions.
- Development of a two-point ray tracing algorithm for complex rays.
- Application of a perturbation method for constructing polynomial phase functions.
- Discrete cosine transform analysis for model representation in complex space.
Main Results:
- Global uniformly asymptotic solutions were determined for models with arbitrarily many caustics.
- Accurate computation of geometrical and uniformly asymptotic solutions.
- Successful application to both a linear layer test model and a realistic velocity model from Yucca Mountain.
Conclusions:
- The combined methods provide a powerful tool for wave propagation modeling in complex geological settings.
- The developed algorithms enhance the accuracy and global applicability of asymptotic solutions.
- This approach is suitable for realistic geophysical models, including those with intricate subsurface structures.
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