Dept. of Geosciences Colloquium: Eigenrays in 3D heterogeneous anisotropic media

Dr. Zvi Koren, Aspen Technology & Tel Aviv University

08 January 2024, 11:00 
Ornstein Building, Room 110 
Dept. of Geosciences Colloquium




The Eigenray method is an enhanced ray-bending method for solving two-point boundary-value ray tracing problems in 3D heterogeneous general anisotropic elastic media (Koren and Ravve, 2021, Ravve and Koren, 2021). It is aimed to provide reliable stationary ray path solutions and their dynamic characteristics (traveltime, amplitude and phase of the asymptotic Green functions), in cases where conventional methods (e.g., initial-value ray shooting methods, followed by numerical convergence techniques) become challenging: Simulating wave/ray propagation through complex geological structures, as well as head-waves and tunneling waves propagating laterally in the shallow model along dominant refractors and through local anomalies.


The kinematic solution corresponds to the vanishing first traveltime variation, using the Euler–Lagrange second-order ordinary differential equation, leading to a stationary path between two fixed endpoints S and R (Fermat’s principle). The solution is based on a finite-element approach.  The unknown variables are discretised by nodal locations and directions along the ray trajectory, where the values between the nodes are accurately and naturally defined with the Hermite polynomial interpolation. 
The computation of the dynamic characteristics along the stationary rays  is based on the second traveltime variation, using the linear second-order Jacobi equation. The same finite-element solver is used for the dynamic ray tracing problem. 


The method is designed for being applied in seismic modeling, tomography, imaging, and inversion. The efficiency and accuracy of the Eigenray method are demonstrated along canonical and realistic models.



Koren, Z., and Ravve, I., 2021, Eigenrays in 3D heterogeneous anisotropic media, Part I: Kinematics, GEOPHYSICAL PROSPECTING, 2021, 69, 3–27, doi: 10.1111/1365-2478.13052

Ravve, I., and Koren, Z., 2021, Eigenrays in 3D heterogeneous anisotropic media, Part II: Dynamics, GEOPHYSICAL PROSPECTING, 2021, 69, 28–52, doi: 10.1111/1365-2478.13053



Event Organizer: Dr. Roy Barkan



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