Seismic imaging is a fundamental tool in the oil and gas industry, but dealing with the complexity of anisotropic geological media has always represented a significant technological challenge. Seismic processing techniques developed over the past century have, for the most part, been adapted for homogeneous and isotropic models, making accuracy in anisotropic environments a difficult task. The advancement of seismic technologies capable of effectively addressing media with anisotropic properties remains a significant technological challenge.
A new article published by HPG Lab members, entitled “Exploring the Velocity‑Spreading Factor and its Consequences Through Dynamic Ray‑Tracing in General Anisotropic Media“, recently accepted in the journal Differential Equations and Dynamical Systems , proposes a crucial advancement in this area and directly addresses the need to understand the influence of anisotropy on seismic wavefronts. To overcome the difficulty imposed by anisotropy, often with the ideal anisotropic model being unknown , the authors utilize paraxial-ray theory in a ray-centered coordinate system. This innovative approach allows for the development of explicit expressions that clearly describe the physics of the problem.
Among the key contributions of the article are:
- The generalization of the relationship between time-migration rays and Dix velocity, incorporating a velocity-spreading factor specific for general anisotropic media;
- The demonstration that the velocity-spreading factor provides valuable information for various applications, including model building, time-imaging, and time-to-depth conversion;
- A physical interpretation of how wavefronts emerge and how anisotropy influences its shape;
- The establishment of a natural connection between Dix velocity and the time-migration wavefront expanding;
- The derivation of a relationship between Dix and group velocities, which can help determine the type and degree of anisotropy in the medium;
- The presentation of explicit expressions for the Hamiltonian, which are fundamental for understanding the physical phenomenon and for the construction of algorithms for modeling, imaging, and time-to-depth conversion.
The methodology based on the explicit formulation in terms of phase velocity and its derivatives offers an in-depth understanding of the contributions of anisotropy and heterogeneity to wave propagation. By converting the problem from Cartesian coordinates to a non-orthogonal ray-centered coordinate system, the work not only simplifies the system of equations but also allows for a qualitative understanding of the propagation phenomenon without the need for complex coordinate transformations. The results show that, even in a homogeneous anisotropic medium, the Dix velocity differs from the migration velocity. This property, which was already known for Vertical Transversely Isotropic (VTI) media, is demonstrated in this work as valid for all types of anisotropic symmetry. This emphasizes that simplistic migration models that ignore velocity spread are inherently inaccurate, even in stratified media where anisotropy is induced by thin layering.
In summary, this work provides new theoretical and computational tools to develop advanced seismic imaging technologies, which are vital for the industry. The solid understanding of the physical phenomenon presented in the article contributes to a deeper insight into the formation of seismic images and paves the way to improve the ability to accurately interpret subsurface features, distinguishing the effects of anisotropy from those of heterogeneity. This article represents a significant step towards the generalization of well-established and validated results in isotropic media to the general anisotropic case, offering a robust foundation for future developments in exploration geophysics.
Article Title: Exploring the Velocity‑Spreading Factor and its Consequences Through Dynamic Ray‑Tracing in General Anisotropic Media
Authors: Tiago A. A. Coimbra, Rodrigo Bloot e Jorge H. Faccipieri Junior
Journal: Differential Equations and Dynamical Systems
DOI: https://doi.org/10.1007/s12591-025-00724-2
