Fresnel volume ray tracing

TLDR

Fresnel volume ray tracing extends standard ray tracing by computing first‑Fresnel‑zone parameters at each ray point, yielding a 3‑D spatial equivalent whose shape varies with source–receiver geometry, intervening structure, wave type, and frequency, and is useful for assessing seismic resolution and ray‑method validity. The study proposes an efficient paraxial‑ray algorithm for Fresnel volume ray tracing. The algorithm evaluates first‑Fresnel‑zone parameters through simple algebraic manipulation of the ray propagator matrix and can be applied to high‑frequency seismic body waves in laterally varying 2‑D or 3‑D layered media. Numerical examples in 2‑D inhomogeneous layered structures demonstrate the method and reveal properties such as a double caustic effect.

Abstract

The concept of “Fresnel volume ray tracing” consists of standard ray tracing, supplemented by a computation of parameters defining the first Fresnel zones at each point of the ray. The Fresnel volume represents a 3-D spatial equivalent of the Fresnel zone that can also be called a physical ray. The shape of the Fresnel volume depends on the position of the source and the receiver, the structure between them, and the type of body wave under consideration. In addition, the shape also depends on frequency: it is narrow for a high frequency and thick for a low frequency. An efficient algorithm for Fresnel volume ray tracing, based on the paraxial ray method, is proposed. The evaluation of the parameters defining the first Fresnel zone merely consists of a simple algebraic manipulation of the elements of the ray propagator matrix. The proposed algorithm may be applied to any high‐frequency seismic body wave propagating in a laterally varying 2-D or 3-D layered structure (P, S, converted, multiply reflected, etc.). Numerical examples of Fresnel volume ray tracing in 2-D inhomogeneous layered structures are presented. Certain interesting properties of Fresnel volumes are discussed (e.g., the double caustic effect). Fresnel volume ray tracing offers numerous applications in seismology and seismic prospecting. Among others, it can be used to study the resolution of the seismic method and the validity conditions of the ray method.