## Fresnel volume ray tracing

**Vlastislav Cerveny** ** & **
**Jose Eduardo P. Soares**
### Summary

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.

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*Geophysics*, **57** (1992), 902-915.

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