Fresnel volumes and Fresnel zones in complex laterally varying structures

Summary

A new method to compute the Fresnel volumes and Fresnel zones of seismic body waves propagating in complex, 2-D and 3-D, laterally varying, layered and blocked structures is proposed. It is based on the network ray tracing. The method is stable and efficient and overcomes limitations of the method based on the paraxial ray approach. Whereas the method based on the paraxial approach can be applied only to regular, zero order seismic body waves (in the terminology of the ray method), the proposed method can be used to compute the Fresnel volumes even for head waves, and for diffracted waves penetrating into shadow zones. The method is also applicable in singular regions of the ray field, and predicts correctly various higher order effect. The limitation of the proposed method is that it is applicable only to waves arriving at the receiver in first arrivals. After some simple modification of the procedure, however, waves reflected from any interface in the model can be treated as first arriving waves. The presented numerical examples show certain interesting properties of Fresnel volumes (splitting of Fresnel volumes, penetration of Fresnel volumes of reflected waves across reflecting interface, penetration of Fresnel volumes of head waves across an interface into a lower velocity medium, etc.).

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