Determination of fresnel zones by traveltime inversion

Abstract

Seismic wave propagation in the high-frequency range is usually described by (zero-order ) ray theory. Its validity conditions are extensively investigated, e.g., by Kravtsov and Orlov (1990) . For finite frequenties a ray can only be viewed as a mathematical concept . There is a ( frequency-dependent) region in its vicinity that influences the wavefield received at the end of the ray . This region is the so-called (first) Fresnel volume of the ray . Any cross-section through it is a Fresnel zone. (Gelchinsky, 1985; Cerveny and Soares, 1992; Knapp, 1991) . In other words, the Fresnel volume is the envelope of all Fresnel zones along the ray. For seismic stratigraphic modeling, usually the Fresnel zone at the reflector is of interest, so as to know which part of it contributes to the reflected field . Fresnel zones are computed very efficiently by forward dynamic ray tracing through a known velocity model (Cerveny and Soares, 1992) . However, exploration geophysicists involved in a stratigraphic analysis would prefer to know the Fresnel zone of a reflecting interface without knowing the details of the reflector overburden, i .e., they are interested in solving an inverse problem . For a plane layered Barth model, it is possible to solve this inverse problem (i e., to calculate the Fresnel zone directly from measured traveltimes, e.g., Erom the rms-velocity) .