The Fresnel zone for P-SV waves

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Abstract
Mode‐converted (P-SV) reflections in field data contain information about an area on the reflecting boundary, rather than a single point. For unmigrated data, the total area contributing to the observed reflection amplitude is approximated by the Fresnel zone. We derive formulas for the P-SV Fresnel‐zone radius for both surface and VSP geometries. In the surface case, the Fresnel radius can be expressed in a form similar to that of the P-P case by substitution of the P-SV single‐layer migration velocity. Numerical modeling shows that the relative changes in size and shape of the P-SV Fresnel zone as a function of offset are not large and are comparable to the P-P case. For a given depth and frequency, the P-SV Fresnel radius is smaller than the P-P Fresnel radius by a factor of about 0.8; hence the lateral resolution of converted‐wave (P-SV) data may be somewhat better than the P-P data. Two sample calculations using field data are presented. For the VSP example, the P-SV Fresnel radius (184 m) is smaller than the corresponding P-P Fresnel radius (231 m), but for the surface example the two are similar (315 m and 295 m, respectively), because of differences in the frequency contents of the reflected P and SV waveforms.

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