AVO theory for non-welded contacts

Tiansheng Chen and Kris Innanen

ABSTRACT

In this paper, a closed formulas of reflected and transmitted wave for incident compressional wave are carried out to analyse the AVO response to nonwelded interface. Based on the boundary conditions for the combined displacement and velocity discontinuity, the reflection coefficients of PP wave and PS wave are both complex function of frequency ω , elastic parameters α, β, ρ across interface and fracture parameters C x , C z describing the interface. The closed formulas are function of elastic parameters contrasts across interface ( r α =Δα/α, r β =Δβ/β and r ρ =Δρ/ρ ), average velocity ratio B 1 and B 2 of two layer respectively and new complex frequency dependent fracture parameters H x and H z . Different from welded interface, the reflection coefficients is not zero when the elastic parameters contrasts are zero. It shows that incident P wave propagating through a nonwelded interface in a single homogeneous medium (e.g., a crack, joint, or fracture) produces both frequency dependent reflected and transmitted P and S wave. The third order truncation approximation in series of fracture parameters and elastic parameter contrasts capture the exact reflected and transmitted coefficient at small incident angle at different frequency. The new closed formulas are convenient to analysis the effect of elastic parameters and fracture parameters on reflected and transmitted coefficients, and can be used to invert the elastic parameter contrasts and fracture parameters by use of linear inversion or series reversion method.

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