Sensitivity Analysis of Amplitude Variation with Offset (avo) in Fractured Media

The variation in seismic P to P reflection amplitude with offset (AVO) caused by a system of fractures embedded in an isotropic background is investigated. Additionally. a sensitivity analysis of AVO parameters with respect to the fracture system parameters is made. The fracture system is assumed to be aligned vertically or horizontally and can be gas filled or fluid filled. Elastic constants are calculated by using formulations of Schoenberg (1988). From the elastic constants, the reflection amplitude as a function of angle is calculated using equations from Ruger (1997). Theoretical results for a single interface between fractured and unfractured media, both with and without lit.hology change, show opportunities for ext.ract.ion of crack density information from seismic Pwave dat.a collected in fractured geothermal or hydrocarbon reservoirs. For vertically oriented fract.ures, wide angle data (> 30°) is crucial for the estimat.ion of fractur,' parameters. INTRODUCTION The behavior of seismic P to P reflection amplitude versus offset (AVO) has been extrllsively studied in the petroleum industry for its usefulness as a hydrocarboll indicator. Laboratory and theoretical research has shown that t.he behavior of seismic P to P reflect.ion amplitudes is anomalous when gas is present in the pore spaces of porous rocks. This result is obtained theoretically by combining the Gassman (1951) equation for bulk compressibilit.y with the Zoeppritz (1919) equations, which predict reflection amplitudes caused by the velocity and density contrasts. The Gassman equations are not readily applicable t.o non-porous rocks, however. There has been less research specifically aimed 4-1