Modeling Reflection Coefficients at a Thin Fluid Layer Representing a Hydraulic Fracture

Abstract

We model a hydraulic fracture by a thin layer of an ideal fluid which is embedded between an elastic and isotropic solid with identical properties on each side of the crack. The main goal is to describe and analyze reflection coefficients for a wave reflected at this thin fluid layer. We present full analytical solutions for the reflections of an incident P-wave, the P-P and P-S reflection coefficients, as well as for an incident S-wave, the S-S and S-P reflection coefficients. We find that for parameters in the range of microseismic needs, which means a layer thickness of h = 0.001 − 0.01m and frequencies of f = 50 − 400Hz, reflection coefficients of an incident S-wave are remarkably high. This allows us to image hydraulic fractures using microseismic events as a source. It also suggests to solve the inverse problem, which means to interpret reflection coefficients extracted from microseismic data in terms of reservoir properties. We compare the analytical solutions for the P-P reflections with synthetic data that is derived using Finite Difference modeling and find that the modeling confirms our theoretical approach.