Publication Date:
2013-07-13
Description:
We have analyzed the angle-dependent reflectivity of microseismic wavefields at a hydraulic fracture, which we modeled as an ideal thin fluid layer embedded in an elastic, isotropic solid rock. We derived 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, and the S-S and S-P reflection coefficients. The rather complex analytical solutions were then approximated and we found that these zero-thickness limit approximations are in good agreement with the linear slip model, representing a fracture at slip contact. We compared the analytical solutions for the P-P reflections with synthetic data that were derived using finite-difference modeling and found that the modeling confirmed our theoretical results. For typical parameters of microseismic monitoring by hydraulic fracturing, e.g., a layer thickness of $$h=0.001\mbox{--}0.01\hbox{ \hspace{0.17em} }\hbox{ \hspace{0.17em} }\mathrm{m}$$ and frequencies of $$f=50\mbox{--}400\hbox{ \hspace{0.17em} }\hbox{ \hspace{0.17em} }\mathrm{Hz}$$ , the reflection coefficients depend on the Poisson’s ratio. Furthermore, the reflection coefficients of an incident S-wave are remarkably high. Theoretical results suggested that it is feasible to image hydraulic fractures using microseismic events as a source and to solve the inverse problem, that is, to interpret reflection coefficients extracted from microseismic data in terms of reservoir properties.
Print ISSN:
0016-8033
Electronic ISSN:
1942-2156
Topics:
Geosciences
,
Physics
Permalink