A Method to Estimate Fracture Parameters From Variation of Elastic Impedance With Azimuth

Abstract

Summary Fracture parameters including fracture density and orientation play a critical role in civil engineering, hydraulic engineering and exploitation. However, it nowadays still remains challenging to concisely and stably estimate those fracture parameters from seismic data. A method based on azimuthally anisotropic elastic impedance (AEI) variation with azimuth is proposed to characterize the fracture distribution. Firstly, the azimuthal AEI equation in terms of truncate Fourier series is derived to reduce the number of unknown parameters in the fracture parameters estimation. In addition, Karhunen-Loeve transformation is used to extract the primary feature of reflection amplitude variation with azimuth. The fracture orientation without 90 degree ambiguity can be estimated by an innovative azimuthal AEI equation incorporating the azimuthal AEI equation in terms of Fourier series and the prior fracture orientation. And the biased estimate for the anisotropic gradient of the azimuthal AEI can be estimated from the second order Fourier coefficient to forecast the fracture density. The model case and a field data example demonstrate the rationality and robustness of the innovative primary wave azimuthal AEI equation and the fracture parameters estimation method even with sparse 30 degrees sampling interval in the azimuth.