Azimuthal fourier coefficients: A simple method to estimate fracture parameters

Abstract

Assuming HTI anisotropy due to one dominant vertical fracture set, the relationship between azimuthal Fourier coefficients and fracture parameters is described. These azimuthal Fourier coefficients can be calculated by performing a Fourier transform of azimuthally sectored seismic data over a particular range of incident angles. Using only the magnitude and phase of the 2nd Fourier coefficient for just one angle of incidence it is possible to calculate the anisotropic gradient and symmetry axis and achieve similar results to that of the near offset Rüger equation. If linear slip theory is assumed, it is then possible using multiple Fourier coefficients and angles of incidence to unambiguously estimate the symmetry axis and the more fundamental normal and tangential fracture weakness parameters. In addition, an unbiased estimate of the anisotropic gradient can be determined. This is demonstrated on synthetic and real seismic data.