Minimization of the 4C Alford Data Matrix for Non-Orthogonal PS-Wave Reflection Modes

Joint inversion of P-waves (compressional waves) and PS-waves (converted P to S-waves) is becoming more important for pore pressure prediction, time-lapse effects and characterizing the stress and fracture state of reservoirs. However accurate results will depend on how well the principal S-wave (shear-wave) directions can be determined in anisotropic media. PS-wave reflection coefficients in azimuthally anisotropic media produce a set of non-orthogonal amplitude modes that can complicate the estimation of principal S-wave directions. <br><br>The purpose of this study is to show that a conventional Alford rotation provides the correct principal direction for non-orthogonal PS-wave modes in azimuthally anisotropic media when reflection coefficients vary azimuthally. Fast and slow S-wave components of 4C (four component) Alford data are examined in terms of azimuthally anisotropic PS-waves reflection coefficients. Results for orthorhombic media illustrate that the Alford data matrix is diagonally dominant when properly aligned with the principal directions. A synthetic data set consisting of a 5-layer model representing vertical fractures of different orientations demonstrates that conventional Alford rotation and layer stripping will give the correct principal directions when the off-diagonal traces are minimized.<br>