Estimation of complex‐valued weaknesses from velocity—attenuation anisotropy data in linear‐slip TI model of fractured media

Abstract

Numerical modeling was performed to find optimal variants of estimating complex-valued weaknesses responsible for velocityattenuation anisotropy in an attenuative linear-slip transversely isotropic (LSTI) model of a fractured medium. Velocities and attenuations of the three wave types (qP, qSV, SH) versus the angle between the symmetry axis and the wave normal were computed for media with different values of the ratio Vs/Vp in the isotropic background and varying values of the real and imaginary parts of the normal and tangential weaknesses. These data were analyzed and then inverted for complexvalued weaknesses. Inversion was made for various combinations of data (velocities, attenuations), wave types and angle intervals (0 o-45 o , 45 o-90 o). The results concerning the optimal ways for estimation the complexvalued weaknesses occurred to be as follows. At first, the values of the real parts neglecting the unknown imaginary parts of the weaknesses are to be determined from the velocity anisotropy, namely, for the normal weakness using qP-wave and for the tangential one using SH-wave. Then with the values of the real parts known, one determines the values of the imaginary parts. For the normal weakness, the qP-wave attenuation anisotropy is used, and for the tangential one SH-wave anisotropy. The velocity and attenuation anisotropy of qSV-wave is recommended to use only in the case of weak anisotropy to avoid cusps at the qSV-wave ray velocity surface. Joint inversion of qP-and SH-wave data can also yield good results.

Cross-correlation-function method for separation of shear waves S 1 and S 2 in azimuthally anisotropic media and an example of its application with real data

“…Such values are typical for anisotropy of naturally fractured carbonate reservoirs we dealt with. We estimated the normal and tangential weaknesses (e.g., Chichinina et al 2009, Obolentseva et al 2011) to be ~0.1, that is, anisotropy was found to be rather weak.…”

Fracture-induced Q-anisotropy: Inversion for fracture parameters

“…We state the inversion problem for estimating the real and imaginary parts of complex-valued weaknesses from the data on phase velocities and attenuations of qP-, qSV-, and SH-waves. The inversion algorithm is described in Dugarov et al (2011) and Obolentseva et al (2011). It has been performed with the use of the least squares method and Wolfram Mathematica-8.…”