On parameterization in monoclinic media with a horizontal symmetry plane

Abstract

I have derived accurate anisotropy parameters for a monoclinic anisotropy model with a horizontal symmetry plane based on normal moveout (NMO) ellipses for P-, S1-, S2-, and converted waves. The NMO velocity ellipse is also defined for all types of converted waves. The parameters are defined in the phase domain and compared with existing approximate monoclinic anisotropy parameters. These parameters are evaluated for two benchmark models consisting of two nonorthogonal fracture sets embedded into a transversely isotropic medium with a vertical symmetry axis. The dependence of monoclinic parameters on the azimuth angle between the fracture sets is analyzed. Being linearized with respect to fracture weaknesses, the monoclinic anisotropy parameters can be decomposed into sine functions of double and quartic azimuth angle between the fracture sets with the weights given by the stiffness coefficients of the background model. The discrimination between the fracture parameters computed from a given set of monoclinic parameters is dependent on the background model and controlled by the azimuth angle between the fracture sets.