On the azimuthal dependence of orthorhombic fractures for vertical seismic profiles using the ellipsoidal approximation

Abstract: The analysis of travel times with move-out velocities represents one of the most widely used seismic signal processing techniques for the exploration and monitoring of Oil and Gas reservoirs. In travel time analysis for anisotropic elastic media with fractures, the knowledge of the conversion point at interfaces with incident longitudinal, and reflected transversal elastic response impulses that take into account the azimuthal dependence is important for seismic data analysis acquired in multicomponent surveys, and for the correct interpretation of seismic in reservoirs. Henceforth, this work shows how to derive analytical expressions for the longitudinal to transverse response impulse $P -S_i$ conversion points using the ellipsoidal approximation for fractured orthorhombic elastic media under kinematical considerations. These expressions can be used for vertical seismic profiles with small polar angles of aperture and azimuthal dependence in orthorhombic media when the elastic slowness is used as a main theoretical tool to solve the Christoffel equation. We also explain some of the differences within the ellipsoidal inversion procedure of the elastic stiffnesses $c_{13}$ and $c_{23}$.