Abstract: The analysis of travel times with moveout 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 taking into account the azimuthal dependence is important for both seismic data
analysis acquired in multicomponent surveys and the correct interpretation of seismic in reservoirs. Henceforth, this
work shows how to derive analytical expressions for the longitudinal to transverse response impulse “P-Si” 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 resolve the Christoffel equation.
We also explain some of the differences within the ellipsoidal inversion procedure of the elastic stiffnesses C13 and C23.
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