Slowness Surface Determination from Slant Stack Curves
A recently developed slant-stack (τ-p) method for determining phase velocity anisotropy from multi-offset and multi-depth downhole seismic observations is further modified and verified. The velocities characterizing the interval between two detector depths are obtained from the difference of the intercept-timer values at constant ray parameter p. This modification provides a continuous measure of the velocity with incidence angle and reduces the propagation of errors inherent to layer stripping methods. The τ-p transformation is a plane wave decomposition; and the method directly provides phase velocities as a function of propagation angle. The nearly continuous measure of the velocity wtih angle allows for a straightforward conversion to the corresponding ray (group) velocities. In tests on synthetic VSP data sets, The compressonal and shear wave phase velocities recovered differ by the known values by less than 0.5% in all cases. In an application to real VSP data acquired in Alberta, one interval consisting of thinly layered sand-shale sequence displays a velocity anisotropy of 12.5% with velocities increasing nom vertical to an incidence near 50°. Consequently, the method can aid in the characterization of depth intervals where sonic logging is not possible due to adverse wellbore conditions.