Error in estimation of arrival direction on offset VSP data

Abstract

Recent advances in high resolution velocity estimation using first-arrivals on multicomponent offset VSP data are crucially dependent upon accurate determination of arrival direction (eg., Esmersoy, 1988). Such methods require post-acquisition orientation of 3-component data by coordinate rotation. Rotation into the direction of maximum P-wave energy in the horizontal plane at each depth of a VSP survey reorients the coordinate system. A second rotation in the vertical plane towards the source establishes the arrival direction and, in addition, separates the P-, SV-, and SH-transmitted waves. An error in the first rotation influences strongly a separation of the wavemodes. The desired rotation angles can be found from an expression which involves cross-products between measured components (DiSiena et al., 1981). The expression assumes there is no phase difference between these components. This will certainly be the case for an isolated P-wave arrival measured on a recording system with identical impulse responses for all three channels. However, non-identical channel responses or overlapping P-wave arrivals introduce, in turn, erroneous estimates of P-wave arrival direction. The present study quantifies the error in arrival direction as a function of phase difference between components and looks closer into the difference between an instantaneous and an average estimate when calculating the rotation angle.