An Exact Solution of the Equation of the Conversion Point for P-SV Converted Wave at a Horizontal Reflector

Abstract

For converted wave stacking and trace selection of common reflection point gathering it is required to accurately calculate the location of conversion points. Tessmer and Behle, Taylor have given an analytic solution of the conversion point for the P-SV converted wave in homogeneous and isotropic media. Because the expression is complicated, it is hardly applied to converted-wave processing. In this paper, by using the Snell's law, we derive a quartic equation for the accurate description of converted waves reflected at a horizontal reflector. From this quartic equation, a unique solution of the conversion point is obtained and determined analytically, expressed as a function of offset, the compressional and shear wave velocities, and the reflector depth at the conversion point. The result is applied to analysis of velocity and stacking of the P-SV converted-wave. The result shows that this simplified formula has a good application value.