## The P-SV conversion point in constant-gradient media

### Michael A. Slawinski, Gary F. Margrave

An analysis of the computation of the P-SV conversion point for the case of constant-gradient (velocity increasing linearly with depth) media is presented. The well known result that raypaths are circular arcs in such media is exploited to derive an implicit sixth order polynomial for r, the distance from the source to the conversion point. An exact expression is then obtained for the asymptotic limiting form as depth of the reflector becomes much larger than the source-receiver separation. The result is formally similar to that for constant velocity case except that the ration of vs/vp is replaced by the ratio of the velocity gradients. It is anticipated that a numerical solution for the nonasymptotic case will yield more significant departures from constant velocity theory.