P-S converted seismic wave exploration plays an important role in detecting complex geologic structures. In this research, we derive two new asymptotic conversion point equations for the P-S converted wave reflected from a dipping reflector. The first is a quadratic asymptotic conversion point equation of the P-S converted wave reflection from a dipping reflector (DACP equation), and the second is a linear asymptotic equation (ADACP equation). DACP and ADACP equations depend on the velocity ratio (VP/VS) of the stratum, the offset (X), the depth (Z) of the conversion point, and the dip angle of the stratum. The last parameter is the most sensitive of the DACP and ADACP equations in determining the conversion point position.
The two new equations can predict the conversion point positions on a deep dipping reflector accurately and directly. The accuracy of the conversion point position at shallow depth determined by the DACP equation is better than using the ADACP equation. For a shallow conversion point, for example Z/X = 0.5, the errors of the conversion point prediction in the horizontal distance (CP error) are less than 2% for the DACP equation, but the CP errors are very large for the ADACP equation. If Z/X is greater than 3, the CP errors of the ADACP equation are less than 3% and this equation is more computationally efficient than the DACP equation.