Estimation of the Conversion Point Position in Elastic Orthorhombic Media

In order to estimate the conversion point in an elastic orthorhombic (ORT) medium, we define an explicit rational form approximation for the radial coordinate of the conversion point for the converted PS1, PS2 and S1S2 waves. In order to obtain the approximation coefficients, the Taylor series approximation in the corresponding vertical slowness for three pure wave modes is applied. The coefficients in our proposed approximation are computed within two vertical symmetry planes. The difference between the acquisition azimuth and the azimuth of the conversion point position is analyzed for different combinations of the wave modes. The accuracy in conversion point position estimation for three ORT models is illustrated in the numerical examples. One can see from the results that for converted PS1 and PS2 waves, the proposed approximation is very accurate in estimating the conversion point position in the tested ORT model. For a converted S1S2 wave, due to the existence of cusps, triplications and shear singularities, the error in conversion point estimation is relatively larger comparing with PS waves in the vicinity of the singularity point.