Estimation of the conversion point position in elastic orthorhombic media

Abstract

Determination of the conversion point position is very important to carry out seismic processing in the common conversion point gather of converted wave data. The anisotropic effect is very obvious for a converted wave when estimating the physical and processing parameters from real data. To estimate the conversion point in an elastic orthorhombic (ORT) medium, we have defined an explicit rational form approximation for the radial coordinate of the conversion point for converted [Formula: see text], [Formula: see text], and [Formula: see text] waves. 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 of the conversion point position estimation for three ORT models is illustrated in the numerical examples. One can see from the results that for converted [Formula: see text] and [Formula: see text] waves, our approximation is very accurate in estimating the conversion point position regardless of the tested ORT model. For a converted [Formula: see text] wave, due to the existence of cusps, triplications, and shear singularities, the error in conversion point estimation is relatively larger compared with PS-waves in the vicinity of the singularity point.