Converted Wave Traveltime Approximation in Elastic Orthorhombic Media

Abstract

Summary In order to approximate the traveltime in an elastic orthorhombic (ORT) medium for converted waves, we define an explicit rational-form approximation for the traveltime of the converted PS1, PS2 and S1S2 waves. For the simplification purpose, The Taylor-series approximation is applied in the corresponding vertical slowness for three pure-wave modes. By using the effective model parameters for PS1, PS2 and S1S2 waves, the coefficients in the converted-wave traveltime approximation can be represented by the anisotropy parameters defined in the elastic ORT model. The accuracy in the converted-wave traveltime for three ORT models is illustrated in numerical examples. One can see from the results that for converted PS1 and PS2 waves, the proposed rational-form approximation is very accurate regardless of the tested ORT model. For a converted S1S2 wave, due to the existence of cusps, triplications, and shear singularities, the error is relatively larger compared with PS waves.