Dip moveout of converted waves and parameter estimation in transversely isotropic media

Abstract

For transverse isotropy with a vertical symmetry axis (VTI media), P-wave reflection data alone are insufficient for building velocity models in depth. Here, we show that all parameters of VTI media responsible for propagation of P- and SV-waves (the P-wave and S-wave vertical velocities VP0 and VS0 and the anisotropic parameters e and δ) can be obtained by combining P-wave traveltimes with the moveout of PS-waves converted at a horizontal and dipping interface. Using converted modes, rather than pure S-waves, avoids the need for expensive shear-wave excitation on land and makes the method suitable for offshore exploration. The inversion algorithm is based on a new analytic description of the dip moveout of PS-waves developed for symmetry planes of anisotropic media (and for any vertical plane in models with weak azimuthal anisotropy). The common-midpoint (CMP) traveltime–offset relationship, derived in a parametric form and represented through the components of the slowness vector of the P- and S-waves, makes it possible to compute the moveout curve of the PS-wave without two-point ray tracing. This formalism also leads to closed-form solutions for moveout attributes, such as the coordinates (xmin, tmin) of the traveltime minimum, the normal-moveout (NMO) velocity defined at x = xmin and the slope of the moveout curve (apparent slowness) at zero offset. The parameter-estimation algorithm operates with reflection moveout of P- and PS-waves from a horizontal and dipping reflector. The NMO velocities of P- and PS-waves from horizontal events and the ratio of the corresponding zero-offset traveltimes yield three equations for the four unknown medium parameters. The remaining parameter is found from an overdetermined system of equations that includes the P-wave NMO velocity and moveout attributes of the PS-wave for a dipping event. Numerical analysis shows that the PS-wave dip-moveout signature plays a crucial role in obtaining accurate estimates of the anisotropic parameters. The joint inversion of P and PS data provides the necessary information not only for P-wave depth imaging in VTI media, but also for the processing of PS-waves, including re-sorting of PS traces into common-reflection-point gathers and transformation to zero offset (TZO).