3D description and inversion of reflection moveout of PS-waves in anisotropic media

Abstract

Common-midpoint moveout of converted waves is generally asymmetric with respect to zero offset and cannot be described by the traveltime series t2(x2) conventionally used for pure modes. Here, we present concise parametric expressions for both common-midpoint (CMP) and common-conversion-point (CCP) gathers of PS-waves for arbitrary anisotropic, horizontally layered media above a plane dipping reflector. This analytic representation can be used to model 3D (multi-azimuth) CMP gathers without time-consuming two-point ray tracing and to compute attributes of PS moveout such as the slope of the traveltime surface at zero offset and the coordinates of the moveout minimum. In addition to providing an efficient tool for forward modelling, our formalism helps to carry out joint inversion of P and PS data for transverse isotropy with a vertical symmetry axis (VTI media). If the medium above the reflector is laterally homogeneous, P-wave reflection moveout cannot constrain the depth scale of the model needed for depth migration. Extending our previous results for a single VTI layer, we show that the interval vertical velocities of the P- and S-waves (VP0 and VS0) and the Thomsen parameters e and δ can be found from surface data alone by combining P-wave moveout with the traveltimes of the converted PS(PSV)-wave. If the data are acquired only on the dip line (i.e. in 2D), stable parameter estimation requires including the moveout of P- and PS-waves from both a horizontal and a dipping interface. At the first stage of the velocity-analysis procedure, we build an initial anisotropic model by applying a layer-stripping algorithm to CMP moveout of P- and PS-waves. To overcome the distorting influence of conversion-point dispersal on CMP gathers, the interval VTI parameters are refined by collecting the PS data into CCP gathers and repeating the inversion. For 3D surveys with a sufficiently wide range of source–receiver azimuths, it is possible to estimate all four relevant parameters (VP0, VS0, e and δ) using reflections from a single mildly dipping interface. In this case, the P-wave NMO ellipse determined by 3D (azimuthal) velocity analysis is combined with azimuthally dependent traveltimes of the PS-wave. On the whole, the joint inversion of P and PS data yields a VTI model suitable for depth migration of P-waves, as well as processing (e.g. transformation to zero offset) of converted waves.