Quartic moveout coefficient: 3D description and application to tilted TI media

摘要

Nonhyperbolic (long-spread) moveout provides essential information for a number of seismic inversion/ processing applications, particularly for parameter estimation in anisotropic media. Here, we present an analytic expression for the quartic moveout coefficient A_4 that controls the magnitude of nonhyperbolic moveout of pure (nonconverted) modes. Our result takes into account reflection-point dispersal on irregular interfaces and is valid for arbitrarily anisotropic, heterogeneous media. All quantities needed to compute A_4 can be evaluated during the tracing of the zero-offset ray, so long-spread moveout can be modeled without time-consuming multioffset, multiazimuth ray tracing. The general equation for the quartic coefficient is then used to study azimuthally varying nonhyperbolic moveout of P-waves in a dipping transversely isotropic (TI) layer with an arbitrary tilt v of the symmetry axis. Assuming that the symmetry axis is confined to the dip plane, we employed the weak-anisotropy approximation to analyze the dependence of A_4 on the anisotropic parameters. The linearized expression for A_4 is proportional to the anellipticity coefficient η≈ε―δ and does not depend on the individual values of the Thomsen parameters. Typically, the magnitude of nonhyperbolic moveout in tilted TI media above a dipping reflector is highest near the reflector strike, whereas deviations from hyperbolic moveout on the dip line are substantial only for mild dips. The azimuthal variation of the quartic coefficient is governed by the tilt v and reflector dip φ and has a much more complicated character than the NMO-velocity ellipse. For example, if the symmetry axis is vertical (VTI media, v = 0) and the dip φ > 30°, A_4 goes to zero on two lines with different azimuths where it changes sign. If the symmetry axis is orthogonal to the reflector (this model is typical for thrust-and-fold belts), the strike-line quartic coefficient is defined by the well-known expression for a horizontal VTI layer (i.e., it is independent of dip), while the dip-line A_4 is proportional to cos~4 φ and rapidly decreases with dip. The high sensitivity of the quartic moveout coefficient to the parameter η and the tilt of the symmetry axis can be exploited in the inversion of wide-azimuth, long-spread P-wave data for the parameters of TI media.