Velocity Analysis for Laterally Heterogeneous Anisotropic Media

Oil, gas, and geothermal reservoirs, and overlying strata are often composed of anisotropic rocks. Proper treatment of anisotropy during the processing of seismic data not only helps to avoid distortions in reservoir imaging, but also provides estimates of the anisotropic coefficients, which carry valuable information about lithology and fracture networks. Accurate estimation of the velocity model is one of the most difficult steps in imaging of seismic data from anisotropic media. Here, I introduce a velocity-analysis method for anisotropic models that can be called stacking-velocity tomography . This technique is designed to invert normal-moveout (NMO) ellipses, zero-offset traveltimes, and reflection time slopes of P and S-waves for interval anisotropic parameters and shapes of reflection interfaces. Examination of a wide range of anisotropic models makes it possible to establish the conditions needed for stable parameter estimation. Results here show that, in many cases, it is possible to build anisotropic velocity models from azimuthally-varying hyperbolic moveouts of P and S-waves alone. For example, the inversion of P -wave NMO velocities makes it possible to estimate the anisotropic parameters of a physical model that includes a bending transversely isotropic (TI) layer with a tilted symmetry axis. However, there are some notable exceptions such as horizontally layered orthorhombic and TI media with vertical axis of symmetry, for which anisotropic parameter estimation requires independent knowledge of the vertical velocities or reflector depth. I also present a general analytic expression for the quartic moveout coefficient A4 that is responsible for the magnitude of nonhyperbolic moveout of pure (non-converted) modes. This expression takes into account reflection-point dispersal on irregular interfaces and is valid for arbitrarily anisotropic, heterogeneous media. All quantities needed to compute A4 can be evaluated during the tracing of a single (zero-offset) ray, so long-spread moveout can be modeled without time-consuming multi-offset, multiazimuth ray tracing. Analysis of the azimuthal dependence of A4 for tilted TI media shows that P -wave nonhyperbolic moveout can help to constrain the orientation of the symmetry axis.