ISO, VTI, TTI
Anisotropy in Time Processing
TGS has mechanisms to compensate for the effects of both VTI and HTI anisotropy in time processing. These mechanisms correct for kinematic distortions (i.e., travel time perturbations), resulting in flatter gathers and a more focused stacked image.
VTI anisotropy compensation is achieved via one of two mechanisms: higher order move out or the so-called "eta" moveout correction. The higher order moveout correction entails retaining fourth or sixth order terms in the well-known Taner and Koehler (1969) power series expansion theory. Strictly speaking, the underlying theory is based on anisotropic earth; however, it is well known that the effects of intrinsic VTI anisotropy and isotropic vertical heterogeneity are hard to separate out on real data, and experience shows that picked interval velocities used in conjunction with a higher order moveout equation can serve as a proxy for both vertical heterogeneity and true anisotropy. The eta moveout equation is based on the work of Grechka and Tsvankin (1998) who added a third term (fourth order in offset) to the conventional NMO equation. Their equation accounts simultaneously for the effects of vertical heterogeneity and intrinsic layer anisotropy via
The eta moveout correction has been incorporated into both our NMO algorithm as well as our prestack time migration, while the higher order moveout correction exists within our prestack time migration only. Note that parameter estimation for either mechanism (i.e., higher order or eta) is performed using our interactive scanning tool which allows the user to scan through various trial percent velocity (and eta) scenarios and pick that velocity (eta) field which best flattens gathers and/or gives optimal stack response. One advantage of the higher order moveout scheme compared to the eta correction is that the former approach entails picking only one free parameter (stacking velocity which is internally converted to interval velocity), whereas the latter approach requires picking two parameters (short spread moveout correction and eta). Conversely, a relative disadvantage of the higher order moveout scheme is that the efficacy of the travel time correction is sensitive with respect to errors in the underlying interval velocity field, a fact which may necessitate the use of a large velocity search range in cases where the reference (i.e., "100%") velocity model is far from the right answer.
HTI anisotropy compensation is achieved via a curve fitting approach in which delta_t time perturbations along an event after nominal (i.e., isotropic) moveout correction are fit to an elliptical velocity function. The underlying theory is based on the work of Tsvankin (1997, Geophysics), who showed that best-fit NMO velocities in an HTI medium exhibit an elliptical variation as a function of source-receiver azimuth. The curve fitting process yields estimates for Vfast, Vslow, and the axis of symmetry of the ellipse at all velocity control points. Once determined, these three parameters are used in conjunction with the observed source-receiver azimuth to perform either an azimuth-dependent NMO correction or a postmigration residual azimuthal moveout correction.
Note that orthorhombic anisotropy can be handled empirically (although not theoretically) by cascaded application of the above VTI n and HTI corrections. Note also that TGS does not handle TTI anisotropic effects in time processing.