Stacking‐velocity tomography with borehole constraints for tilted TI media

Abstract

We present a 2D inversion methodology for transversely isotropic media with a tilted symmetry axis (TTI) based on combining reflection moveout with borehole information. The input data include P‐wave normal‐moveout (NMO) velocities, zero‐offset traveltimes and reflection time slopes, as well as traveltimes of a check shot, reflector depths and dips measured in a borehole. For a dipping TTI layer with the symmetry axis confined to the dip plane of the reflector, estimation of the symmetry‐direction velocity , the anisotropy parameters ε and δ, and the tilt ν of the symmetry axis proves to be ambiguous despite the borehole constraints. If the symmetry axis is orthogonal to the reflector (a model typical for dipping shale layers), and δ can be recovered with high accuracy, even when the symmetry axis deviates by ±5° from the reflector normal. The parameter ε, however, cannot be constrained for dips smaller than 60° without using nonhyperbolic moveout. To invert for the interval parameters of layered TTI media, we apply 2D stacking‐velocity tomography supplemented with the same borehole constraints. If the symmetry axis is orthogonal to the reflector in each layer, estimation of the interval parameters and δ remains stable in the presence of Gaussian noise in the input data. Our algorithm can be used to build an accurate initial TTI model for migration velocity analysis.