Moveout inversion of wide‐azimuth P‐wave data for tilted TI media

Abstract

In a previous publication, we discussed 2D stacking‐velocity inversion for the interval parameters of TTI (transversely isotropic with a tilted symmetry axis) media composed of homogeneous layers separated by plane interfaces. Here, this 2D algorithm is extended to 3D wide‐azimuth data by including P‐wave NMO ellipses and two horizontal slowness components (time slopes) in the objective function. If the symmetry axis is perpendicular to the bottom of each layer, it is possible to estimate the interval symmetry‐direction velocity VP0, anisotropy parameter δ, and the reflector orientation using only one borehole constraint—the reflector depths. The algorithm can tolerate small (1/10 of the dip) deviation of the symmetry axis from the reflector normal. However, as is the case for the 2D problem, the parameter ε can seldom be constrained without using nonhyperbolic moveout inversion. If the symmetry axis deviates from the reflector normal but is confined to the dip plane, stable parameter estimation requires a relationship between the tilt and dip in each layer. When the tilt represents a free parameter, the input data have to be supplemented by wide‐azimuth VSP traveltimes with the offset reaching at least 1/4 of the maximum reflector depth. Moreover, the additional angle coverage provided by VSP data may help resolve the parameter ε in the upper part of the model.