Weakly-Anelliptical Traveltime Analysis: Ambiguity between Subsurface and Elasticity

The building of a subsurface and (anisotropic) velocity model from a single gather of reflection traveltime (kinematic) data is inherently ambiguous since the processing of such data can only determine a horizontal slowness component, not a vertical one. Based thereon I derive a simple algorithm that generates an infinite series of combinations of subsurface - velocity models, all of which will show nearly the same seismic kinematic response, as further demonstrated by simulating wave propagation through a model with different interface dips. This algorithm assumes, firstly, all interface dips remain constant over the distance considered and, secondly, an approximation of the elasticity model – that is, linearization of a phase velocity – valid for weak anisotropy can be used. Furthermore, when applied at the classic, and analytically solvable, case of traveltime analysis for a stack of flat layers with weak transverse isotropy, the algorithm explains theoretically the combination of anisotropy parameters that govern the non-hyperbolic term of a traveltime series: the established [Formula: see text] and its new counterpart [Formula: see text] for a [Formula: see text] - and [Formula: see text] -wave, respectively.