A proposed power-gradient velocity model incorporates several well-known velocity models as special cases. The model covers a wide range of possible velocity distributions and has four parameters, giving more flexibility in velocity-model manipulation. For this nonlinear model, the kinematic characteristics — offset-traveltime parameteric equations, traveltime parameters, relative geometric spreading, and propagator phase — are computed. The characteristics are investigated with respect to a parameter responsible for nonlinearity of velocity distribution. The inversion of travel-time parameters was studied in three- and four-parameter frameworks.

The velocity model is very important for seismic modeling and inversion. To invert the kinematic parameters obtained in velocity analysis into model parameters, the model must be defined properly. The uncertainty in the velocity model is very important for inversion, interpretation (Hajnal and Sereda, 1981; Bickel, 1990; Lines, 1993; Al-Chalabi, 1997; Kosloff and Sudman, 2001), and imaging (Fomel and Landa, 2005).

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