Models of geological structures are very often described by values specified at discrete points. A description much more suitable for ray tracing is the parameterization of the model by smooth functions. Such models may be constructed using the method of minimizing the selected objective function.
The efficiency of ray tracing in the constructed model can be evaluated in terms of the average Lyapunov exponent. The exponent may be approximated by the square root of the corresponding Sobolev norm of the model. Including the Sobolev norm in the selected objective function thus allows models suitable for ray tracing to be constructed.
The method is very briefly reviewed and then it is illustrated by constructing two models, which are suitable for ray tracing, and fit the SEG/EAGE 3-D Salt Model data set.
Model specification, smoothing, inversion, ray methods, Sobolev norm, Lyapunov exponent, SEG/EAGE 3-D Salt Model.
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