Representation of discontinuous seismic velocity fields by sigmoidal functions for ray tracing and traveltime modelling

SUMMARY Wave-modelling methods based on asymptotic ray theory have a lower computational cost than full wave-equation methods but require a smooth velocity field, though discontinuities may be handled by imposing interface conditions between adjacent blocks. We propose to approximate discontinuous velocity fields with model parametrizations based on smooth, rapidly varying functions known as sigmoidal functions. We have implemented the proposed technique on Cartesian grids using the wavelet theory formalism. Numerical experiments with 2-D and 3-D initial-value and two-point ray tracing in heterogeneous media show that the ray paths and traveltimes produced with the sigmoidal representation are consistent with the results produced by conventional ray tracing in block structures, broadening the scope of classical algorithms based on smooth velocity fields.