Traveltime data profiles obtained using seismic ray tracing methods for the continental slope model parameterized by polynomials

Geological structures known as continental shelf break, also called continental slope, are represented by seismic models characterized by two-dimensional, heterogeneous and isotropic velocity fields. By means of a polynomial parameterization of such fields, a smooth version of the model is generated with a strong variation near discontinuities that are, generally, associated to the seismic interfaces. In this kind of parameterization, all geometric and kinematics complications of the model are compacted in the polynomial coefficients, which are obtained by the least squares method. Traveltimes are calculated on the rays that represent paths for the seismic wave during its travel through the model. Seismic rays are connecting source positions to arrival points on the observation surface and they are traced by means of numerical approximations of ray equations (expansions of Taylor of second order). The calculated data tells us something about the geologic features of the considered seismic velocity field, such as: low lateral variation of velocity in one half of the model, predominance of low velocities in another half, break of model symmetry due to the increase of declivity of the layers in the accentuated slope region, increase of velocities with deep, etc. The same model is represented by different polynomial functions, it is observed that the increase of the polynomial degree produces an improvement on the representation when quantity and distribution of chosen points for polynomial adjustment are not altered. The used continental slope model comes from literature and, in this first approach, just its main features are considered. We believe that better results will be produced considering finer discrete models or polynomials of higher degree. Modeling traveltimes, such as it is done in this work, allows us the accomplishment of seismic inversions, in which the polynomials coefficients are the model parameters to be estimated.