Aproximações não-hiperbólicas do tempo de trânsito utilizando aproximantes de Padé

Abstract

Traveltime approximation is a fundamental tool of the stack and migration steps in seismic data processing. To increase the accuracy of these approximations, we propose new traveltime approximations based on Padé approximants, to CMP and CRS gathers. Hyperbolic approximations such as normal moveout (NMO) and comom reflection surface (CRS) are taylor series approximations of second order of the reflection traveltime. Padé approximants appear as an alternative to Taylor series, because they converge quickly to the desired function, and they have a major radius of convergence improving approximations acuracy. They can be obtained through the proper Taylor serie of the approximated function. This new approximation is obtained from the [2/2] Padé approximation of the generalized moveout equation; and from [2/2] Padé approximation of the Taylor series expansions of fourth order of the CRS surface. The acuracy of Padé approximation is superior when compared with other convencional approximations: normal moveout, shifted hyperbola and Transversal isotropic medium with vertical symetry axis (VTI). CMP gather Padé approximations depend just only one more parameter than normal moveout approximation and they keep the acuracy for long offsets. CRS gather non hyperbolic approximations, non hyperbolic CRS, fourth order CRS and Padé CRS, have major acuracy than hyperbolic CRS, increasing the convergence of the approximation for offset and CMP domain. The quadratic approximation of fourth order CRS is superior than non hyperbolic CRS approximation, producing less error in least square CRS parameter inversion.