La teoría del rayo paraxial en la sismica de pozo: Aproximación de segundo orden en los tiempos de tránsito

Abstract

Using the paraxial ray approximation of the named geometric optics a set of numerical expressions were found, these expressions characterize reflecting events recorded in detectors placed in a borehole. One of them is the characteristic travel time function which estimates the travel times of reflecting events in a vertical seismic profile configuration with sources placed in surface in the vicinity of the boreholes´s top. This characteristic VSP function can be numerically estimated using at least six measurements of appropriated selected travel times.

Others expressions were deduced to allow the transformation of the VSP travel time function in the equivalent COP travel time function corresponding to reflecting events recorded in surface in a common midpoint array. The use of this result will make possible to solve the inverse problem in the neighborhood of the borehole by the application of downward continuation techniques of the travel time function. The results are valid only in the approximation of the second order of the travel times in models which consist of a pile of homogeneous and isotropic layers of any velocities and densities, separated by smooth interfaces arbitrarily curved.