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Abstract

An analytical method for the approximate solution of the n-layer refraction problem is described. Its main advantage is the speed and ease with which solutions can be obtained. An estimate is made of the error of the method by comparing the exact and approximate solutions for the two-layer case.

Abstract

This paper deals with an approximation modification of F. W. Hales'1 graphical method and its execution by a computer program for relatively small dips.

From available velocity information, “paper plots” of time-distance and raypath-distance are made to determine the optimum shot-to-cable location for a particular refractor. These results are tested by field shooting. After determination of the “window” for shooting, a program of data lines is shot and recorded on magnetic tapes which are playback processed; tilted, filtered, and phase corrected.

Data analysis includes the necessary corrections to datum and the analysis of all reversed time ties and subsequent listing on “shift-plot” sheets. Data, times, and distances from these sheets for forward and reverse shots are input independently into the electronic computer program whose output is a scaled vertical section of both sets of data and their average. The program is versatile in that the refractor may be solved as a two-layer problem or the shallower horizons may be stripped off prior to solving for the particular horizon. Model studies show the results for an asymmetrical anticline, a fault example, and a multilayer problem.

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