AN ALGORITHM FOR THE BEST FIT SOLUTION OF A SYSTEM OF LINEAR REGRESSION EQUATIONS FOR SEISMIC REFRACTION DATA

Abstract

A statistical method of best fitting several line segments has been successfully applied to shallow refraction data. Adjacent regression line segments either may be joined at a distance which is between two data points or may be constrained to join at a distance corresponding to one data point which is shared by two regression lines. The calculation of wave slowness, time intercept, and residual sum of squares for each line segment may be found for either join point case. Several tests have been found which eliminate the calculation of many combinations of data in the second join point case. The over‐all residual sum of squares is found by adding the local residual sum of squares for each connected line segment, and the best fit is the combination of line segments which has the best total residual sum of squares. An algorithm has been found which reduces the number of possible combinations of data for three or more line segments to a manageable number by successively searching for one join point on sections of the data, rather than calculating regression fits for all possible combinations of the data.