Signal processing method for determining the number of exponential decay parameters in multiexponentially decaying signals and its application to nuclear magnetic resonance well logging

摘要

A method of determining the number of exponential decay modes in spin echo amplitude signals from a nuclear magnetic resonance well logging instrument. The method includes dividing the time interval between initiation and termination of measurement of the spin echo amplitude signals into 2r-1 equal length segments, where r is a positive integer. Integrals of the spin echo amplitude signals with respect to time in each of the segments are calculated. Best fit functions are calculated for the spin echo amplitude signals, and integrals with respect to time of apparent amplitudes of the best fit functions at each time corresponding to a time at which the spin echo amplitude signals were generated. The integrals of the spin echo amplitude signals and the integrals of the apparent amplitudes from each segment are arranged into symmetric matrices each having dimensions r×r. A norm and a standard deviation of the matrix of the spin echo amplitude integrals is calculated. If the norm of the determinant of the matrix of the integrals of the spin echo amplitude signals is less than or equal to a selected confidence factor multiplied by the standard deviation of the determinant of the matrix of the integrals of the spin echo amplitude signals, then the number of exponential decay modes in the spin echo amplitude is equal to r-1. If the inequality is not satisfied, r is increased by one and the process is repeated.