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METHOD FOR FITTING A SUM OF EXPONENTIALS TO EXPERIMENTAL DATA BY LINEARIZATION USING A NUMERICAL INTEGRATION APPROXIMATION, AND ITS APPLICATION TO WELL LOG DATA
METHOD FOR FITTING A SUM OF EXPONENTIALS TO EXPERIMENTAL DATA BY LINEARIZATION USING A NUMERICAL INTEGRATION APPROXIMATION, AND ITS APPLICATION TO WELL LOG DATA
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机译:数值积分法线性化拟合指数与实验数据的方法及其在测井数据中的应用
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摘要
A method for analyzing formations using measurements from a detector in response to energy imparted therein. The measurements have characteristics which exponentially reduce in magnitude with time. The method includes (a) determining, an N-th order integral of the value of each measurement from an initial time to the time of each measurement, wherein N represents a number of exponentially decaying characteristics; b) determining a solution to a system of linear equations relating the measurements to the integrals, the solution representing polynomials of order N related to a decay rate and an initial measurement amplitude for each component; (c) solving the polynomials to determine the decay rate and the initial amplitude for each component; (d) determining if the decay rates and initial amplitudes are within possible limits; and (e) incrementing N and repeating (a) through (d) until the decay rates or the initial amplitudes are not within possible limits.
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