Computer-implemented method of using a non-transitory computer readable memory device with a pre programmed neural network and a trained neural network computer program product for obtaining a true borehole sigma and a true formation sigma

1. A computer-implemented method of using a non-transitory computer readable memory device with a pre-programmed neural network and a trained neural network computer program product both with three layers each, to perform the operations of obtaining a true borehole sigma and a true formation sigma, the operations of the computer-implemented method comprising:

initializing a non-transitory computer readable memory device having a pre-programmed neural network on an above-surface processing system, wherein the above-surface processing system is coupled to a memory resource, an above-surface telemetry system, a communication bus, a multi-channel analyzer, and a computing system device;

initializing a nuclear logging tool wireline or logging-while-drilling system having a deuterium-tritium (D-T) neutron generator or a deuterium-deuterium (D-D) neutron generator neutron source coupled with at least three dual-function radiation detectors, wherein each dual-function radiation detector is pre-programmed through a non-transitory computer-readable memory device using pulsed shape discrimination technique, a high-voltage supplier, a sub-surface telemetry system, an electronic instrument, and a sub-surface non-transitory computer readable memory device;

pulsing the deuterium-tritium (D-T) neutron generator or the deuterium-deuterium (D-D) neutron generator neutron source, for at least two pulses;

measuring neutrons and neutron-induced gamma rays after each of the at least two pulses from each of at least three dual-function radiation detectors;

separating signals of the measured neutrons and neutron-induced gamma rays into thermal neutrons and neutron-induced capture gamma rays, using the at least three dual-function radiation detectors pre-programmed through the non-transitory computer-readable memory device using pulsed shape discrimination technique;

sending the separated signals of thermal neutrons and neutron-induced capture gamma rays to the multi-channel analyzer using the sub-surface telemetry system and using the at least three dual-function radiation detectors pre-programmed through the non-transitory computer-readable memory device;

generating a thermal neutron time-spectrum and a neutron-induced capture gamma rays time-spectrum for each of the three dual-function radiation detectors, wherein the thermal neutron time-spectrum essentially consists of a time-decay curve of thermal neutrons, and the neutron-induced capture gamma rays time-spectrum essentially consists of a time-decay curve of neutron-induced capture gamma rays, using the pre-programmed neural network on an above-surface processing system;

computing curve fitting using two exponential decays of the time-decay curve of thermal neutrons from a time immediately after pulsing the deuterium-tritium (D-T) neutron generator or the deuterium-deuterium (D-D) neutron generator neutron source, using two exponential decays, using the pre-programmed neural network on an above-surface processing system;

computing curve-fitting using two exponential decays of the time-decay curve of neutron-induced capture gamma rays from a time immediately after pulsing the deuterium-tritium (D-T) neutron generator or the deuterium-deuterium (D-D) neutron generator neutron source, using the pre-programmed neural network on an above-surface processing system;

acquiring from the computed curve-fitting of the time-decay curve of thermal neutrons and from the computed curve-fitting of the time-decay curve of neutron-induced capture gamma rays, a neutron-induced apparent borehole time-decay constant, and an apparent formation time-decay constant for each of the at least three dual-function radiation detectors, using the pre-programmed neural network on an above-surface processing system;

training a first input-layer of the non-transitory computer readable memory device having a pre-programmed neural network for using, as input, the acquired neutron-induced apparent borehole time-decay constant and the apparent formation time-decay constant;

training three, second-processing hidden layers of the non-transitory computer readable memory device having a pre-programmed neural network with a weighted nonlinear regression algorithm and a weighted regression algorithm;

training a third output-layer of the non-transitory computer readable memory device having a pre-programmed neural network to output an apparent borehole sigma using a weighted linear regression algorithm and to output an apparent formation sigma using a weighted regression algorithm, and then comparing said outputs of said third layer to known values of a true borehole sigma and a true formation sigma;

repeating the operations of pulsing the deuterium-tritium (D-T) neutron generator or the deuterium-deuterium (D-D) neutron generator neutron source, measuring neutrons and neutron-induced gamma rays, separating signals of the measured neutrons and the measured neutron-induced gamma rays from each other, sending the separated thermal neutrons and neutron-induced capture gamma rays to the multi-channel analyzer, acquiring a neutron-induced apparent borehole time-decay constant and an apparent formation time-decay constant, training of the first layer, training of the three, second-processing hidden layers, and training of the third layer of the non-transitory computer readable memory device having a pre-programmed neural network, until a relative difference between an output of the third layer and the known values of a true borehole sigma and a true formation sigma are less than 1 percent;

generating a trained neural network computer program product, having three layers, using the non-transitory computer-readable memory device having a pre-programmed neural network on an above-surface processing system;

storing the generated trained neural network computer program product having three layers, on a memory resource on the above-surface processing system;

replacing the pre-programmed neural network of the non-transitory computer-readable memory device on an above-surface processing system, with the stored trained neural network computer program product, having three layers;

pulsing the deuterium-tritium (D-T) neutron generator or the deuterium-deuterium (D-D) neutron generator neutron source, for at least two pulses;

measuring neutrons and neutron-induced gamma rays after each of the at least two pulses from each of at least three dual-function radiation detectors;

separating signals of the measured neutrons and neutron-induced gamma rays into thermal neutrons and neutron-induced capture gamma rays, using the at least three dual-function radiation detectors pre-programmed through the non-transitory computer-readable memory device using pulsed shape discrimination technique;

sending the separated thermal neutrons and neutron-induced capture gamma rays to the multi-channel analyzer using the sub-surface telemetry system and using the at least three dual-function radiation detectors pre-programmed through the non-transitory computer-readable memory device;

generating a thermal neutron time-spectrum and a neutron-induced capture gamma rays time-spectrum for each of the three dual-function radiation detectors, wherein the thermal neutron time-spectrum essentially consists of a time-decay curve of thermal neutrons, and the neutron-induced capture gamma rays time-spectrum essentially consists of a time-decay curve of neutron-induced capture gamma rays, using the pre-programmed neural network on an above-surface processing system;

computing curve fitting using two exponential decays of the time-decay curve of thermal neutrons from a time immediately after pulsing the deuterium-tritium (D-T) neutron generator or the deuterium-deuterium (D-D) neutron generator neutron source, using two exponential decays, using the non-transitory computer readable memory device having the trained neural network computer program product;

computing curve-fitting using two exponential decays of the time-decay curve of neutron-induced capture gamma rays from a time immediately after pulsing the deuterium-tritium (D-T) neutron generator or the deuterium-deuterium (D-D) neutron generator neutron source, using the non-transitory computer readable memory device having the trained neural network computer program product;

acquiring from the computed curve-fitting of the time-decay curve of thermal neutrons and from the computed curve-fitting of the time-decay curve of neutron-induced capture gamma rays, a neutron-induced apparent borehole time-decay constant, and an apparent formation time-decay constant for each of the at least three dual-function radiation detectors, using the non-transitory computer readable memory device having the trained neural network computer program product;

inputting into a first input-layer of the non-transitory computer readable memory device having the trained neural network computer program product, the acquired neutron-induced apparent borehole time-decay constant and the acquired apparent formation time-decay constant for each of the at least three dual-function radiation detectors;

processing in one of the three, second-processing hidden layers of the non-transitory computer readable memory device having the trained neural network computer program product, the acquired neutron-induced apparent borehole time-decay constant and the acquired apparent formation time-decay constant for each of the at least three dual-function radiation detectors using the weighted nonlinear regression algorithm;

processing in a second of the three, second-processing hidden layers of the non-transitory computer readable memory device having the trained neural network computer program product, the acquired neutron-induced apparent borehole time-decay constant and the acquired apparent formation time-decay constant for each of the at least three dual-function radiation detectors using the weighted nonlinear regression algorithm;

processing in a third of the three, second-processing hidden layers of the non-transitory computer readable memory device having the trained neural network computer program product the acquired neutron-induced apparent borehole time-decay constant and the acquired apparent formation time-decay constant for each of the at least three dual-function radiation detectors using the weighted linear regression algorithm; and

computing in a third output-layer of the non-transitory computer readable memory device having the trained neural network computer program product, a true borehole sigma and a true formation sigma using the weighted linear regression algorithms;

generating a true borehole sigma and a true formation sigma using the weighted linear regression algorithms of the trained third output-layer of the non-transitory computer readable memory device having the trained neural network computer program product.

2. The method of claim 1 , wherein processing in one of the three, second-processing hidden layers of the non-transitory computer readable memory device having the trained neural network computer program product, the acquired neutron-induced apparent borehole time-decay constant for each of the at least three dual-function radiation detectors using the weighted nonlinear regression algorithm, further comprises the expression:

τ

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(

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3. The method of claim 1 , wherein processing in one of the three, second-processing hidden layers of the non-transitory computer readable memory device having the trained neural network computer program product, the acquired apparent formation time-decay constant for each of the at least three dual-function radiation detectors using the weighted nonlinear regression algorithm, further comprises the expression:

τ

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4. The method of claim 1 , wherein processing in a second of the three, second-processing hidden layers of the non-transitory computer readable memory device having the trained neural network computer program product, the acquired neutron-induced apparent borehole time-decay constant for each of the at least three dual-function radiation detectors using the weighted nonlinear regression algorithm, further comprises the expression:

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5. The method of claim 1 , wherein processing in a second of the three, second-processing hidden layers of the non-transitory computer readable memory device having the trained neural network computer program product, the acquired apparent formation time-decay constant for each of the at least three dual-function radiation detectors using the weighted nonlinear regression algorithm, further comprises the expression:

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6. The method of claim 1 , wherein processing in a third of the three, second-processing hidden layers of the non-transitory computer readable memory device having the trained neural network computer program product the acquired neutron-induced apparent borehole time-decay constant and the acquired apparent formation time-decay constant for each of the at least three dual-function radiation detectors using the weighted linear regression algorithm, further comprises the expression:

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7. The method of claim 1 , wherein generating a true borehole sigma using the weighted linear regression algorithms of the trained third output-layer of the non-transitory computer readable memory device having the trained neural network computer program product, further comprises the expression:

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8. The method of claim 1 , wherein generating a true formation sigma using the weighted linear regression algorithms of the trained third output-layer of the non-transitory computer readable memory device having the trained neural network computer program product, further comprises the expression:

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