Calculation method of pulse neutron logging gamma-ray spectrum broadening coefficient

Abstract

The invention relates to a method for calculating a broadening coefficient of a pulse neutron logging gamma-ray energy spectrum. The method is mainly used for calculating the broadening coefficient of the gamma-ray energy spectrum acquired by pulse neutron logging. The broadening of the gamma-ray energy spectrum can be regarded as the convolution of a Gaussian response matrix and an unbroadened energy spectrum, the characteristic gamma ray energy of different elements is used as priori knowledge to set additional weights for channel addresses in a characteristic peak area in the energy spectrum, and a calculation scheme of additional weight values is designed. And meanwhile, a broadening coefficient calculation objective function with energy spectrum feature constraint is provided by combining a weighted least square method. The objective function is solved by adopting a swarm intelligent optimization method, the broadening coefficient is determined, the method is an accurate and efficient gamma-ray spectrum quantitative analysis method, accurate calculation of the broadening coefficient of the gamma-ray spectrum is achieved, and a foundation is laid for follow-up pulsed neutron logging spectrum data analysis and stratum attribute evaluation.

Description

Technical Field

[0001] The present invention relates to a method for calculating the broadening coefficient of a pulsed neutron logging gamma spectrum, which is mainly used to determine the broadening coefficient of energy spectrum data such as an inelastic gamma spectrum and a captured gamma spectrum collected by pulsed neutron logging. The pulsed neutron logging instrument uses a scintillator detector to measure the secondary gamma-ray response spectrum induced by neutrons in the well, and determines the properties of the formation, such as mineral components, oil and gas saturation, porosity, etc., by analyzing the gamma spectrum. However, due to the different types of scintillator detector detection crystals used in the logging instrument, the characteristics of the corresponding gamma-ray response spectrum are significantly different, which is mainly reflected in the detection efficiency, peak-to-Compton ratio (total energy peak to Compton platform count ratio) and peak width of characteristic peaks (energy resolution). The peak width of the characteristic peak in the gamma spectrum can be determined by the broadening coefficient, so accurately calculating the broadening coefficient of the pulsed neutron logging gamma spectrum is the basis for realizing gamma spectrum analysis, and is also the key prerequisite for subsequent quantitative evaluation and interpretation of formation parameters. The present invention proposes a broadening coefficient calculation objective function with energy spectrum characteristic constraints, uses the characteristic gamma-ray energy of different elements as prior knowledge to set constraints, and then adopts a swarm intelligence optimization method to solve the objective function and determine the broadening coefficient. It is an accurate and efficient gamma energy spectrum quantitative analysis method, which realizes the accurate calculation of the gamma energy spectrum broadening coefficient and lays a foundation for subsequent pulse neutron logging energy spectrum data analysis and formation property evaluation. Background Art

[0002] Pulsed neutron logging is an important logging method for evaluating formation mineral composition, oil and gas saturation, porosity and other properties. The logging instrument has a pulsed neutron source that can emit fast neutrons with an energy of 14MeV into the formation downhole. After entering the formation, the fast neutrons can emit a series of nuclear reactions such as inelastic scattering, elastic scattering, and radiation capture with the nuclei of the formation elements. Among them, inelastic scattering and radiation capture nuclear reactions can stimulate the target nuclei, causing them to release gamma rays. These gamma rays are transported in the formation and collected and recorded by the scintillator gamma detector on the logging instrument. Since the gamma rays generated by the stimulation of nuclei of different elements have different energies, that is, the characteristic energy of the element, the inversion of formation parameters can be achieved by analyzing the proportion of gamma rays of different energies. However, according to the measurement mechanism of the instrument's scintillator detector, the response energy spectrum corresponding to the gamma rays is not a pulse signal, but a continuous spectrum with a certain energy distribution. Factors such as the non-uniform luminous efficiency of the detector's scintillation crystals and the statistical fluctuations of the charge generated by the internal ionization of the detector will cause the corresponding characteristic gamma rays to form characteristic peaks with a certain peak width in the energy spectrum, which can be well approximated by a Gaussian function. This phenomenon is called Gaussian broadening. Usually, as the energy of the gamma ray increases, the peak width of the characteristic peak also increases. This is the measurement law of the scintillator detector, and the half-width (FWHM) of the characteristic peak and the incident gamma energy will conform to a certain mathematical model. The coefficient in this model is the broadening coefficient. The magnitude of the broadening is related to the properties of the scintillator detector and can be determined by the corresponding broadening coefficient.

[0003] In the qualitative and quantitative analysis of gamma energy spectra, the magnitude of energy spectrum broadening is an important indicator for evaluating the performance of pulsed neutron logging gamma-ray measurement systems, which can reflect the ability of the detector to distinguish between two gamma rays with similar energies. Therefore, determining the broadening coefficient of the instrument's scintillator detector is of great significance for the extraction and analysis of complex formation composition information. For energy spectra measured by different scintillator detectors, the characteristic peaks may be well separated, partially overlapped, or mostly overlapped, which is mainly limited by the magnitude of energy spectrum broadening. Accurately determining the broadening coefficient of the gamma energy spectrum is of great significance for energy spectrum processing and analysis such as energy spectrum resolution enhancement, rapid component identification, and energy spectrum deconvolution.

[0004] The common method for calculating the gamma spectrum broadening coefficient is to use a Gaussian function to fit the peak shape of different characteristic peaks. By calculating the FWHM of multiple characteristic peaks in the gamma spectrum, the broadening coefficient can be fitted using a mathematical model between the FWHM of the characteristic peak and the incident gamma energy. The most commonly used method for peak shape fitting is the nonlinear iteration method. However, the main difficulty of this method is that it tends to converge to a local optimal solution in a multidimensional case, especially when a bad initial solution is given. In addition, due to the influence of spectrum broadening and Compton scattering, a higher background background will appear in the low-energy region of the measured gamma spectrum, and some weak peaks will be submerged in the background, making it difficult to accurately fit their shapes. In this case, additional background correction processing is required to obtain the net peak, such as the SNIP method, asymmetric least squares method, etc., which obviously increases the complexity of the processing.

[0005] With the development of numerical simulation technology, the Monte Carlo method plays an increasingly important role in the calculation of gamma spectrum broadening coefficients. By establishing a simulation model consistent with the measurement system, the optimization method is used to minimize the error between the simulated spectrum and the actual measured spectrum, thereby obtaining the optimal broadening coefficient. However, in the absence of effective constraints, even if the adaptability of the objective function is satisfactory, traditional optimization methods are prone to derive unreasonable solutions. Although the optimization performance can be improved by restarting the algorithm multiple times or increasing the number of iterations, the optimization efficiency will also be reduced.

[0006] The present invention proposes a method for calculating the broadening coefficient based on energy spectrum characteristic constraints. The Monte Carlo simulation technology is used to obtain the theoretical response energy spectrum of the actual gamma-ray measurement system when it is not broadened. Then, the characteristic gamma-ray intrinsic energy of different elements is used as prior knowledge, and the constraint conditions reflecting the energy spectrum characteristics are set and the optimization objective function is established in combination with the scintillator gamma detector measurement mechanism. Afterwards, in order to ensure that the broadening size of the simulated energy spectrum matches that of the actual energy spectrum, a swarm intelligence optimization algorithm is introduced to solve the objective function, thereby calculating the optimal gamma energy spectrum broadening coefficient. Summary of the invention

[0007] The purpose of the present invention is to provide a method for calculating the gamma spectrum broadening coefficient of pulsed neutron logging, which is mainly based on the gamma spectrum characteristics collected by pulsed neutron logging, calculates the corresponding gamma spectrum broadening coefficient, and realizes the quantitative calculation of the peak width of the characteristic peak of typical elements in the spectrum, laying a foundation for subsequent spectrum analysis and formation parameter inversion.

[0008] The broadening principle of the gamma spectrum of pulsed neutron logging can be regarded as the convolution operation between the unbroadened spectrum and the Gaussian response function. For discrete data, the convolution operation can be expressed as:

[0009]

[0010] Where x(k) is the original input signal, h(i) is the response function, s(i) is the response signal, N and M are the lengths of the input signal and the response function, respectively. An output signal with the same length as the input signal can be obtained by discarding the boundary value of the response signal.

[0011] In actual measurement, noise is an inevitable influencing factor. Therefore, the response energy spectrum of the scintillator detector of the pulsed neutron logging tool can be written as the following matrix equation:

[0012] s=Hx+n (2)

[0013] Where s is the scintillator detector response energy spectrum vector, x is the incident unbroadened energy spectrum vector, n is the noise vector, and H is the Gaussian response matrix.

[0014] The magnitude of the gamma spectrum broadening is determined by the Gaussian response matrix, which can be written as:

[0015]

[0016] Where m is the length of the response energy spectrum vector, and the element G in the matrix H is ij It can be expressed as:

[0017]

[0018] Formula (4) can be regarded as energy E j The gamma-ray energy spectrum of E i The contribution of the count on the channel address corresponding to the energy. And σ in formula (4) can be expressed as:

[0019]

[0020] Where, FWHM is the half-height width of the characteristic peak of the energy spectrum, which is a function of the broadening coefficients a, b, and c, and E is the energy represented by the corresponding channel address.

[0021] Therefore, the matrix H can be viewed as a series of normalized Gaussian distributions centered on the diagonal elements of the matrix.

[0022] Based on the above theory, a method for calculating the gamma spectrum broadening coefficient of pulsed neutron logging is characterized by comprising the following steps:

[0023] Step 1: Conduct a standard calibration well experiment to collect gamma energy spectra.

[0024] The standard calibration well is an artificial simulation well with known formation and borehole composition and well structure parameters, and is often used to carry out physical simulation experiments related to pulsed neutron logging. During the experiment, the pulsed neutron logging instrument is placed in the borehole of the simulation well, and multiple gamma energy spectra are continuously collected. Due to the influence of inherent statistical fluctuations in radioactive measurements, there are slight differences in the counts between the energy spectra. Therefore, multiple gamma energy spectra are accumulated and the average value of each channel is calculated to reduce the influence of radioactive statistical fluctuations. The accumulated average spectrum obtained is used as the measured gamma energy spectrum of the pulsed neutron logging instrument in the standard calibration well, as shown in formula (6).

[0025]

[0026] In the formula, C ij is the j-th channel count of the measured i-th energy spectrum, NN is the number of gamma energy spectra collected, C j is the j-th channel count of the cumulative average spectrum.

[0027] Step 2: Establish a Monte Carlo simulation model based on the experimental conditions of the standard calibration well and simulate the incident gamma energy spectrum without broadening.

[0028] A Monte Carlo numerical simulation model is established based on the composition and structural parameters of the standard calibration well in the calibration well experiment and the specific parameters of the pulsed neutron logging instrument in the experiment. The Monte Carlo numerical simulation technology is used to simulate the unbroadened gamma energy spectrum measured by the scintillator detector of the logging instrument in the standard calibration well experiment. Although the response process of the scintillator detector cannot be avoided in actual measurement, the response of the scintillator detector can be eliminated through numerical simulation methods, thereby obtaining the unbroadened gamma energy spectrum measured by the scintillator detector.

[0029] Step 3: Establish the energy spectrum characteristic weight matrix based on the characteristic gamma-ray energy of the incident element.

[0030] Since the composition in the standard calibration well is known, the typical characteristic peak in the gamma energy spectrum can be determined based on the characteristic gamma energy of the element. In theory, the broadening coefficient determines the peak width of the characteristic peak, so within the range of the characteristic peak, the broadened gamma energy spectrum is required to have a high degree of consistency with the actual measured energy spectrum. This requires adding a higher weight to the channel address within the characteristic peak range. This additional weight can be obtained through the energy spectrum characteristic weight matrix W 1 To achieve this, the matrix can be expressed as:

[0031]

[0032] Where n is the number of selected characteristic peaks, m is the length of the gamma spectrum, is the pth characteristic peak in the region where the nth characteristic peak is located. k The additional weight that the road has.

[0033] When designing the matrix, only the channel data within the FWHM of the selected peak area have additional weights. Therefore, a nonlinear weighting scheme is designed to calculate the additional weight value of each channel within the FWHM. The weighting scheme can be expressed as:

[0034]

[0035] In the formula, w ip is the additional weight value of the pth channel in the ith peak area, d ip is the distance between the peak track address in the ith peak area and the pth track in the peak area.

[0036] In the designed weighting scheme, the weight of each channel in the peak area is determined by the distance from the channel to the peak channel, and gradually decreases with the increase of distance. The peak channel has the largest additional weight, and the boundary channel of FWHM has the smallest weight.

[0037] Step 4: Construct the objective function based on the weighted least squares method and the energy spectrum feature weight matrix.

[0038] The main part of the objective function is the sum of squares of the channel-by-channel errors between the calculated energy spectrum and the measured energy spectrum. Since the statistical accuracy of each channel of the measured energy spectrum is different, the variance of the high energy channel count is larger than the variance of the low energy channel count. Therefore, in order to ensure that each energy channel is calculated with equal accuracy, the weight corresponding to each channel in the weighted least squares method is:

[0039]

[0040] In the formula, u 1 …u m Counts each channel of the gamma spectrum.

[0041] Combining the least squares method with the energy spectrum characteristic weight matrix, the objective function for calculating the broadening coefficient can be constructed:

[0042]

[0043] In the formula, s i and u i are the calculated broadened energy spectrum and the count of the i-th channel of the actually measured energy spectrum, respectively. λ is the weighting coefficient, which reflects the importance of the additional constraints constructed by the energy spectrum feature weight matrix in the entire objective function. n is the number of characteristic peaks selected, and p is the number of characteristic peaks selected. jk is the number of channels in the peak area of ​​the jth characteristic peak, w 2i is the weight value of the ith channel, w 1ji is the additional weight value of the ith channel in the jth peak area.

[0044] Combined with the weighted least squares weight matrix W2 And the energy spectrum feature weight matrix W 1 The objective function (10) can be written in matrix form:

[0045] F(s)=(us) T W 2 (us)+λ(us) T W 1 T W 1 (us) (11)

[0046] Since the broadened energy spectrum can be calculated based on the Gaussian response matrix of the scintillator detector, the matrix form of the objective function can be rewritten as a function of the Gaussian response matrix:

[0047] F(H)=(u-Hx) T W 1 (u-Hx)+λ(u-Hx) T W 2 T W 2 (u-Hx) (12)

[0048] The gamma spectrum broadening coefficient can be obtained by calculating the optimal Gaussian response matrix.

[0049] Step 5: Solve the optimal broadening coefficient through swarm intelligence optimization algorithm.

[0050] According to the broadening mechanism of the instrument scintillator detector, it can be seen that there is a strong correlation between the elements in the Gaussian response matrix. Therefore, the matrix equation shown in equation (12) can be regarded as a function of the broadening coefficients a, b, and c. The calculation process of the broadening coefficient can be regarded as a high-dimensional constrained optimization problem, expressed as equation (13):

[0051]

[0052] Where M is the number of standard scale well experiments, function f i (a, b, c) are the objective functions established by measuring the energy spectrum of the i-th standard calibration well experiment.

[0053] The swarm intelligence optimization algorithm is an iterative method that updates feasible solutions based on the fitness of the objective function. Its advantage is that it does not rely on initial guesses and does not require the calculation of the derivatives of the objective function. Therefore, the particle swarm optimization (PSO), a typical swarm intelligence algorithm, is used to calculate the global optimal solution of the objective function and obtain the optimal gamma spectrum broadening coefficient.

[0054] Particle swarm optimization is a classic optimization algorithm inspired by bird predation behavior. Particle swarm optimization algorithm first initializes a set of particles as potential solutions, and the fitness of the solution is determined by the objective function. In the kth iteration, the i-th particle tracks the individual optimal position P i k and the global optimal position To update its own speed V i k and location To find the optimal solution, as shown in equations (14) and (15).

[0055]

[0056] Where ω is the inertia weight, c 1 and c 2 is the acceleration factor, r 1 and r 2 is a random number distributed in the range [0, 1].

[0057] Monte Carlo simulation is used to obtain the unbroadened gamma energy spectrum in the scintillator detector in the standard calibration well experiment. Under the preset energy spectrum characteristic constraints, the sum of square errors between the measured gamma energy spectrum and the calculated gamma energy spectrum is solved according to the established objective function. In order to ensure that the measured energy spectrum and the calculated energy spectrum are in the same order of magnitude, they need to be normalized during the calculation process. The sum of squares of the errors between the two is the adaptability evaluation criterion in the iteration of the particle swarm algorithm. Finally, when the algorithm converges, the optimal gamma energy spectrum broadening coefficient can be obtained.

[0058] The present invention proposes a method for calculating the broadening coefficient of the gamma spectrum of pulsed neutron logging. The method flow chart is as follows: Figure 1 As shown in the figure. When calculating the broadening coefficient of the pulsed neutron logging gamma spectrum, the well logging instrument is first used to carry out a physical simulation experiment of a standard scale well, and the neutron-induced gamma spectrum is collected in a simulated formation with known composition and structural parameters. Then, the characteristic gamma energy of typical elements in the spectrum is determined according to the formation composition, and the energy spectrum characteristic weight matrix is ​​established based on this. Based on the weighted least squares principle and the established energy spectrum characteristic weight matrix, the objective function for solving the broadening coefficient is constructed. Finally, the calculation of the gamma spectrum broadening coefficient is realized through the swarm intelligence optimization algorithm.

[0059] Beneficial Effects

[0060] Compared with the prior art, the present invention has the following significant advantages: (1) The calculation results are highly accurate. The energy spectrum characteristic weight matrix is ​​constructed using the characteristic gamma rays of elements with known energies in the energy spectrum, and is used as an additional constraint term for solving the objective function of the broadening coefficient. The existence of the additional constraint term will give the channel address in the characteristic peak area a higher weight, thereby ensuring that the calculation results of the characteristic peak area are more consistent with the actual measurement results, which also makes the calculated broadening coefficient more accurate. (2) The algorithm design is reasonable and stable. The objective function is regarded as a high-dimensional optimization problem and a swarm intelligence optimization algorithm is used to solve the objective function. The global optimization capability of this type of algorithm is used to search for the optimal broadening coefficient. The search is performed through certain iterative rules to ensure the stability of the solution process. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 The present invention provides a flow chart of a method for calculating the gamma spectrum broadening coefficient of pulsed neutron logging.

[0062] Figure 2 Schematic diagram of the standard scale well experiment simulation model in the application example.

[0063] Figure 3 This is a comparison chart of the normalized experimental measured total spectrum and the calculated total spectrum.

[0064] Figure 4 Comparison diagram of normalized experimental measured capture spectrum and calculated capture spectrum. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0066] Application examples:

[0067] In this embodiment, a pulsed neutron logging instrument is used to carry out a standard calibration well experiment. The experimental instrument uses a DT neutron source to emit fast neutrons to stimulate the element nuclei in the simulated formation components of the standard calibration well to release gamma rays, and uses a scintillator detector to obtain the corresponding gamma energy spectrum. The experimental pulsed neutron logging instrument is placed in different standard calibration wells for measurement, and the composition and structural parameters of these calibration wells are also known. The standard calibration well is composed of pure rock or elemental single substance. The filling materials include aluminum (Al), graphite (C), limestone (LS), fresh water (H 2 O) Four. The instrument is inserted into a 200 mm diameter wellbore filled with fresh water and measures neutron-induced gamma rays.

[0068] According to the actual structure of the experimental instrument and the configuration of the standard calibration well, a Monte Carlo simulation model is constructed to simulate the unbroadened gamma energy spectrum in the detector scintillation crystal. Figure 2 As shown. The instrument has a diameter of 41mm and a length of 2358mm. The DT neutron source consists of two parts: an acceleration system and a neutron production target. The instrument has three scintillator detectors with different detector-source distances of 29cm, 59cm, and 91cm, respectively. There is a tungsten shield between the source and the near detector. Both the far and near detectors use cylindrical LaBr3 crystals with crystal dimensions of 27.5mm×152mm and 27.5mm×38mm (diameter×length), respectively. The ultra-far detector uses NaI crystals with dimensions of 27mm×152mm. The ultra-far detector has the largest source distance, so it is mainly used to collect natural gamma rays rather than neutron-induced gamma rays. In the experiment, considering the influence of radioactive statistical fluctuations in gamma-ray energy spectrum measurement, the energy spectrum collected by the detector at a near source distance was selected to verify the proposed method.

[0069] According to the nuclear reaction mechanism between fast neutrons and atomic nuclei, both inelastic scattering and radiation capture nuclear reactions can produce secondary gamma rays. The pulsed neutron logging instrument uses a special measurement sequence to measure inelastic gamma rays and captured gamma rays. The DT neutron source of the instrument can periodically emit neutrons with an energy of 14MeV. A complete measurement cycle is 20ms, consisting of 200 100μs sub-cycles. The neutron source emits neutrons in the first 40μs of each sub-cycle, and the neutron source does not work in the last 60μs. The gamma rays measured and recorded during the burst phase of the pulsed neutron source are mainly inelastic gamma rays, but also contain a certain amount of captured gamma rays. The gamma rays collected during the period when the neutron source stops working are captured gamma rays, and then the energy spectra recorded in all sub-cycles are accumulated to obtain the final energy spectrum. The gamma energy spectrum obtained during the burst phase of the pulsed neutron source is called the total spectrum, which contains inelastic gamma rays and captured gamma rays, while the gamma energy spectrum obtained during the shutdown phase of the pulsed neutron source is called the capture spectrum, which only contains captured gamma rays.

[0070] The pulse neutron logging gamma spectrum broadening coefficient calculation method proposed in this invention is used to process two gamma spectra measured in four standard calibration wells. The total spectrum processing results are shown in Figure 3As shown. It can be seen that there is an obvious characteristic peak with an energy of 2.23MeV in each total spectrum, which is produced by the radiation capture nuclear reaction of hydrogen in the fluid in the well. In addition, some characteristic peaks of other elements can be found in the total spectrum, such as the inelastic characteristic peaks of oxygen and carbon in the fresh water calibration well and the graphite calibration well. All the characteristic peaks of the main elements, including the corresponding escape peaks, can be used as useful prior knowledge to construct the energy spectrum feature weight matrix and set additional weights. The objective function is established using all the total spectra and capture energy spectra measured in the four standard calibration wells to solve the broadening coefficient of the gamma energy spectrum. The calculation results are a=0.0253, b=0.0048, c=52.562.

[0071] The root mean square error (RMSE) and correlation coefficient (R-Square) between the characteristic peaks selected in each total spectrum, the normalized experimental measured gamma energy spectrum and the normalized calculated gamma energy spectrum are shown in Table 1. In the experiment, some obvious characteristic peaks were selected from the gamma energy spectrum measured in each standard scale well to set the energy spectrum characteristic weight matrix. The results show that the experimental energy spectrum has a good correlation with the calculated energy spectrum. The broadening coefficient calculated by the method proposed in the present invention makes the correlation coefficient between the experimental measured gamma energy spectrum and the calculated gamma energy spectrum above 0.99, and the average RMSE is only 4.22e-4.

[0072] Similarly, the comparison between the normalized experimentally measured captured gamma spectrum and the normalized calculated captured gamma spectrum is shown in Figure 4 The captured gamma spectrum processing results in four standard scale wells are shown in Table 2. The results show that the calculated gamma spectrum and the measured gamma spectrum also have a good correlation. The correlation coefficients are all greater than 0.99, and the average RMSE is 4.03e-4. The processing results of the captured gamma spectrum also prove the adaptability of the present invention in the calculation of the gamma spectrum broadening coefficient.

[0073] Table 1 Comparison of normalized experimental measured total spectrum and calculated total spectrum

[0074]

[0075] Table 2 Comparison of normalized experimentally measured capture spectra and calculated capture spectra

[0076]

Claims

1. A method for calculating the broadening coefficient of the gamma spectrum of pulsed neutron logging is characterized by The method comprises the following steps: Step 1: Carry out a standard calibration well experiment to collect gamma energy spectrum. The standard calibration well is an artificial simulation well with known formation and borehole composition and well structure parameters. During the experiment, the pulsed neutron logging instrument is placed in the borehole of the simulation well, and multiple gamma energy spectra are continuously collected. The multiple gamma energy spectra are accumulated and the average value of each channel is calculated to reduce the influence of radioactive statistical fluctuations. The accumulated average spectrum obtained is used as the measured gamma energy spectrum of the pulsed neutron logging instrument in the standard calibration well, as shown in formula (1): In the formula, C ij is the j-th channel count of the measured i-th energy spectrum, NN is the number of gamma energy spectra collected, is the j-th channel count of the cumulative average spectrum; Step 2: Establish a Monte Carlo simulation model based on the experimental conditions of the standard calibration well and simulate the unbroadened incident gamma energy spectrum. Establish a Monte Carlo numerical simulation model based on the composition and structural parameters of the standard calibration well in the calibration well experiment and the specific parameters of the pulsed neutron logging instrument in the experiment. Use the Monte Carlo numerical simulation technology to simulate the unbroadened gamma energy spectrum measured by the scintillator detector of the logging instrument in the standard calibration well experiment. Although the response process of the scintillator detector cannot be avoided in actual measurement, the response of the scintillator detector can be eliminated through numerical simulation. Step 3: Establish the energy spectrum characteristic weight matrix based on the characteristic gamma ray energy of the incident element. Since the components in the standard calibration well are known, the typical characteristic peaks in the gamma energy spectrum are determined according to the characteristic gamma energy of the element. In theory, the broadening coefficient determines the peak width of the characteristic peak. Within the range of the characteristic peak, the broadened gamma energy spectrum is required to have a high degree of consistency with the actual measured energy spectrum. Therefore, a higher weight is added to the channel address within the characteristic peak range. This additional weight is realized through the energy spectrum characteristic weight matrix W1, which can be expressed as: In the formula, n is the number of selected characteristic peaks, m is the length of the gamma spectrum, is the pth characteristic peak in the region where the nth characteristic peak is located. k The additional weight of the channel. When designing the matrix, only the channel address data within the FWHM of the selected peak area has additional weight. Therefore, a nonlinear weighting scheme is designed to calculate the additional weight value of each channel address within the FWHM. The weighting scheme can be expressed as: In the formula, w ip is the additional weight value of the pth channel in the ith peak area, d ip is the distance between the peak track address in the ith peak area and the pth track in the peak area; Step 4: Construct the objective function based on the weighted least squares method and the energy spectrum feature weight matrix. The main part of the objective function is the sum of squares of the channel-by-channel errors between the calculated energy spectrum and the measured energy spectrum. To ensure that each energy channel is calculated with equal accuracy, the weight corresponding to each channel in the weighted least squares method is: In the formula, u1...u m By counting the addresses of the gamma spectrum and combining the least square method with the spectrum feature weight matrix, the objective function for calculating the broadening coefficient can be constructed: In the formula, s i and u i are the calculated broadened energy spectrum and the count of the i-th channel of the actually measured energy spectrum, respectively. λ is the weighting coefficient, which reflects the importance of the additional constraints constructed by the energy spectrum feature weight matrix in the entire objective function. n is the number of characteristic peaks selected, and p is the number of characteristic peaks selected. jk is the number of channels in the peak area of ​​the jth characteristic peak, w 2i is the weight value of the ith channel, w 1ji is the additional weight value of the ith channel in the jth peak area. Combining the weighted least squares weight matrix W2 and the energy spectrum feature weight matrix W1, the objective function (5) can be written in matrix form: F(s)=(u-s) T W2(u-s)+λ(u-s) T W1 T W1(u-s) (6) Since the broadened energy spectrum can be calculated based on the Gaussian response matrix of the scintillator detector, the matrix form of the objective function can be rewritten as a function of the Gaussian response matrix: The gamma spectrum broadening coefficient can be obtained by calculating the optimal Gaussian response matrix; Step 5: Solve the optimal broadening coefficient through the swarm intelligence optimization algorithm. According to the broadening mechanism of the instrument scintillator detector, there is a strong correlation between the elements in the Gaussian response matrix. Therefore, the matrix equation shown in formula (7) can be regarded as a function of the broadening coefficients a, b, and c. The calculation process of the broadening coefficient is regarded as a high-dimensional constrained optimization problem, which can be expressed as: sta,b,c≥0 Where M is the number of standard scale well experiments, function f i (a, b, c) is the objective function established by the energy spectrum measured by the i-th standard calibration well experiment. The particle swarm algorithm, a typical swarm intelligence algorithm, is used to calculate the global optimal solution of the objective function and obtain the optimal gamma spectrum broadening coefficient. The particle swarm algorithm first initializes a group of particles as potential solutions. The fitness of the solution is determined by the objective function. In the k-th iteration, the i-th particle tracks the individual optimal position P i k and the global optimal position To update its own velocity V i k and location To find the optimal solution, as shown in equations (9) and (10): Where ω is the inertia weight, c1 and c2 are acceleration factors, r1 and r2 are random numbers distributed in the range of [0, 1]. Monte Carlo simulation is used to obtain the unbroadened gamma energy spectrum in the scintillator detector in the standard calibration well experiment. Under the preset energy spectrum characteristic constraints, the sum of square errors between the measured gamma energy spectrum and the calculated gamma energy spectrum is solved according to the established objective function. In order to ensure that the measured energy spectrum and the calculated energy spectrum are in the same order of magnitude, they need to be normalized during the calculation process. The sum of squares of the errors between the two is the adaptability evaluation criterion in the iteration of the particle swarm algorithm. Finally, when the algorithm converges, the optimal gamma energy spectrum broadening coefficient can be obtained.

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