A method for calculating a gamma energy spectrum broadening coefficient of a pulsed neutron logging

Abstract

The present application relates to a kind of impulse neutron logging gamma spectrum broadening coefficient calculation method, mainly for calculating the broadening coefficient of gamma spectrum collected by impulse neutron logging.Gamma spectrum broadening can be regarded as the convolution of Gaussian response matrix and un-broadened spectrum, the present application uses the characteristic gamma ray energy of different elements as prior knowledge to set additional weight for channel address in characteristic peak area of spectrum, and designs the calculation scheme of additional weight value.At the same time, a broadening coefficient calculation objective function with spectrum characteristic constraint is proposed combining with weighted least squares method.Furthermore, swarm intelligence optimization method is used to solve the objective function, and the broadening coefficient is determined, which is an accurate and efficient gamma spectrum quantitative analysis method, realizes the accurate calculation of gamma spectrum broadening coefficient, and lays a foundation for subsequent impulse neutron logging spectrum data analysis and formation property evaluation.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of impulse neutron logging gamma spectrum broadening coefficient calculation method, mainly used to determine the broadening coefficient of non elastic gamma spectrum, capture gamma spectrum etc. Spectrum data collected by impulse neutron logging. Impulse neutron logging instrument uses scintillator detector to measure the secondary gamma ray response spectrum induced by neutron underground, and determines the properties of formation, such as mineral composition, oil and gas saturation, porosity etc. By analyzing gamma spectrum. But due to the different types of scintillator detector detection crystal used by logging instrument, the characteristics of corresponding gamma ray response spectrum exist obvious difference, which is mainly reflected in the detection efficiency, peak-to-compton ratio (full energy peak and compton platform count ratio) and characteristic peak width (energy resolution) etc. The peak width of characteristic peak in gamma spectrum can be determined by broadening coefficient, so accurate calculation of impulse neutron logging gamma spectrum broadening coefficient is the basis of realizing gamma spectrum analysis, and is also the key prerequisite for subsequent formation parameter quantitative evaluation and interpretation. The present application proposes a broadening coefficient calculation objective function with spectrum characteristic constraint, uses the characteristic gamma ray energy of different elements as prior knowledge to set constraint condition, and then uses swarm intelligence optimization method to solve the objective function, determines the broadening coefficient, is a kind of accurate and efficient gamma spectrum quantitative analysis method, realizes the accurate calculation of gamma spectrum broadening coefficient, and lays a foundation for subsequent impulse neutron logging spectrum data analysis and formation property evaluation. BACKGROUND

[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, which can emit fast neutrons with an energy of 14 MeV into the formation. After the fast neutrons enter the formation, they can emit a series of nuclear reactions such as inelastic scattering, elastic scattering, and radiative capture with the atomic nuclei of the formation elements. Among them, inelastic scattering and radiative capture nuclear reactions can excite the target nuclei, so that they release gamma rays. These gamma rays are transported in the formation and are collected and recorded by the scintillator gamma detector on the logging instrument. Since the gamma rays excited by different element nuclei have different energies, i.e. the characteristic energy of the element, the proportion of gamma rays of different energies can be analyzed to realize the inversion of formation parameters. However, according to the measurement mechanism of the instrument 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 light-emitting efficiency of the detector scintillator crystal and the statistical fluctuation of the ionization charge generated inside 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. Generally, as the energy of the gamma rays increases, the peak width of the characteristic peak also increases, which is the measurement rule of the scintillator detector, and the full width at half maximum (FWHM) of the characteristic peak and the incident gamma energy will conform to a certain mathematical model, and the coefficient in the model is the broadening coefficient. The size of the broadening is related to the properties of the scintillator detector and can be determined by the corresponding broadening coefficient.

[0003] In gamma spectrum qualitative and quantitative analysis, the size of the energy spectrum broadening is an important indicator for evaluating the performance of the pulsed neutron logging gamma ray measurement system, which can reflect the ability of the detector to distinguish two gamma rays with similar energy. Therefore, determining the broadening coefficient of the instrument scintillator detector is of great significance for extracting and analyzing complex formation composition information. For energy spectra measured by different scintillator detectors, the characteristic peaks may be well separated, partially overlapping, or mostly overlapping, which is mainly limited by the size of the energy spectrum broadening. Accurate determination of the broadening coefficient of the gamma spectrum is of great significance for energy spectrum resolution enhancement, rapid component identification, energy spectrum deconvolution and other energy spectrum processing and analysis.

[0004] The common method for calculating the gamma spectrum broadening coefficient is to use Gaussian function to fit the peak shape of different characteristic peaks. The FWHM of multiple characteristic peaks in the gamma spectrum is calculated. The mathematical model between the FWHM of the characteristic peak and the incident gamma energy can be used to fit the broadening coefficient. The most commonly used method for peak shape fitting is the nonlinear iterative method. However, the main difficulty of this method is that it is easy to converge to a local optimal solution in a multi-dimensional case, especially when a poor initial solution is given. In addition, due to the influence of spectrum broadening and Compton scattering, a higher background base will appear in the low-energy region of the measured gamma spectrum, and some weak peaks will be submerged in the background, and their shapes are difficult to accurately fit. In this case, additional background correction processing is needed to obtain the net peak, such as the SNIP method, the 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 the gamma spectrum broadening coefficient. By establishing a simulation model consistent with the measurement system, the error between the simulation spectrum and the actual measured spectrum is minimized by using the optimization method, thereby obtaining the optimal broadening coefficient. However, in the absence of effective constraints, even if the adaptability of the objective function is satisfactory, the traditional optimization method is easy to derive an unreasonable solution. 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 application proposes a broadening coefficient calculation method based on spectrum feature constraints. The Monte Carlo simulation technology is used to obtain the theoretical response spectrum of the actual gamma ray measurement system without broadening. Then, the characteristic gamma ray eigenenergy of different elements is used as prior knowledge to set the constraint condition reflecting the spectrum feature and establish the optimization objective function combined with the measurement mechanism of the scintillator gamma detector. Then, in order to ensure that the broadening size of the simulation spectrum matches the actual spectrum, the swarm intelligence optimization algorithm is introduced to solve the objective function, thereby calculating the optimal gamma spectrum broadening coefficient. SUMMARY

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

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

[0009]

[0010] In the formula, 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. The output signal with the same length as the input signal can be obtained by discarding the boundary values of the response signal.

[0011] In actual measurement, noise is an inevitable influencing factor. Therefore, the response spectrum of the scintillator detector of the pulsed neutron logging instrument can be written in the form of a matrix equation as follows:

[0012] s = Hx + n (2)

[0013] In the formula, s is the response spectrum vector of the scintillator detector, x is the incident unexpanded spectrum vector, n is the noise vector, and H is the Gaussian response matrix.

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

[0015]

[0016] In the formula, m is the length of the response spectrum vector, and the elements G ij in the matrix H can be represented as:

[0017]

[0018] Formula (4) can be regarded as the contribution of the counts at the channel corresponding to the E i energy in the spectrum of the gamma ray pair with energy E j . And σ in formula (4) can be represented as:

[0019]

[0020] In the formula, FWHM is the full width at half maximum of the spectrum characteristic peak, which is a function of the expansion coefficients a, b and c, and E is the energy size corresponding to the channel.

[0021] Therefore, the matrix H can be regarded 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 expansion coefficient of a pulsed neutron logging instrument comprises the following steps:

[0023] Step 1: Collect gamma spectra through standard calibration well experiments.

[0024] The standard calibration well is an artificial simulation well with known formation and borehole composition and well structure parameters, which is often used for physical simulation experiments related to pulsed neutron logging. In 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 inherent statistical fluctuations in radioactive measurement, there are slight differences in the counts between the energy spectra. Therefore, the multiple gamma energy spectra are accumulated and the average values of each channel are calculated to reduce the influence of radioactive statistical fluctuations. The accumulated average spectrum obtained is taken as the measured gamma energy spectrum of the pulsed neutron logging instrument in the standard calibration well, as shown in equation (6).

[0025]

[0026] In the formula, Cij is the count of the jth channel of the ith measured energy spectrum, NN is the number of collected gamma energy spectra, Cj is the count of the jth channel of the accumulated average spectrum. ij j k

[0027] Step 2: Establish a Monte Carlo simulation model according to the experimental conditions of the standard calibration well and simulate the unspread incident gamma energy spectrum.

[0028] A Monte Carlo numerical simulation model is established according to the composition and structure 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 unspread 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, thereby obtaining the unspread gamma energy spectrum measured by the scintillator detector.

[0029] Step 3: Establish a spectrum feature 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 peaks in the gamma energy spectrum can be determined according to the characteristic gamma energy of the element. In theory, the spread coefficient determines the peak width of the characteristic peak, so the spread gamma energy spectrum and the actual measured energy spectrum should have a high degree of agreement in the range of the characteristic peak. Therefore, higher weights need to be added to the channel addresses in the range of the characteristic peak. This additional weight can be realized through the spectrum feature weight matrix W1, which can be represented as:

[0031]

[0032] In the formula, n is the number of selected characteristic peaks, m is the length of the gamma energy spectrum, is the additional weight of the pth channel in the region of the nth characteristic peak. k ​​

[0033] In the design of the matrix, only the channel data within the FWHM of the selected peak region has additional weight. Therefore, a non-linear weighting scheme is designed to calculate the additional weight value of each channel in the FWHM, which can be expressed as:

[0034]

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

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

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

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

[0039]

[0040] In the formula, u1…u m is the count of each channel of the gamma spectrum.

[0041] Combined with the least squares method and the spectral feature 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 counts of the ith channel of the calculated broadening spectrum and the actual measured spectrum, respectively, λ is the weighting coefficient, which reflects the importance of the additional constraint constructed by the spectral feature weight matrix in the entire objective function, n is the number of selected characteristic peaks, p jk is the number of channels in the peak region 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 region.

[0044] The objective function (10) can be written in matrix form by combining the weighted least squares weight matrix W2 and the spectral feature weight matrix W1:

[0045] F(s) = (u - s) T W2(u - s) + λ(u - s) T W1 T W1(u - s) (11)

[0046] Since the spread spectrum can be calculated according to 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 W1(u - Hx) + λ(u - Hx) T W2 T W2(u - Hx) (12)

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

[0049] Step 5: Solve the optimal spread coefficient by swarm intelligence optimization algorithm.

[0050] According to the spread 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 spread coefficients a, b, and c. The calculation process of the spread coefficient can be regarded as a high-dimensional constrained optimization problem, which is represented by equation (13):

[0051]

[0052] In the formula, M is the number of standard calibration well experiments, and the function f i (a, b, c) is the objective function established by the measured spectrum of the i-th standard calibration well experiment.

[0053] Swarm intelligence optimization algorithm is an iterative method for updating feasible solutions based on the fitness of the objective function. Its advantages are that it does not depend on the initial guess and does not need to calculate the derivative of the objective function. Therefore, a typical swarm intelligence algorithm, particle swarm optimization (PSO), is used to realize the global optimal solution calculation of the objective function and obtain the optimal gamma spectrum spread coefficient.

[0054] Particle swarm optimization algorithm is a classical optimization algorithm inspired by the hunting behavior of birds. Particle swarm optimization algorithm first initializes a group of particles as potential solutions, and the fitness of the solution is determined by the objective function. In the k-th iteration, the i-th particle is updated by tracking the individual optimal position P i k and the global optimal position to update its own speed V i k and position to find the optimal solution, as shown in formula (14) and formula (15).

[0055]

[0056] In the formula, omega is an inertia weight, c1 and c2 are acceleration factors, and r1 and r2 are random numbers distributed in the range of [0, 1].

[0057] The un-broadened gamma energy spectrum in the scintillator detector in the standard calibration well experiment is obtained by using the Monte Carlo simulation, under the preset spectrum feature constraint condition, the error square sum between the measured gamma energy spectrum and the calculated gamma energy spectrum is solved according to the established target function. In order to ensure that the measured energy spectrum and the calculated energy spectrum are in the same order of magnitude, it is necessary to normalize the two in the calculation process. The square sum of the error between the two channels is the adaptability evaluation criterion in the iteration of the particle swarm algorithm. Finally, the optimal gamma energy spectrum broadening coefficient can be obtained when the algorithm converges.

[0058] The present application proposes a kind of pulse neutron logging gamma spectrum broadening coefficient calculation method, and its method flow chart is as Figure 1 When calculating the gamma spectrum broadening coefficient of pulse neutron logging, first, the standard calibration well physical simulation experiment is carried out using logging instrument, and the induced gamma spectrum of neutron is collected in the simulation formation with known composition and structure parameters. Then, the typical element characteristic gamma energy existing in the energy spectrum is determined according to the formation composition, and the energy spectrum feature weight matrix is established based on this. Based on the weighted least square principle, the objective function for solving the broadening coefficient is constructed combined with the established energy spectrum feature weight matrix. Finally, the calculation of gamma spectrum broadening coefficient is realized through group intelligence optimization algorithm.

[0059] Beneficial effects

[0060] Compared with the prior art, the present application has the following advantages: (1) high calculation result precision. The energy spectrum feature weight matrix is constructed using the known energy element characteristic gamma ray in the energy spectrum, and is used as an additional constraint term of the objective function for solving the broadening coefficient. Due to the existence of the additional constraint term, the channel address in the characteristic peak area has higher weight, thereby ensuring that the calculation result of the characteristic peak area has higher coincidence degree with the actual measurement result, which also makes the calculated broadening coefficient have higher precision. (2) Reasonable and stable algorithm design. The objective function is regarded as a high-dimensional optimization problem, and the group intelligence optimization algorithm is used to solve the objective function, the global optimization ability of the algorithm is used to search for the optimal broadening coefficient. The stability of the solving process is ensured by searching according to certain iteration rules. BRIEF DESCRIPTION OF DRAWINGS

[0061] Figure 1A flow chart of a method for calculating a gamma energy spectrum broadening coefficient of a pulsed neutron logging is provided.

[0062] Figure 2 A standard calibration well experimental simulation model schematic diagram is provided in the application example.

[0063] Figure 3 A normalized experimental measurement total spectrum and a calculated total spectrum comparison chart is provided.

[0064] Figure 4 A normalized experimental measurement capture spectrum and a calculated capture spectrum comparison chart is provided. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application is further described in detail below with examples. It should be understood that the specific examples described herein are only used to explain the present application and not to limit the present application.

[0066] Application example:

[0067] In this example, a pulsed neutron logging instrument is used to carry out standard calibration well experiments. The experimental instrument uses a D-T neutron source to emit fast neutrons, which excite the element nuclei in the standard calibration well simulation formation components to release gamma rays, and a scintillator detector is used 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 substance. The filling materials include aluminum (Al), graphite (C), limestone (LS), and fresh water (H2O). The instrument is inserted into a 200mm diameter well filled with fresh water, and the neutron-induced gamma rays are measured.

[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 un-broadened gamma energy spectrum in the scintillation crystal of the detector. The simulation model is shown in Figure 2 The instrument has a diameter of 41mm and a length of 2358mm. The D-T neutron source consists of two parts: an acceleration system and a neutron production target. The instrument has three scintillator detectors with different source-to-detector distances, 29cm, 59cm, and 91cm, respectively. There is a tungsten shield between the source and the near detector. The far and near detectors both use cylindrical LaBr3 crystals with sizes of 27.5mm x 152mm and 27.5mm x 38mm (diameter x length), respectively. The ultra-far detector uses a NaI crystal with a size of 27mm x 152mm. The ultra-far detector has the largest source-to-detector distance, so it is mainly used to collect natural gamma rays, rather than neutron-induced gamma rays. During the experiment, considering the influence of radioactive statistical fluctuations in gamma ray energy spectrum measurement, the energy spectrum collected by the near source distance detector is selected to verify the proposed method.

[0069] According to the nuclear reaction mechanism between fast neutrons and atomic nuclei, both inelastic scattering and radiative capture nuclear reactions can generate secondary gamma rays. A pulsed neutron logging instrument can measure inelastic gamma rays and capture gamma rays by using a special measurement timing. The D-T neutron source of the instrument can periodically emit neutrons with an energy of 14 MeV. A complete measurement cycle is 20 ms, which is composed of 200 sub-cycles of 100 μs. The neutron source emits neutrons in the first 40 μs of each sub-cycle and does not work in the following 60 μs. The gamma rays measured and recorded in the burst stage of the pulsed neutron source are mainly inelastic gamma rays, but also contain a certain amount of capture gamma rays. The gamma rays collected in the period when the neutron source stops working are capture gamma rays. Then, the energy spectra recorded in all sub-cycles are accumulated to obtain the final energy spectrum. The gamma spectrum obtained in the burst stage of the pulsed neutron source is called the total spectrum, which contains inelastic gamma rays and capture gamma rays. The gamma spectrum obtained in the period when the pulsed neutron source stops working is called the capture spectrum, which only contains capture gamma rays.

[0070] The two kinds of gamma spectra measured in four standard calibration wells are processed by using the pulsed neutron logging gamma spectrum broadening coefficient calculation method proposed in the present application. The total spectrum processing results are shown in Figure 3 It can be seen that there is an obvious characteristic peak with an energy of 2.23 MeV in each total spectrum, which is generated by the radiative 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 elements 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 characteristic weight matrix and set the additional weight. The total spectrum and the capture spectrum measured in the four standard calibration wells are used to establish the objective function to solve the broadening coefficient of the gamma spectrum. The calculation results are a=0.0253, b=0.0048, and c=52.562.

[0071] The root mean square error (RMSE) and the correlation coefficient (R-Square) between the selected characteristic peaks in each total spectrum, the normalized experimental gamma spectrum and the normalized calculated gamma spectrum are shown in Table 1. Some obvious characteristic peaks are selected in the measured gamma spectrum in each standard calibration well to set the energy spectrum characteristic weight matrix. The results show that the experimental spectrum and the calculated spectrum have good correlation. The broadening coefficient calculated by using the method proposed in the present application makes the correlation coefficient between the experimental measured gamma spectrum and the calculated gamma spectrum all above 0.99, and the average RMSE is only 4.22e-4.

[0072] Similarly, the comparison between the normalized experimental capture gamma spectrum and the normalized calculated capture gamma spectrum is shown in Figure 4The results of the capture gamma spectrum processing in the four standard calibration wells are shown in Table 2. The results show that the calculated gamma spectrum has good correlation with the measured gamma spectrum. The correlation coefficient is greater than 0.99, and the average RMSE is 4.03e-4. The processing results of the capture gamma spectrum also prove the adaptability of the application in the calculation of the gamma spectrum broadening coefficient.

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

[0074]

[0075] Table 2 Comparison of normalized experimental measurement capture spectrum and calculated capture spectrum

[0076]

Claims

1.A method for calculating a gamma-ray energy spectrum broadening factor of a pulsed neutron logging, characterized in that The method comprises the following steps: Step 1: carry out 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, in 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 fluctuation, and the accumulated average spectrum obtained is taken 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 jth count of the ith measured energy spectrum, N is the number of gamma energy spectra collected, is the jth count of the cumulative average spectrum; Step 2: establish a Monte Carlo simulation model according to the standard calibration well experimental conditions and simulate the unspread incident gamma energy spectrum, a Monte Carlo numerical simulation model is established according to the composition and structure parameters of the standard calibration well in the calibration well experiment and the specific parameters of the pulsed neutron logging instrument in the experiment, and the unspread gamma energy spectrum measured by the scintillator detector of the logging instrument in the standard calibration well experiment is simulated by using the Monte Carlo numerical simulation technology, although the response process of the scintillator detector cannot be avoided in actual measurement, but the response of the scintillator detector can be eliminated by numerical simulation method; Step 3: establish a spectrum feature weight matrix based on the characteristic gamma ray energy of the incident element, since the composition in the standard calibration well is known, the typical characteristic peak in the gamma energy spectrum is determined according to the characteristic gamma energy of the element, in theory, the spread coefficient determines the peak width of the characteristic peak, and the spreaded gamma energy spectrum is required to have a high degree of coincidence with the actual measured spectrum in the range of the characteristic peak, therefore, higher weight is added to the channel address in the range of the characteristic peak, and the additional weight is realized by the spectrum feature weight matrix W1, which can be expressed as: In the formula, n is the number of selected characteristic peaks, and m is the length of the gamma spectrum. For the region containing the nth characteristic peak, the pth peak k The additional weights of each channel are determined by the FWHM (Front-Wide Harrow) of the characteristic peaks in the energy spectrum. When designing this matrix, only channel address data within the FWHM of the selected peak regions have additional weights. Therefore, a nonlinear weighting scheme based on the Sigmoid function is designed to calculate the additional weight values ​​for each channel address within the FWHM. This weighting scheme can be expressed as: wherein w ip is the additional weight value of the pth track in the ith peak region, d ip is the distance between the peak track address in the ith peak region and the pth track in the ith peak region. Step 4: construct an objective function based on the weighted least square method and the spectrum feature weight matrix, the main part of the objective function is the square sum of the channel error between the calculated energy spectrum and the measured energy spectrum, in order to ensure that each channel is calculated with equal precision, the weight corresponding to each channel in the weighted least square method is: In the formula, u1u m The least square method and the characteristic weight matrix of the gamma spectrum are used to construct the objective function for calculating the spread coefficient. where s i and u i are the calculated broadened and the actually measured spectrum counts of the ith channel, λ is the weighting factor, reflecting the importance of the additional constraints constructed by the spectrum feature weight matrix in the whole objective function, n is the number of selected feature peaks, p jk is the number of channel positions in the jth feature peak region, 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 region. The objective function (5) can be written in matrix form by combining the weighted least squares weight matrix W2 and the spectrum feature weight matrix W1: F(s) = (u - s) T W2(u - s) + λ(u - s) T W1 T W1(u - s) (6) Since the spreaded energy spectrum can be calculated according to 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: F(H) = (u - Hx) T W2(u - Hx) + λ(u - Hx) T W1 T W1(u - Hx) (7) The optimal Gaussian response matrix is calculated to obtain the gamma energy spectrum spread coefficient; Step 5: solve the optimal spread coefficient by using swarm intelligence optimization algorithm, according to the spread mechanism of the instrument scintillator detector, there is a strong correlation between the elements in the Gaussian response matrix H, therefore, the matrix equation shown in formula (7) can be regarded as a function of the spread coefficients a, b and c, and the calculation process of the spread coefficient is regarded as a high-dimensional constrained optimization problem, which is represented as: In the formula, M is the number of standard calibration well experiments, and f is the function i (a, b, c) is the objective function established by the measured energy spectrum of the i-th standard calibration well experiment, and a typical swarm intelligence algorithm, particle swarm optimization, is used to realize the global optimal solution calculation of the objective function, so as to obtain the optimal gamma energy spectrum broadening coefficient. The particle swarm optimization firstly initializes a group of particles as potential solutions, and the fitness of the solution is determined by the objective function. In the k-th iteration, the i-th particle updates its own speed V i k and the global optimal position to update its own speed V i k and position to find the optimal solution, as shown in formula (9) and formula (10): In the formula, ω is the inertial weight, c1 and c2 are the acceleration factors, r1 and r2 are random numbers distributed in the range of [0, 1], the un-broadened gamma spectrum in the scintillator detector in the standard calibration well experiment is obtained by using the Monte Carlo simulation, under the preset spectrum feature constraint condition, the error square sum between the measured gamma spectrum and the calculated gamma spectrum is solved according to the established target function, in order to ensure that the measured spectrum and the calculated spectrum are in the same order of magnitude, it is necessary to normalize the two in the calculation process, the square sum of the error between the two channels is the adaptability evaluation criterion in the particle swarm algorithm iteration, and finally the optimal gamma spectrum broadening coefficient can be obtained after the algorithm converges.

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