A solar high-energy particle source region injection profile inversion fitting method, fitting device, storage medium and terminal

Abstract

The application provides a solar energetic particle (SEP) source region injection profile inversion fitting method, a fitting device, a storage medium and a terminal. The inversion fitting method provided by the application comprises constructing an inversion fitting equation. The inversion fitting equation uniformly describes the symmetric and asymmetric source region injection profile by introducing a continuously adjustable logarithmic Gaussian function with a shape parameter. The function is embedded in a physical framework that comprehensively considers the energy-dependent propagation delay and the instrument limited energy channel integration. The inversion fitting method provided by the application can improve the inversion accuracy and universality of the source region injection profile of various SEP events, and provides a key and reliable source parameter input for space weather physical prediction.

Description

Technical Field

[0001] This invention relates to the field of space environment exploration data processing technology, specifically to an inversion fitting method, fitting device, storage medium, and terminal for an injection profile of a solar high-energy particle source region. Background Technology

[0002] Solar energetic particle (SEP) events are direct manifestations of the rapid energy release in eruptive phenomena such as solar flares and coronal mass ejections. They typically contain protons, electrons, and heavy ions with energies ranging from tens of keV to GeV. These events are not only key probes for revealing the physical processes of solar eruptions but also major sources of space weather hazards that affect the near-Earth space environment, threaten the on-orbit safety of spacecraft, and endanger the health of astronauts. Therefore, accurately diagnosing the underlying physical processes of SEP events is of irreplaceable value for ensuring the safety of space activities and understanding the Sun-Earth space relationship.

[0003] The SEP time profile observed at a single point in the heliosphere is essentially the result of multiple physical processes, including particle acceleration, injection, and subsequent propagation and scattering in interplanetary space. On one hand, particle propagation is significantly influenced by the solar wind background magnetic field, irregular turbulence, and pitch angle scattering. On the other hand, the onset time, enhancement rate, decay, and duration of the observed profile largely preserve key information about the particle injection history in the solar source region. Therefore, the SEP time profile is not only a tracer of propagation effects but also provides important clues for retrieving the particle release process in the solar source region. Accurately characterizing and retrieving the ion injection profile of the solar source region is crucial for understanding the acceleration mechanism of SEP (such as the relative contributions of flare acceleration and CME shock acceleration), the timescale of particle release, and the physical relationship between SEP events and solar eruptive activity. Furthermore, reliable source region injection models can help improve the predictive ability of SEP events, thus serving space weather forecasting.

[0004] However, to extract pure source injection information from mixed observation signals, current mainstream inversion methods include velocity dispersion analysis (VDA). This method assumes that particles of different energies are released at the same time and have the same propagation path length in the source region. Linear fitting yields the release time and propagation distance of ions. However, despite its simplicity, this method has several limitations: ① Overly idealistic assumptions; the release times of particles with different energies are often inconsistent, and the VDA assumption cannot accurately reflect the energy dependence of the release. ② This method fails to fully consider the instrument's energy response to particles; the observation energy channel usually has a certain broadening, but a representative energy must be assumed in VDA fitting, which may lead to instrument bias. Subsequent studies using symmetric trigonometric function-based injection profile fitting revealed that the release times of particles with different energies are not entirely the same, indicating that the assumption of a fixed release time is not always valid. ③ However, this method is still mainly applicable to time-symmetric events, with limited ability to describe complex or asymmetric injection processes, severely limiting its universality. In summary, current methods either rely on simplified models that deviate from physical reality or are limited by insufficient mathematical expression capabilities, failing to consistently, accurately, and universally reflect the injection profile of the solar source region from single-point in-situ observation data. Summary of the Invention

[0005] In view of the problem that the existing technology cannot consistently reflect the injection profile of the solar source region from single-point in-situ observation data, this application provides an inversion fitting method and apparatus for the injection profile of the solar high-energy particle source region, which can consistently invert the injection time structure of the solar source region while taking into account the propagation delay dependent on particle energy.

[0006] To achieve the above and other related objectives, the present invention provides, in one aspect, an inversion fitting method for injection profiles of solar high-energy particle source regions, comprising:

[0007] Construct an inversion fitting equation, which is as follows:

[0008] (1);

[0009] Acquire target solar high-energy particle SEP events within a preset energy range [E min E max Within [the data set], N sets of observational data points showing the change of electron flux at various energies over time. The N sets of observation data points follow a functional distribution. ;

[0010] From the N sets of observation data points, n sets of data points within the time period from the initial rise of electron flux to the end of the rapid decay phase are selected as the fitting input data;

[0011] The fitting input data is input into the inversion fitting equation to obtain the fitting result;

[0012] Where t is time, Let be the theoretical particle flux at time t. Let y0 be the shape function, and y0 be the background flux of the instrument. and Here, A represents the lower and upper limits of the energy range used for fitting, E represents the particle energy, β represents the spectral index of the particle energy spectrum within the stated energy range, and L represents the propagation path length of the particle from the solar source region to the observation point. Let t be the particle velocity corresponding to energy E. p The time of peak particle injection in the solar source region is represented by Δ, the duration of particle injection in the solar source region is represented by σ, and σ is the asymmetry controlling the shape of the injection profile. Let m be a vector of m parameters, where m is the number of parameters to be fitted, and m=5.

[0013] Optionally, the shape function The standard logarithmic Gaussian function is obtained by shifting and normalizing. The formula is as follows:

[0014] (2).

[0015] Optionally, inputting the fitting input data into the inversion fitting equation to obtain the fitting result further includes:

[0016] Calculate the chi-square statistic of the residuals of the n sets of data points. The calculation is shown in the following formula:

[0017] (3);

[0018] According to the above formula (3), the minimum is obtained. The corresponding parameter is ;

[0019] Where m is the number of parameters to be fitted. , , , , yes , , Standard deviation, x i y i , z i These are the observations of the first independent variable, the second independent variable, and the dependent variable for i data points. This represents the theoretically calculated value of the inversion fitting equation.

[0020] Alternatively, the minimum can be obtained according to the above formula (3). The corresponding parameters also include the following steps:

[0021] Substitute the N sets of data points into the formula (3) for iterative calculation;

[0022] Approximation is achieved by using the gradient information obtained in each iteration. The positive definite Hessian matrix;

[0023] In the initial value Perform a linear search along the descent direction in the vicinity, stopping when a minimum point is encountered. The parameters at this point are... ;

[0024] The uncertainty of the parameter is: ,in It is a Hessian matrix.

[0025] This application also provides an inversion fitting device for the injection profile of a solar high-energy particle source region, comprising:

[0026] The equation construction module is used to construct the inversion fitting equation, which is as follows:

[0027] (1);

[0028] The data acquisition module acquires the target solar high-energy particle SEP event within a preset energy range [E]. min E max Within [the data set], N sets of observational data points showing the change of electron flux at various energies over time. The N sets of observation data points follow a functional distribution. ;

[0029] The data selection module selects a portion of the data from the N sets of observation data points acquired by the data acquisition module, from the initial rise of the electron flux to the end of the rapid decay phase, as the fitting input data.

[0030] The data fitting module takes the fitting input data selected by the data selection module and substitutes it into the inversion fitting equation constructed by the equation construction module to obtain the fitting result.

[0031] The output module acquires and outputs the fitting results from the data fitting module.

[0032] Where t is time, Let yt be the theoretical particle flux at time t, and y0 be the background flux of the instrument. and Here, A represents the lower and upper limits of the energy range used for fitting, E represents the particle energy, β represents the spectral index of the particle energy spectrum within the stated energy range, and L represents the propagation path length of the particle from the solar source region to the observation point. Let t be the particle velocity corresponding to energy E.p The time of peak particle injection in the solar source region is represented by Δ, the duration of particle injection in the solar source region is represented by σ, and the asymmetry of the injection profile shape is controlled by σ.

[0033] Optionally, the data fitting module further includes a calculation unit, which is used to calculate the chi-square statistic of the residuals of the N sets of observed data points. The chi-square statistic is shown in the following formula:

[0034] (4);

[0035] The minimum value is obtained according to the above formula (4). The corresponding parameter is ;in, , , yes , The standard deviation.

[0036] Another aspect of this application provides a storage medium storing a computer program that, when executed by a processor, implements the inversion fitting method for the injection profile of the solar high-energy particle source region as described in any one of claims 1 to 4.

[0037] Another aspect of this application provides a terminal, which includes: a processor and a memory;

[0038] The memory is used to store computer programs;

[0039] The processor is used to execute the computer program stored in the memory, so that the terminal performs the inversion fitting method for the injection profile of the solar high-energy particle source region as described in any one of claims 1 to 4.

[0040] As described above, the inversion fitting method and inversion fitting device for the injection profile of solar high-energy particle source region provided by the present invention have at least the following beneficial technical effects:

[0041] The inversion fitting method for the injection profile of solar high-energy particle source regions in this invention constructs an inversion fitting equation that uses a log-Gaussian function with continuously adjustable shape parameter σ as the injection profile model, replacing the fixed symmetric trigonometric function. This model can describe the more common asymmetric injection process of rapid rise and slow decay, and has universality. Furthermore, it incorporates the concept of energy propagation delay and simulates the finite-channel response of a real detector by integrating over the energy range. Attached Figure Description

[0042] Figure 1 The flowchart shown is a process for inverting and fitting the injection profile of the solar high-energy particle source region provided in Example 1.

[0043] Figure 2 The diagram shown is a schematic representation of the inversion fitting equation displayed on a linear scale, as provided in this embodiment.

[0044] Figure 3 The diagram shown is a schematic representation of the inversion fitting equation displayed on a logarithmic scale as provided in this embodiment.

[0045] Figure 4 The diagram shown is a schematic representation of the fitting results displayed on a linear scale, as provided in this embodiment.

[0046] Figure 5 The diagram shown is a logarithmic scale representation of the fitting results provided in this embodiment. Detailed Implementation

[0047] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0048] It should be noted that the illustrations provided in this embodiment are only schematic representations of the basic concept of the present invention. Although the illustrations only show components related to the present invention and are not drawn according to the actual number, shape and size of the components, the shape, quantity, positional relationship and proportion of each component can be arbitrarily changed under the premise of realizing the technical solution of this invention, and the layout of the components may also be more complex.

[0049] Example 1

[0050] This embodiment provides an inversion fitting method for the injection profile of a solar high-energy particle source region, such as... Figure 1 The diagram shown is a flowchart of an inversion fitting method for an injection profile of a solar high-energy particle source region provided in this embodiment.

[0051] S1: Construct the inversion fitting equation, which is as follows:

[0052] (1);

[0053] S2: Obtain N sets of observational data points on the electron flux at each energy level within a preset energy range [Emin, Emax] for the target solar high-energy particle SEP event as a function of time. The N sets of observation data points follow a functional distribution. ;

[0054] S3: Select n sets of data from the N sets of observation data points during the period from the initial rise of electron flux to the end of the rapid decay phase as the fitting input data;

[0055] S4: Input the fitting input data into the inversion fitting equation to obtain the fitting result;

[0056] Where t represents time, and J(t) represents the theoretical particle flux at time t calculated by the inversion fitting equation. Let y0 be the shape function, representing the instrument's background flux. and Let A and E represent the lower and upper limits of the energy range used for fitting, respectively. Let A characterize the overall intensity or amplitude of the injection event, E represent the particle energy, and β represent the energy level obtained by fitting the in-situ observed energy spectrum at that energy level, which is the energy range [E]. min E max The energy spectrum slope (spectral index) within the range, where L represents the propagation path length of the particle from the solar source region to the observation instrument. t represents the velocity of a particle with energy E. p Δ represents the peak moment of the inverted particle injection process in the solar source region, Δ represents the main duration of the inverted particle injection process in the solar source region, σ represents the asymmetry of the core shape function controlling the model, and its value determines whether the injection time profile is symmetrical or asymmetrical. n is the number of data points. Let N be a vector of m parameters, where m is the number of parameters to be fitted (m=5), N is the total number of all observed data points, and n is the number of data points used for fitting.

[0057] Generally speaking, and Based on the energy spectrum characteristics of the SEP event and the inversion target, the lower and upper limits of the selected effective energy range are determined. This range should be within the effective detection capability of the observation instrument. In this embodiment, and These represent the lowest and highest energies measured by the instrument, respectively. Specifically, [E min E max [30 KeV, 50 KeV].

[0058] In functional relations In this example, x and y represent the independent variables of the data points. In this embodiment, the independent variables are time t and energy E; z represents the dependent variable. In this embodiment, the dependent variable is the flux observation value. The parameter vector described in this method... Specifically, it includes the physical parameters of the source region 5: y0, A, t p Vectors of , Δ, and σ.

[0059] Specifically, shape function The standard logarithmic Gaussian function is obtained by shifting and normalizing. The formula is as follows:

[0060] (2)

[0061] Specifically, S1: Constructing the inversion fitting equation includes the following steps: The inversion fitting equation is as follows:

[0062] (1);

[0063] Shape parameters A continuously adjustable shape function is used to characterize the symmetrical and asymmetrical morphology of the injection profile in the source region. Characterizing the number of particles received at observation time t, relative to the peak injection time t in the source region. p Energy-dependent propagation delay deducted The relative time afterwards.

[0064] Constructing the inversion fitting equation includes the following steps:

[0065] S11: The standard logarithmic Gaussian function is selected as the basis for constructing the inversion fitting equation. The standard logarithmic Gaussian function is:

[0066] (3);

[0067] The standard logarithmic Gaussian function in When the maximum value is obtained .

[0068] Because in order to uniformly describe symmetric and asymmetric injection profiles, the standard form of the logarithmic Gaussian function has the property of describing a right-skewed distribution (rapid rise, slow decay).

[0069] S12: The peak value of function (3) is shifted to x=0 by variable substitution;

[0070] Specifically, through variable substitution: ,Will Substituting the variable x in formula (3), we get :

[0071] (4);

[0072] The function changes with the parameters It fluctuates with the change of x.

[0073] S13: Normalize the maximum value of function (4) to 1 and eliminate the parameter. ;

[0074] Specifically, the function Multiply the whole by the normalization factor In this process, the position parameter μ is eliminated, and the final function form is controlled only by a single shape parameter σ, resulting in the shape function. :

[0075] (5);

[0076] Furthermore, supplement the shape function. Domain: when hour, =0.

[0077] The complete formula for the shape function is:

[0078] (2);

[0079] The function describes the relative profile of the source region particle injection rate over time, and consists of only one parameter. Simultaneously control the width and asymmetry of the function, and when As → 0, the function approaches a symmetric Gaussian form; when When the value is greater than 0, the function exhibits an asymmetric right-skewed shape.

[0080] S14: Form the complete inversion fitting equation;

[0081] Specifically, the modified shape function described above As the core formula describing the time profile of source region injection, it is embedded in the consideration of energy-dependent propagation delay. In the physical framework of the instrument energy channel integral ∫, and add the background term y0.

[0082] S141: Suppose a particle in the source region is at t in The particle is injected at a constant speed. If the flight distance L is to reach the observation point, then the propagation time is... This particle will be at t=t in + A particle is observed at time t; conversely, a particle observed at time t should have been injected into its source region at time t. in =t- .

[0083] Among them, particle velocity Based on the relativistic energy-velocity relation, the particle velocity is determined. The expression is:

[0084] (6);

[0085] Where C is the speed of light and m0 is the rest mass of a high-energy particle from the sun.

[0086] Shape function This describes the change in source region injection rate over time. Its independent variable, x, is the dimensionless relative time of the source region. The relative time of the source region is defined as: (Source region injection time - peak injection time) / duration. From the previous step, we know: Source region injection time = t - Therefore, the shape function independent variable .

[0087] Ensure that when the observation time t satisfies When x=0, the function Take the maximum value, which corresponds to the particles injected from the peak moment of the source region.

[0088] S142: Consider the instrument's response capability.

[0089] The detector measures not a single particle with a single energy E, but an energy range [E]. min E max The total flux within [E]. At energy E, the number of injected particles per unit energy interval is proportional to E. -β (Obeying a power-law energy spectrum); these particles move at a rate It is injected. Therefore, the observed total flux needs to be integrated over the entire channel range:

[0090] Flux ∝

[0091] coefficient Used to normalize and calibrate the integral results, so that A directly represents the intensity of the event.

[0092] S143: Add a background item. Characterize the instrument background flux. The inversion fitting equation can then be obtained.

[0093] (1);

[0094] By subtracting the energy-dependent propagation delay, Describe the release process of the solar source region itself; add The parameters allow the model to separate the signal and background simultaneously during fitting, thereby more accurately reproducing the true form of the source region process and improving the reliability of the fitting method.

[0095] like Figure 2 As shown, this is a schematic diagram of the inversion fitting equation presented in a linear scale according to this embodiment; as... Figure 3As shown, this is a schematic diagram of the inversion fitting equation presented on a logarithmic scale according to this embodiment. Figure 2 and Figure 3 The horizontal axis represents time: 00:30 to 00:35 on October 17, 2025 (UT). With a 5-minute time window, the 5-minute window covers the core stages of a simulated SEP event from its onset, peak, to early decay, demonstrating the fitting ability of the fitted equation to fit transient and rapid processes. Figure 2 and Figure 3 The vertical axis represents particle flux. Figure 2 Display the main temporal structure, peak positions, and shapes of events using a linear scale; Figure 3 Highlight details of low-flux regions (such as the initial rise and decay tail) on a logarithmic scale.

[0096] This simulation uses the solar high-energy electron injection event at 00:00:00 UTC on October 17, 2025 as the simulation data. Specific parameters include: source region parameters; injection peak time t. p The event duration is 00:00:00, the characteristic duration is Δ = 50 s, the asymmetry is σ = 0.5, and the event amplitude is A = 2 × 10⁻⁶. 7 Propagation and spectral parameters: propagation path length L = 1.2 AU, spectral index β = 3, simulated energy channel [E min E max ] = [23 keV, 30 keV], Instrument background flux y 0= 15(cm²·sr·s·keV)⁻¹, particle rest mass m0.

[0097] Figure 2 and Figure 3 The cluster of red dots and lines represents the preset energy range [E]. min E max Within [the image], the theoretical differential flux time profiles corresponding to a series of particles with different energies are shown. For each red dotted line, the integrand within the integral sign of the fitting equation is represented as follows: Its physical meaning is: a particle with energy E experiences a peak time t in the solar source region. p After the injection process, defined by duration Δ and asymmetry σ, and following the energy-related propagation delay... The flux variation over time upon arrival at the observation point. The overall morphology of the red dotted cluster is uniformly controlled by the source region parameter σ.

[0098] Figure 2 and Figure 3 The black lines in the image represent the preset energy range [E]. min E maxWithin the inversion fitting equation (1), the theoretical total flux is obtained by integrating multiple red data representing the physical characteristics of the source region. Through integration, the inversion fitting equation can integrate the energy-dependent propagation delay, power-law energy spectrum, and detector finite channel integral into a unified physical-mathematical framework, enabling the theoretical prediction to be directly and accurately compared with the original observation data.

[0099] Step S2: Obtain N sets of observational data points showing the change of electron flux at each energy level over time within a preset energy range [Emin, Emax] for the target solar high-energy particle SEP event. The N sets of observation data points follow a functional distribution. .

[0100] Specifically, such as Figure 4 and Figure 5 As shown, Figure 4 The diagram shown is a schematic representation of the fitting results displayed on a linear scale, as provided in this embodiment. Figure 5 The diagram shown is a logarithmic scale representation of the fitting results provided in this embodiment. Figure 4 and Figure 5 The horizontal axis represents Universal Time (UT), showing the time period from 14:20 to 15:00 on October 20, 2002. The vertical axis represents particle flux. Figure 5 The vertical axis is a logarithmic scale, which can more clearly show the details of flux changes across several orders of magnitude.

[0101] This embodiment uses an electron event observed by the Wind satellite on October 20, 2002, as an example. The energy range is selected as [30 keV, 50 keV], which corresponds to a specific energy channel of the instrument. The black line represents the observation data, with the center energy of this energy channel being 40 keV, and its effective detection energy range covering approximately [30 keV, 50 keV]. Therefore, the black curve represents the change in particle integral flux of the detector over time within this complete energy range; the blue data points represent the fitting input data selected from the complete observation data points for inversion fitting, specifically the data from the initial rise to the end of rapid decay; the red line represents the fitting data obtained using the fitting method provided in this application. Specifically, from the obtained N sets of observation data points ( In, where x i y i , z i These are the first independent variable observation, the second independent variable observation, and the dependent variable observation for i data points; in this embodiment, x i Represents the observation time t i ;y i Represents particle energy; z i Observations representing flux .

[0102] Step S3: Select n sets of data points from the N sets of observation data points, from the initial rise of electron flux to the end of the rapid decay phase, as the fitting input data.

[0103] Specifically, the purpose of selecting n sets of data points from N sets of observation data points as the fitting input data is to retain, as far as possible, the signal directly dominated by the solar source region injection process, while minimizing the interference of the signal dominated by complex interplanetary propagation effects. Therefore, the target period for the fitting input data includes the period from the initial rise to the end of the rapid decay. During this stage, the dramatic changes in particle flux (rapid increase and rapid decrease) are mainly driven by the instantaneous processes of particle acceleration and release in the source region. Inverting the data during this stage can most directly obtain the source region parameter t. p Constraints of Δ and σ.

[0104] Specifically, the data filtering steps include:

[0105] S31: Determine the time window: Identify the moment when flux begins to rise significantly and the end of the rapid decline phase through algorithms.

[0106] S32: Identify and identify anomalous mutation points: Within the initial selection window, detect and remove outliers from the flux time series. Optionally, the rate of change of flux within the local time window (first-order difference) can be calculated. When the rate of change of flux at a certain data point (such as the rate of decrease) deviates significantly from the trend formed by its preceding and following adjacent data points, the point is determined to be a mutation data that needs to be removed.

[0107] The fitting input data also includes: particle rest mass m0, which in this embodiment uses electron mass as an example; and the propagation path length L from the particle solar source region to the observation satellite, which in this embodiment is based on a typical estimate of the satellite orbit, L=1.2AU. In this embodiment, the inversion energy range is selected as [30 keV, 50 keV], and the spectral index β=3 for this range.

[0108] Step S4: Input the fitting input data into the inversion fitting equation to obtain the fitting result.

[0109] Obtaining the fitting results specifically refers to solving the problem using an optimization algorithm to obtain a set of optimal source region physical parameters that achieve the best match between the inversion fitting model and the inversion input data. These parameters include background flux y0, event amplitude A, and peak injection time t in the source region. p The data includes the injection duration Δ and the profile asymmetry σ. This set of data defines a mathematically well-defined and physically interpretable particle injection time profile in the solar source region. These parameters represent the quantitative inversion results of the injection profile in the source region of solar high-energy particle events.

[0110] For illustrative purposes, this embodiment uses the least squares method to fit and obtain the optimal parameters. Specifically, it includes the following steps:

[0111] S41: Select n sets of data points from N sets of observed data points as inversion fitting data, and calculate the chi-square statistic of the residuals of the n sets of data points. The calculation is shown in the following formula:

[0112] (3);

[0113] Where n is the number of input data points to be fitted, and m is the number of parameters to be fitted. , , , , yes , , Standard deviation, x i y i , z i These are the observations of the first independent variable, the second independent variable, and the dependent variable for i data points. This represents the theoretically calculated value of the inversion fitting equation.

[0114] S42: The BFGS algorithm from the Broyden family of quasi-Newton methods is used to evaluate the objective function. Minimize.

[0115] When the chi-square statistic of the above residuals The minimum value is considered the optimal fit result, and the search for the minimum value in the parameter space is performed. That set of parameters is Specifically, the gradient information calculated during the iteration process is used to approximate the gradient. The Hessian matrix, and the parameter vector a at initial values. (initial value after k iterations) Perform a linear search in the descent direction near the point until convergence to the minimum point, at which point the parameter is... .

[0116] Step S43: The parameter uncertainty is given by the Hessian matrix. .

[0117] in Let be the i-th diagonal element of the Hessian matrix, and the uncertainty of the parameter is given by [the parameter is missing here]. Scope of credibility: [ , The smaller the uncertainty, the better the fitted parameters. The more accurate.

[0118] Applying the above method to invert the event of October 20, 2002, the optimal source region physical parameters are finally obtained as follows:

[0119] Peak time t p : 2002-10-20 / 14:15:34; Duration Δ: 291 seconds; Asymmetry σ: 0.37; Amplitude A: 2.87×10 3 Background y0: 1.13×10⁻²(cm²·sr·s·keV)⁻¹;

[0120] like Figure 4 and Figure 5 As shown, the fitted theoretical curve closely matches the observed data during the main phase of the event. Figure 4 In the linear scaling plot, the fitted curve accurately reproduces the rapid rise and peak structure of the flux; Figure 5 In the logarithmic scaling plot, the fitted curve closely follows the data points, accurately depicting the rising and falling phases of flux across multiple orders of magnitude, with no systematic deviations observed, especially in the lower flux region. The parameter σ = 0.37 > 0 clearly quantifies the asymmetry of the event injection profile, demonstrating the ability of this method to surpass traditional symmetric models and characterize real physical processes. The uncertainties of all parameters are within a reasonable range, indicating that the inversion results are robust and reliable.

[0121] Example 2

[0122] This embodiment provides an inversion fitting device for the injection profile of a solar high-energy particle source region. This fitting device is used to realize the inversion fitting process of the injection profile of a solar high-energy particle source region. The fitting device includes:

[0123] The equation construction module is used to construct the inversion fitting equation, which is as follows:

[0124] (1);

[0125] The data acquisition module acquires N sets of observational data points showing the change of electron flux at each energy level over time within a preset energy range [Emin, Emax] for the target solar high-energy particle SEP event. The N sets of observation data points follow a functional distribution. ;

[0126] The data selection and parameter extraction module selects a portion of the data from the N sets of observation data points obtained by the data acquisition module, within the time period from the initial rise of the electron flux to the end of the rapid decay phase, as the fitting input data.

[0127] The data fitting module takes the fitting input data selected by the data selection module and substitutes it into the inversion fitting equation constructed by the equation construction module to obtain the fitting result.

[0128] The output module acquires and outputs the fitting results from the data fitting module.

[0129] Where t is time, Let yt be the theoretical particle flux at time t, and y0 be the background flux of the instrument. and Here, A represents the lower and upper limits of the energy range used for fitting, E represents the particle energy, β represents the spectral index of the particle energy spectrum within the stated energy range, and L represents the propagation path length of the particle from the solar source region to the observation point. Let t be the particle velocity corresponding to energy E. p The time of peak particle injection in the solar source region is represented by Δ, the duration of particle injection in the solar source region is represented by σ, and the asymmetry of the injection profile shape is controlled by σ.

[0130] Specifically, the equation construction module includes an equation construction unit and a parameter initialization unit. The equation construction unit is used to generate the inversion fitting equation, and the parameter initialization unit is used to receive the preset parameters required for the operation of the inversion fitting device. The preset parameters include: particle mass m0, propagation path length L, inversion energy range [Emin, Emax], energy spectrum index β, and the source region parameters to be determined (y0, A, t). p , Δ, σ).

[0131] Specifically, the data acquisition module interfaces with external data sources (such as satellite data warehouses and real-time data streams) to acquire observation data input. Specifically, the data selection module processes the raw observation data, including data calibration and the removal of outlier data.

[0132] Specifically, the data fitting module further includes a calculation unit, which is used to calculate the chi-square statistic of the residuals of the n sets of data points. The formula for the chi-square statistic is as follows:

[0133] (3);

[0134] According to the above formula (3), the minimum is obtained. The corresponding parameter is ;

[0135] Where m is the number of parameters to be fitted. , , , , yes , , Standard deviation, x i y i , z i These are the observations of the first independent variable, the second independent variable, and the dependent variable for i data points. This represents the theoretically calculated value of the inversion fitting equation.

[0136] Specifically, the output module organizes and visualizes the fitting results. For example... Figure 4 and Figure 5 As shown, the observed data and the inversion fitting data are automatically plotted into curves for intuitive display.

[0137] The specific fitting method of the inversion fitting device for the solar high-energy particle source region injection profile provided in this embodiment can be found in the detailed description of Embodiment 1, and will not be repeated in this embodiment.

[0138] Example 3

[0139] This embodiment provides a storage medium on which a computer program is stored. When the computer program is executed by a processor, it implements the inversion fitting method for the injection profile of the solar high-energy particle source region provided in Embodiment 1.

[0140] This embodiment also provides a terminal, which includes: a processor and a memory; the memory is used to store a computer program; the processor is used to execute the computer program stored in the memory, so that the terminal executes the inversion fitting method for the injection profile of the high-energy particle source region of the sun provided in Embodiment 1.

[0141] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in the present invention should still be covered by the claims of the present invention.

Claims

1. A method for inverting and fitting the injection profile of a solar high-energy particle source region, characterized in that, include: Construct an inversion fitting equation, which is as follows: （1）； Acquire target solar high-energy particle SEP events within a preset energy range [E min E max Within [the data set], N sets of observational data points showing the change of electron flux at various energies over time. The N sets of observation data points follow a functional distribution. ; From the N sets of observation data points, n sets of data points within the time period from the initial rise of electron flux to the end of the rapid decay phase are selected as the fitting input data; The fitting input data is input into the inversion fitting equation to obtain the fitting result; Where t is time, Let be the theoretical particle flux at time t. Let y0 be the shape function, and y0 be the background flux of the instrument. and Here, A represents the lower and upper limits of the energy range used for fitting, E represents the particle energy, β represents the particle energy spectrum index within the energy range, and L represents the propagation path length of the particle from the solar source region to the observation point. Let t be the particle velocity corresponding to energy E. p The time of peak particle injection in the solar source region is represented by Δ, the duration of particle injection in the solar source region is represented by σ, and σ is the asymmetry controlling the shape of the injection profile. Let m be a vector of m parameters, where m is the number of parameters to be fitted, and m=5.

2. The inversion fitting method for the injection profile of a solar high-energy particle source region according to claim 1, characterized in that, The shape function The standard logarithmic Gaussian function is obtained by shifting and normalizing. The formula is as follows: （2）。 3. The inversion fitting method for the injection profile of a solar high-energy particle source region according to claim 1, characterized in that, The process of inputting the fitting input data into the inversion fitting equation to obtain the fitting result further includes: Calculate the chi-square statistic of the residuals of the n sets of data points. The calculation is shown in the following formula: （3）； The minimum value is obtained according to the above formula (3). The corresponding parameter is ; Where m is the number of parameters to be fitted. , , , , yes , , Standard deviation, x i y i , z i These are the observations of the first independent variable, the second independent variable, and the dependent variable for i data points. This represents the theoretically calculated value of the inversion fitting equation.

4. The inversion fitting method for the injection profile of a solar high-energy particle source region according to claim 3, characterized in that, The minimum value is obtained according to the above formula (3). The corresponding parameters also include the following steps: Substitute the N sets of data points into the formula (3) for iterative calculation; Approximation is achieved by using the gradient information obtained in each iteration. The positive definite Hessian matrix; In the initial value Perform a linear search along the descent direction in the vicinity, stopping when a minimum point is encountered. The parameters at this point are... ; The uncertainty of the parameter is: ,in It is a Hessian matrix.

5. An inversion and fitting device for injection profiles of solar high-energy particle source regions, characterized in that, include: The equation construction module is used to construct the inversion fitting equation, which is as follows: （1）； The data acquisition module acquires the target solar high-energy particle SEP event within a preset energy range [E]. min E max Within [the data set], N sets of observational data points showing the change of electron flux at various energies over time. The N sets of observation data points follow a functional distribution. ; The data selection module selects a portion of the data from the N sets of observation data points acquired by the data acquisition module, from the initial rise of the electron flux to the end of the rapid decay phase, as the fitting input data. The data fitting module takes the fitting input data selected by the data selection module and substitutes it into the inversion fitting equation constructed by the equation construction module to obtain the fitting result. The output module acquires and outputs the fitting results from the data fitting module. Where t is time, Let yt be the theoretical particle flux at time t, and y0 be the background flux of the instrument. and Here, A represents the lower and upper limits of the energy range used for fitting, E represents the particle energy, β represents the spectral index of the particle energy spectrum within the stated energy range, and L represents the propagation path length of the particle from the solar source region to the observation point. Let t be the particle velocity corresponding to energy E. p The time of peak particle injection in the solar source region is represented by Δ, the duration of particle injection in the solar source region is represented by σ, and the asymmetry of the injection profile shape is controlled by σ.

6. The inversion and fitting device for the injection profile of a solar high-energy particle source region according to claim 5, characterized in that, The data fitting module further includes a calculation unit, which is used to calculate the chi-square statistic of the residuals of the N sets of observed data points. The chi-square statistic is shown in the following formula: （4）； The minimum value is obtained according to the above formula (4). The corresponding parameter is ;in, , , yes , The standard deviation.

7. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the inversion fitting method for the injection profile of the solar high-energy particle source region as described in any one of claims 1 to 4.

8. A terminal, characterized in that, include: Processor and memory; The memory is used to store computer programs; The processor is used to execute the computer program stored in the memory, so that the terminal performs the inversion fitting method for the injection profile of the solar high-energy particle source region as described in any one of claims 1 to 4.

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