Age signal platform automated depth profile analysis method based on change point analysis

Abstract

The application provides an age signal platform automatic deep profile analysis method based on a change point analysis, and belongs to the technical field of stratum age profile analysis. The method comprises the following steps: obtaining an original age depth sequence, pre-processing the original age depth sequence to obtain depth profile time sequence data; establishing an improved penalty value, and using a pruning accurate linear time algorithm to identify change points through dynamic programming and backtracking to obtain an optimal change point sequence and define an initial age signal platform; screening the initial age signal platform based on age background, internal difference, analysis duration and crystallization sequence to obtain a screened age signal platform; and performing inversion calculation on the screened age signal platform based on the optimal change point sequence by using a Bayesian segmentation regression model to obtain a verified age signal platform. The application solves the problems of the existing age signal platform interpretation method, such as lack of unified quantitative standard, low processing efficiency, difficulty in scaling and limited identification accuracy.

Description

Technical Field

[0001] This invention belongs to the field of stratigraphic age profile analysis technology, and particularly relates to an automated depth profile analysis method for an age signal platform based on variable point analysis. Background Technology

[0002] Deep profiling is a key micro-area in-situ analysis technique that uses laser ablation or ion beam ablation to ablate material layer by layer from the surface (edge) of a mineral toward the core, thereby obtaining isotope ratios or elemental content data that change continuously with ablation time (ablation depth).

[0003] However, accurately interpreting geologically significant "age signal plateaus" from complex time-series data remains a challenge in this field. Currently, mainstream interpretation methods still heavily rely on manual visual inspection of isotope / ratio spectra, with researchers manually delineating plateaus based on experience. This traditional approach has the following drawbacks: Lack of unified quantitative standards: The identification of platform boundaries lacks standardized mathematical definitions, and the interpretation results often vary from person to person, resulting in strong subjective bias and limiting the repeatability of data analysis. Low processing efficiency and difficulty in scaling: The manual division process is extremely labor-intensive, and manual processing is too inefficient when faced with large-scale data analysis tasks (such as large-scale zircon dating data). Limited recognition accuracy: It is difficult to capture subtle changes in signals by visual observation alone. For complex signals that are not visually obvious, have a low signal-to-noise ratio, or involve multiple superimposed stages, manual recognition is prone to information loss or misjudgment. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, this invention provides an automated depth profile analysis method for age signal platforms based on change point analysis. This method solves the problems of existing age signal platform interpretation methods, such as lack of unified quantitative standards, low processing efficiency, difficulty in scaling, and limited recognition accuracy.

[0005] To achieve the above objectives, the technical solution adopted by this invention is: an automated depth profiling analysis method for an age signal platform based on change point analysis, comprising the following steps: S1. Based on the original depth profile data, the original age depth sequence is obtained. Through outlier detection, discordant age screening, outlier correction and data smoothing, the original age depth sequence is processed to obtain depth profile time series data. S2. Based on the depth profile time series data, establish the scaling Akaike information criterion, and use the pruned exact linear time algorithm to identify the change points through dynamic programming and backtracking, obtain the optimal change point sequence, and define the initial age signal platform. S3. Based on the initial age signal platform, the initial age signal platform is screened according to age background, internal differences, resolution time and crystallization sequence to obtain the screened age signal platform. S4. Based on the optimal change point sequence, the selected age signal platform is inverted using a Bayesian piecewise regression model to obtain a validated age signal platform, thus completing the automated in-depth profile analysis of the age signal platform.

[0006] The beneficial effects of this invention are as follows: This invention achieves rapid, objective and repeatable segmentation of age signal platforms through data optimization, automatic segmentation of age signal platforms, screening of age signal platforms and Bayesian verification. It determines the standardized mathematical definition of platform boundary recognition, improves processing efficiency and achieves scalability, and greatly improves recognition accuracy. It also realizes quantitative analysis of deep profile data and effectively solves the core pain points of traditional technology, which are highly dependent on human experience, highly subjective and lack repeatability. By integrating core algorithms for data optimization, automatic age signal segmentation, and platform objective identification, the precise definition of growth zones and standardized calculation of uranium-lead ages have been achieved.

[0007] Further, S1 includes the following steps: S1 includes the following steps: S101. Based on the original depth profile data, obtain the original age depth sequence; S102. Based on the non-seasonal autoregressive difference moving average model, the difference order of the non-seasonal autoregressive difference moving average model is determined by the unit root test algorithm, and the autoregressive order and moving average order are determined by the stepwise algorithm and the Akaike information criterion method, thus obtaining the non-seasonal autoregressive difference moving average model with determined order. S103. Using a non-seasonal autoregressive differential moving average model of a certain order, outlier detection is performed on the original age depth sequence by fitting a preset age, and an age depth sequence with outliers removed is obtained. S104. Remove age data in the age depth sequence that has a preset age inconsistency greater than a preset probability, and determine the optimal age to obtain the age depth sequence with the optimal age. S105. Using an odd-length window, perform mean filtering on the age depth sequence that determines the optimal age to obtain the filtered age depth sequence. S106. Using ten-fold cross-validation and Bayesian information criterion, evaluate the local weighted regression smoothing method to obtain the optimal span value. S107. Based on the optimal span value, the filtered age depth sequence is smoothed using the local weighted regression smoothing method to obtain depth profile time series data.

[0008] The beneficial effects of the above-mentioned further solutions are as follows: By employing outlier detection, discordant age screening, outlier correction, and data smoothing, the present invention optimizes the original age depth sequence, thereby achieving accurate reconstruction and improved reliability of the original age data.

[0009] Furthermore, S2 includes the following steps: S201. Based on the number of data points in the depth profile time series data, establish the scaled Akaike information criterion. S202. Using the pruning precise linear time algorithm and combining it with the scaling Akaike information criterion, the minimum cost is calculated through dynamic programming. S203. In response to the pruning precise linear time algorithm, the data is segmented and linearly standardized on the depth profile time series data to obtain the standardized age series. S204. Based on minimum cost, identify the change points of the standardized age sequence, and determine the optimal change point sequence through backtracking. S204. Based on the optimal change point sequence, the average value of the data between every two adjacent change points is defined as the initial age signal platform.

[0010] Furthermore, the expression for the scaling Akaike information criterion is as follows: ; in, This indicates the scaling criteria for Akaike Information. This refers to the Akaike Information Criteria. Indicates the scaling factor. This indicates the number of data points.

[0011] The beneficial effects of the above-mentioned further solutions are as follows: By designing an improved scaling Akaike information criterion for penalty values ​​and utilizing a pruned exact linear time algorithm, the present invention treats the identification of depth profile platforms as a variable point detection problem, thereby achieving efficient and accurate detection and identification of variable points on depth profile platforms, significantly reducing computational complexity, and improving processing speed and noise resistance under large-scale data.

[0012] Furthermore, step S3 includes the following steps: S301. Based on the initial age signal platform and the age background, by setting a preset age filtering range, age signal platforms whose ages do not match the known geological background are removed, and age signal platforms after age background removal are obtained. S302. Based on the age signal platforms that have been removed from the age background, and based on the internal differences, calculate the variance of each age signal platform that has been removed from the age background and the variance of the sample set, and remove age signal platforms whose variance is greater than the preset percentile of the variance of the sample set, to obtain age signal platforms that have been removed from the internal differences. S303. Based on the age signal platform after internal difference elimination, and based on the preset minimum resolution time, age signal platforms shorter than the minimum resolvable time are eliminated to obtain the age signal platform after the elimination resolution time. S304. Based on the crystallization sequence from the core to the edge, age signal platforms with edge ages greater than those of the core or mantle are removed, and the age signal platforms with the removed analysis time are simplified to obtain simplified age signal platforms. S305. By pre-screening particles under a microscope to avoid inclusions, and in response to screening the initial age signal platform, based on the simplified age signal platform, using trace element data, the regions affected by inclusions are identified and excluded to obtain the screened age signal platform.

[0013] Furthermore, S304 specifically includes: Based on the crystallization sequence from the core to the edge, an age rule is derived that the age of the edge is less than that of the core or mantle. Based on the age rule, in response to the addition of age to the edge or the absence of a clear age pattern, the age signal platform after the parsing time is removed is simplified by retaining the first age signal platform immediately adjacent to the edge and removing the remaining age signal platforms, thus obtaining the simplified age signal platform.

[0014] The beneficial effects of the above-mentioned further solutions are as follows: Through rigorous screening based on four geological and statistical standards, the present invention achieves automated and accurate identification of age signal platforms, effectively eliminates interfering data and meaningless outliers, and significantly improves the objectivity and reliability of dating results.

[0015] Furthermore, step S4 includes the following steps: S401. Based on the optimal change point sequence, a Bayesian piecewise regression model is used to model the complete initial age signal plateau sequence, and the modeled complete initial age signal plateau sequence is sampled to obtain the inversion result of the age signal plateau. S402. Based on the inversion results of the age signal platform, Gibbs sampling is used to numerically approximate the inversion results of the age signal platform, and a sample chain that conforms to the posterior distribution is generated by gradually updating the conditional distribution of each parameter in the age signal platform. S403. Using a sample chain that conforms to the posterior distribution, the screened age signal platform is validated to obtain the validated age signal platform, and the automated depth profile analysis of the age signal platform is completed.

[0016] Furthermore, S401 specifically includes: Based on the number of change points in the optimal change point sequence, a Bayesian piecewise regression model is used, combined with the change points, to connect the linear trends of a preset set of standardized platform age items, thus obtaining the complete initial age signal platform structure. Using the complete initial age signal platform structure, the complete initial age signal platform is modeled, and based on the standardization conditions, the age values ​​are sampled by calculating the complete age signal platform sequence to obtain the inversion result of the age signal platform.

[0017] The beneficial effects of the above-mentioned further solutions are as follows: the present invention achieves the repeatability of data processing and eliminates human interference errors through Bayesian posterior and Gibbs sampling. Attached Figure Description

[0018] Figure 1 This is a flowchart of the method of the present invention.

[0019] Figure 2 This is a flowchart illustrating the automated depth profiling analysis method for the age signal platform based on change point analysis in this embodiment.

[0020] Figure 3 This is a comparison chart of the age and integration time results of the pruning exact linear time algorithm and the Markov chain Monte Carlo method in this embodiment. Detailed Implementation

[0021] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0022] Before describing this embodiment, the following terms will be explained: SAIC: Scaling Akaike Information Criteria; ARIMA model: Autoregressive integral moving average model; LOESS: Locally weighted regression smoothing method; Span: span; BIC: Bayesian Information Criterion; PELT: Pruning Exact Linear Time Algorithm; MCMC: Markov Chain Monte Carlo Method; Gibbs sampling; Gelman-Rubin diagnostic criteria: a convergence diagnostic method based on multi-chain MCMC sampling.

[0023] Example This embodiment provides a method for quantitative analysis of depth profile data. From a mathematical perspective, the identification of age signal plateaus in depth profiles can be viewed as a change point detection problem in time series data. Based on this concept, an automated workflow has been developed: an automated depth profile analysis method for age signal plateaus based on change point analysis. This technology employs a change point analysis method based on dynamic programming, comprising three steps: data optimization, automatic segmentation of age signal plateaus, and screening of age signal plateaus. Finally, the results are validated using Bayesian methods. The aim is to achieve rapid, objective, and repeatable segmentation of age signal plateaus, with the core objective of quantitatively classifying depth profile data plateaus.

[0024] like Figure 1 As shown, this invention provides an automated depth profiling analysis method for an age signal platform based on change point analysis, the implementation of which is as follows: S1. Based on the original depth profile data, obtain the original age-depth sequence. Process the original age-depth sequence through outlier detection, discordant age filtering, outlier correction, and data smoothing to obtain the depth profile time series data. The specific steps are as follows: S101. Based on the original depth profile data, obtain the original age depth sequence; S102. Based on the non-seasonal autoregressive difference moving average model, the difference order of the non-seasonal autoregressive difference moving average model is determined by the unit root test algorithm, and the autoregressive order and moving average order are determined by the stepwise algorithm and the Akaike information criterion method, thus obtaining the non-seasonal autoregressive difference moving average model with determined order. S103. Using a non-seasonal autoregressive differential moving average model of a certain order, outlier detection is performed on the original age depth sequence by fitting a preset age, and an age depth sequence with outliers removed is obtained.

[0025] In this embodiment, as Figure 2 As shown, since the raw depth profile data may be affected by instrument noise, analytical uncertainty, insufficient fractionation correction, and inclusion or fracture signals, the raw age-depth (integration time) sequence is optimized through outlier detection, dissonant age screening, outlier correction, and data smoothing. An ARIMA model is then used to identify outliers. Zircon depth profile U-Pb isotope data are typical time series data. Therefore, this invention employs the ARIMA model, which is designed to capture the autocorrelation structure and trend characteristics of time series data, to identify outliers in the data. The ARIMA model consists of three parts: AR (Autoregressive), I (Differential), and MA (Moving Average). For time series data on age, the ARIMA model can be considered non-seasonal. Process model, in which, Indicates the order of autoregression. Indicates the difference order. Indicates the order of the moving average. , , All are non-negative integers; The expression for the ARIMA model is as follows: ; in, express order difference, Indicates a point in time Time series, Indicates the current time point, Represents a constant term. Represents the autoregressive coefficient. Indicates a point in time The previous At a certain point in time, Indicates a point in time Time series, Represents the moving average coefficient. Indicates a point in time Error term, Indicates a point in time Error term; To determine the autoregressive order of parameters in a nonseasonal ARIMA model Moving average order Sum of difference order This invention employs a unit root test algorithm to determine the order of difference. The autoregressive order was determined using a stepwise algorithm and the Akaike Information Criterion (AIC) method. and moving average order The order of; Based on the statistical properties of residuals, outliers are identified and handled. Theoretically, the fitting residuals of the ARIMA model should conform to a normal distribution. Based on this principle, outliers are identified and handled separately. age, Age and For age, an ARIMA model is fitted. If the difference between the predicted point and the data point exceeds twice the standard deviation, such data points are classified as outliers and removed, resulting in an age depth sequence with outliers removed.

[0026] S104. Remove age data in the age depth sequence that has a preset age inconsistency greater than a preset probability, and determine the optimal age to obtain the age depth sequence with the optimal age. S105. Using an odd-length window, perform mean filtering on the age depth sequence that determines the optimal age to obtain the filtered age depth sequence. S106. Using ten-fold cross-validation and Bayesian information criterion, evaluate the local weighted regression smoothing method to obtain the optimal span value. S107. Based on the optimal span value, the filtered age depth sequence is smoothed using the local weighted regression smoothing method to obtain depth profile time series data.

[0027] In this embodiment, discordant ages are eliminated. Specifically, to ensure the reliability of the selected ages, [the following steps are taken]. and Dating data with a discordance exceeding 10% were discarded. Additionally, when the zircon age was less than 1000 Ma, [the data was selected]. Age is considered the optimal age; when the zircon age is greater than 1000 Ma, then [the appropriate age is selected]. Age is used as the optimal age to obtain an age depth sequence that determines the optimal age; Mean filtering handles outliers. Specifically, after removing outliers using the ARIMA model and disharmony degree, mean filtering is applied to smooth the data. To preserve initial age information as much as possible and prevent over-smoothing of the original data, an odd-length window is used to ensure symmetry, including the outliers themselves, and avoid data shift. The calculation expression for mean filtering is shown below: ; in, Indicates the smoothed-out first... The value of each data point. Indicates the current data point position. Indicates the window radius. Indicates that the original sequence is located at Location observations; when At that time, smoothing is not strong enough to resist outliers; while At this time, it may lead to excessive smoothing of the data, i.e., narrower borders. Age or similar nucleus-mantle-rime age Information loss, this invention adopts The parameters for mean filtering are used to obtain the filtered age depth sequence; Data smoothing is performed by using LOESS to smooth the filtered age-depth sequence to obtain depth profile time series data. In the LOESS method, the parameter span determines the size of the neighborhood used for fitting in each local regression (the proportion of data points participating in the local fitting). To select the optimal span value, 10-fold cross-validation and BIC are used for evaluation. 10-fold cross-validation can effectively measure the model's generalization ability and help reduce the risk of overfitting. BIC is a standard used to measure the balance between model fit and complexity. The calculation expression of BIC is as follows: ; in, Represents the Bayesian information criterion. Indicates sample size. Represents the natural logarithm. The mean square error of the residuals. Indicates the number of model parameters; Of the 4615 zircons in the Himalayan leucite granite with the best Span values, 64% of the zircons had a Span value of [missing value]. Within the range, it approximately follows The Span parameter in the LOESS method is selected as the mean of the distribution 0.15, which follows a normal distribution.

[0028] S2. Based on the depth profile time series data, establish the scaling Akaike information criterion, and use the pruned exact linear time algorithm to identify change points through dynamic programming and backtracking, obtain the optimal change point sequence, and define the initial age signal plateau. The specific steps are as follows: S201. Based on the number of data points in the depth profile time series data, establish the scaled Akaike information criterion. S202. Using the pruning precise linear time algorithm and combining it with the scaling Akaike information criterion, the minimum cost is calculated through dynamic programming. S203. In response to the pruning precise linear time algorithm, the data is segmented and linearly standardized on the depth profile time series data to obtain the standardized age series. S204. Based on minimum cost, identify the change points of the standardized age sequence, and determine the optimal change point sequence through backtracking. S204. Based on the optimal change point sequence, the average value of the data between every two adjacent change points is defined as the initial age signal platform.

[0029] In this embodiment, the identification of depth profile platforms is treated as a change point detection problem. For dividing age signal platforms in the depth profile, it is necessary to consider not only the accuracy and efficiency of age signal platform division but also to avoid excessive parameter settings. Based on the high computational efficiency, ease of operation, and excellent division accuracy of the PELT algorithm, it is used to identify change points in the zircon depth profile time series data, obtaining the optimal change point sequence. The average data between every two adjacent change points is defined as the initial age signal platform. The expression of the PELT algorithm is as follows: ; in, Indicates the number of variable points. Indicates the first A turning point, Represents the cost function, From the Point to number Subsets of data between point observations Indicates the point of change The starting position, Indicates the point of change The end position, Indicates the scaling criteria for Akaike Information; The PELT algorithm calculates the minimum cost through dynamic programming and determines the optimal change point sequence through backtracking. During the calculation process, the sensitivity of the change points can be controlled by adjusting the penalty term, thereby balancing the goodness of fit and complexity of the model. However, since the magnitude of the penalty term has a significant impact on the identification of the number of change points, it is difficult to identify all change points in the depth profile data when the penalty value is relatively large (based on AIC). This invention establishes an improved penalty value SAIC, the expression of which is as follows: ; in, This indicates the scaling criteria for Akaike Information. This refers to the Akaike Information Criteria. This represents the scaling factor, designed to reduce the impact of the number of data points on the size of the penalty term. Indicates the number of data points; During the PELT data segmentation process, linear normalization is applied to the complete age sequence formed by the depth profiles of individual zircons to reduce the influence of numerical magnitude and depth fractionation effects on change point identification. The expression for linear normalization is shown below: ; in, This represents data values ​​that have been linearly standardized. Represents the original data value. Describes the minimum value function. This represents the maximum value function.

[0030] S3. Based on the initial age signal platform, and considering factors such as age background, internal differences, resolution time, and crystallization sequence, the initial age signal platform is screened to obtain the screened age signal platform. The specific steps are as follows: S301. Based on the initial age signal platform and the age background, by setting a preset age filtering range, age signal platforms whose ages do not match the known geological background are removed, and age signal platforms after age background removal are obtained. S302. Based on the age signal platforms that have been removed from the age background, and based on the internal differences, calculate the variance of each age signal platform that has been removed from the age background and the variance of the sample set, and remove age signal platforms whose variance is greater than the preset percentile of the variance of the sample set, to obtain age signal platforms that have been removed from the internal differences. S303. Based on the age signal platform after internal difference elimination, and based on the preset minimum resolution time, age signal platforms shorter than the minimum resolvable time are eliminated to obtain the age signal platform after the elimination resolution time. S304. Based on the crystallization sequence from the core to the edge, age signal platforms with edge ages greater than those of the core or mantle are removed. The removed age signal platforms with longer resolution times are then simplified to obtain the simplified age signal platforms, specifically: Based on the crystallization sequence from the core to the edge, an age rule is derived that the age of the edge is less than that of the core or mantle. Based on the age rule, in response to the increase of age to the edge or the absence of a clear age pattern, the age signal platform after the removal of parsing time is simplified by retaining the first age signal platform immediately adjacent to the edge and removing the remaining age signal platforms, thus obtaining the simplified age signal platform. S305. By pre-screening particles under a microscope to avoid inclusions, and in response to screening the initial age signal platform, based on the simplified age signal platform, using trace element data, the regions affected by inclusions are identified and excluded to obtain the screened age signal platform.

[0031] In this embodiment, to ensure geological reliability, the initial age signal platform identified by PELT must undergo rigorous screening based on four geological and statistical criteria. First, age signal plateaus whose ages do not match the known geological background (e.g., ages less than the emplacement age or greater than the protolith or sedimentary age) are removed, as these discrepancies are often caused by lead loss, alteration, or trapped xenografts, which can cause U-Pb age records to deviate from their true values. The default parameter for age range filtering is set to 0 Ma (lower limit) to 45.4 Ga (upper limit), and users can adjust this parameter through the web application or settings panel to obtain age signal plateaus after age background removal. Secondly, age signal platforms with excessively large internal differences (potentially due to instability, contamination, or incorrect segmentation) will be flagged. This is done by calculating the variance of each linearly normalized age signal platform and removing those with variances exceeding 75% of the overall sample set variance. th Percentile age signal plateau; this threshold is determined empirically to effectively filter out outliers while retaining most of the continuous age signal plateau. It is worth noting that it is unclear whether the threshold used in this invention is applicable to magmatic systems other than leucogranite. Users can use the code provided in this paper to recalculate the variance threshold based on their own datasets. The variances of the plateau ages of the Himalayan leucogranite zircon depth profile data are similar after linear standardization; therefore, this invention uses 75 for them. th Using a percentile of 0.1192 as the screening criterion for fluctuating age, an age signal plateau was obtained after internal differences were removed; Third, age signal plateaus shorter than the minimum resolvable duration are excluded, as this duration is constrained by analytical limitations (such as beam size and ablation rate) and statistical factors. Signal mixing occurs when the laser radius exceeds the thickness of a single age domain within the mineral. Furthermore, current depth-profiling laser ablation uses a vertical ablation method, making precise control of the ablation rate impossible. Additionally, the radius of the ablation pits produced may be larger than the laser radius, and sufficient data is lacking to determine the corresponding variation patterns. Therefore, the impact of analytical limitations on the resolution of the minimum age signal plateau cannot be quantitatively assessed. The minimum age signal plateau resolution is defined as the statistical threshold between the longest and shortest age signal plateau lengths (based on statistical analysis) observed in the same and similar samples, with 5 s selected as the minimum resolution. This invention assumes that the LA-ICP-MS (laser ablation inductively coupled plasma mass spectrometry) system is purged in a timely and effective manner, thereby preventing signal mixing. In addition, the user needs to provide an effective integration interval setting during execution, which ensures that signal tails that may be caused by insufficient rinsing in a single laboratory can be eliminated, resulting in age signal plateaus with resolution time removed. Fourth, considering the crystallization sequence from the core to the edge, the edge age should be less than the core or mantle age. For age signal platforms that violate this principle under different alteration scenarios (age increasing towards the edge or irregularly), selective screening will be performed to retain the most reliable age information; specifically, for scenarios where the age increases towards the edge, only the first age signal platform immediately adjacent to the edge will be retained, and the remaining age signal platforms will be discarded. For scenarios without a clear age pattern, only the first age signal plateau immediately adjacent to the edge is retained. The above processing method may remove geologically significant data (e.g., recrystallization time and age reset events of zircons in complex zoning), but for large-scale datasets, it is a necessary simplification to obtain simplified age signal plateaus. Finally, the automatic screening described above did not address the potential impact of mineral inclusions. Inclusions cannot be fully identified based solely on age data. Small inclusions that cause sharp age anomalies may be filtered out, but larger, plateau-shaped inclusions may be mixed in. Therefore, supplementary measures were taken: particles were pre-screened under a microscope to avoid inclusions, and trace element data (such as Ti, Fe, P, and La) were used during the processing to identify and exclude regions affected by inclusions, resulting in a screened age signal plateau.

[0032] S4. Based on the optimal change point sequence, the selected age signal platform is inverted using a Bayesian piecewise regression model to obtain the validated age signal platform, thus completing the automated depth profile analysis of the age signal platform. The specific steps are as follows: S401. Based on the optimal change point sequence, a Bayesian piecewise regression model is used to model the complete initial age signal plateau sequence, and the modeled complete initial age signal plateau sequence is sampled to obtain the inversion result of the age signal plateau, specifically: Based on the number of change points in the optimal change point sequence, a Bayesian piecewise regression model is used, combined with the change points, to connect the linear trends of a preset set of standardized platform age items, thus obtaining the complete initial age signal platform structure. Using the complete initial age signal platform structure, the complete initial age signal platform is modeled, and based on the standardization conditions, the age values ​​are sampled by calculating the complete age signal platform sequence to obtain the inversion result of the age signal platform; S402. Based on the inversion results of the age signal platform, Gibbs sampling is used to numerically approximate the inversion results of the age signal platform, and a sample chain that conforms to the posterior distribution is generated by gradually updating the conditional distribution of each parameter in the age signal platform. S403. Using a sample chain that conforms to the posterior distribution, the screened age signal platform is validated to obtain the validated age signal platform, and the automated depth profile analysis of the age signal platform is completed.

[0033] In this embodiment, to verify the reliability of the zircon age signal plateau segmentation method, a Bayesian piecewise regression model is used to invert the age signal plateaus. The inversion results are then compared with those segmented by the PELT algorithm. In the Bayesian piecewise regression model, the complete initial age signal plateau sequence is first modeled. Then, based on the modeling results, sampling is performed according to the recovered age values ​​to obtain the inversion results of the age signal plateaus. Specifically, for the complete age signal plateau sequence calculated by the PELT algorithm under normalization conditions, the complete age signal plateau sequence is modeled as a structure composed of multiple linear trends (containing only intercept terms, where the intercept represents the age of each normalized plateau) connected by variable points. The number of variable points is equal to the number of variable points identified in the PELT algorithm. This modeling method facilitates comparison with the results of the PELT algorithm and improves the efficiency of data analysis. The modeling expression is shown below: ; in, The normalized age signal plateau sequence of zircon, Indicates the initial undetermined intercept. This indicates the indicator function, specifically the function at time point. When the value falls within the corresponding interval, the Bayesian piecewise regression model takes the corresponding intercept value. Represents a standardized age signal plateau sequence The corresponding time point, This indicates the first variable point. Indicates the first undetermined intercept. This indicates the second variable point. Indicates the first Undetermined intercept This indicates the total number of variable points. Indicates the first A turning point, Indicates the first A turning point, Represents a standardized age signal plateau sequence The corresponding error term; We employ a Gibbs sampling algorithm to numerically approximate the posterior distribution of a Bayesian piecewise regression model. Gibbs sampling, a commonly used MCMC method, generates a sample chain that conforms to the posterior distribution by progressively updating the conditional distribution of each parameter.

[0034] like Figure 3 As shown, although the MCMC method can perform posterior validation of the age of a depth profile platform, it still has significant limitations in practical applications, according to the Gelman-Rubin diagnostic criteria ( ,in, According to the Gelman-Rubin diagnostic criteria, only 49% of MCMC chains achieve complete convergence, and 51% of chains exhibit suboptimal convergence. When comparing platform ages based on MCMC, the ages of the first four platforms showed a high degree of consistency with the age of the platform of this invention. ), more than 85% of the posterior mean ages are within 1 root mean square error (RMSE); However, the consistency of integration time is reduced (R 2 The R² decreased from 0.87 to 0.52, and even with more than 84% of the posterior integration time remaining within 1x RMSE, the difference between the proposed method and MCMC stems from two factors: MCMC's convergence limitations: the proposed method struggles to achieve optimal convergence in a single run, especially in terms of integration time, where stable convergence may be difficult; data sensitivity and sample size impact: as the data volume gradually decreases across 1 to 4 platforms, R²... 2 The sensitivity to outliers increases during RMSE calculation, thereby reducing the robustness of the comparison results. Due to the above limitations, Bayesian analysis becomes a supplementary verification tool, and the final result is determined by the calculation results of this invention.

[0035] In this embodiment, quantitative analysis of depth profile data is realized, effectively solving the core pain points of traditional technology, which is highly dependent on human experience, subjective, and lacks repeatability. Compared with the manual processing mode in the background technology, which is inefficient and prone to identification bias, the automated depth profile analysis method of age signal platform based on change point analysis developed in this invention integrates core algorithms such as data optimization, automatic age signal segmentation, and platform objective identification, realizing accurate definition of growth zone and standardized calculation of U-Pb age. Bayesian posterior results show that the Bayesian posterior validation of the results obtained in this invention shows that more than 84% of the data fall within one standard deviation of the root mean square error (RMSE), achieving repeatability of data processing and eliminating human interference errors. In terms of computational efficiency, this invention demonstrates significant advantages: the analysis time for a single zircon is reduced to less than 1 second, and processing a large dataset containing 4615 zircons takes less than 10 minutes, while traditional manual analysis usually takes 2 to 3 weeks to complete the same amount of work, greatly reducing time costs.

Claims

1. An automated depth profiling analysis method for an age signal platform based on change point analysis, characterized in that, Includes the following steps: S1. Based on the original depth profile data, the original age depth sequence is obtained. Through outlier detection, discordant age screening, outlier correction and data smoothing, the original age depth sequence is processed to obtain depth profile time series data. S2. Based on the depth profile time series data, establish the scaling Akaike information criterion, and use the pruned exact linear time algorithm to identify the change points through dynamic programming and backtracking, obtain the optimal change point sequence, and define the initial age signal platform. S3. Based on the initial age signal platform, the initial age signal platform is screened according to age background, internal differences, resolution time and crystallization sequence to obtain the screened age signal platform. S4. Based on the optimal change point sequence, the selected age signal platform is inverted using a Bayesian piecewise regression model to obtain a validated age signal platform, thus completing the automated in-depth profile analysis of the age signal platform.

2. The automated depth profiling analysis method for age signal platforms based on change point analysis according to claim 1, characterized in that, S1 includes the following steps: S101. Based on the original depth profile data, obtain the original age depth sequence; S102. Based on the non-seasonal autoregressive difference moving average model, the difference order of the non-seasonal autoregressive difference moving average model is determined by the unit root test algorithm, and the autoregressive order and moving average order are determined by the stepwise algorithm and the Akaike information criterion method, thus obtaining the non-seasonal autoregressive difference moving average model with determined order. S103. Using a non-seasonal autoregressive differential moving average model of a certain order, outlier detection is performed on the original age depth sequence by fitting a preset age, and an age depth sequence with outliers removed is obtained. S104. Remove age data in the age depth sequence that has a preset age inconsistency greater than a preset probability, and determine the optimal age to obtain the age depth sequence with the optimal age. S105. Using an odd-length window, perform mean filtering on the age depth sequence that determines the optimal age to obtain the filtered age depth sequence. S106. Using ten-fold cross-validation and Bayesian information criterion, evaluate the local weighted regression smoothing method to obtain the optimal span value. S107. Based on the optimal span value, the filtered age depth sequence is smoothed using the local weighted regression smoothing method to obtain depth profile time series data.

3. The automated depth profiling analysis method for age signal platforms based on change point analysis according to claim 1, characterized in that, S2 includes the following steps: S201. Based on the number of data points in the depth profile time series data, establish the scaled Akaike information criterion. S202. Using the pruning precise linear time algorithm and combining it with the scaling Akaike information criterion, the minimum cost is calculated through dynamic programming. S203. In response to the pruning precise linear time algorithm, the data is segmented and linearly standardized on the depth profile time series data to obtain the standardized age series. S204. Based on minimum cost, identify the change points of the standardized age sequence, and determine the optimal change point sequence through backtracking. S204. Based on the optimal change point sequence, the average value of the data between every two adjacent change points is defined as the initial age signal platform.

4. The automated depth profiling analysis method for age signal platforms based on change point analysis according to claim 3, characterized in that, The expression for the scaling Akaike information criterion is as follows: in, This indicates the scaling criteria for Akaike Information. This refers to the Akaike Information Criteria. Indicates the scaling factor. This indicates the number of data points.

5. The automated depth profiling analysis method for age signal platforms based on change point analysis according to claim 1, characterized in that, S3 includes the following steps: S301. Based on the initial age signal platform and the age background, by setting a preset age filtering range, age signal platforms whose ages do not match the known geological background are removed, and age signal platforms after age background removal are obtained. S302. Based on the age signal platforms that have been removed from the age background, and based on the internal differences, calculate the variance of each age signal platform that has been removed from the age background and the variance of the sample set, and remove age signal platforms whose variance is greater than the preset percentile of the variance of the sample set, to obtain age signal platforms that have been removed from the internal differences. S303. Based on the age signal platform after internal difference elimination, and based on the preset minimum resolution time, age signal platforms shorter than the minimum resolvable time are eliminated to obtain the age signal platform after the elimination resolution time. S304. Based on the crystallization sequence from the core to the edge, age signal platforms with edge ages greater than those of the core or mantle are removed, and the age signal platforms with the removed analysis time are simplified to obtain simplified age signal platforms. S305. By pre-screening particles under a microscope to avoid inclusions, and in response to screening the initial age signal platform, based on the simplified age signal platform, using trace element data, the regions affected by inclusions are identified and excluded to obtain the screened age signal platform.

6. The automated depth profiling analysis method for age signal platforms based on change point analysis according to claim 5, characterized in that, Specifically, S304 is: Based on the crystallization sequence from the core to the edge, an age rule is derived that the age of the edge is less than that of the core or mantle. Based on the age rule, in response to the addition of age to the edge or the absence of a clear age pattern, the age signal platform after the parsing time is removed is simplified by retaining the first age signal platform immediately adjacent to the edge and removing the remaining age signal platforms, thus obtaining the simplified age signal platform.

7. The automated depth profiling analysis method for age signal platforms based on change point analysis according to claim 1, characterized in that, S4 includes the following steps: S401. Based on the optimal change point sequence, a Bayesian piecewise regression model is used to model the complete initial age signal plateau sequence, and the modeled complete initial age signal plateau sequence is sampled to obtain the inversion result of the age signal plateau. S402. Based on the inversion results of the age signal platform, Gibbs sampling is used to numerically approximate the inversion results of the age signal platform, and a sample chain that conforms to the posterior distribution is generated by gradually updating the conditional distribution of each parameter in the age signal platform. S403. Using a sample chain that conforms to the posterior distribution, the screened age signal platform is validated to obtain the validated age signal platform, and the automated depth profile analysis of the age signal platform is completed.

8. The automated depth profiling analysis method for age signal platforms based on change point analysis according to claim 7, characterized in that, Specifically, S401 is: Based on the number of change points in the optimal change point sequence, a Bayesian piecewise regression model is used, combined with the change points, to connect the linear trends of a preset set of standardized platform age items, thus obtaining the complete initial age signal platform structure. Using the complete initial age signal platform structure, the complete initial age signal platform is modeled, and based on the standardization conditions, the age values ​​are sampled by calculating the complete age signal platform sequence to obtain the inversion result of the age signal platform.

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