Groundwater long-term correlation analysis method based on geostatistics and fractal theory combined model

Abstract

The invention discloses an underground water long-term correlation analysis method based on a geostatistics and fractal theory combined model, and the method comprises the steps: obtaining the initial underground water long-sequence burial depth monitoring data of a research region, and carrying out the processing of the underground water long-sequence burial depth monitoring data based on a space-time Kriging interpolation method, and obtaining the average burial depth data of underground water; and constructing a geostatistics and fractal theory combined model, inputting the initial groundwater long sequence burial depth monitoring data and the groundwater average burial depth data into the geostatistics and fractal theory combined model for processing to obtain an output result, and analyzing the long-term correlation of the groundwater burial depth of the research area through the output result. According to the method, a more accurate and reliable prediction result is provided, and a more scientific basis is provided for groundwater resource management and planning.

Description

Technical Field

[0001] The present invention relates to the cross-technical fields of groundwater hydrology, spatial data analysis, mathematical modeling, and the like, and in particular to a groundwater long-term correlation analysis method based on a joint model of geostatistics and fractal theory. Background Art

[0002] In the management and research of groundwater resources, the long-term change characteristics of groundwater levels are crucial for prediction and planning. However, traditional groundwater observation data often come from limited scattered observation stations, which makes it difficult to conduct a comprehensive analysis of the long-term changes in groundwater in non-observation areas.

[0003] Although there are more and more studies on the prediction of groundwater dynamic changes, traditional interpolation methods can usually only provide predictions for local areas and cannot effectively capture the global long-term change trend of groundwater levels. In particular, the accuracy and effectiveness of interpolation methods are limited when conducting long-term correlation analysis. Therefore, it is necessary to explore and construct a theoretical framework for analyzing the spatiotemporal evolution of groundwater depth by combining geostatistics and fractal theory to form a systematic, complete and reliable groundwater depth dataset. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes a groundwater long-term correlation analysis method based on a joint model of geostatistics and fractal theory, aiming to solve the limitations of traditional geostatistical methods in capturing the long-term variation laws of groundwater depth data, introduce the Hurst exponent to optimize the interpolation results, and improve the accuracy and reliability of groundwater depth prediction.

[0005] To achieve the above object, the present invention provides a groundwater long-term correlation analysis method based on a joint model of geostatistics and fractal theory, comprising:

[0006] Obtain initial groundwater long-sequence burial depth monitoring data in the study area, process the groundwater long-sequence burial depth monitoring data based on the spatiotemporal Kriging interpolation method, and obtain a groundwater average burial depth dataset;

[0007] A joint model of geostatistics and fractal theory is constructed, and the initial groundwater long-series depth monitoring data and the average groundwater depth data are input into the joint model of geostatistics and fractal theory for processing to obtain output results, and the long-term correlation of the groundwater depth in the study area is analyzed through the output results.

[0008] Preferably, obtaining the average groundwater depth dataset includes:

[0009] Calculate the empirical semivariogram, optimize the empirical semivariogram using the covariance function, and select the function that best expresses the correlation of variables in time, space, and spatiotemporal;

[0010] Determine the grid size and obtain the groundwater depth difference of each grid center point by calculation;

[0011] The groundwater depth difference of each grid center point is assigned to the grid, and the grid is converted into a raster with the same spatial resolution to obtain a groundwater average depth dataset.

[0012] Preferably, constructing the joint model of geostatistics and fractal theory includes:

[0013] Using a spectral analysis sequence to eliminate the influence of periodicity and trend items in the average groundwater depth data set, and determining the length of the Hurst exponent calculation data;

[0014] Based on the Hurst index calculation data length, the Hurst index of groundwater depth is calculated by re-scaling range analysis method;

[0015] According to the groundwater depth distribution and the Hurst index, the correlation between the change of the Hurst index and the change of the groundwater depth is analyzed to obtain the joint model of geostatistics and fractal theory.

[0016] Preferably, using a spectral analysis sequence to eliminate the influence of periodicity and trend items in the average groundwater depth data set includes:

[0017] The average groundwater depth dataset is preprocessed to remove obvious trend items or perform differential processing. Fourier transform is applied to convert the processed data into the frequency domain, and frequency components related to periodicity and trend are identified through spectral analysis. In the frequency domain, a band-stop filter is used to filter out periodic frequency components, and frequency components without periodic fluctuations are retained. The processed spectrum is converted back to the time domain through inverse Fourier transform to obtain the screened average groundwater depth dataset.

[0018] Preferably, the Hurst index of groundwater depth is calculated by re-scaling range analysis method, including:

[0019] The mean sequence of the screened groundwater average depth data set is defined as X τ :

[0020]

[0021] Calculate X τ The cumulative deviation X(t,τ):

[0022] X(t,τ)=∑ u＝1 (X(u)-X τ )1≤t≤τ

[0023] Calculate X τThe extreme deviation R(τ):

[0024]

[0025] Calculate X τ The standard deviation S(τ):

[0026]

[0027] Analyzing the statistical law of R(τ) / S(τ)=R / S, we can obtain:

[0028]

[0029] Where T is the number of data points in X(t), τ is any positive integer, τ ≥ 1, X(t) is a given time series, and H is the Hurst exponent;

[0030] Among them, the least squares method is used to draw the τ and R / S relationship lines in the logarithmic grid, H is the slope of the relationship line, and X(u) is the time series with a length of u.

[0031] Preferably, the Hurst index of groundwater depth is calculated by the rescaled range analysis method, and the long-term correlation of groundwater depth is analyzed, including:

[0032] The length of the time series is increased successively to calculate the Hurst exponent corresponding to different samples, and the number of samples when the Hurst exponent is stable is obtained as the sliding time series;

[0033] Based on the Hurst calculation results and time period changes, the trend of groundwater depth changes is predicted.

[0034] Preferably, analyzing the long-term correlation of the groundwater depth in the study area through the output results includes:

[0035] The long-term correlation of groundwater depth in the study area is analyzed by correlation function D(t) and Hurst index H:

[0036] If the given time series {X(t)} is an independent random sequence with finite variance, then the exponent H = 0.5, and H depends on the correlation function D(t):

[0037] D(t)=2 2H-1 -1;

[0038] If H>0.5, D(t)>0, it has a positive persistence characteristic, and the future trend of the time series will be consistent with the historical data; if H<0.5, D(t)<0, it has an opposite persistence characteristic, and the future trend of the time series will be opposite to the past data.

[0039] Compared with the prior art, the present invention has the following advantages and technical effects:

[0040] The present invention effectively utilizes the spatial local interpolation technology in geostatistics to optimize the spatial distribution of data, and uses fractal theory to accurately model groundwater dynamics. Compared with traditional methods, the present invention reduces the prediction error caused by sparse or uneven data distribution, and enhances the adaptability of the model to groundwater dynamics under complex geological conditions. By introducing the multi-scale characteristics of fractal theory, this method can better capture the subtle characteristics of groundwater changes, provide more accurate and reliable prediction results, and provide a more scientific basis for groundwater resource management and planning. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0042] Figure 1 This is a flow chart of a method for analyzing long-term groundwater correlation based on a joint model of geostatistics and fractal theory according to an embodiment of the present invention;

[0043] Figure 2 The groundwater level changes in the study area and typical funnel area of ​​the embodiment of the present invention;

[0044] Figure 3 It is a contour map of the Hurst index of the study area of ​​the embodiment of the present invention;

[0045] Figure 4 A schematic diagram of the change of Hurst index in the statistical sequence study area and the typical funnel area in an embodiment of the present invention;

[0046] Figure 5 This is a comparison chart of different cities according to an embodiment of the present invention. DETAILED DESCRIPTION

[0047] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0048] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0049] This paper proposes a groundwater long-term correlation analysis method based on a joint model of geostatistics and fractal theory. Figure 1 ,include:

[0050] Obtain initial groundwater long-sequence burial depth monitoring data in the study area, process the groundwater long-sequence burial depth monitoring data based on the spatiotemporal Kriging interpolation method, and obtain a groundwater average burial depth dataset;

[0051] A joint model of geostatistics and fractal theory is constructed, and the initial groundwater long-series depth monitoring data and the average groundwater depth data are input into the joint model of geostatistics and fractal theory for processing to obtain output results, and the long-term correlation of the groundwater depth in the study area is analyzed through the output results.

[0052] This embodiment effectively uses the spatial local interpolation technology in geostatistics to optimize the spatial distribution of data, and uses fractal theory to accurately model groundwater dynamics. Compared with traditional methods, this embodiment reduces the prediction error caused by sparse or uneven data distribution, and enhances the adaptability of the model to groundwater dynamics under complex geological conditions. By introducing the multi-scale characteristics of fractal theory, it can better capture the subtle characteristics of groundwater changes, provide more accurate and reliable prediction results, and provide a more scientific basis for groundwater resource management and planning.

[0053] Furthermore, the average groundwater depth dataset is obtained, including:

[0054] Calculate the empirical semivariogram, optimize the empirical semivariogram using the covariance function, and select the function that best expresses the correlation of variables in time, space, and spatiotemporal;

[0055] Determine the grid size and obtain the groundwater depth difference of each grid center point by calculation;

[0056] The groundwater depth difference of each grid center point is assigned to the grid, and the grid is converted into a raster with the same spatial resolution to obtain a groundwater average depth dataset.

[0057] Specifically, the spatiotemporal Kriging interpolation method is used to simulate the groundwater level in the study area in spatiotemporal interpolation. The empirical semivariogram is calculated using the existing spatiotemporal data, which can preliminarily reflect the relationship between groundwater in time and space. The empirical semivariogram is optimized according to the three covariance functions of separability, sum metric and product sum, and the optimal function is selected to express the relationship between groundwater in space, time and space-time. After the grid size is finally determined, the groundwater depth of each unknown point at each time point is calculated.

[0058] The main steps are as follows:

[0059] Step 1: Calculate the empirical semivariogram. This function can preliminarily reflect the relationship between groundwater in time and space, that is, the time hysteresis and spatial distance of groundwater. When t = 1, it is a pure spatial variogram.

[0060] Step 2: Use covariance function optimization. Consider groundwater as a random function defined in the space-time domain to establish a space-time covariance function to express the space-time correlation of variables. A variety of space-time covariance functions are often used to optimize the empirical semivariogram, and finally select the function with the best effect in time, space and space-time.

[0061] Step 3: Interpolation grid screening. The size of the grid determines the interpolation accuracy, but the smaller the grid scale, the greater the amount of calculation of the space-time Kriging model and the longer the model calculation time.

[0062] Step 4: Obtain the groundwater distribution map of the study area in each time period. Assign the calculated groundwater depth interpolation data of each grid center point to the grid, and finally convert the grid into a raster with the same spatial resolution to obtain the average groundwater depth dataset.

[0063] As a geostatistical technique, the space-time kriging method can make full use of the space-time correlation of groundwater level data and predict groundwater levels at different time and space points by constructing a space-time model. This method can not only fill the data gaps between observation stations, but also generate accurate groundwater level distribution maps in unobserved areas, thereby predicting the long-term change characteristics of these areas. Combined with fractal theory, the space-time kriging method further improves the level of refinement of the analysis. Fractal theory can reveal the long-term correlation characteristics of groundwater level data by studying the self-similarity and long-term dependence of groundwater level data. The high-resolution data provided by the space-time kriging method enables fractal theory to more accurately calculate the long-range correlation of groundwater levels.

[0064] Furthermore, the geostatistics and fractal theory joint model is constructed, including:

[0065] Using a spectral analysis sequence to eliminate the influence of periodicity and trend items in the average groundwater depth data set, and determining the length of the Hurst exponent calculation data;

[0066] Based on the Hurst index calculation data length, the Hurst index of groundwater depth is calculated by re-scaling range analysis method;

[0067] According to the groundwater depth distribution and the Hurst index, the correlation between the change of the Hurst index and the change of the groundwater depth is analyzed to obtain the joint model of geostatistics and fractal theory.

[0068] Specifically, the input of the joint model of geostatistics and fractal theory is the initial long-series groundwater depth monitoring data and the average groundwater depth data set. The Hurst index of groundwater depth is calculated by the rescaled range analysis method, which is used to analyze the long-term correlation of groundwater depth.

[0069] Model construction is mainly divided into three steps:

[0070] The first step is to determine the length of the Hurst index calculation data. In this embodiment, according to the groundwater depth statistical series, the length of the time series is increased in sequence to calculate the Hurst index corresponding to different samples, and the number of samples when the Hurst index is stable is found as a sliding time series and slid with 1 year as the sliding step.

[0071] The second step is to calculate the Hurst index. The monthly groundwater depth of the station and the regional groundwater statistical depth sliding time series are imported into the rescaled range analysis calculation program to calculate the Hurst index of the station and the groundwater depth statistical series.

[0072] The third step is to study the fluctuation of Hurst index. According to the distribution of groundwater depth and the calculated Hurst index, the correlation between the change of Hurst index and the change of groundwater depth is analyzed, and certain predictions are made.

[0073] Furthermore, a spectral analysis sequence is used to eliminate the influence of periodicity and trend items in the average groundwater depth data set, including:

[0074] The average groundwater depth dataset is preprocessed to remove obvious trend items or perform differential processing. Fourier transform is applied to convert the processed data into the frequency domain, and frequency components related to periodicity and trend are identified through spectral analysis. In the frequency domain, a band-stop filter is used to filter out periodic frequency components, and frequency components without periodic fluctuations are retained. The processed spectrum is converted back to the time domain through inverse Fourier transform to obtain the screened average groundwater depth dataset.

[0075] Specifically, before calculating the Hurst exponent of the groundwater depth time series, two aspects need to be considered: First, the existence of periodicity and trend terms in the time series has a great impact on the calculation of the Hurst exponent. Therefore, it is necessary to use a spectral analysis sequence to eliminate the influence of periodicity and trend terms in the time series. Second, the stability conditions of the calculated Hurst exponent time series should be explored. The stability of the Hurst exponent affects the accuracy of the long-term correlation.

[0076] This embodiment designs the following two groups of experiments to solve the second problem. In the first group of experiments, ten groups of random numbers with undetermined sample sizes that conform to uniform distribution and normal distribution are used to calculate the Hurst index. The Hurst index calculated from a large number of random numbers should be close to 0.5. The more samples there are, the closer the calculated Hurst index is to 0.5. According to this principle, the number of samples of random numbers is increased in sequence, and when the Hurst index tends to be stable, the number of samples is determined. In the second group of experiments, the Hurst index is calculated using the preprocessed groundwater depth time series. The length of the time series is increased in sequence to calculate the Hurst index corresponding to different samples. This experiment selected 5 representative stations in each provincial administrative region in the study area, 3 representative stations in the typical funnel area, and the depth statistical series of the study area, the typical funnel area, and the three cities in the typical funnel area for trial calculation. In the first group of experiments, when the number of random samples was less than 110, the Hurst index value fluctuated greatly and then tended to be stable. In the second set of experiments, when the sample number is greater than 160, the Hurst exponents of the eight selected groundwater monitoring stations and five statistical series tend to be stable as the sample number changes.

[0077] Furthermore, the Hurst index of groundwater depth is calculated by rescaling range analysis method, including:

[0078] The mean sequence of the screened groundwater average depth data set is defined as X τ :

[0079]

[0080] Calculate X τ The cumulative deviation X(t,τ):

[0081] X(t,τ)=∑ u＝1 (X(u)-X τ )1≤t≤τ

[0082] Calculate X τ The extreme deviation R(τ):

[0083]

[0084] Calculate X τ The standard deviation S(τ):

[0085]

[0086] Analyzing the statistical law of R(τ) / S(τ)=R / S, we can obtain:

[0087]

[0088] Where T is the number of data points in X(t), τ is any positive integer, τ ≥ 1, X(t) is a given time series, and H is the Hurst exponent;

[0089] Among them, the least squares method is used to draw the τ and R / S relationship lines in the logarithmic grid, H is the slope of the relationship line, and X(u) is the time series with a length of u.

[0090] Specifically, after obtaining the length of the research time series and the sliding step in the previous step, this step imports the long-term burial depth data of the groundwater station into the calculation program to obtain the Hurst index of the station in different time series. In addition, based on the statistical burial depth data, the Hurst index of the average burial depth of regional groundwater is calculated.

[0091] Furthermore, the Hurst index of groundwater depth is calculated by the rescaled range analysis method, and the long-term correlation of groundwater depth is analyzed, including:

[0092] The length of the time series is increased successively to calculate the Hurst exponent corresponding to different samples, and the number of samples when the Hurst exponent is stable is obtained as the sliding time series;

[0093] Based on the Hurst calculation results and time period changes, the trend of groundwater depth changes is predicted.

[0094] Furthermore, the long-term correlation of groundwater depth in the study area is analyzed through the output results, including:

[0095] The long-term correlation of groundwater depth in the study area is analyzed by correlation function D(t) and Hurst index H:

[0096] If the given time series {X(t)} is an independent random sequence with finite variance, then the exponent H = 0.5, and H depends on the correlation function D(t):

[0097] D(t)=2 2H-1 -1

[0098] If H>0.5, D(t)>0, it has a positive persistence characteristic, and the future trend of the time series will be consistent with the historical data; if H<0.5, D(t)<0, it has an opposite persistence characteristic, and the future trend of the time series will be opposite to the past data.

[0099] In order to more clearly express the technical solution of the present invention, the following specific embodiments are provided to introduce the solution:

[0100] The study area of ​​this example is located in the North China Plain, which belongs to the warm temperate semi-arid monsoon climate zone on the east coast of Eurasia. The average annual precipitation is 525 mm, with large seasonal differences in precipitation, mainly concentrated in June to September, and the evaporation of the water surface is 1100 to 2000 mm. According to statistics, there are nearly 60 large and small rivers in the study area, and the average annual runoff of the upper reaches of the main rivers in the mountainous area is 2.4 to 2.91 billion m 3 , the average annual runoff has dropped by 20% to 80% in the past 10 years. Precipitation infiltration is the main source of groundwater recharge in the study area. Lateral recharge in front of the mountain, river leakage, canal leakage, irrigation water backseepage, and top support recharge from the lower aquifer are also recharge sources. The monthly depth data of groundwater monitoring stations in the area from January 2000 to December 2021 were used as characteristic data. Based on the collection and collation of groundwater level depth data since 2000, the groundwater monitoring station network in the study area was statistically analyzed. From 2000 to 2017, water level depth data of 967 shallow groundwater artificial monitoring stations (including unified measurement stations) were collected.

[0101] Firstly, the data are analyzed to see whether they meet the requirements of the Kriging interpolation method. Then, an appropriate semivariogram function is selected to establish a model for fitting. In this way, the groundwater depth distribution map of the study area for that month is obtained and rasterized. Finally, the data set for subsequent long-term correlation analysis is established by statistically analyzing the grid mean, i.e., the average groundwater depth data set.

[0102] Based on the groundwater average depth dataset, the average groundwater depth change map of the study area and typical funnel area was drawn. Figure 2 , the thin solid line in the figure is the linear trend line of the buried depth fitting, and the thick solid line is the five-year sliding average change line. From the above analysis, it can be seen that since the 21st century, the precipitation in the study area and the typical funnel area has alternated between high and low, and extreme high precipitation occurred in 2021. Groundwater extraction was higher than the multi-year average before 2014. At the end of 2014, the middle route of the South-to-North Water Diversion Project was put into operation, providing conditions for large-scale pressure extraction in the comprehensive management of groundwater overexploitation carried out in the same year. After 2018, water replenishment conditions have improved.

[0103] In this embodiment, the input of the joint model of geostatistics and fractal theory is the long-series groundwater depth monitoring data and the average groundwater depth data set. The Hurst index of groundwater depth is calculated by the rescaled range analysis method to analyze the long-term correlation of groundwater depth.

[0104] Considering the stability of the Hurst index and the change of groundwater depth in years, this embodiment uses a sliding time series, with 21 years of monthly groundwater depth data points in the study area as the total length of the time series, 15 years of monthly groundwater depth time series and a step length of 1 year for sliding, to calculate the Hurst index. Specifically, the first Hurst index is calculated based on the groundwater depth time series from 2000 to 2014, the second Hurst index is calculated based on the groundwater depth time series from 2001 to 2015, and so on, thereby providing a set of Hurst index sequences with a length of 8.

[0105] After obtaining the length of the research time series and the sliding step in the previous step, in this step, the long-term burial depth data of the groundwater station is imported into the calculation program to obtain the Hurst index of the station in different time series. In addition, based on the statistical burial depth data, the Hurst index of the average burial depth of regional groundwater is calculated, see Table 1.

[0106] Table 1

[0107]

[0108] According to the calculated changes in the Hurst index of the sliding sequence in the study area and the typical funnel area, Figure 4 shown.

[0109] from Figure 4 It can be concluded that the Hurst index in the study area is generally on a downward trend, and after the time series reached the maximum value of the Hurst index from 2003 to 2017, the Hurst index has been declining, but it is still greater than 0.5, reflecting that the long-term correlation of groundwater depth in the study area has declined. The depth will still be affected by the previous time series, but the degree of influence is decreasing. It is speculated that the reason is that after the ecological water replenishment of rivers and lakes, the study area received a large amount of external water supplement, the surface available water increased, the water use contradiction in the study area was alleviated, and the groundwater level decline rate slowed down. It can be concluded that water diversion has a certain impact on groundwater depth. It can be predicted that under the influence of the South-to-North Water Diversion Project and the Grand Canal water replenishment, the groundwater depth in the study area will continue to increase, but the growth rate will decrease.

[0110] Figure 3It is the contour map of Hurst index in the study area. Overall, the Hurst index in the study area is greater than 0.5 in all 6 time series, showing a more obvious persistence feature. The study area is divided into three parts according to the type of change in the Hurst index: the area where the Hurst index increases, the area where the Hurst index remains basically unchanged, and the area where the Hurst index decreases. For the sliding Hurst index, the increase in the Hurst index indicates that the time series better "remembers" the trend of groundwater depth in the later period, while the decrease in the Hurst index indicates that the time series better "remembers" the trend of groundwater depth in the early period. It can be roughly determined that in areas where the Hurst index increases, the groundwater depth will continue to increase due to overexploitation for some time in the future. In contrast, the groundwater depth in the other two areas will continue to fluctuate up and down, and the trend is not obvious.

[0111] The Hurst index of the typical funnel area shows an overall upward trend. After the 2005-2019 time series, there is a continuous downward trend, reflecting that the groundwater depth in the previous period still has a significant impact on the later period. However, with the ecological replenishment of rivers and lakes starting in 2019, the impact of the previous groundwater depth on the later period is gradually weakening.

[0112] In order to verify whether the regional Hurst index can represent the change of the Hurst index of the city, the average burial depth of the three cities in the typical funnel area after Kriging interpolation was used to calculate the Hurst index with the data of the station with the maximum burial depth in the area. The comparison of the Hurst index calculated by the two sets of data is shown in Table 2 and Figure 5 .

[0113] Table 2

[0114]

[0115] Depend on Figure 5 It can be seen that the difference between the Hurst index calculated from the average burial depth of the regional surface and the Hurst index calculated from the burial depth of the representative regional station is within 0.06. In most time series, the change of the regional Hurst index is consistent with the change of the station Hurst index, especially the trend of the prefecture-level city 1 is almost the same, which shows that the change of the Hurst index calculated by the station can represent the change trend of the regional Hurst index to a certain extent.

[0116] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A groundwater long-term correlation analysis method based on a joint model of geostatistics and fractal theory, characterized in that: include: Obtain initial groundwater long-sequence burial depth monitoring data in the study area, process the groundwater long-sequence burial depth monitoring data based on the spatiotemporal Kriging interpolation method, and obtain a groundwater average burial depth dataset; A joint model of geostatistics and fractal theory is constructed, and the initial groundwater long-series depth monitoring data and the average groundwater depth data are input into the joint model of geostatistics and fractal theory for processing to obtain output results, and the long-term correlation of the groundwater depth in the study area is analyzed through the output results.

2. The groundwater long-term correlation analysis method based on the joint model of geostatistics and fractal theory according to claim 1 is characterized in that: The average groundwater depth dataset is obtained, including: Calculate the empirical semivariogram, optimize the empirical semivariogram using the covariance function, and select the function that best expresses the correlation of variables in time, space, and spatiotemporal; Determine the grid size and obtain the groundwater depth difference of each grid center point by calculation; The groundwater depth difference of each grid center point is assigned to the grid, and the grid is converted into a raster with the same spatial resolution to obtain a groundwater average depth dataset.

3. The groundwater long-term correlation analysis method based on the joint model of geostatistics and fractal theory according to claim 1 is characterized in that: Constructing the joint model of geostatistics and fractal theory, including: Using a spectral analysis sequence to eliminate the influence of periodicity and trend items in the average groundwater depth data set, and determining the length of the Hurst exponent calculation data; Based on the Hurst index calculation data length, the Hurst index of groundwater depth is calculated by re-scaling range analysis method; According to the groundwater depth distribution and the Hurst index, the correlation between the change of the Hurst index and the change of the groundwater depth is analyzed to obtain the joint model of geostatistics and fractal theory.

4. The groundwater long-term correlation analysis method based on the joint model of geostatistics and fractal theory according to claim 3 is characterized in that: The spectral analysis sequence is used to eliminate the influence of periodicity and trend terms in the average groundwater depth data set, including: The average groundwater depth dataset is preprocessed to remove obvious trend items or perform differential processing. Fourier transform is applied to convert the processed data into the frequency domain, and frequency components related to periodicity and trend are identified through spectral analysis. In the frequency domain, a band-stop filter is used to filter out periodic frequency components, and frequency components without periodic fluctuations are retained. The processed spectrum is converted back to the time domain through inverse Fourier transform to obtain the screened average groundwater depth dataset.

5. The groundwater long-term correlation analysis method based on the joint model of geostatistics and fractal theory according to claim 4 is characterized in that: The Hurst index of groundwater depth is calculated by re-scaling range analysis method, including: The mean sequence of the screened groundwater average depth data set is defined as <x> τ ：< / x> calculate <X τ The cumulative deviation X(t,τ): X(t,τ)=∑ u＝1 (X(u)- <x> τ )1≤t≤τ< / x> calculate <X τ The extreme deviation R(τ): calculate <x> τ The standard deviation S(τ):< / x> Analyzing the statistical law of R(τ) / S(τ)=R / S, we can obtain: Where T is the number of data points in X(t), τ is any positive integer, τ ≥ 1, X(t) is a given time series, and H is the Hurst exponent; Among them, the least squares method is used to draw the τ and R / S relationship lines in the logarithmic grid, H is the slope of the relationship line, and X(u) is the time series with a length of u.

6. The groundwater long-term correlation analysis method based on the joint model of geostatistics and fractal theory according to claim 5 is characterized in that: The Hurst index of groundwater depth is calculated by the rescaled range analysis method, and the long-term correlation of groundwater depth is analyzed, including: The length of the time series is increased successively to calculate the Hurst exponent corresponding to different samples, and the number of samples when the Hurst exponent is stable is obtained as the sliding time series; Based on the Hurst calculation results and time period changes, the trend of groundwater depth changes is predicted.

7. The groundwater long-term correlation analysis method based on the joint model of geostatistics and fractal theory according to claim 1 is characterized in that: The output results are used to analyze the long-term correlation of groundwater depth in the study area, including: The long-term correlation of groundwater depth in the study area is analyzed by correlation function D(t) and Hurst index H: If the given time series {X(t)} is an independent random sequence with finite variance, then the exponent H = 0.5, and H depends on the correlation function D(t): D(t)=2 2H-1 -1; If H>0.5, D(t)>0, it has a positive persistence characteristic, and the future trend of the time series will be consistent with the historical data; if H<0.5, D(t)<0, it has an opposite persistence characteristic, and the future trend of the time series will be opposite to the past data.

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