A method for analyzing long-term correlation of groundwater based on a joint model of geostatistics and fractal theory

Abstract

The present invention discloses a method for analyzing long-term groundwater correlation based on a joint model of geostatistics and fractal theory. The method comprises the following steps: obtaining initial long-sequence groundwater depth monitoring data for a study area; processing the data using a spatiotemporal kriging interpolation method to obtain average groundwater depth data; constructing a joint model of geostatistics and fractal theory, inputting the initial long-sequence groundwater depth monitoring data and the average groundwater depth data into the joint model for processing to obtain an output result; and analyzing the long-term correlation of groundwater depth in the study area using the output result. The present invention provides more accurate and reliable prediction results, offering a more scientific basis for groundwater resource management and planning.

Description

Technical Field

[0001] The present invention relates to interdisciplinary technical fields such as groundwater hydrology, spatial data analysis, and mathematical modeling, 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 variation characteristics of groundwater levels are crucial for prediction and planning. However, traditional groundwater observation data often come from a limited number of scattered observation stations, making it difficult to conduct a comprehensive analysis of long-term groundwater changes in non-observed areas.

[0003] Despite a growing body of research on predicting groundwater dynamics, traditional interpolation methods typically only provide localized predictions and struggle to effectively capture global, long-term trends in groundwater levels. This is particularly true when analyzing long-term correlations. Therefore, it is necessary to explore a theoretical framework for analyzing the spatiotemporal evolution of groundwater depth that combines geostatistics with fractal theory to generate a systematic, comprehensive, and reliable groundwater depth dataset. Summary of the Invention

[0004] To solve the above technical problems, the present invention proposes a long-term groundwater correlation analysis method based on a joint model of geostatistics and fractal theory, aiming to address the limitations of traditional geostatistical methods in capturing the long-term variation patterns 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 objectives, the present invention provides a groundwater long-term correlation analysis method based on a combined model of geostatistics and fractal theory, comprising:

[0006] Obtain initial long-sequence groundwater depth monitoring data in the study area, process the long-sequence groundwater depth monitoring data based on the spatiotemporal kriging interpolation method, and obtain a groundwater average 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 it using the covariance function, and select the function that best expresses the correlation of variables in time, space, and spatiotemporal terms;

[0010] Determine the grid size and obtain the groundwater depth difference of each grid center point through 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 terms 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 the groundwater depth is calculated by rescaling the 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 terms in the average groundwater depth dataset 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 trends 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 exponent of groundwater depth is calculated by rescaled range analysis method, including:

[0019] The mean sequence of the filtered groundwater average depth dataset is defined as <x> τ :

[0020]

[0021] calculate <x> τ The cumulative deviation X(t,τ):

[0022]

[0023] calculate <x> τ The 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] The least squares method is used to draw the τ and R / S relationship lines on the logarithmic grid, H is the slope of the relationship line, and X(u) is the time series with length u.

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

[0032] The Hurst exponent corresponding to different samples is calculated by increasing the length of the time series in sequence, 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 using the correlation function D(t) and the 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] This method effectively utilizes spatial local interpolation techniques from geostatistics to optimize the spatial distribution of data, while simultaneously applying fractal theory to accurately model groundwater dynamics. Compared with traditional methods, this method reduces prediction errors caused by sparse or unevenly distributed data and enhances the model's adaptability to groundwater dynamics under complex geological conditions. By incorporating the multi-scale properties of fractal theory, this method can better capture subtle characteristics of groundwater changes, providing more accurate and reliable predictions and offering a more scientific basis for groundwater resource management and planning. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying 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 This is a contour map of the Hurst index of the study area of ​​an embodiment of the present invention;

[0045] Figure 4 Schematic diagram of the Hurst exponent changes 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 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 of the embodiments in this 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 long-sequence groundwater depth monitoring data in the study area, process the long-sequence groundwater depth monitoring data based on the spatiotemporal kriging interpolation method, and obtain a groundwater average 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 utilizes spatial local interpolation techniques from geostatistics to optimize the spatial distribution of data, while simultaneously applying fractal theory to accurately model groundwater dynamics. Compared with traditional methods, this embodiment reduces prediction errors caused by sparse or unevenly distributed data and enhances the model's adaptability to groundwater dynamics under complex geological conditions. By incorporating the multi-scale properties of fractal theory, it can better capture subtle characteristics of groundwater fluctuations, providing more accurate and reliable prediction results and providing 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 it using the covariance function, and select the function that best expresses the correlation of variables in time, space, and spatiotemporal terms;

[0055] Determine the grid size and obtain the groundwater depth difference of each grid center point through 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 is calculated at each time point.

[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 spatiotemporal domain and establish a spatiotemporal covariance function to express the spatiotemporal correlation of variables. Multiple spatiotemporal covariance functions are often used to optimize the empirical semivariogram, ultimately selecting the function with the best performance in time, space, and space-time.

[0061] Step 3: Interpolation grid selection. The grid size determines the interpolation accuracy, but the smaller the grid size, the greater the computational complexity of the space-time kriging model and the longer the model calculation time.

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

[0063] Space-time kriging, a geostatistical technique, can fully exploit the spatiotemporal correlations in groundwater level data. By constructing a spatiotemporal model, it can predict groundwater levels at different points in time and space. This method not only fills data gaps between observation stations but also generates accurate groundwater level maps in unobserved areas, thereby predicting long-term variations in these areas. Incorporating fractal theory, space-time kriging further refines the analysis. Fractal theory, by studying the self-similarity and long-term dependence of groundwater level data, can reveal its long-term correlation characteristics. The high-resolution data provided by space-time kriging enables fractal theory to more accurately calculate long-range correlations in 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 terms 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 the groundwater depth is calculated by rescaling the 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 geostatistical and fractal theory model is the initial long-series groundwater depth monitoring data and the average groundwater depth dataset. The Hurst exponent of groundwater depth is calculated through 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 data length for calculating the Hurst exponent. In this example, based on the groundwater depth statistical series, the Hurst exponent is calculated for different samples with increasing time series length. The number of samples at which the Hurst exponent stabilizes is used as a sliding time series, and the sliding step is one year.

[0071] The second step is to calculate the Hurst index. The monthly groundwater depth of the station and the regional groundwater depth statistical 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 the Hurst index. Based on the groundwater depth distribution and the calculated Hurst index, the correlation between the changes in the Hurst index and the changes in 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 terms in the average groundwater depth dataset, including:

[0074] The average groundwater depth dataset was preprocessed to remove obvious trend items or perform differential processing. Fourier transform was applied to convert the processed data into the frequency domain, and frequency components related to periodicity and trend were identified through spectral analysis. In the frequency domain, a band-stop filter was used to filter out periodic frequency components, and frequency components without periodic fluctuations were retained. The processed spectrum was 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 for a groundwater depth time series, two aspects need to be considered: First, the presence of periodicity and trend terms in the time series significantly impacts the calculation of the Hurst exponent. Therefore, a spectral analysis sequence is needed to eliminate the effects of these periodicity and trend terms. Second, the stability conditions for the calculated Hurst exponent should be explored, as the stability of the Hurst exponent affects the accuracy of long-term correlations.

[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 successively, 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 successively to calculate the Hurst index corresponding to different samples. This experiment selected 5 representative stations of 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 is less than 110, the Hurst index value fluctuates greatly and then tends to be stable. In the second set of experiments, when the number of samples was greater than 160, the Hurst exponents of the eight selected groundwater monitoring stations and the five statistical series tended to be stable with the change of sample number.

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

[0078] The mean sequence of the filtered groundwater average depth dataset is defined as <x> τ :

[0079]

[0080] calculate <x> τ The cumulative deviation X(t,τ):

[0081]

[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] The least squares method is used to draw the τ and R / S relationship lines on the logarithmic grid, H is the slope of the relationship line, and X(u) is the time series with length 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 measuring 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 Hurst exponent corresponding to different samples is calculated by increasing the length of the time series in sequence, 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 using the correlation function D(t) and the 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 variations, mainly concentrated from June to September. The evaporation rate is 1100 to 2000 mm. According to statistics, there are nearly 60 rivers and streams in the study area. 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 sharply 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 back-infiltration, and top-up 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 were collected from 967 shallow groundwater artificial monitoring stations (including unified monitoring stations).

[0101] First, we analyzed whether the data met the requirements of the Kriging interpolation method. Then, we selected an appropriate semivariogram function to establish a model for fitting. This method obtained the groundwater depth distribution map of the study area for that month and performed rasterization processing. Finally, we established a dataset for subsequent long-term correlation analysis by statistically analyzing the grid mean, namely, the average groundwater depth dataset.

[0102] Based on the groundwater average depth dataset, the groundwater average depth change map of the study area and typical funnel area was drawn. Figure 2 The thin solid line in the figure represents the linear trend line fitted by the depth, and the thick solid line represents the five-year sliding average. The above analysis shows that since the 21st century, the study area and the typical funnel region have experienced alternating periods of high and low rainfall, with extremely high rainfall occurring in 2021. Groundwater extraction was consistently above the multi-year average before 2014. The South-to-North Water Diversion Project's Middle Route commenced operation at the end of 2014, paving the way for large-scale reductions in groundwater overexploitation as part of the comprehensive groundwater overexploitation control program launched that same year. After 2018, water replenishment conditions 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 dataset. The Hurst exponent of groundwater depth is calculated by the rescaled range analysis method, which is used to analyze the long-term correlation of groundwater depth.

[0104] Considering the stability of the Hurst index and the annual variation of groundwater depth, this example uses a sliding time series, with 21 years of monthly groundwater depth data points for the study area as the total length of the time series, a 15-year monthly groundwater depth time series, and a 1-year step size 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. This provides a set of Hurst index sequences with a length of 8.

[0105] After obtaining the length of the study time series and the sliding step in the previous step, in this step, the long-term burial depth data of the groundwater monitoring 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 The Hurst index for the study area shows an overall downward trend. After reaching its maximum value in the 2003-2017 time series, the Hurst index has continued to decline, but remains above 0.5. This reflects a decline in the long-term correlation of groundwater depth in the study area. While the depth is still affected by the previous time series, the degree of influence is decreasing. This is presumably due to the large amount of external water diversion received by the study area after ecological water replenishment from rivers and lakes. This has increased surface water availability, alleviated water use conflicts in the study area, and slowed the rate of groundwater level decline. This suggests that water diversion has a certain impact on groundwater depth. It is predictable that, due to the South-to-North Water Diversion Project and the Grand Canal water diversion project, groundwater depth in the study area will continue to increase, but at a slower rate.

[0110] Figure 3 This is a contour map of the Hurst index for the study area. Overall, the Hurst index for all six time series is greater than 0.5, demonstrating a strong persistence pattern. The study area is divided into three regions based on the type of Hurst index change: areas with increasing Hurst index, areas with essentially unchanged Hurst index, and areas with decreasing Hurst index. For the sliding Hurst index, an increasing Hurst index indicates that the time series better "remembers" later groundwater depth trends, while a decreasing Hurst index indicates that the time series better "remembers" earlier groundwater depth trends. It can be roughly determined that in areas with increasing Hurst index, groundwater depth will continue to increase due to overexploitation for some time to come. In contrast, groundwater depth in the other two regions will continue to fluctuate, with no clear trend.

[0111] The Hurst index of the typical funnel area showed an overall upward trend. After the 2005-2019 time series, there was a continuous downward trend, reflecting that the groundwater depth in the previous period still had a relatively significant impact on the later period. However, with the ecological water replenishment of rivers and lakes starting in 2019, the impact of the early 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 largest 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]

[0116] Depend on Figure 5 As can be seen from the data, the Hurst index calculated from the regional average depth and the Hurst index calculated from the depth of the representative regional station are within 0.06. For most of the time series, the changes in the regional Hurst index are consistent with those at the station. In particular, the trends in the prefecture-level city 1 are almost identical, indicating that the changes in the Hurst index calculated at the station can, to a certain extent, represent the regional Hurst index trend.

[0117] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.< / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x>

Claims

1. A groundwater long-term correlation analysis method based on a joint model of geostatistics and fractal theory, characterized by: include: Obtain initial long-sequence groundwater depth monitoring data in the study area, process the long-sequence groundwater depth monitoring data based on the spatiotemporal kriging interpolation method, and obtain a groundwater average depth dataset; Constructing a joint model of geostatistics and fractal theory, inputting the initial groundwater long-series depth monitoring data and the average groundwater depth data into the joint model of geostatistics and fractal theory for processing, obtaining output results, and analyzing the long-term correlation of the groundwater depth in the study area through the output results; Obtaining the average groundwater depth dataset includes: Calculate the empirical semivariogram, optimize the empirical semivariogram using the covariance function, and select the function that best expresses the correlation between variables in time, space, and spatiotemporal; Determine the grid size and obtain the groundwater depth difference of each grid center point through calculation; Assigning the groundwater depth difference of each grid center point to the grid, and converting the grid into a raster with the same spatial resolution to obtain a groundwater average depth dataset; Constructing the joint model of geostatistics and fractal theory includes: Using a spectral analysis sequence to eliminate the influence of periodicity and trend terms 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 the groundwater depth is calculated by rescaling the 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; A spectral analysis sequence is used to eliminate the influence of periodicity and trend terms in the average groundwater depth dataset, including: Preprocessing the average groundwater depth dataset to remove obvious trend items or perform differential processing, applying Fourier transform to convert the processed data into the frequency domain, and identifying frequency components related to periodicity and trends through spectral analysis. In the frequency domain, using a band-stop filter to filter out periodic frequency components and retain frequency components without periodic fluctuations. The processed spectrum is converted back to the time domain through inverse Fourier transform to obtain a filtered average groundwater depth dataset; The Hurst index of groundwater depth is calculated by rescaled range analysis method, including: The mean sequence of the filtered groundwater average depth dataset is defined as <x> τ ：< / x> calculate <x> τ The cumulative deviation X(t,τ):< / x> calculate <x> τ The extreme deviation R(τ):< / x> 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 relationship line between τ and R / S is drawn on the logarithmic grid using the least squares method, H is the slope of the relationship line, and X(u) is the time series with length u; 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 Hurst exponent corresponding to different samples is calculated by increasing the length of the time series in sequence, 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.

2. The groundwater long-term correlation analysis method based on the combined 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 using the correlation function D(t) and the 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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