GNSS thermo-elastic deformation estimation method based on hierarchical full-spectrum finite element model

Abstract

The application discloses a GNSS thermal-elastic deformation estimation method based on a layered full-spectrum finite element model, which constructs a thermal-elastic coupling finite element model of a multi-layer medium of "shallow soil-deep bedrock", uses reanalysis soil temperature data with a resolution of 6 hours as temperature forcing, carries out site modeling in combination with site layered parameters (such as thermal / mechanical parameters and thickness of soil and bedrock), and adopts multi-UTC time solving and vector averaging to inhibit time sequence bias caused by fixed UTC sampling; in numerical solving, diurnal, seasonal to interannual full-band thermal-elastic responses are solved by explicit analysis, and the vertical displacement estimation sequence of the GNSS site and the correction field are output, so that the method is used for non-structure signal separation and precision improvement of the GNSS coordinate time sequence, and has global promotion and engineering application feasibility.

Description

Technical Field

[0001] This invention belongs to the field of satellite geodesy, and particularly relates to nonlinear deformation modeling of GNSS station coordinate time series, specifically to a GNSS thermoelastic deformation estimation method based on a layered full-spectrum finite element model. Background Technology

[0002] The shallow crustal medium expands and contracts with temperature fluctuations, resulting in minute but continuous deformations near the monitoring station. This type of deformation is commonly referred to as thermoelastic displacement. In regions with significant seasonal or diurnal temperature variations, and against the backdrop of global warming and increasingly frequent extreme weather events, the thermoelastic effect becomes increasingly pronounced in GNSS coordinate time series. Without proper modeling, it can easily be superimposed or confused with other geophysical signals, leading to misjudgments of long-term trends and nonlinear components. The systematic deviation can reach approximately ±0.2 mm / yr.

[0003] Since the mid-to-late 20th century, two main modeling approaches have emerged in academia regarding the thermoelastic effects of GNSS stations:

[0004] (1) Analytical solution model (half-space / harmonic model): Using a half-space elastic body as an approximation and employing periodic forcing by the surface temperature, an analytical expression for displacement is obtained. This type of model is simple in form and highly efficient in computation, but it usually requires the input field to be relatively smooth in space, and its ability to characterize the coupling between complex station structures and media layers is limited. Some studies have further considered the station burial depth and structural type, but the description of realistic factors such as shallow and deep stratification and the variation of thermal parameters with depth is still insufficient.

[0005] (2) Finite Element (FEM) numerical model: FEM can solve elastic-thermal coupling problems under complex geometry and heterogeneous medium conditions, and has a natural advantage in characterizing interlayer coupling. However, existing site-scale applications mostly treat the thermal and mechanical parameters of the site as a homogeneous medium with constant depth, which limits the physical reality of the "shallow soil-deep bedrock" layered structure; in some coastal and complex surface environments, the relative performance of homogeneous FEM and analytical solutions also varies regionally.

[0006] Existing GNSS thermoelastic modeling methods mostly employ half-space analytical solutions or homogeneous FEM assumptions, which are insufficient to characterize the depth heterogeneity and interlayer coupling of shallow soil and deep bedrock in terms of thermal / mechanical parameters. To simplify implementation, daily-scale temperatures at fixed UTC times are commonly used as forcing, omitting diurnal and semi-diurnal frequency band information and easily leading to frequency folding and amplitude-phase bias. Using a single UTC sample at different latitudes and longitudes also introduces regional temporal system biases, resulting in insufficient consistency of the correction field globally. At the same time, there is limited use of reanalysis soil temperature data and site stratification parameters, which restricts the physical realism, generalizability, and robust identification of nonlinear trends of the model. Summary of the Invention

[0007] To overcome the shortcomings of the existing technologies, this invention provides a GNSS thermoelastic vertical displacement estimation method based on a layered full-spectrum finite element model. This method constructs a thermo-elastic coupled finite element model of a multi-layered medium consisting of shallow soil and deep bedrock. It uses reanalysis soil temperature data at 6-hour resolution as temperature forcing, and combines site layering parameters (such as the thermal / mechanical parameters and thickness of soil and bedrock) for site-specific modeling. Multiple UTC time-series solutions and vector averaging are employed to suppress the temporal bias caused by fixed UTC sampling. In the numerical solution, the thermoelastic response across the entire frequency band, including day / night, seasonal, and interannual periods, is explicitly analyzed. The method outputs the vertical displacement estimation sequence of the GNSS station and its correction field, which can then be used for non-structural signal separation and accuracy improvement of GNSS coordinate time series. This method is feasible for global promotion and engineering applications.

[0008] According to one aspect of the present invention, a method for estimating GNSS thermoelastic deformation based on a hierarchical full-spectrum finite element model is provided, characterized in that it includes:

[0009] Model the finite element temperature field to obtain the time-varying layered underground temperature field;

[0010] Based on the obtained layered underground temperature field, the thermoelastic strain of each layer of medium due to temperature changes is calculated.

[0011] Determine the vertical strain amplification factor under lateral rigid constraint, and determine the actual vertical thermal strain based on the vertical strain amplification factor;

[0012] Integrating the magnified vertical thermal strain of each layer along the depth yields a thermoelastic vertical displacement time series.

[0013] Based on the modeled finite element temperature field, surface temperature forcing is applied at different times of the day to obtain multiple thermoelastic vertical displacement time series, and the long-term variation trend and periodic term of each thermoelastic vertical displacement time series are decomposed.

[0014] The decomposed periodic terms are synthesized by vector averaging of harmonic components.

[0015] The high-frequency residual signals of each sequence after removing long-term variation trends and periodic terms are averaged in the frequency domain to obtain the comprehensive high-frequency residual signal.

[0016] Based on the long-term trend, the synthesized periodic term, and the comprehensive high-frequency residual signal, the comprehensive thermoelastic vertical displacement time series is reconstructed and the long-term trend is extracted.

[0017] As a further technical solution, modeling the finite element temperature field also includes:

[0018] A one-dimensional layered finite element model was used to simulate the temperature field at a preset depth underground. The preset depth was divided into several layers corresponding to the standard layer depth of ERA5 soil temperature. A bedrock layer was added between the maximum value of the standard layer depth and the preset depth to capture the thermo-elastic coupling effect of shallow and deep layers at the same time.

[0019] As a further technical solution, modeling the finite element temperature field also includes:

[0020] At the interface between adjacent layers, the continuity conditions of temperature and heat flux are satisfied. The surface temperature at the upper boundary is directly assigned by the surface air temperature from the ERA5 reanalysis, and the temperature at the lower boundary is fixed as the long-term average temperature of the deepest soil layer, so as to achieve an approximate mixed adiabatic-isothermal boundary condition.

[0021] As a further technical solution, the magnified vertical thermal strain of each layer is integrated along the depth to obtain a thermoelastic vertical displacement time series, which includes the layer-by-layer accumulation of the vertical strain increments of all finite element elements of the underground profile from the surface to the bottom according to the following formula:

[0022] ,

[0023] in, For a moment The total vertical displacement, The total number of layers, For the first The number of finite element elements in the layer division. For the first Layer The thickness of each unit For the first Each unit at time average temperature For reference temperature, and The first The coefficient of thermal expansion and Poisson's ratio of the medium.

[0024] As a further technical solution, after obtaining multiple thermoelastic vertical displacement time series, the following is also included:

[0025] Each thermoelastic vertical displacement time series is represented as a superposition of long-term variation trend, periodic terms, and high-frequency residuals.

[0026] As a further technical solution, the decomposed periodic terms are synthesized by vector averaging of harmonic components, including:

[0027] For each harmonic component, amplitude-phase vector averaging is performed across multiple thermoelastic vertical displacement time series to synthesize a unified periodic term.

[0028] As a further technical solution, frequency domain vector averaging is performed on the high-frequency residual signals of each sequence after removing long-term trends and periodic terms, including:

[0029] Perform a discrete Fourier transform on the high-frequency residual signal of each sequence to obtain its spectral representation;

[0030] In the frequency domain, the corresponding frequency components of multiple sequences are averaged.

[0031] An inverse Fourier transform is performed on the averaged spectrum to reconstruct the composite high-frequency residual signal in the time domain.

[0032] As a further technical solution, the reconstructed comprehensive thermoelastic vertical displacement time series is divided into each trend segment. The inner representation is as follows:

[0033] ,

[0034] in, To synthesize the displacement of the thermoelastic vertical displacement time series, and Segmentation The average initial offset and the slope of the linear trend. and The first and second parts after vector average synthesis are respectively Harmonic amplitude and phase, For the high-frequency residual terms of the synthesis, For the time of the nth sampling point, For the first The angular frequency of harmonics.

[0035] As a further technical solution, after reconstructing the comprehensive thermoelastic vertical displacement time series, it also includes:

[0036] By applying a change point detection algorithm, the sequence is divided into several segments according to the points of change in deformation trend, and the slope of the linear trend of each segment is fitted.

[0037] The slope of each segment is weighted by time length to obtain the overall multi-year trend estimate.

[0038] According to one aspect of the present invention, a GNSS thermoelastic deformation estimation device based on a hierarchical full-spectrum finite element model is provided for implementing the method, comprising:

[0039] The first main module is used to model the finite element temperature field and obtain the layered underground temperature field that varies with time.

[0040] The second main module is used to calculate the thermoelastic strain of each layer of medium due to temperature changes based on the obtained layered underground temperature field.

[0041] The third main module is used to determine the vertical strain amplification factor under lateral rigid constraint, and to determine the actual vertical thermal strain based on the vertical strain amplification factor.

[0042] The fourth main module is used to integrate the amplified vertical thermal strain of each layer along the depth to obtain a thermoelastic vertical displacement time series.

[0043] The fifth main module is used to apply surface temperature forcing at different times of the day based on the modeled finite element temperature field, obtain multiple thermoelastic vertical displacement time series, and decompose the long-term variation trend and periodic term of each thermoelastic vertical displacement time series.

[0044] The sixth main module is used to synthesize the harmonic components of the decomposed periodic terms by vector averaging, and obtain the synthesized periodic terms.

[0045] The seventh main module is used to perform frequency domain vector averaging on the high-frequency residual signals of each sequence after removing long-term variation trends and periodic terms, so as to obtain a comprehensive high-frequency residual signal.

[0046] The eighth main module is used to reconstruct the comprehensive thermoelastic vertical displacement time series and extract the long-term trend based on the long-term change trend, the synthesized periodic term, and the comprehensive high-frequency residual signal.

[0047] Compared with existing half-space analytical models and homogeneous FEMs, the advantages of this invention are as follows:

[0048] This invention employs a layered, full-spectrum finite element model of "shallow soil to deep bedrock" to realistically depict deep heterogeneous media and interlayer coupling. By using 6-hour temperature forcing combined with multi-UTC (00 / 06 / 12 / 18) calculations and amplitude-phase vector averaging, it significantly reduces amplitude-phase distortion and regional temporal bias caused by diurnal sampling and fixed UTC sampling. It outputs station-level vertical displacement sequences and correction fields, which can be directly integrated into GNSS post-processing to improve the robustness of height sequence WRMS and trend estimation. The method relies on standard data such as ERA5 and SoilGrids, is parameterized and transparent, and can be produced in parallel batches, possessing global promotion and engineering application value. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1The flowchart illustrates the GNSS thermoelastic vertical displacement estimation method based on a layered full-spectrum finite element model, as provided in this embodiment of the invention.

[0051] Figure 2 This is a schematic diagram of the thermoelastic displacement time series of the method provided in the embodiments of the present invention at four different UTC periods. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0053] Figure 1 This is a flowchart illustrating the GNSS thermoelastic vertical displacement estimation method based on a hierarchical full-spectrum finite element model, according to an embodiment of the present invention. The system demonstrates the complete steps from temperature forcing input, finite element modeling, to multi-time vector averaging and trend extraction. This embodiment of the present invention provides a GNSS thermoelastic deformation estimation method based on a hierarchical full-spectrum finite element model, the specific implementation process of which is as follows:

[0054] Step 1: Finite element temperature field modeling.

[0055] A one-dimensional layered finite element model was used to simulate the temperature field at a depth of 0–50 m underground. The 0–50 m depth was divided into five layers, corresponding to the standard depths of ERA5 soil temperatures (0–7 cm, 7–28 cm, 28–100 cm, 100–255 cm). An additional bedrock layer was added below 255 cm up to 50 m to simultaneously capture the thermo-elastic coupling effects of both shallow (diurnal cycle, monthly cycle) and deep (annual cycle, multi-year trend) layers. The temperature evolution of each layer satisfies the one-dimensional heat conduction governing equation:

[0056] ,

[0057] in, Indicates the first Layer medium at depth Location, Time Instantaneous temperature (°C) at that time. For the first Thermal diffusivity of the layer medium (m² / s). For time, For depth, This is the internal heat source or latent heat flux term (taken as 0 in this embodiment). The interface between adjacent layers (the interface along the layer thickness direction) satisfies the continuity conditions for temperature and heat flux. Regarding boundary conditions: the upper boundary surface ( =0) Temperature is directly assigned from the surface air temperature obtained from ERA5 reanalysis (6-hour time series data), lower boundary ( The temperature at a depth of 50m is fixed at the long-term average temperature of the fourth layer (the deepest soil layer) to achieve an approximate mixed adiabatic-isothermal boundary condition. Through this modeling, the time-varying stratified subsurface temperature field can be obtained.

[0058] Step 2: Calculate the thermoelastic strain of each layer.

[0059] Using the layered temperature field obtained in step one, the thermoelastic strain of each layer of the medium due to temperature changes can be calculated. For the first... The layer, whose one-dimensional linear free thermal expansion strain is expressed as:

[0060] ,

[0061] in, For the first Vertical thermal strain of the layer (dimensionless). The coefficient of linear thermal expansion of this medium is K⁻¹. For the first Layer at time temperature, This is the multi-year average temperature of the medium layer (used as a thermal expansion reference temperature). According to the formula above, the temperature of a certain layer relative to the reference temperature... An increase in temperature leads to positive thermal expansion strain (material stretching), while a decrease in temperature results in negative thermal expansion strain (material contraction). The greater the temperature change, the greater the strain value.

[0062] Step 3: Lateral constraint effect and vertical strain amplification.

[0063] Because the underground medium is subjected to approximately rigid lateral constraints in the horizontal direction, the free thermal expansion strain calculated for each layer will be amplified in the vertical direction. This amplification effect can be expressed using Poisson's ratio. The function is used to characterize it. For the ... The vertical strain amplification factor under lateral rigid constraint is defined as follows:

[0064] ,

[0065] in, This is the Poisson's ratio of the medium layer. The actual vertical thermal strain is approximately equal to the free strain multiplied by this amplification factor. The amplification factor mentioned above originates from the deformation enhancement effect of a one-dimensional vertical column under fully lateral constraints. When the Poisson's ratios of the various medium layers are similar and the horizontal scale of the site is much larger than the layer thickness, this factor can be used as an approximate estimate of the vertical strain amplification.

[0066] Step 4: Calculate the vertical displacement by integrating along the depth.

[0067] Integrating the magnified vertical thermal strain of each layer along the depth yields the total vertical displacement change at the surface, i.e., the thermoelastic vertical displacement time series. Specifically, the vertical strain increments of all finite element elements in the underground profile from the surface to the bottom are accumulated layer by layer:

[0068] ,

[0069] in, For a moment The total vertical displacement, The total number of layers, For the first The number of finite element elements in the layer division. For this layer The thickness of each unit For this unit at time... average temperature For reference temperature (e.g., long-term average ground temperature). and The first The thermal expansion coefficient and Poisson's ratio of the layer medium. The physical meaning of the above summation is clear: for each depth element, its instantaneous vertical elongation is approximately the magnified strain plus the element thickness. The product of the units; by accumulating the minute elongations of all units along the depth direction, we obtain the sum of the vertical displacement changes caused by thermal expansion and contraction at the observation point, which is a thermoelastic vertical displacement time series.

[0070] Step 5: Construction and decomposition of displacement sequences under multi-time forcing.

[0071] Using the aforementioned finite element temperature field model, surface temperature forcing is applied at different times of the day to obtain multiple thermoelastic vertical displacement time series. In this embodiment, 6-hour resolution ERA5 air temperature data is used to drive the model at 0:00, 6:00, 12:00, and 18:00 UTC, respectively, resulting in four corresponding daily cyclic displacement series (thermoelastic vertical displacement time series). Since thermoelastic displacement exhibits periodic variation characteristics, each UTC-specific displacement time series is represented as a superposition of long-term variation trend, periodic term, and high-frequency residuals for subsequent processing.

[0072] ,

[0073] in, Indicates the first Displacement sequence at UTC time ( =1,2,3,4 correspond to UTC 0:00, 6:00, 12:00, and 18:00 respectively. For this sequence in segments Linear trend term within, and These are the first and second digits of the sequence, respectively. The amplitude and initial phase of each harmonic component, For the first The angular frequency of harmonics The number of harmonics to be explicitly modeled (e.g., including two harmonic terms: annual and semi-annual). This represents the high-frequency residuals (variations and noise other than the trend and main periodic components). Using the time series decomposition model described above, the long-term trend of each displacement sequence can be distinguished from the periodic oscillation components.

[0074] Step 6: Vector average synthesis of harmonic components.

[0075] For each harmonic component, amplitude-phase vector averaging is performed across four UTC-specific displacement time series to synthesize a unified periodic term. Specifically, the first step is to... No. 1 in the sequence The amplitude and phase of each harmonic component are represented as vectors in the complex plane:

[0076]

[0077] Then to =Average of the corresponding vectors of the 4 sequences:

[0078]

[0079] in, It is the first The first of the sequence The representation of harmonics in the complex plane (the real part and the imaginary part correspond to the cosine component and the sine component, respectively). This is the synthesized complex vector after vector averaging of the harmonic. The amplitude-phase vector averaging method can avoid the amplitude cancellation or phase distortion that occurs when the same periodic components of different sequences are directly added due to phase inconsistency, thus more accurately synthesizing the periodic deformation signals of each sequence.

[0080] Step 7: Frequency domain vector averaging of the high-frequency residual signal.

[0081] For the high-frequency residuals remaining after removing trends and major harmonics in each sequence The synthesis process is performed using the frequency domain vector averaging method. Specifically, the residual signal of each sequence is subjected to a Discrete Fourier Transform (FFT) to obtain its spectral representation. Then, in the frequency domain, the corresponding frequency components of the M=4 sequences are averaged:

[0082]

[0083] in, Indicates the first The residual signal of the sequence at angular frequency The complex amplitude value at that point, This represents the complex amplitude value after vector averaging of the corresponding frequency components. Finally, the spectrum after vector averaging... An inverse Fourier transform (IFFT) is performed to reconstruct the composite high-frequency residual signal in the time domain. This method of vector averaging the high-frequency residual in the frequency domain avoids the cancellation caused by the different phases of the sequences when directly adding high-frequency signals, thus more fully preserving the amplitude information of the high-frequency variation components.

[0084] Step 8: Reconstruct the composite displacement sequence and extract the long-term trend.

[0085] By superimposing the obtained average linear trend (i.e., long-term trend), synthetic harmonic components (i.e., unified periodic terms), and high-frequency residuals, the final comprehensive thermoelastic vertical displacement time series can be reconstructed. This comprehensive series is divided into segments based on each trend. The interior can be represented as:

[0086]

[0087] in, The displacement is the amount of displacement in the overall displacement sequence. and Segmentation The average initial offset and the slope of the linear trend. and The first and second parts after vector average synthesis are respectively Harmonic amplitude and phase, This represents the high-frequency residual terms from the synthesis. Next, a robust change-point detection algorithm is applied to the synthesized sequence, dividing it into segments based on the points of change in deformation trend, and then fitting the linear trend slope of each segment. Finally, a weighted average of the slopes of each segment is calculated based on the time length to obtain an overall multi-year trend estimate:

[0088]

[0089] in, For the first The duration of the segment. The trend extraction method described above integrates the sequence information of multiple forced moments, which can effectively estimate the long-period deformation components of GNSS stations and be used to assess the long-term stability of the station's vertical displacement.

[0090] By comparing the method of this invention with the traditional homogeneous finite element model, the advantages of this invention in GNSS thermoelastic deformation modeling and correction can be clearly demonstrated. A comparison of the amplitudes of the GNSS thermoelastic vertical displacement estimated by the method of this invention and the traditional homogeneous finite element model at annual and semi-annual frequencies shows that the estimations of the two models differ significantly, and the method of this invention is better able to characterize the true amplitude features. Figure 2 The thermoelastic displacement time series obtained using the method of this invention at four different UTC periods are presented, demonstrating that the method can capture and distinguish systematic differences caused by different sampling times. By comparing the changes in WRMS (weighted root mean square) of the GNSS elevation time series before and after correction, it is shown that after correction using the method of this invention, the fluctuation of the series is significantly reduced, effectively improving the GNSS vertical positioning accuracy and the robustness of long-term trend estimation.

[0091] The implementation of the various embodiments of the present invention is based on programmed processing by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of the present invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of the present invention provide a GNSS thermoelastic deformation estimation device based on a hierarchical full-spectrum finite element model. This device is used to execute a GNSS thermoelastic deformation estimation method based on a hierarchical full-spectrum finite element model from the above method embodiments.

[0092] The device includes: a first main module for modeling a finite element temperature field to obtain a time-varying layered underground temperature field; a second main module for calculating the thermoelastic strain of each layer of medium due to temperature changes based on the obtained layered underground temperature field; a third main module for determining the vertical strain amplification factor under lateral rigid constraints and determining the actual vertical thermal strain based on the vertical strain amplification factor; a fourth main module for integrating the amplified vertical thermal strain of each layer along the depth to obtain a thermoelastic vertical displacement time series; and a fifth main module for implementing [the process] at different times of the day based on the modeled finite element temperature field. Surface temperature forcing yields multiple thermoelastic vertical displacement time series, and the long-term trend and periodic term of each thermoelastic vertical displacement time series are decomposed. The sixth main module is used to synthesize the decomposed periodic term by vector averaging of harmonic components to obtain the synthesized periodic term. The seventh main module is used to perform frequency domain vector averaging on the high-frequency residual signal of each series after removing the long-term trend and periodic term to obtain the comprehensive high-frequency residual signal. The eighth main module is used to reconstruct the comprehensive thermoelastic vertical displacement time series and extract the long-term trend based on the long-term trend, the synthesized periodic term, and the comprehensive high-frequency residual signal.

[0093] This invention provides a GNSS thermoelastic deformation estimation device based on a layered full-spectrum finite element model. Addressing the limitations of existing GNSS thermoelastic modeling methods that often employ half-space analytical solutions or homogeneous FEM assumptions, which struggle to characterize the deep heterogeneity and interlayer coupling of thermal / mechanical parameters between shallow soil and deep bedrock, this invention utilizes several modules to construct a thermo-elastic coupled FEM in a multi-layered medium of shallow soil and deep bedrock. High temporal resolution (6-hour) reanalysis data is used as forcing, and site-layered parameters are introduced to achieve site-specific modeling. To suppress temporal bias caused by fixed UTC sampling, a strategy of solving at multiple UTCs (e.g., four times) and performing vector averaging is employed to explicitly analyze the full-spectrum response across day / night, season, and year, reducing frequency folding and regional inconsistencies. The device generates a site-specific vertical thermoelastic displacement estimation sequence and its correction field, which can be used for robust estimation of unstructured signals, amplitude, phase, and trends in GNSS coordinate time series, possessing global scalability and engineering application value.

[0094] It should be noted that the device embodiments provided by the present invention, in addition to implementing the methods in the above method embodiments, are also used to implement the methods in other method embodiments provided by the present invention. The difference lies only in setting corresponding functional modules, and their principles are basically the same as those of the above device embodiments provided by the present invention. As long as those skilled in the art, based on the above device embodiments and referring to the specific technical solutions in other method embodiments, obtain corresponding technical means and technical solutions constituted by these technical means by combining technical features, and improve the device in the above device embodiments while ensuring the practicality of the technical solutions, they can obtain corresponding device-type embodiments for implementing the methods in other method-type embodiments. For example:

[0095] In summary, the purpose of this invention is to provide a GNSS thermoelastic vertical displacement estimation method based on a layered full-spectrum finite element model. This method constructs a thermo-elastic coupled finite element model of a multi-layered medium consisting of shallow soil and deep bedrock. It uses reanalysis soil temperature data at a 6-hour resolution as temperature forcing, and combines site-specific parameters (such as the thermal / mechanical parameters and thickness of soil and bedrock) for site-specific modeling. Multiple UTC time-series solutions and vector averaging are employed to suppress the temporal bias caused by fixed UTC sampling. In the numerical solution, the thermoelastic response across the entire frequency band, including day / night, seasonal, and interannual periods, is explicitly analyzed. The method outputs the vertical displacement estimation sequence of the GNSS station and its correction field, which can be used for non-structural signal separation and accuracy improvement of GNSS coordinate time series. This method is feasible for global promotion and engineering applications.

[0096] The terms “comprising” and “having”, and any variations thereof, in the specification, claims, and accompanying drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0097] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for estimating the thermoelastic deformation of GNSS based on a hierarchical full-spectrum finite element model, characterized in that, include: Model the finite element temperature field to obtain the time-varying layered underground temperature field; Based on the obtained layered underground temperature field, the thermoelastic strain of each layer of medium due to temperature changes is calculated. Determine the vertical strain amplification factor under lateral rigid constraint, and determine the actual vertical thermal strain based on the vertical strain amplification factor; Integrating the magnified vertical thermal strain of each layer along the depth yields a thermoelastic vertical displacement time series. Based on the modeled finite element temperature field, surface temperature forcing is applied at different times of the day to obtain multiple thermoelastic vertical displacement time series, and the long-term variation trend and periodic term of each thermoelastic vertical displacement time series are decomposed. The decomposed periodic terms are synthesized by vector averaging of harmonic components. Frequency domain vector averaging is performed on the high-frequency residual signals of each sequence after removing long-term variation trends and periodic terms. This includes: performing discrete Fourier transform on the high-frequency residual signal of each sequence to obtain its spectral representation; averaging the corresponding frequency components of multiple sequences in the frequency domain; and performing inverse Fourier transform on the averaged spectrum to reconstruct the comprehensive high-frequency residual signal in the time domain. Based on the long-term trend, the synthesized periodic term, and the comprehensive high-frequency residual signal, the comprehensive thermoelastic vertical displacement time series is reconstructed and the long-term trend is extracted; wherein, the reconstructed comprehensive thermoelastic vertical displacement time series is represented in each trend segment p as follows: ， in, To synthesize the displacement of the thermoelastic vertical displacement time series, and Segmentation The average initial offset and the slope of the linear trend. and The first and second parts after vector average synthesis are respectively Harmonic amplitude and phase, For the high-frequency residual terms of the synthesis, For the time of the nth sampling point, For the first The angular frequency of harmonics.

2. The GNSS thermoelastic deformation estimation method based on a layered full-spectrum finite element model according to claim 1, characterized in that, Modeling the finite element temperature field also includes: A one-dimensional layered finite element model was used to simulate the temperature field at a preset depth underground. The preset depth was divided into several layers corresponding to the standard layer depth of ERA5 soil temperature. A bedrock layer was added between the maximum value of the standard layer depth and the preset depth to capture the thermo-elastic coupling effect of shallow and deep layers at the same time.

3. The GNSS thermoelastic deformation estimation method based on a layered full-spectrum finite element model according to claim 2, characterized in that, Modeling the finite element temperature field also includes: At the interface between adjacent layers, the continuity conditions of temperature and heat flux are satisfied. The surface temperature at the upper boundary is directly assigned by the surface air temperature from the ERA5 reanalysis, and the temperature at the lower boundary is fixed as the long-term average temperature of the deepest soil layer, so as to achieve an approximate mixed adiabatic-isothermal boundary condition.

4. The GNSS thermoelastic deformation estimation method based on a layered full-spectrum finite element model according to claim 1, characterized in that, Integrating the magnified vertical thermal strain of each layer along the depth yields a thermoelastic vertical displacement time series, which includes the layer-by-layer accumulation of vertical strain increments from all finite element elements of the underground profile from the surface to the bottom, according to the following formula: ， in, For a moment The total vertical displacement, The total number of layers, For the first The number of finite element elements in the layer division. For the first Layer The thickness of each unit For the first Each unit at time... average temperature For reference temperature, and The first The coefficient of thermal expansion and Poisson's ratio of the medium.

5. The GNSS thermoelastic deformation estimation method based on a layered full-spectrum finite element model according to claim 1, characterized in that, After obtaining multiple thermoelastic vertical displacement time series, the following is also included: Each thermoelastic vertical displacement time series is represented as a superposition of long-term variation trend, periodic terms, and high-frequency residuals.

6. The GNSS thermoelastic deformation estimation method based on a layered full-spectrum finite element model according to claim 1, characterized in that, The vector average synthesis of harmonic components from the decomposed periodic terms includes: For each harmonic component, amplitude-phase vector averaging is performed across multiple thermoelastic vertical displacement time series to synthesize a unified periodic term.

7. The GNSS thermoelastic deformation estimation method based on a layered full-spectrum finite element model according to claim 1, characterized in that, After reconstructing the comprehensive thermoelastic vertical displacement time series, it also includes: By applying a change point detection algorithm, the sequence is divided into several segments according to the points of change in deformation trend, and the slope of the linear trend of each segment is fitted. The slope of each segment is weighted by time length to obtain the overall multi-year trend estimate.

8. A GNSS thermoelastic deformation estimation device based on a hierarchical full-spectrum finite element model, used to implement the method described in any one of claims 1-7, characterized in that, include: The first main module is used to model the finite element temperature field and obtain the layered underground temperature field that varies with time. The second main module is used to calculate the thermoelastic strain of each layer of medium due to temperature changes based on the obtained layered underground temperature field. The third main module is used to determine the vertical strain amplification factor under lateral rigid constraint, and to determine the actual vertical thermal strain based on the vertical strain amplification factor. The fourth main module is used to integrate the amplified vertical thermal strain of each layer along the depth to obtain a thermoelastic vertical displacement time series. The fifth main module is used to apply surface temperature forcing at different times of the day based on the modeled finite element temperature field, obtain multiple thermoelastic vertical displacement time series, and decompose the long-term variation trend and periodic term of each thermoelastic vertical displacement time series. The sixth main module is used to synthesize the harmonic components of the decomposed periodic terms by vector averaging, and obtain the synthesized periodic terms. The seventh main module is used to perform frequency domain vector averaging on the high-frequency residual signals of each sequence after removing long-term variation trends and periodic terms, so as to obtain a comprehensive high-frequency residual signal. The eighth main module is used to reconstruct the comprehensive thermoelastic vertical displacement time series and extract the long-term trend based on the long-term change trend, the synthesized periodic term, and the comprehensive high-frequency residual signal.

Images