InSAR atmospheric delay correction method and device for water body load deformation

Abstract

The application relates to the field of geodetic surveying, and provides an InSAR atmospheric delay correction method and equipment for water body load deformation, which comprises the following steps: unwrapping differential interferograms generated by all SAR images to obtain unwrapped interferograms; identifying and correcting phase jumps of the unwrapped interferograms to obtain corrected interferograms; decoupling and removing stratified atmospheric delay phases and phase slopes in the corrected interferograms to obtain optimized interferograms corresponding to the corrected interferograms; modeling nonlinear deformation signals based on all the optimized interferograms to obtain turbulent atmospheric delay error of each SAR image; and removing the turbulent atmospheric delay error in the optimized interferograms based on the turbulent atmospheric delay error of all the SAR images to obtain final interferograms of a water body load influence area. The method can improve the accuracy of InSAR atmospheric delay correction for water body load deformation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of geodesy, in particular to an InSAR atmospheric delay correction method and equipment for water body load deformation. BACKGROUND

[0002] Satellite-borne synthetic aperture radar interferometry (InSAR, Interferometric Synthetic Aperture Radar) has the advantages of wide coverage, high spatial resolution, high accuracy of ground deformation monitoring, and is a common space geodetic technique for obtaining ground load-driven deformation. However, under natural conditions, the load change of the ground water body is relatively slow, and the ground deformation driven thereby is relatively small (~ 10 mm / yr), while the atmospheric delay noise, which is considered as the main error of InSAR deformation extraction, can introduce an error of up to 5.6 cm, and in addition, the water body covered area often shows the characteristics of mutual coupling of deformation, terrain and error, so it is difficult to separate the small ground deformation from the complex atmospheric delay error, which is a major problem in the field of InSAR water body load deformation monitoring at present.

[0003] Generally speaking, the interference phase in the InSAR interferogram can be expressed as: wherein is the deformation phase caused by the displacement of the ground surface during the two SAR acquisition times, is the atmospheric delay phase caused by the difference in atmospheric conditions at the two times, which can be divided into tropospheric delay and ionospheric delay, wherein the ionospheric delay often shows a long-wave trend, but the influence on short-wavelength (such as C-band Sentinel-1 satellite) sensors is smaller, and the tropospheric delay error is considered to be the main error source of InSAR observation, which can be mainly divided into a randomly distributed turbulent component in time and a stratified component showing seasonal fluctuations but related to terrain height; is the orbit error phase caused by inaccurate satellite orbit attitude data, which, like the ionospheric delay, shows a long-wave error in the interferogram; is a noise term, which is caused by many reasons in the ground water body covered area, such as unwrapping error and spatio-temporal decorrelation error.

[0004] The current mainstream atmospheric delay error correction methods can be divided into two categories: one is the use of auxiliary atmospheric data set or model of interference phase correction method; Another is based on the space-time distribution characteristics of atmospheric delay, from the interference phase itself modeling correction method. For the external data-based atmospheric delay error correction method, because the atmospheric delay phase and synthetic aperture radar (SAR, Synthetic Aperture Radar) satellite observation time of atmospheric temperature, humidity and pressure and other factors related, in many external data products, meteorological data is considered to be the most reliable one. At the same time, meteorological data can also be combined with high-precision global navigation satellite system (GNSS, Global Navigation Satellite System) data to estimate the InSAR interference phase of atmospheric delay error, but due to the low spatial resolution of the weather model, the global positioning system (GPS, Global Positioning System) data is affected by the regional station layout density, the accuracy of the correction cannot be guaranteed, so there are certain limitations.

[0005] The methods based on the phase of interferogram itself have obvious advantages, i.e. no need to rely on external data and can be adjusted according to the environmental characteristics of the study area, but these methods still have certain limitations in InSAR water load deformation monitoring. For ionospheric delay and orbit error showing long-wave trend, the common correction method is to remove it by polynomial fitting phase plane, but this method may cause over-fitting. And due to the differences in topographic features of the study area, the terrain distribution in the SAR scene of some study areas also shows long-wave trend, and the long-wave error and the terrain-related atmosphere are coupled, so the method of estimating the phase slope in the interferogram using the phase plane will cause part of the tropospheric delay error to be incorrectly estimated as long-wave error. At the same time, for the water load area, because the surface water (such as natural lakes and artificial reservoirs) is mostly in the basin, the surface deformation field driven by the mass change is often related to the terrain, and the layered components of the tropospheric delay are also related to the terrain height, so the surface deformation and the tropospheric delay error are also coupled, and the commonly used linear or power-law analysis model of phase terrain may cause the layered atmospheric components to be incorrectly estimated, and the traditional phase terrain correlation analysis result is not always accurate and is very susceptible to long-wave error in the interferogram. For the more complex random distribution characteristics in time of the turbulent component, various methods have been applied in actual production, but each has its limitations. For the phase stacking and space-time filtering methods, because the atmospheric delay is not Gaussian distributed, it may cause some local deformation signals in space-time to be incorrectly estimated as atmospheric noise, and the selection of the filtering window has strong empirical guidance, if the filtering window is too large, the deformation signal may be smoothed out, and if it is too small, it is difficult to remove the atmospheric delay noise; for the common scene image stacking (CSS, Common Scene Stacking) method and Tikhonov regularization method, although these two methods greatly improve the accuracy of atmospheric delay estimation, one of the important assumptions of these methods is that the deformation changes linearly in time, which is obviously not applicable to the nonlinear deformation in response to the fluctuation of the water load, and another important assumption of the traditional CSS method is that the atmospheric delay error is randomly distributed in time, which does not consider the differences in the distribution characteristics of the layered components and the turbulent components in the time dimension. For the turbulent component, the error is randomly distributed in time, but the layered component is not randomly distributed in time but shows seasonal periodic oscillation, and this method cannot well model and estimate the layered atmospheric noise. Therefore, for the extraction of the surface deformation driven by the water load change, because the deformation level is very small, it is easily disturbed by the atmospheric delay error, and the deformation, terrain and error are coupled, resulting in poor accuracy of InSAR atmospheric delay correction for water load deformation. SUMMARY

[0006] The application provides an InSAR atmospheric delay correction method and device for water load deformation, which can solve the problem of poor accuracy of InSAR atmospheric delay correction for water load deformation.

[0007] In a first aspect, the embodiments of the application provide an InSAR atmospheric delay correction method for water load deformation, which comprises the following steps:

[0008] SAR images of a water load affected area at multiple time points are used to generate multiple differential interferograms, and all the differential interferograms are unwrapped to obtain an unwrapped interferogram set; the unwrapped interferogram set comprises multiple unwrapped interferograms;

[0009] Phase jumps of each unwrapped interferogram are identified and corrected to obtain a corrected interferogram corresponding to each unwrapped interferogram;

[0010] Layered atmospheric delay phases and phase slopes in each corrected interferogram are decoupled, and the layered atmospheric delay phases are removed to obtain an optimized interferogram corresponding to each corrected interferogram;

[0011] Nonlinear deformation signal modeling is performed based on all the optimized interferograms to obtain turbulent atmospheric delay errors of each SAR image;

[0012] Based on the turbulent atmospheric delay errors of all the SAR images, the turbulent atmospheric delay errors in each optimized interferogram are removed to obtain a final interferogram corresponding to each optimized interferogram of the water load affected area.

[0013] In a second aspect, the embodiments of the application provide an InSAR atmospheric delay correction device for water load deformation, which comprises the following modules:

[0014] An unwrapping module is configured to generate multiple differential interferograms from SAR images of a water load affected area at multiple time points, and unwrap all the differential interferograms to obtain an unwrapped interferogram set; the unwrapped interferogram set comprises multiple unwrapped interferograms;

[0015] A correction module is configured to identify and correct phase jumps of each unwrapped interferogram to obtain a corrected interferogram corresponding to each unwrapped interferogram;

[0016] A decoupling module is configured to decouple layered atmospheric delay phases and phase slopes in each corrected interferogram, and remove the layered atmospheric delay phases to obtain an optimized interferogram corresponding to each corrected interferogram;

[0017] A nonlinear deformation signal modeling module is configured to perform nonlinear deformation signal modeling based on all the optimized interferograms to obtain turbulent atmospheric delay errors of each SAR image;

[0018] The removal module is used to remove the turbulent atmospheric delay error from each optimized interferogram based on the turbulent atmospheric delay error of all SAR images, so as to obtain the final interferogram corresponding to each optimized interferogram of the water load-affected area.

[0019] Thirdly, embodiments of this application provide a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the aforementioned InSAR atmospheric delay correction method for water load deformation.

[0020] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned InSAR atmospheric delay correction method for water load deformation.

[0021] The above-mentioned solution in this application has the following beneficial effects:

[0022] In the embodiments of this application, multiple differential interferograms are generated from SAR images of the water load-affected area at multiple times. All differential interferograms are unwrapped to obtain an unwrapped interferogram set. Then, phase jump identification and correction are performed on each unwrapped interferogram to obtain a corrected interferogram corresponding to each unwrapped interferogram. Next, the layered atmospheric delay phase and phase slope in each corrected interferogram are decoupled and the layered atmospheric delay phase is removed to obtain an optimized interferogram corresponding to each corrected interferogram. Then, nonlinear deformation signal modeling is performed based on all optimized interferograms to obtain the turbulent atmospheric delay error of each SAR image. Finally, based on the turbulent atmospheric delay error of all SAR images, the turbulent atmospheric delay error in each optimized interferogram is removed to obtain the final interferogram corresponding to each optimized interferogram of the water load-affected area. Among these methods, phase jump identification and correction of the interferogram can reduce the error caused by phase jump in the interferogram. Decoupling and removing the stratified atmospheric delay phase and phase slope takes into account the influence of the phase slope on the atmospheric delay phase estimation and effectively decouples the two to improve the accuracy of removing the stratified atmospheric delay phase. The removal of turbulent atmospheric delay error in the optimized interferogram further reduces the atmospheric delay of deformation information in the interferogram, realizes the accurate representation of water load deformation, and thus improves the accuracy of InSAR atmospheric delay correction for water load deformation.

[0023] Other beneficial effects of this application will be described in detail in the following detailed description section. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 A flowchart of an InSAR atmospheric delay correction method for water load deformation provided in an embodiment of this application;

[0026] Figure 2 A phase terrain relationship estimation comparison diagram provided in an embodiment of this application;

[0027] Figure 3 A comparison diagram of surface deformation under water load provided in an embodiment of this application;

[0028] Figure 4 This is a schematic diagram of a triangular phase closed loop provided in an embodiment of this application;

[0029] Figure 5 This is a schematic diagram of the delay correction result provided in an embodiment of this application;

[0030] Figure 6 A schematic diagram of STD comparison of interferograms provided in an embodiment of this application;

[0031] Figure 7 This is a schematic diagram comparing LOS-oriented surface deformation according to an embodiment of this application;

[0032] Figure 8 This is a schematic diagram of the InSAR atmospheric delay correction device for water load deformation provided in an embodiment of this application.

[0033] Figure 9 This is a schematic diagram of the structure of a terminal device provided in an embodiment of this application. Detailed Implementation

[0034] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0035] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0036] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0037] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrases "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0038] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0039] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0040] To address the issue of poor accuracy in existing InSAR atmospheric delay corrections for water load deformation, this application provides an InSAR atmospheric delay correction method for water load deformation. This method generates multiple differential interferograms from SAR images of the water load-affected area at multiple times, unwraps all differential interferograms to obtain an unwrapped interferogram set, identifies and corrects phase jumps in each unwrapped interferogram to obtain a corrected interferogram. Then, it decouples the layered atmospheric delay phase and phase slope in each corrected interferogram and removes the layered atmospheric delay phase to obtain an optimized interferogram for each corrected interferogram. Based on all optimized interferograms, it models nonlinear deformation signals to obtain the turbulent atmospheric delay error for each SAR image. Finally, based on the turbulent atmospheric delay error of all SAR images, it removes the turbulent atmospheric delay error from each optimized interferogram to obtain the final interferogram corresponding to each optimized interferogram of the water load-affected area. Among these methods, phase jump identification and correction of the interferogram can reduce the error caused by phase jump in the interferogram. Decoupling and removing the stratified atmospheric delay phase and phase slope takes into account the influence of the phase slope on the atmospheric delay phase estimation and effectively decouples the two to improve the accuracy of removing the stratified atmospheric delay phase. The removal of turbulent atmospheric delay error in the optimized interferogram further reduces the atmospheric delay of deformation information in the interferogram, realizes the accurate representation of water load deformation, and thus improves the accuracy of InSAR atmospheric delay correction for water load deformation.

[0041] The following is an exemplary description of the InSAR atmospheric delay correction method for water load deformation provided in this application.

[0042] like Figure 1 As shown, the InSAR atmospheric delay correction method for water load deformation provided in this application includes the following steps:

[0043] Step 11: Generate multiple differential interferograms from SAR images of the water load-affected area at multiple times, and unwrap all differential interferograms to obtain an unwrapped interferogram set.

[0044] The unwrapped interferogram set includes multiple unwrapped interferograms.

[0045] The aforementioned water load-affected areas refer to the regions affected by water loads requiring deformation monitoring, such as the area where a lake is located. The multiple time points refer to specific moments within historical time periods during which deformation monitoring of the water load-affected areas is required. For example, if the deformation of a lake needs to be monitored from March 1st to July 1st, and the number of time points is 5, then the 5 time points are: March 1st, April 1st, May 1st, June 1st, and July 1st.

[0046] In some embodiments of this application, SAR images can be acquired by taking pictures of the water load-affected area by a satellite that collects SAR images (such as Sentinel-1). Multiple differential interferograms can be generated using methods such as Differential InSAR (DInSAR). All differential interferograms can be unwrapped using methods such as region growing and least squares to obtain multiple unwrapped interferograms.

[0047] Step 12: Perform phase transition identification and correction on each unwrapped interferogram to obtain the corrected interferogram corresponding to each unwrapped interferogram.

[0048] Phase jump refers to the phenomenon where the phase value changes discontinuously in the generated unwrapped interferogram.

[0049] For example, phase transitions can be identified using a phase triangle closed loop, expressed as:

[0050] ;

[0051] in, Indicates the phase closure error. Indicates the first The SAR image and the first Unwrapped interferogram between SAR images Indicates the first The SAR image and the first Unwrapped interferogram between SAR images Indicates the first The SAR image and the first Unwrapped interferogram between SAR images.

[0052] If there is no phase jump, the phase closure error should be zero. If the phase closure error is not zero, it means that there is a phase jump region. The phase jump in the unwrapped interferogram needs to be corrected (the phase jump can be corrected by adjusting the unwrapping algorithm to obtain the unwrapped interferogram again until there is no phase jump region in the obtained unwrapped interferogram).

[0053] Step 13: Decouple the layered atmospheric delay phase and phase slope in each corrected interferogram and remove the layered atmospheric delay phase to obtain the optimized interferogram corresponding to each corrected interferogram.

[0054] Atmospheric delay phase refers to the phase change in the interferogram caused by the influence of the atmosphere on the propagation speed of electromagnetic waves (especially microwaves). Phase slope, or long-wave error, refers to phase errors on a larger scale that affect the interferogram. These errors are usually manifested in the low-frequency (long-wave) part of the interferogram, such as orbital errors and ionospheric delay errors.

[0055] In some embodiments of this application, the steps of decoupling the layered atmospheric delay phase and phase slope in each corrected interferogram and removing the layered atmospheric delay phase to obtain the optimized interferogram corresponding to each corrected interferogram include:

[0056] The first step is to remove the phase ramp from each corrected interferogram to obtain the second-order corrected interferogram and the corresponding linear regression slope.

[0057] Specifically, first, the initial phase ramp of the corrected interferogram is calculated, and then the initial phase ramp is removed from the corrected interferogram to obtain the initial removed interferogram.

[0058] Through the formula:

[0059] ;

[0060] Calculate the first The SAR image and the first Initial phase ramp of the corrected interferogram between SAR images .

[0061] in, , and Represents the fitting coefficient. Indicates the first The SAR image and the first The x-coordinates of each pixel in the corrected interferogram between SAR images Indicates the first The SAR image and the first The vertical coordinates of each pixel in the corrected interferogram between SAR images. , , This represents the set of SAR image numbers.

[0062] For example, the initial phase ramp can be removed by subtracting it from the corrected interferogram.

[0063] Then, a global linear regression of phase and terrain is performed on the initial removed interferogram to obtain the initial linear regression slope of the initial removed interferogram.

[0064] The initial linear regression slope describes the slope of the linear relationship between phase and terrain in the initial removed interferogram. By performing a global linear regression on the initial removed interferogram for phase and terrain, the linear relationship between phase and terrain is obtained, and the slope of this linear relationship is calculated, which is the initial linear regression slope.

[0065] Then, based on the initial linear regression slope, the phase terrain correlation in the initial removed interferogram is removed to obtain the secondary removed interferogram.

[0066] For example, phase-topographic correlation refers to the relationship between the phase difference of radar signals and ground elevation. This is achieved by performing a global linear regression analysis of the interferometric phase and ground elevation outside of deformation zones, and calculating the phase-topographic correlation based on the initial linear regression slope.

[0067] ;

[0068] In the formula Indicates the interference phase. Indicates terrain (i.e., ground elevation). and are linear regression coefficients, representing the slope and intercept of the correlation between phase and elevation, respectively.

[0069] Subtracting the phase terrain correlation from the initial removal interferogram yields the secondary removal interferogram.

[0070] The initial phase ramp of the second removal interferogram is then calculated, and the initial phase ramp of the second removal interferogram is removed from the second removal interferogram to obtain the third removal interferogram.

[0071] For example, the expression for calculating the initial phase ramp of the secondary removed interferogram is the same as the expression for calculating the initial phase ramp of the corrected interferogram above.

[0072] Then, the phase terrain correlation in the initial removal interferogram is added to the three removal interferograms to obtain the summed interferogram.

[0073] Finally, increment the iteration count by 1 and check if the iteration count is greater than or equal to the preset iteration count.

[0074] For example, the initial value for the number of iterations is 0.

[0075] If so, the added interferogram is used as the second-corrected interferogram, and the initial phase slope of the second-removed interferogram is used as the linear regression slope corresponding to the second-corrected interferogram.

[0076] Otherwise, the summed interferogram is used as the initial removed interferogram, and the steps of performing a global linear regression of phase and terrain on the initial removed interferogram are returned to obtain the initial linear regression slope of the initial removed interferogram.

[0077] The second step is to calculate the phase topographic linear regression slope of each SAR image based on the linear regression slopes corresponding to all secondary corrected interferograms.

[0078] Specifically, through the formula:

[0079] ;

[0080] ;

[0081] The matrix for calculating the phase topographic linear regression slope of all SAR images. .

[0082] in, The matrix representing the initial phase topographic linear regression slope of all SAR images. The matrix representing the relative slope correction values ​​for all SAR images. Represents the design matrix. Represents the transpose of a matrix. The matrix representing the linear regression slopes corresponding to all quadratic corrected interferograms. Representing the pseudo-inverse matrix:

[0083] ;

[0084] ;

[0085] ;

[0086] in, Representing the coefficient matrix of the normal equation, Describes a right singular vector matrix. This represents a left singular vector matrix.

[0087] The third step is to calculate the final linear regression slope corresponding to each quadratic corrected interferogram based on the phase topographic linear regression slope of all SAR images.

[0088] Specifically, through the formula:

[0089] ;

[0090] Calculate the first The SAR image and the first The final linear regression slope of the quadratic corrected interferogram between SAR images.

[0091] in, Indicates the first The slope of phase topographic linear regression of a SAR image. Indicates the first The slope of phase topographic linear regression of a SAR image.

[0092] The fourth step is to multiply the final linear regression slope of each second-corrected interferogram by the topography of the second-corrected interferogram to obtain the atmospheric delay phase, and then remove the atmospheric delay phase from the second-corrected interferogram to obtain the optimized interferogram.

[0093] The terrain data in the above-mentioned secondary corrected interferogram is ground elevation data.

[0094] For example, the atmospheric delay phase is subtracted from the secondary corrected interferogram to obtain the optimized interferogram.

[0095] Step 14: Based on all optimized interferograms, perform nonlinear deformation signal modeling to obtain the turbulent atmospheric delay error for each SAR image.

[0096] The aforementioned turbulent atmospheric delay error refers to the fluctuation in the propagation speed of electromagnetic waves caused by atmospheric turbulence (i.e., irregular airflow), resulting in changes in the phase or amplitude of the radar signal. Compared to the atmospheric delay of layered components, the turbulent atmospheric delay has a smaller impact on InSAR deformation extraction in terms of amplitude, but its temporal randomness makes it difficult to model and is considered a major source of error in InSAR deformation monitoring. Although the traditional CSS method greatly improves the estimation accuracy of atmospheric delay error, this method is based on two important assumptions: the atmospheric delay is randomly distributed in time and the deformation is linearly distributed in time. For the first assumption, the layered components, which are not randomly distributed in time, have already been well estimated in step 13. For the second assumption, this application achieves the purpose of modeling the nonlinear deformation signal by performing SBAS time-series calculation and stacking interferograms of common images with the same time span, thereby accurately estimating the turbulent atmospheric delay signal of the common master image.

[0097] In some embodiments of this application, the step of modeling nonlinear deformation signals based on all optimized interferograms to obtain the turbulent atmospheric delay error for each SAR image includes:

[0098] For each SAR image, perform the following steps:

[0099] The first step is to stack all optimized interferograms with SAR imagery as the main image, and then eliminate the turbulent atmospheric delay term and random distribution error term of the sub-image in the stacking result to obtain the stacked result after elimination.

[0100] The optimized interferogram of the SAR image as the main image is the corresponding interferogram calculated from the SAR image and other SAR images.

[0101] If multiple interferograms are obtained by unwrapping the same SAR image with other SAR images, then the SAR image is the master image of these interferograms. For example, for the interferogram between the 1st and 3rd SAR images, the interferogram between the 2nd and 3rd SAR images, the interferogram between the 3rd and 4th SAR images, and the interferogram between the 3rd and 5th SAR images, each interferogram is obtained based on the 3rd SAR image, then the master image of these four interferograms is the 3rd SAR image.

[0102] Specifically, the stacking result is as follows:

[0103] ;

[0104] ;

[0105] in, Indicates the first The optimized interferogram is in the first... The SAR image and the first Optimized interferogram between SAR images Indicates the first The optimized interferogram is in the first... The SAR image and the first Optimized interferogram between SAR images Indicates the first The number of optimized interferogram pairs of a SAR image as the main image. This represents the deformation term in the stacked result. Indicates the first The SAR image and the first Deformation terms between SAR images Indicates the first The SAR image and the first Deformation terms between SAR images For the turbulent atmospheric delay term in the sub-image of the stacked result, Indicates the first Turbulent atmospheric delay term of a SAR image. Indicates the first Turbulent atmospheric delay term of a SAR image. Indicates the first Turbulent atmospheric delay term of a SAR image. This represents the random distribution error term in the stacked results. , This represents the set of SAR image IDs. , , Indicates the first The set of numbers for all other SAR images, including all optimized interferograms of the main SAR image.

[0106] It should be noted that an optimized interferogram pair consists of any two of the optimized interferograms of the SAR image as the primary image. Based on the assumption that turbulent atmosphere is randomly distributed over time, when a sufficient number of optimized interferogram pairs are involved in stacking, the delay term of the turbulent atmosphere in the secondary image will be reduced. It can be eliminated for the random distribution error term. Similarly, based on this, the atmospheric delay term and random distribution error term of the secondary image are directly subtracted from the stacking result to obtain the stacked result after elimination.

[0107] The second step involves inverting the displacement vector increments of multiple SAR images from all optimized interferograms with SAR images as the main image.

[0108] The displacement vector increment is the vector increment of the surface displacement between the acquisition times of two SAR images.

[0109] Specifically, through the formula:

[0110] ;

[0111] The matrix for calculating the displacement vector increments of multiple SAR images ;

[0112] in, This represents a matrix containing all optimized interferograms derived from a SAR image as the primary image. Represents the relation matrix The right singular vector matrix after singular value decomposition. It is a diagonal matrix whose main diagonal elements are singular values. Represents the relation matrix The left singular vector matrix after singular value decomposition:

[0113] ;

[0114] in, This represents the transpose of a matrix.

[0115] It should be noted that the matrix The matrix includes displacement vector increments of multiple SAR images. The elements in the matrix are the displacement vector increments of SAR images. The multiple SAR images are all other SAR images of all optimized interferograms of the main image. The multiple displacement vector increments correspond one-to-one with the multiple SAR images.

[0116] The third step is to calculate the deformation term in the stacked result based on the increments of all displacement vectors, and then remove the deformation term from the stacked result after elimination to obtain the final stacked result.

[0117] Specifically, by subtracting the displacement vector increments of the SAR images, the deformation phase (i.e., deformation term) of each interferogram can be obtained. Substituting all deformation terms into... The deformation term in the stacked result is obtained, and the deformation term is subtracted from the expression of the stacked result to obtain the final stacked result.

[0118] The fourth step is to solve the final stacking result to obtain the turbulent atmospheric delay error of the SAR image.

[0119] Specifically, the expression for the final stacking result is:

[0120] ;

[0121] Solving for it yields the turbulent atmospheric delay error of the SAR image. .

[0122] It should be noted that the final stacking result effectively reduces the turbulent atmospheric delay error of the source image while amplifying the turbulent atmospheric delay error of the main image. This allows for accurate estimation of the turbulent atmospheric delay error in the main image. To model the nonlinear deformation term during stacking, this step involves performing a Satellite-Based Augmentation System (SBAS) time-series calculation on the interferogram, thereby removing the deformation term and achieving the goal of enhancing the turbulent atmospheric signal in the main image through stacking.

[0123] Step 15: Based on the turbulent atmospheric delay error of all SAR images, remove the turbulent atmospheric delay error from each optimized interferogram to obtain the final interferogram corresponding to each optimized interferogram of the water load-affected area.

[0124] Specifically, for each optimized interferogram, the turbulent atmospheric delay error of the two corresponding SAR images is differentially calculated to obtain the turbulent atmospheric delay error in the optimized interferogram. The turbulent atmospheric delay error is then subtracted from the optimized interferogram to obtain the final interferogram of the water load-affected area.

[0125] It should be noted that, to improve the accuracy of removing turbulent atmospheric delay errors, steps 14 and 15 can be iterated multiple times. The optimized interferogram after removing turbulent atmospheric delay errors is used as the optimized interferogram in step 14, and step 14 is executed again. In each iteration, the accuracy of deformation extraction is continuously improved, and residual turbulent atmospheric delay errors are continuously removed, finally obtaining the interferogram after removing turbulent atmospheric delay errors. Correcting the atmospheric delay in the interferogram reduces the error in the terrain deformation information caused by atmospheric delay, ensuring that the interferogram only represents the actual terrain deformation, providing accurate terrain deformation information for water load deformation monitoring.

[0126] It is worth mentioning that phase jump identification and correction of interferograms can reduce the errors caused by phase jumps in the interferograms. By decoupling and removing atmospheric delay phase and phase slope, the influence of phase slope on atmospheric delay phase estimation is taken into account, and the two are effectively decoupled to improve the accuracy of removing atmospheric delay phase and phase slope. In the optimized interferogram, the turbulent atmospheric delay error is removed, which further reduces the atmospheric delay of deformation information in the interferogram, realizes the accurate representation of water load deformation, and thus improves the accuracy of InSAR atmospheric delay correction for water load deformation.

[0127] The purpose of this application is to address the problem in existing atmospheric error correction techniques where the coupling between atmospheric delay error and long-wavelength error, as well as between these errors and nonlinear deformation, makes accurate estimation of atmospheric delay error difficult. This aims to improve the extraction accuracy of surface water load deformation in InSAR, and has significant scientific and practical value. The main technical problems are as follows:

[0128] Lakeshore Phase Jumps and Discontinuities: In areas such as lakes and reservoirs, the presence of water can easily lead to severe phase jumps in InSAR interferograms. Errors caused by phase jumps can be as dominant as atmospheric delay errors in the interferogram. The method proposed in this application relies on the interferometric phase to estimate atmospheric delay errors. Therefore, this application uses a dense network strategy and a phase triangulation closed-loop method for unwrapping error correction. Sufficient redundant observations ensure that phase jump regions can be accurately identified and corrected.

[0129] The coupling problem between stratified atmospheric delay and long-wavelength errors: In interferograms, stratified atmospheric delay noise and long-wavelength errors (such as orbital errors and ionospheric delay errors) are coupled. Traditional linear phase topography models are highly susceptible to the influence of long-wavelength errors, leading to incorrect estimation of the correlation between phase topography caused by stratified atmosphere. This application considers the impact of long-wavelength errors on the estimation of stratified atmospheric delay, effectively decoupling the two, and thus accurately estimating the stratified components of atmospheric delay errors.

[0130] Nonlinear load deformation modeling problem: Surface deformation driven by water loads often exhibits nonlinear characteristics with seasonal and irregular fluctuations. Traditional turbulent atmospheric correction methods rely on the assumption that deformation changes linearly over time, making it difficult to model nonlinear deformation signals and therefore unsuitable for turbulent atmospheric delay correction of water load deformation. This application achieves the goal of modeling nonlinear deformation signals by iteratively performing SBAS time-series solution on stacked common image interferograms.

[0131] Regarding the correction of atmospheric delay stratification components, compared to traditional methods using linear models for phase-topographic correlation estimation, this application's method iteratively performs long-wavelength error fitting and phase-topographic correlation analysis. This effectively decouples long-wavelength errors from stratified atmospheric delay, significantly reducing the impact of long-wavelength errors on topographic-related atmospheric delay estimation and effectively improving the estimation accuracy of stratified atmosphere, which accounts for the largest proportion of atmospheric delay amplitude in interferograms. Simulation experiments show that, compared to traditional stratified atmospheric delay estimation models, the estimation residual of the phase-topographic linear regression slope of this application's method is significantly improved. Increased to This method improves accuracy by 32% compared to traditional methods.

[0132] Compared to the traditional CSS method, this application's method considers the temporal differences in the layered components and turbulent components of the atmospheric delayed phase. First, it removes the seasonally oscillating layered atmosphere from the interferograms. Then, based on the assumption of a temporally random distribution of turbulent atmosphere, it stacks interferogram pairs with common images. Simultaneously, this method considers the nonlinear temporal characteristics of water load deformation, iteratively performing inversion during the stacking process to model the nonlinear deformation signal, thus independent of the assumption of a linear deformation distribution. Simulation experiments show that the deformation extraction results using this method have a root mean square error (RMSE) of only 2.11 mm, while the traditional CSS method has an RMSE of 4.58 mm, improving accuracy by approximately 54%. Furthermore, the traditional CSS method adds strong linear constraints to the deformation, leading to the smoothing out of some seasonal deformation signals.

[0133] In a real-world water body load deformation verification, the error correction method proposed in this application significantly improves the overall quality of the interferograms compared to the commonly used GPS Atmospheric Column Observation System (GACOS) plus phase filtering method, and significantly reduces the noise in the interferograms. The standard deviation (STD) of the interferograms decreased from 11.03 mm to 3.04 mm, improving accuracy by 72%. The extracted surface deformation results were verified with GNSS time-series data. The RMSE of the commonly used GACOS external data correction method was as high as 11.74 mm, while the RMSE of the deformation extraction time-series results from the method in this application was as low as 2.91 mm, improving accuracy by 75%.

[0134] The method of this application will be illustrated below with a specific example.

[0135] Based on the water level changes and underwater topography of a lake area over the past decade, an elastic stratified model of water load was constructed. Forward modeling was used to simulate the surface deformation field of the region from 2014 to 2024 as the true deformation value. Based on this, an interferometric atlas with a dense spatiotemporal baseline network was created. A phase slope was added to the interferogram to simulate long-wavelength errors, and a layered atmosphere exhibiting seasonal oscillations and high correlation with topography was added. Finally, fractal functions were used to simulate temporally random but spatially correlated turbulent atmospheric delays, resulting in unwrapped interferograms of simulated hybrid deformation signals and multi-source errors. Error correction and deformation extraction were performed on the same interferometric atlas using a traditional linear phase topographic model with phase filtering, as well as the method proposed in this application.

[0136] Comparison of phase terrain relationship estimation methods using different methods is shown in the figure below. Figure 2 As shown, the horizontal axis represents the date, and the vertical axis Topo APS represents the linear correlation coefficient of phase / elevation of each SAR acquisition time relative to the first SAR image, used to characterize the relative stratified atmospheric delay error of each SAR acquisition time relative to the first time, in mm / m. b_SAR_sim represents the true value of the simulated phase-topographic linear regression coefficient, b_SAR_trad represents the result of the traditional linear model estimation, and b_SAR_mod represents the estimation result of the method in this application. It can be seen that the traditional method does not consider the influence of long-wavelength errors in the interferogram on the phase-topographic correlation. In most cases, long-wavelength errors in the interferogram are incorrectly estimated as stratified atmospheric delay errors, resulting in an overestimation of the phase-topographic correlation coefficient, with an RMSE of 5.7 e-3 mm / m. In contrast, this application, by considering the influence of long-wavelength errors on the stratified atmospheric delay of the image, estimates the regression coefficient more accurately, reducing the RMSE to 3.9 e-3 mm / m, and improving the accuracy by 32%.

[0137] A comparison diagram of water load and surface deformation is shown below. Figure 3 As shown, the horizontal axis represents the date, and the vertical axis represents the surface deformation along the line of sight (LOS), in millimeters (mm). The simulated true value represents the true value of the simulated LOS-to-surface deformation. The linear CSS method represents the LOS-to-surface deformation value obtained using the CSS method. The method of this invention represents the LOS-to-surface deformation value obtained using the method of this application. The results show that the deformation characteristics are well recovered in terms of both deformation amplitude and temporal evolution trend through the correction of the method of this application, with an RMSE of only 2.11 mm, while the RMSE of the traditional CSS method is as high as 4.58 mm. The accuracy of the method of this application is improved.

[0138] The following example uses real InSAR data covering a lake area from 2014 to 2024 to further illustrate this point.

[0139] Following the methodology of this proposal, a dense spatiotemporal baseline network was first constructed, generating 2950 interferometric pairs from 236 SAR images. The interferograms were then unwrapped to obtain unwrapped interferograms. First, a triangular phase closure loop was used to correct the unwrapping error in the interferograms. The triangular phase closure loop is as follows: Figure 4 As shown, Figure 4 (a) to Figure 4 (e) consists entirely of interferograms. Figure 4 (f) and Figure 4 (g) is a schematic diagram of the phase closure error calculation results. Figure 4 (h) part Figure 4 (i) part Figure 4 (j) consists of an original interferogram, the calculated phase closure error corresponding to the interferogram, and the corrected interferogram. Figure 5 It demonstrates that the presence of water caused severe phase jumps on both the north and south sides, which were identified and corrected through a phase closed loop.

[0140] A diagram illustrating the results of delayed correction is shown below. Figure 5 As shown, Figure 5 (a) and Figure 5 (d) is the interferogram before correction. Figure 5 (b) The atmospheric delay phase estimated by the method of this application. Figure 5 (e) is the atmospheric delay phase estimated using the method of GACOS products. Figure 5 (c) is the interference diagram after the method correction of this application. Figure 6(f) shows the interferogram after correction using the GACOS product. For short-time baseline interferograms of water load deformation, due to the short time span, the interferogram usually does not contain obvious deformation signals and is dominated by multi-source errors. From the perspective of correction effect, the method of this application effectively estimates the error signals in the interferogram, and there are no obvious error residues in the results. However, a large number of error signals remain in the interferogram after GACOS correction.

[0141] Interferograms before and after correction by different methods (STD comparison) Figure 6 As shown, Figure 6 (a) The original interferogram set STD is divided into three levels: excellent, medium, and poor, corresponding to STDs of 0-5 mm, 5-10 mm, and greater than 10 mm, respectively. Figure 6 (b) STD of the interferogram after GACOS method correction. Figure 7 (c) shows the STD plot of the method of this application. Regarding the atmospheric delay error (STD) of the interferograms, the GACOS correction played a role, reducing the mean STD from 16.88 mm to 11.03 mm, achieving an improvement of approximately 34.65%. While the STD of the interferogram set was improved to some extent, many interferograms still exhibited poor quality. However, the method of this invention demonstrates a greater advantage, further reducing the mean STD of the interferograms to 3.04 mm, achieving an accuracy improvement of up to 82.00% compared to the original interferograms. All poor-quality interferograms in the interferogram set were improved, representing a significant improvement of 72.44% compared to the results after GACOS correction.

[0142] LOS-related surface deformation, for example Figure 7 As shown, the horizontal axis represents the date, and the vertical axis represents the LOS value of surface deformation, in millimeters (mm). Figure 7 (a) is a schematic diagram comparing surface deformation using the method of this application. GNSS data represents the LOS-to-surface deformation data, and the method of this invention represents the LOS-to-surface deformation value obtained through the method of this application. Figure 8 (b) is a schematic diagram comparing surface deformation using the GACOS method. GNSS data represents the LOS-directed surface deformation data, and GACOS data represents the LOS-directed surface deformation value obtained using the GACOS method. The results show that, compared to the GACOS-corrected method, the proposed method significantly reduces the signal noise figure, produces smoother deformation, and achieves higher deformation estimation accuracy. Using GNSS data as the true value, the RMSE of the proposed method is 2.91 mm, while the RMSE of GACOS is as high as 11.74 mm, representing a 75% improvement in accuracy.

[0143] The following is an exemplary description of the InSAR atmospheric delay correction device for water load deformation provided in this application.

[0144] like Figure 9 As shown, this application provides an InSAR atmospheric delay correction device for water body load deformation. The InSAR atmospheric delay correction device 800 includes:

[0145] The unwrapping module 801 is used to generate multiple differential interferograms from SAR images of the water load-affected area at multiple times, and to unwrap all the differential interferograms to obtain an unwrapped interferogram set; the unwrapped interferogram set includes multiple unwrapped interferograms.

[0146] The correction module 802 is used to identify and correct phase jumps in each unwrapped interferogram to obtain the corrected interferogram corresponding to each unwrapped interferogram.

[0147] The decoupling module 803 is used to decouple the layered atmospheric delay phase and phase slope in each corrected interferogram and remove the layered atmospheric delay phase to obtain the optimized interferogram corresponding to each corrected interferogram.

[0148] The nonlinear deformation signal modeling module 804 is used to model nonlinear deformation signals based on all optimized interferograms to obtain the turbulent atmospheric delay error for each SAR image.

[0149] Module 805 is used to remove the turbulent atmospheric delay error from each optimized interferogram based on all SAR images, so as to obtain the final interferogram corresponding to each optimized interferogram of the water load-affected area.

[0150] It should be noted that the information interaction and execution process between the above-mentioned devices / units are based on the same concept as the method embodiments of this application. For details on their specific functions and technical effects, please refer to the method embodiments section, and they will not be repeated here.

[0151] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0152] like Figure 9 As shown, an embodiment of this application provides a terminal device, wherein the terminal device D10 of this embodiment includes: at least one processor D100 ( ​ The diagram shows only one processor, a memory D101, and a computer program D102 stored in the memory D101 and executable on the at least one processor D100, wherein the processor D100 executes the computer program D102 to implement the steps in any of the above method embodiments.

[0153] Specifically, when the processor D100 executes the computer program D102, it generates multiple differential interferograms from SAR images of the water load-affected area at multiple times, unwraps all differential interferograms to obtain an unwrapped interferogram set, then identifies and corrects phase jumps in each unwrapped interferogram to obtain a corrected interferogram corresponding to each unwrapped interferogram, then decouples the layered atmospheric delay phase and phase slope in each corrected interferogram and removes the layered atmospheric delay phase to obtain an optimized interferogram corresponding to each corrected interferogram, then models nonlinear deformation signals based on all optimized interferograms to obtain the turbulent atmospheric delay error of each SAR image, and finally removes the turbulent atmospheric delay error in each optimized interferogram based on the turbulent atmospheric delay error of all SAR images to obtain the final interferogram corresponding to each optimized interferogram of the water load-affected area. Among these methods, phase jump identification and correction of the interferogram can reduce the error caused by phase jump in the interferogram. Decoupling and removing the stratified atmospheric delay phase and phase slope takes into account the influence of the phase slope on the atmospheric delay phase estimation and effectively decouples the two to improve the accuracy of removing the stratified atmospheric delay phase. The removal of turbulent atmospheric delay error in the optimized interferogram further reduces the atmospheric delay of deformation information in the interferogram, realizes the accurate representation of water load deformation, and thus improves the accuracy of InSAR atmospheric delay correction for water load deformation.

[0154] The processor D100 can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0155] In some embodiments, the memory D101 may be an internal storage unit of the terminal device D10, such as a hard disk or memory of the terminal device D10. In other embodiments, the memory D101 may be an external storage device of the terminal device D10, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the terminal device D10. Furthermore, the memory D101 may include both internal and external storage units of the terminal device D10. The memory D101 is used to store the operating system, applications, bootloader, data, and other programs, such as the program code of the computer program. The memory D101 can also be used to temporarily store data that has been output or will be output.

[0156] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps described in the various method embodiments above.

[0157] This application provides a computer program product that, when run on a terminal device, enables the terminal device to implement the steps described in the various method embodiments above.

[0158] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying the computer program code to an InSAR atmospheric delay correction method device / terminal device for water load deformation, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, such as a USB flash drive, a portable hard drive, a magnetic disk, or an optical disk.

[0159] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0160] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0161] The above description is the preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principles described in this application, and these improvements and modifications should also be considered within the scope of protection of this application.

Claims

1. An InSAR atmospheric delay correction method for water body load deformation, characterized in that, include: Multiple differential interferograms are generated from SAR images of the water load-affected area at multiple times, and all differential interferograms are unwrapped to obtain an unwrapped interferogram set; the unwrapped interferogram set includes multiple unwrapped interferograms. Each unwrapped interferogram is identified and corrected for phase transitions to obtain a corrected interferogram corresponding to each unwrapped interferogram. The layered atmospheric delay phase and phase slope in each of the corrected interferograms are decoupled, and the layered atmospheric delay phase is removed to obtain the optimized interferogram corresponding to each corrected interferogram. Based on all optimized interferograms, nonlinear deformation signal modeling is performed to obtain the turbulent atmospheric delay error for each SAR image; Based on the turbulent atmospheric delay error of all SAR images, the turbulent atmospheric delay error in each optimized interferogram is removed to obtain the final interferogram corresponding to each optimized interferogram of the water load-affected area; The process of decoupling the layered atmospheric delay phase and phase slope in each corrected interferogram and removing the layered atmospheric delay phase to obtain the optimized interferogram corresponding to each corrected interferogram includes: For each of the corrected interferograms, the phase ramp is removed from the corrected interferogram to obtain the secondary corrected interferogram and the corresponding linear regression slope; The phase topographic linear regression slope of each SAR image is calculated based on the linear regression slope corresponding to all secondary corrected interferograms. The final linear regression slope corresponding to each secondary corrected interferogram is calculated based on the phase topographic linear regression slope of all SAR images. For each quadratic corrected interferogram, the final linear regression slope corresponding to the quadratic corrected interferogram is multiplied by the terrain of the quadratic corrected interferogram to obtain the layered atmospheric delay phase. The layered atmospheric delay phase is then removed from the quadratic corrected interferogram to obtain the optimized interferogram.

2. The InSAR atmospheric delay correction method according to claim 1, characterized in that, The step of removing the phase ramp from the corrected interferogram to obtain the second-corrected interferogram and the corresponding linear regression slope of the second-corrected interferogram includes: Calculate the initial phase slope of the corrected interferogram, and remove the initial phase slope from the corrected interferogram to obtain the initial removed interferogram; A global linear regression of phase and terrain is performed on the initial removed interferogram to obtain the initial linear regression slope of the initial removed interferogram; The phase terrain correlation in the initial removed interferogram is removed based on the initial linear regression slope to obtain the secondary removed interferogram; Calculate the initial phase ramp of the second-order removal interferogram, and remove the initial phase ramp from the second-order removal interferogram to obtain the third-order removal interferogram; The phase terrain correlation in the initial removal interferogram is added to the three removal interferograms to obtain the summed interferogram; Increment the iteration count by 1, and determine whether the iteration count is greater than or equal to the preset iteration count; If so, the added interferogram is used as the second-corrected interferogram, and the initial phase slope of the second-removed interferogram is used as the linear regression slope corresponding to the second-corrected interferogram. Otherwise, the summed interferogram is used as the initial removed interferogram, and the step of performing a global linear regression of phase and terrain on the initial removed interferogram to obtain the initial linear regression slope of the initial removed interferogram is returned.

3. The InSAR atmospheric delay correction method according to claim 2, characterized in that, The calculation of the initial phase ramp of the corrected interferogram includes: Through the formula: ； Calculate the first The SAR image and the first Initial phase ramp of the corrected interferogram between SAR images ; in, , and Represents the fitting coefficient. Indicates the first The SAR image and the first The x-coordinates of each pixel in the corrected interferogram between SAR images Indicates the first The SAR image and the first The vertical coordinates of each pixel in the corrected interferogram between SAR images. , , This represents the set of SAR image numbers.

4. The InSAR atmospheric delay correction method according to claim 3, characterized in that, The calculation of the phase topographic linear regression slope for each SAR image based on the linear regression slopes corresponding to all secondary corrected interferograms includes: Through the formula: ； ； The matrix for calculating the phase topographic linear regression slope of all SAR images. ; in, The matrix representing the initial phase topographic linear regression slope of all SAR images. The matrix representing the relative slope correction values ​​for all SAR images. Represents the design matrix. Represents the transpose of a matrix. The matrix representing the linear regression slopes corresponding to all quadratic corrected interferograms. Representing the pseudo-inverse matrix: ； ； ； in, Representing the coefficient matrix of the normal equation, Describes a right singular vector matrix. This represents a left singular vector matrix.

5. The InSAR atmospheric delay correction method according to claim 4, characterized in that, The nonlinear deformation signal modeling based on all optimized interferograms yields the turbulent atmospheric delay error for each SAR image, including: For each SAR image, perform the following steps: All optimized interferograms with the SAR image as the main image are stacked, and the turbulent atmospheric delay term and random distribution error term of the sub-image in the stacking result are eliminated to obtain the stacked result after elimination. The displacement vector increments of multiple SAR images are obtained by inversion from all optimized interferograms with the SAR image as the main image; The deformation term in the stacking result is calculated based on the increments of all displacement vectors, and the deformation term is removed from the stacking result after elimination to obtain the final stacking result; The turbulent atmospheric delay error of the SAR image is obtained by solving the final stacking result.

6. The InSAR atmospheric delay correction method according to claim 5, characterized in that, The stacking result is as follows: ； in, Indicates the first The optimized interferogram is in the first... The SAR image and the first Optimized interferogram between SAR images Indicates the first The optimized interferogram is in the first... The SAR image and the first Optimized interferogram between SAR images Indicates the first The number of optimized interferogram pairs of a SAR image as the main image. This represents the deformation term in the stacked result. Indicates the first The SAR image and the first Deformation terms between SAR images Indicates the first The SAR image and the first Deformation terms between SAR images For the turbulent atmospheric delay term in the sub-image of the stacked result, Indicates the first Turbulent atmospheric delay term of a SAR image. Indicates the first Turbulent atmospheric delay term of a SAR image. Indicates the first Turbulent atmospheric delay term of a SAR image. This represents the random distribution error term in the stacked results. , This represents the set of SAR image IDs. , , Indicates the first The set of numbers for all other SAR images, including all optimized interferograms of the main SAR image.

7. The InSAR atmospheric delay correction method according to claim 6, characterized in that, The process of inverting the displacement vector increments of multiple SAR images from all optimized interferograms of the SAR image as the primary image includes: Through the formula: ； The matrix for calculating the displacement vector increments of multiple SAR images ; in, This represents a matrix of all optimized interferograms derived from the SAR image as the primary image. Represents the relation matrix The right singular vector matrix after singular value decomposition. It is a diagonal matrix whose main diagonal elements are singular values. Represents the relation matrix The left singular vector matrix after singular value decomposition: ； in, This represents the transpose of a matrix.

8. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the InSAR atmospheric delay correction method for water load deformation as described in any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the InSAR atmospheric delay correction method for water load deformation as described in any one of claims 1 to 7.

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