Time sequence InSAR method suitable for landslide multi-dimensional deformation monitoring

Abstract

The invention provides a time sequence InSAR (Interferometric Synthetic Aperture Radar) method suitable for landslide multi-dimensional deformation monitoring, which comprises the following steps of: firstly, acquiring an upward deformation observed quantity of a to-be-detected landslide, and then inputting the upward deformation observed quantity into a monitoring model containing a fractal dimension composite structure deformation constraint model, thereby obtaining deformation time sequences of a landslide body in a vertical direction, an east-west direction, a down-slope direction and a vertical down-slope direction; the method has remarkable advantages, deformation time sequence characteristics of the landslide in four dimensions including the vertical direction, the east-west direction, the down-slope direction and the vertical down-slope direction can be obtained at the same time, the constructed model covers linear, accelerated speed, periodicity, high frequency and thermal expansion deformation, the complexity of landslide deformation is fully considered, and adaptability is high. Moreover, the model pays attention to the difference between the vertical deformation and the east-west deformation as well as between the down-slope deformation and the vertical down-slope deformation, different constraint conditions are constructed respectively, and mutually independent deformation model constraints are formed, so that the deformation in each direction can be accurately constrained, the model fits the reality, and the precision of a calculation result is effectively improved.

Description

Technical Field

[0001] The invention relates to the technical field of data processing, and specifically provides a time series InSAR method suitable for multi-dimensional deformation monitoring of landslides. Background Art

[0002] Landslide refers to an adverse geological phenomenon in which part or all of the soil and rock mass slides downward along the weak surface or weak zone of the slope strata under the action of gravity. Landslide disasters are a combination of various types of landslides, collapses, and mudslides, which are mainly caused by factors such as earthquakes, volcanic movements, river scouring, freeze-thaw, precipitation, and human activities. It is of great practical significance to carry out pre-identification of landslide hazard points in landslide-prone areas. One of the important characteristics of landslide hazard points is the instability of the slope, which will shift in space, that is, surface deformation. Therefore, landslide deformation monitoring is carried out in landslide-prone areas. According to the deformation measurement results, the mountain slope with high instability can be located, and the landslide hazard level can be delineated according to the deformation rate. In addition, a deformation prediction model can be constructed based on the deformation measurement results in the time series to predict the evolution trend of slope deformation over time, providing richer and more detailed reference information for the identification of landslide hazard points and the classification of hazard levels. Among them, accurately extracting the real deformation of the slope space is the most critical process.

[0003] In terms of landslide deformation monitoring, time-series InSAR measurement has shown great technical advantages and potential, with the advantages of high spatial resolution, high efficiency, low cost, strong adaptability, and can avoid possible safety accidents during on-site testing. However, since InSAR technology extracts deformation by interfering with data obtained by side-looking synthetic aperture radar (SAR) sensors, and side-looking SAR sensors can only detect one-dimensional information along the observation direction, the existing time-series InSAR technology can only obtain a single displacement component of the landslide deformation along the radar line of sight (LOS), and cannot obtain the true deformation information of the landslide.

[0004] In terms of landslide deformation monitoring technology in different dimensions, existing technologies are mostly based on InSAR data from different tracks or platforms. The observation equation is established through the intersection principle to solve the static two-dimensional deformation rate, such as the static deformation rate in the vertical and east-west directions, along the slope and vertical directions, along the slope and vertical along the slope. However, the static two-dimensional deformation rate cannot trace back the temporal deformation characteristics of the landslide, which makes the landslide deformation information incomplete and affects the subsequent analysis and evaluation. For landslides with more significant deformation, time-series pixel offset tracking POT or time-series POT combined with time-series InSAR can obtain vertical and horizontal two-dimensional deformation time series. However, POT technology converts the pixel offset of different SAR image pairs into deformation information. Due to the large error corresponding to the pixel offset, the deformation monitoring accuracy is low, and the error reaches more than 5 cm. Therefore, it is only suitable for deformations of larger magnitude, such as deformations of 50 cm / year and above. However, the temporal deformation of general landslides is only 5-20 cm per year, and the time-series POT technology is not applicable. Moreover, since the SAR image offset only corresponds to the horizontal direction, this technology can only monitor horizontal deformation, and cannot monitor vertical, downslope, and vertical downslope deformation. In terms of multidimensional time-series deformation monitoring technology, the multidimensional small baseline set MSBAS interferometric deformation monitoring technology constructs a two-dimensional time-series deformation monitoring model based on ascending and descending orbit time-series InSAR results and regularization constraints, which can be applied to landslide time-series two-dimensional deformation monitoring to obtain vertical and east-west landslide two-dimensional deformation time series. However, the characteristics of landslide deformation are mainly manifested as downslope sliding and vertical downslope sliding, while the MSBAS technology can only obtain vertical and east-west two-dimensional deformation time series, and cannot obtain the true downslope and vertical downslope landslide time-series deformation characteristics. In addition, this technology does not consider the thermal expansion and contraction deformation of the monitoring target and the physical mechanism of deformation, which affects the deformation monitoring accuracy. Summary of the invention

[0005] In order to overcome the above-mentioned defects, the present invention is proposed to provide a solution or at least partially solve the problem of being unable to obtain the true along-slope and vertical along-slope landslide deformation characteristics.

[0006] The invention provides a time series InSAR method suitable for multi-dimensional deformation monitoring of landslides, comprising: obtaining deformation observations of a landslide to be measured in the upward direction of the line of sight; inputting the deformation observations of the landslide to be measured in the upward direction of the line of sight into a monitoring model to obtain deformation time series of the landslide body in the vertical direction, the east-west direction, the along-slope direction, and the vertical along-slope direction; wherein the monitoring model at least comprises a fractal-dimensional composite structure deformation constraint model; a first constraint condition constructed based on the fractal-dimensional composite structure deformation constraint model respectively constrains the vertical and east-west deformations, and a second constraint condition constructed based on the fractal-dimensional composite structure deformation constraint model respectively constrains the along-slope and vertical along-slope deformations.

[0007] In a technical solution of the above-mentioned time-series InSAR method suitable for multi-dimensional deformation monitoring of landslides, the fractal-dimensional composite structure deformation constraint model includes a first constraint model and a second constraint model; the first constraint model is a constraint model for vertical and east-west time-series deformation, and the second constraint model is a constraint model for along-slope and vertical along-slope time-series deformation; the method at least includes the following steps to construct the fractal-dimensional composite structure deformation constraint model: the mathematical models of surface deformation in different types of regions are used to construct the first constraint model and the second constraint model in the form of a full combination.

[0008] In a technical solution of the above-mentioned time-series InSAR method suitable for multi-dimensional deformation monitoring of landslides, the process of constructing the first constraint model and the second constraint model in the form of a full combination of mathematical models of surface deformation in different types of regions at least includes: obtaining the first parameter of the fractal composite structure deformation constraint model, the first parameter including: the vertical and east-west deformations corresponding to the m-th moment, the parameters of the vertical deformation constraint model, the parameters of the east-west deformation constraint model, the acquisition time of the first SAR image, the acquisition time of the m-th SAR image, the vertical and east-west thermal expansion deformation coefficients, and the m-th moment; The temperature difference between the time when the SAR image is acquired and the starting time; the first constraint model is constructed based on the first parameter; the second parameter of the fractal composite structure deformation constraint model is obtained, and the second parameter includes: the along-slope and vertical along-slope deformations corresponding to the m-th moment, the parameters of the along-slope deformation constraint model, the parameters of the vertical along-slope deformation constraint model, the acquisition time of the first SAR image, the acquisition time of the m-th SAR image, the along-slope and vertical along-slope thermal expansion deformation coefficients, and the temperature difference between the time when the m-th SAR image is acquired and the starting time; the second constraint model is constructed based on the second parameter.

[0009] In a technical solution of the above-mentioned time-series InSAR method suitable for multi-dimensional deformation monitoring of landslides, the monitoring model also includes a first observation equation and a second observation equation; the deformation observation quantity of the landslide to be measured in the upward direction of sight is input into the monitoring model to obtain the deformation time series of the landslide body in the vertical direction, the east-west direction, the slope direction, and the vertically upward slope direction, which at least includes: based on the first constraint model, constraining the vertical deformation and the east-west deformation respectively, and then constructing the first observation equation of the independent deformation model constraint conditions; based on the second constraint model, constraining the along-slope direction and the vertical along-slope direction deformation respectively, and then constructing the second observation equation of the independent deformation model constraint conditions; based on the first observation equation, solving the vertical and east-west time-series deformation of the landslide body; based on the second observation equation, solving the along-slope and vertically upward slope time-series deformation.

[0010] In a technical solution of the above-mentioned time-series InSAR method suitable for multi-dimensional deformation monitoring of landslides, the deformation observations of the landslide to be measured in the upward direction of the line of sight are input into the monitoring model to obtain the deformation time series of the landslide body in the vertical direction, the east-west direction, the downslope direction, and the vertical upslope direction. The process also includes: based on the vertical and east-west time-series deformation, the vertical and east-west deformation time series are obtained by integrating the time dimension; based on the downslope and vertical upslope time-series deformation, the downslope and vertical upslope deformation time series are obtained by integrating the time dimension; different platforms are weighted by using the variance component estimation method, and the deformation time series is gradually refined by the weight selection iteration method.

[0011] Compared with the prior art, the time series InSAR method for multi-dimensional deformation monitoring of landslide provided by the present invention has the following beneficial effects: the method fully considers the complexity of landslide deformation, and the constructed fractal composite structure deformation constraint model not only includes linear deformation (first order term), deformation acceleration (second order term) and periodic deformation (sine and cosine terms), but also considers high frequency deformation (third order term) and thermal expansion deformation, and has better adaptability to complex landslide deformation. At the same time, the model considers the difference between vertical and east-west deformation, and adopts different constraint models for the two dimensions: based on the fractal composite structure deformation constraint model, the vertical and east-west deformations are constrained respectively, which can better consider the difference between vertical and east-west deformations, and can form constraints on vertical and east-west deformations respectively, and also considers the difference between along-slope and vertical along-slope deformations, and constrains along-slope and vertical along-slope deformations respectively, thereby constructing independent deformation model constraint conditions, which is more in line with the actual situation and improves the accuracy of the solution result.

[0012] Furthermore, the adopted fractal-dimensional composite structure deformation constraint model does not need to project the two to the line of sight when constructing the constraint conditions, thus avoiding the problem of angle value selection and improving the accuracy and stability of the solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The disclosure of the present invention will become more easily understood with reference to the accompanying drawings. It is easy for those skilled in the art to understand that these drawings are only for illustrative purposes and are not intended to limit the scope of protection of the present invention. In addition, similar numbers in the figures are used to represent similar components, among which:

[0014] Figure 1 1 is a schematic flow chart of main steps of a time-series InSAR method suitable for multi-dimensional deformation monitoring of landslides according to an embodiment of the present invention;

[0015] Figure 2 It is a schematic diagram of the sliding surface coordinate system of the landslide and its relationship with the three-dimensional spatial coordinate system;

[0016] Figure 3 It is a schematic diagram of the geometric relationship between the sliding surface coordinate system and the "northeast high" coordinate system. DETAILED DESCRIPTION

[0017] Some embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood by those skilled in the art that these embodiments are only used to explain the technical principles of the present invention and are not intended to limit the protection scope of the present invention.

[0018] Embodiment 1

[0019] like Figure 1 As shown, a time-series InSAR method suitable for multi-dimensional deformation monitoring of landslides in an embodiment of the present invention mainly includes the following steps S1 to S2.

[0020] Step S1, obtaining the visually upward deformation observation value of the landslide to be measured.

[0021] Step S2, inputting the deformation observation amount of the landslide to be measured in the line of sight upward into the monitoring model, and obtaining the deformation time series of the landslide body in the vertical direction, the east-west direction, the slope direction, and the vertical along the slope direction; wherein the monitoring model at least includes a fractal composite structure deformation constraint model; the first constraint condition constructed based on the fractal composite structure deformation constraint model constrains the vertical and east-west deformations respectively, and the second constraint condition constructed based on the fractal composite structure deformation constraint model constrains the along the slope direction and the vertical along the slope direction respectively.

[0022] In this embodiment, the deformation observation can be the deformation in the line of sight direction obtained by monitoring the SAR image data of different satellites; it can also be the line of sight deformation presented by a SAR satellite in a certain orbit at a specific moment in two different states: ascending orbit and descending orbit. The vertical direction is perpendicular to the horizontal plane, and the east-west direction is within the horizontal plane. Due to the difference in vertical and east-west deformations, different constraint models are used for the two dimensions: based on the fractal composite structure deformation constraint model, the vertical and east-west deformations are constrained respectively, which can better consider the difference in vertical and east-west deformations, and can form constraints on the vertical and east-west deformations respectively. The difference in along-slope and vertical along-slope deformations is also considered, and the along-slope and vertical along-slope deformations are constrained respectively, thereby constructing independent deformation model constraint conditions, which are more in line with the actual situation and improve the accuracy of the solution results.

[0023] In one embodiment, the fractal-dimensional composite structure deformation constraint model includes a first constraint model and a second constraint model; the first constraint model is a constraint model for vertical and east-west time-series deformation, and the second constraint model is a constraint model for along-slope and vertical along-slope time-series deformation; the method at least includes the following steps to construct the fractal-dimensional composite structure deformation constraint model: the mathematical models of surface deformation in different types of regions are used to construct the first constraint model and the second constraint model in the form of a full combination.

[0024] In this embodiment, the first constraint model is used to constrain the vertical and east-west time series deformation. The second constraint model mainly focuses on the constraints of the time series of along-slope and vertical along-slope deformation. Specifically, the mathematical models of surface deformation in different types of regions are shown in Table 1. The physical meaning of each parameter of the model in the table is: t is the time relative to the starting moment (the first SAR image), v is the linear deformation rate, a is the deformation acceleration, b represents the change in acceleration, A1 and A2 are the seasonal change intensity of the deformation, T is the period of the trigonometric function model (can be 1 year), α is the thermal expansion coefficient, and γ is the temperature change value relative to the starting moment.

[0025] Table 1

[0026]

[0027]

[0028] Taking into account the complexity of natural phenomena and processes, in order to ensure that the constructed deformation model has a wider adaptability, the constraint models of vertical and east-west temporal deformation are constructed respectively in the form of a full combination of the mathematical models in Table 1, that is, the first constraint model is obtained.

[0029] Similarly, considering that the variation of landslide deformation in the time dimension is relatively complex, the same constraint model as the first constraint model is used in the solution, based on which the corresponding second constraint model can be obtained.

[0030] Specifically, the expression of the first constraint model is:

[0031]

[0032] Among them, d m，U and d m，E are the vertical and east-west deformations corresponding to the mth moment respectively; a0 to a3, A1 and A2 are the parameters of the vertical deformation constraint model, b0 to b3, B1 and B2 are the parameters of the east-west deformation constraint model; t0 is the starting time, that is, the time when the first SAR image is obtained; t m is the mth moment, i.e., the moment when the mth SAR image is acquired; α U and α E are the thermal expansion coefficients in the vertical and east-west directions respectively (which will be used to exclude non-stress deformation components later); Υ m Get the time t for the mth SAR image m Temperature difference relative to the starting time t0.

[0033] The expression of the second constraint model is:

[0034]

[0035] Among them, d m，K and d m，T are the slope-direction and vertical-slope-direction deformations corresponding to the mth moment, respectively; p0 to p3, H1 and H2 are the parameters of the slope-direction deformation constraint model; q0 to q3, I1 and I2 are the parameters of the vertical-slope-direction deformation constraint model; t0 is the starting time, i.e., the time when the first SAR image is acquired; t m is the mth moment, i.e., the moment when the mth SAR image is acquired; α K and α T are the thermal expansion coefficients along the slope and perpendicular to the slope (which will be used to exclude non-stress deformation components later); γ m Get the time t for the mth SAR image m Temperature difference relative to the starting time t0.

[0036] In one embodiment, the monitoring model also includes a first observation equation and a second observation equation; the deformation observation quantity of the landslide to be measured in the upward direction of sight is input into the monitoring model to obtain the deformation time series of the landslide body in the vertical direction, the east-west direction, the slope direction, and the vertical slope direction. The process at least includes: based on the first constraint model, constraints are formed on the vertical deformation and the east-west deformation respectively, and then the first observation equation of the deformation model constraint conditions that are independent of each other is constructed; based on the second constraint model, constraints are formed on the slope direction and the vertical slope direction deformation respectively, and then the second observation equation of the deformation model constraint conditions that are independent of each other is constructed; based on the first observation equation, the time series deformation of the landslide body in the vertical direction and the east-west direction is solved; based on the second observation equation, the time series deformation of the landslide body in the vertical direction and the east-west direction is solved. Based on the second observation equation, the time series deformation of the slope direction and the vertical slope direction is solved.

[0037] In this embodiment, the inconsistency of vertical and east-west deformation, along-slope and vertical along-slope deformation laws is taken into consideration, and independent constraint models are constructed. This can reduce mutual interference among models during the calculation process, and at the same time, more accurate fitting can be performed based on the actual characteristics of deformation in each direction and data features.

[0038] Specifically, the expression of the one-dimensional constraint model is:

[0039] d m，LOS =a0+a1(t m -t0)+a2(t m -t0) 2 +a3sin(2πt m / T)+a4cos(2πt m / T)

[0040] Where, d m，LOS is the time-series deformation of the line of sight corresponding to the mth (m=0, 1, 2, ..., M) moment after the two platforms are merged, and d0，LOS =0; t0 is the starting time, i.e. the time when the first SAR image is acquired; t m is the mth moment (i.e., the moment when the mth SAR image is acquired); T is the period of the sine and cosine functions, which can generally be taken as 1 year; a0 to a4 are model parameters.

[0041] The matrix form of the temporal two-dimensional deformation solution equation group of the same-name point i under the constraints of a single deformation model is:

[0042]

[0043] In the formula, in the first term on the left side of the equal sign, the upper part of the solid horizontal line is the coefficient matrix of the time series two-dimensional deformation solution equation group. The lower part of the solid horizontal line is the constraint condition constructed based on the deformation model, which is divided into three parts by two vertical dashed lines, namely the projection coefficient matrix from the vertical direction to the line of sight, the projection coefficient matrix from the east-west direction to the line of sight, and the matrix composed of the coefficients of the elements in the constraint model parameter X to be estimated. The vertical dashed lines divide the upper and lower parts into three parts, which are respectively related to Δd U , Δd E Multiply by X. The upper part of the solid horizontal line in the vector on the right side of the equal sign is the line-of-sight deformation observation value corresponding to the interference of the two platforms, and the 0 value under the solid horizontal line is the virtual observation value required to construct the constraint condition. U =D mat ·*R U , G E =D mat ·*R E , X=[a0, a1, a2, a3, a4] T ;c m =(t m -t0), m=1, 2,..., M, f m =sin(2πt m / T), m=1,2,…,M,g m =cos(2πt m / T), m=1, 2, ..., M; u m = cosθ i , m=1,2,…,M; θ i and are respectively the radar wave incident angle and satellite flight azimuth corresponding to the i-th point of the same name (different ground targets correspond to different angle values).

[0044] According to the above solution equations based on one-dimensional deformation constraints, the expression of the first observation equation based on two-dimensional composite model constraints can be expanded as follows:

[0045]

[0046] In the formula, G U =D mat ·*R U , G E =D mat ·*R E ;X1=[a0,a1,a2,a3,A1,A2,α U ] T ,X2=[b0,b1,b2,b3,B1,B2,α E ] T , are the parameters of the vertical and east-west deformation constraint models respectively; c m =(t m -t0), m=1, 2,..., M, f m =sin(2πt m / T), m=1, 2, ..., M; g m =cos(2πt m / T), m=1, 2, ..., M.

[0047] For landslides, vertical and east-west deformations are the apparent reflection of along-slope deformations and vertical along-slope deformations. Only obtaining the vertical and east-west time series deformations of landslides is not enough to characterize the movement characteristics of landslides, while the along-slope and vertical along-slope deformations are the most intuitive indicators to characterize their dynamic changes. The existing technology can only obtain the deformation rate of the along-slope and vertical along-slope directions of the landslide, but cannot obtain the deformation time series, and cannot support the analysis of the changing laws of landslide deformation and the dynamic risk assessment. Starting from the observation geometry of ascending and descending SAR satellites, the three-dimensional spatial geometry of the surface and the relative relationship with the geometry of the landslide sliding surface, this method constructs the two-dimensional deformation and solution of the along-slope and vertical along-slope time series.

[0048] like Figure 2 As shown in the figure, the sliding body moves downward on the sliding surface. The sliding surface coordinate system is composed of three unit orthogonal vectors, including the downslope axis, the vertical downslope axis and the normal axis, which are represented by OK, OT and OI respectively. The direction indicated by the downslope axis is the slope direction of the sliding surface, and the direction indicated by the normal axis is the normal direction of the sliding surface. It is stipulated that downward movement along the downslope axis is positive, right movement along the vertical downslope axis is positive, and movement outside the sliding surface along the normal axis is positive. The deformation of the sliding body can also be represented by the "north-east-high" coordinate system composed of three directions: north-south direction (ON), east-west direction (OE) and vertical direction (OH). Therefore, the geometric relationship between the two coordinate systems can be constructed through slope and slope direction.

[0049] Figure 3 The figure shows the geometric relationship between the sliding surface coordinate system and the "northeast height" coordinate system. K , D T and D Irepresents the temporal deformation on the three axes of the sliding surface coordinate system OK, OT, and OI (i.e., deformation along the slope, deformation perpendicular to the slope, and normal deformation), respectively. N , D E and D H They represent the temporal deformation on the three axes of the “North-East-High” coordinate system, and α and β represent the slope and slope direction of the sliding surface. According to their geometric relationship, there is D K and D I The deformation projection of the slope axis OK and the normal axis OI are in the same vertical plane, so D K and D I The deformation projections on the horizontal plane should overlap, and D T Perpendicular to the plane OPK, the deformation projection in the vertical direction is zero. T Located in the horizontal plane, there are deformation projections in the east-west direction and the north-south direction, from which the projection relationship matrix of the deformation between the sliding surface coordinate system and the "north-east-high" coordinate system can be obtained, that is:

[0050]

[0051] The displacement towards the satellite is defined as positive, and the displacement away from the satellite is defined as negative. Based on the radar satellite imaging geometry, the deformation of the surface along the LOS direction can be known as D LOS It is actually the deformation of the earth's surface in the east-west direction. E , deformation in the north-south direction D N and vertical deformation (vertically upward or downward) D H The sum of the projections in the LOS direction is shown in the following formula:

[0052]

[0053] Where θ is the incident angle of the radar wave, is the heading angle of the satellite.

[0054] Therefore, the projection relationship matrix of the deformation in the sliding surface slope coordinate system and the radar satellite LOS direction can be obtained:

[0055]

[0056] Where a, b, and c are the projection coefficients of the deformation along the slope direction, along the perpendicular slope direction, and along the normal direction, respectively.

[0057] In the natural environment, the sliding body usually moves downward along the sliding surface under the action of gravity. In the absence of obvious external forces, the deformation along the normal direction of the sliding surface is much smaller than the deformation in other directions. Therefore, the time series deformation along the normal direction D IIgnore. The above formula can be simplified into a two-dimensional estimation model of along-slope deformation and vertical along-slope deformation in the sliding surface:

[0058]

[0059] The process of modeling the time series of downslope deformation and vertical downslope deformation is similar to the modeling and solving of vertical and east-west two-dimensional deformation time series. The average downslope and vertical downslope deformations in the time interval between two adjacent SAR images or the deformation increment between two moments are still used as the estimated parameters for modeling and solving. Here, "two adjacent SAR images" refer to the two SAR images that are adjacent in time after the M+1 SAR images are combined from the two platforms and arranged in chronological order. Still taking the i-th point of the same name as an example, based on the estimation model of the two-dimensional downslope and vertical downslope deformation in the sliding surface, the basic observation equations for solving its time series two-dimensional deformation are constructed, which are expressed in the form of a matrix:

[0060]

[0061] In the formula, Δd LOS is composed of all Δd i.k.LOS (ifg j ) is constructed by constructing the Y-order LOS deformation observation column vector, and arranged in the order of different platform numbers k; Δd K and Δd T are the M-order column vectors composed of the temporal deformation along the slope and perpendicular to the slope within the time interval between two adjacent images in the M+1 SAR image set; D mat is a Y×M-order design matrix, consisting of 0 and 1, where 1 corresponds to the time interval between adjacent SAR images contained in a certain interferogram time span, and the rest of the elements are 0; R K =a k , R T =b k (k=1, 2) are the Z×M-order matrices composed of the projection coefficients of different platforms along the slope and perpendicular to the slope to the LOS direction; a k and b k They represent the conversion parameters corresponding to the kth platform (see formula (4)), and are arranged in the order of the platform numbers k; "·*" represents the multiplication of the elements at the corresponding positions of the two matrices, and "·" represents the matrix multiplication. Assuming that the equation system (5) is solvable, when Δd K and Δd TAfter that, the time-dimensional integration of the internal elements of the two can obtain the time series deformation along the slope and vertical along the slope. However, since the acquisition time of SAR images from different platforms does not completely overlap, the equation group (5) is rank-deficient and cannot be solved normally. Therefore, the second constraint condition is constructed for the time series of along-slope deformation and the time series of vertical along-slope deformation. Combining (1), (4), (5) and we can get:

[0062]

[0063] In the formula, G K =D mat ·*R K ; G T =D mat ·*R T ;Y1=[p0, p1, p2, p3, H1, H2, α K ] T , Y2=[q0, q1, q2, q3, I1, I2, α T ] T , are the parameters of the deformation constraint model along the slope and perpendicular to the slope, respectively; c m =(t m -t0), m=1, 2,..., M, f m =sin(2πt m / T), m=1, 2, ..., M; g m =cos(2πt m / T), m=1, 2,…,M.

[0064] In one embodiment, the deformation observation amount of the line of sight upward of the landslide to be measured is input into the monitoring model to obtain the deformation time series of the landslide body in the vertical direction, the east-west direction, the downslope direction, and the vertical upslope direction, and the process also includes: based on the vertical and east-west time series deformation, the vertical and east-west deformation time series are obtained by integrating the time dimension; based on the downslope and vertical upslope time series deformation, the downslope and vertical upslope deformation time series are obtained by integrating the time dimension; different platforms are weighted by using the variance component estimation method, and the deformation time series is gradually refined by the weight selection iteration method.

[0065] In this embodiment, since the vertical and east-west deformations are constrained separately, they do not need to be projected to the sight line when constructing the constraint conditions, so the u in equation group (2) can be avoided. m = cosθ i and The problem of selecting the angle value can be directly replaced by the constant "1". Then the least squares or SVD method can be used to solve the vertical and east-west time series deformation within the time interval of adjacent SAR images. The deformation time series in the two directions can be obtained by integrating the time dimension. Similarly, the deformation time series along the slope and vertically along the slope can be obtained based on the above method.

[0066] It should be pointed out that the accuracy levels of deformation observations in the line of sight of different platforms are different. Therefore, firstly, the standard deviation of the noise of the differential interferogram of each platform is used as the initial weight (the weight matrix estimated before the test) for pre-adjustment processing, and the residual of the observation value obtained after adjustment is used to estimate the variance of the observation values ​​of different platforms. The weights are re-determined according to the estimated variance, and the initial value of the weight matrix in the first adjustment is improved. The adjustment is performed again according to the re-determined weight matrix, and this process is repeated until the variances of different observations tend to be consistent, and finally the weighted adjustment estimates of the vertical and east-west deformation time series are obtained.

[0067] So far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the original technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

Claims

1. A time-series InSAR method suitable for multi-dimensional deformation monitoring of landslides, characterized in that: include: Obtaining the visually upward deformation observation of the landslide to be measured; The deformation observation quantity of the landslide to be measured in the line of sight upward is input into the monitoring model to obtain the deformation time series of the landslide body in the vertical direction, the east-west direction, the along-slope direction, and the vertical along-slope direction; wherein the monitoring model at least includes a fractal-dimensional composite structure deformation constraint model; the first constraint condition constructed based on the fractal-dimensional composite structure deformation constraint model respectively constrains the vertical and east-west deformations, and the second constraint condition constructed based on the fractal-dimensional composite structure deformation constraint model respectively constrains the along-slope and vertical along-slope deformations.

2. The method according to claim 1, characterized in that The fractal-dimensional composite structure deformation constraint model includes a first constraint model and a second constraint model; the first constraint model is a constraint model for vertical and east-west time-series deformation, and the second constraint model is a constraint model for along-slope and vertical along-slope time-series deformation; The method at least comprises the following steps to construct the fractal-dimensional composite structure deformation constraint model: constructing a first constraint model and a second constraint model in the form of a full combination of mathematical models of surface deformation in different types of regions.

3. The method according to claim 2, characterized in that The process of constructing the first constraint model and the second constraint model in the form of a full combination of the surface deformation mathematical models of different types of regions at least includes: Acquire the first parameter of the fractal-dimensional composite structure deformation constraint model, wherein the first parameter includes: the vertical and east-west deformations corresponding to the m-th moment, the parameters of the vertical deformation constraint model, the parameters of the east-west deformation constraint model, the acquisition time of the first SAR image, the acquisition time of the m-th SAR image, the vertical and east-west thermal expansion deformation coefficients, and the temperature difference between the acquisition time of the m-th SAR image and the starting time; constructing a first constraint model based on the first parameter; Acquire the second parameter of the fractal-dimensional composite structure deformation constraint model, wherein the second parameter includes: the along-slope and vertical along-slope deformations corresponding to the m-th moment, the parameters of the along-slope deformation constraint model, the parameters of the vertical along-slope deformation constraint model, the acquisition time of the first SAR image, the acquisition time of the m-th SAR image, the along-slope and vertical along-slope thermal expansion deformation coefficients, and the temperature difference between the acquisition time of the m-th SAR image and the starting time; A second constraint model is constructed based on the second parameter.

4. The method according to claim 3, characterized in that The monitoring model also includes a first observation equation and a second observation equation. The process of inputting the deformation observation amount of the landslide to be measured in the upward direction of sight into the monitoring model to obtain the deformation time series of the landslide body in the vertical direction, the east-west direction, the slope direction, and the vertical slope upward direction at least includes: Based on the first constraint model, constraints are respectively formed on the vertical deformation and the east-west deformation, and then the first observation equations of the mutually independent deformation model constraint conditions are constructed; Based on the second constraint model, the deformation along the slope and the deformation perpendicular to the slope are constrained respectively, and then the second observation equations of the independent deformation model constraint conditions are constructed; Based on the first observation equation, the time-series deformation of the landslide body in the vertical direction and the east-west direction is calculated; Based on the second observation equation, the temporal deformation along the slope and vertically along the slope is calculated.

5. The method according to claim 4, characterized in that The process of inputting the visually upward deformation observation of the landslide to be measured into the monitoring model to obtain the deformation time series of the landslide body in the vertical direction, the east-west direction, the slope direction, and the vertically upward slope direction also includes: Based on the vertical and east-west temporal deformation, the vertical and east-west deformation time series are obtained through the integration of the time dimension; Based on the temporal deformation along the slope and vertically along the slope, the deformation time series along the slope and vertically along the slope are obtained by integrating the time dimension. The variance component estimation method is used to determine the weights of different platforms, and the deformation time series is gradually refined through the weight selection iteration method.

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