A time-series InSAR method suitable for multi-dimensional landslide deformation monitoring

Abstract

The present invention provides a time-series InSAR method suitable for multi-dimensional deformation monitoring of landslides. First, the deformation observations of the landslide to be measured in the upward direction of the line of sight are obtained, and then the observations are input into a monitoring model containing a fractal-dimensional composite structure deformation constraint model, thereby obtaining the deformation time series of the landslide body in the vertical, east-west, along-slope, and vertical along-slope directions. This method has significant advantages. It can simultaneously obtain the deformation time series characteristics of the landslide along four dimensions, namely, vertical, east-west, along-slope, and vertical along-slope. The constructed model covers linear, acceleration, periodic, high-frequency, and thermal expansion deformations, fully considers the complexity of landslide deformation, and has strong adaptability. Moreover, the model attaches importance to the differences between vertical and east-west, along-slope and vertical along-slope deformations, and constructs different constraint conditions respectively to form independent deformation model constraints. It can not only accurately constrain deformation in all directions, but also fit the reality and effectively improve the accuracy of the solution results.

Description

Technical Field

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

[0002] A landslide is a geological phenomenon in which part or all of a soil or rock mass slides downward along a weak surface or zone in a slope under the influence of gravity. Landslide hazards are a combination of various types of landslides, collapses, and debris flows, primarily caused by earthquakes, volcanic activity, river erosion, freeze-thaw cycles, precipitation, and human activities. Preemptive identification of landslide hazard points in landslide-prone areas is of great practical significance. One of the key characteristics of landslide hazard points is slope instability, which results in spatial displacement, or surface deformation. Therefore, landslide deformation monitoring is conducted in landslide-prone areas. Deformation measurement results can be used to locate slopes with high instability and to determine landslide hazard levels based on deformation rates. Furthermore, deformation prediction models can be constructed based on time series deformation measurements to predict the temporal evolution of slope deformation, providing richer and more detailed information for identifying landslide hazard points and categorizing hazard levels. Accurately extracting the slope's true spatial deformation is crucial for this process.

[0003] Time-series InSAR (Inspur SAR) measurements have demonstrated significant technical advantages and potential for landslide deformation monitoring, offering high spatial resolution, high efficiency, low cost, and strong adaptability, while also avoiding potential safety incidents during on-site testing. However, because InSAR technology extracts deformation by interfering with data acquired by side-looking synthetic aperture radar (SAR) sensors, which only detect one-dimensional information along the observation direction, existing time-series InSAR technology can only capture a single displacement component of the landslide along the radar's line of sight (LOS), failing to capture true landslide deformation information.

[0004] Existing technologies for monitoring landslide deformation in different dimensions are mostly based on InSAR data from different orbits or platforms. Using the intersection principle, observation equations are established to calculate static two-dimensional deformation rates, such as those in the vertical and east-west directions, downslope and vertical directions, and downslope and vertical downslope directions. However, static two-dimensional deformation rates cannot trace the temporal deformation characteristics of the landslide, resulting in incomplete landslide deformation information and hindering subsequent analysis and assessment. 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 deformation information by obtaining pixel offsets from different SAR image pairs. Due to the large errors associated with pixel offsets, deformation monitoring accuracy is low, reaching errors of more than 5 cm. Therefore, it is only suitable for large-scale deformation, such as deformations of 50 cm / year or more. However, typical landslides experience temporal deformation of only 5-20 cm per year, making POT technology unsuitable. Furthermore, because SAR image offsets correspond only to the horizontal direction, this technology can only monitor horizontal deformation and cannot monitor vertical, downslope, and perpendicular-to-downslope deformation. Regarding 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. This model can be applied to two-dimensional landslide time-series deformation monitoring, obtaining vertical and east-west two-dimensional landslide deformation time series. However, landslide deformation is primarily characterized by downslope sliding and perpendicular-to-downslope sliding, while MSBAS technology can only obtain vertical and east-west two-dimensional deformation time series, failing to capture the true downslope and perpendicular-to-downslope landslide time-series deformation characteristics. Furthermore, this technology does not consider the thermal expansion and contraction deformation of the monitored target and the physical mechanisms of deformation, which affects 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 perpendicular along-slope landslide deformation characteristics.

[0006] The present 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 an upward direction of sight; inputting the deformation observations of the landslide to be measured in an upward direction 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 includes 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 perpendicular-to-slope time-series deformation; the method includes at least 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 parameters of the fractal composite structure deformation constraint model, the first parameters 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, the m-th moment The temperature difference between the time when the SAR image is acquired and the starting time; a 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; a 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 the line of sight is input into the monitoring model to obtain the time series of deformation of the landslide body in the vertical direction, the east-west direction, the downslope direction, and the vertical upslope direction, and the process 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 mutually independent deformation model constraint conditions; based on the second constraint model, constraining the downslope direction and the vertical upslope direction deformation respectively, and then constructing the second observation equation of the mutually independent deformation model constraint conditions; solving the time series deformation of the landslide body in the vertical direction and the east-west direction based on the first observation equation; solving the time series deformation in the downslope direction and the vertical upslope direction based on the second observation equation.

[0010] In one 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 direction and the vertical upslope time-series deformation, the downslope direction and the vertical upslope deformation time series are obtained by integrating the time dimension; different platforms are weighted using the variance component estimation method, and the deformation time series is gradually refined through the weight selection iteration method.

[0011] Compared with the prior art, the present invention provides a time-series InSAR method suitable for multi-dimensional landslide deformation monitoring, which has the following beneficial effects: This method fully considers the complexity of landslide deformation. The constructed fractal-dimensional composite structural deformation constraint model not only includes linear deformation (linear term), deformation acceleration (quadratic term), and periodic deformation (sine and cosine terms), but also takes into account high-frequency deformation (cubic term) and thermal expansion deformation, which has better adaptability to complex landslide deformation. At the same time, the model considers the differences between vertical and east-west deformation, adopting different constraint models for the two dimensions: constraining vertical and east-west deformation based on the fractal-dimensional composite structural deformation constraint model separately, can better account for the differences in vertical and east-west deformation, and can form constraints for vertical and east-west deformation separately. It also considers the differences in along-slope and perpendicular along-slope deformation, and constrains along-slope and perpendicular along-slope deformation separately, thereby constructing mutually independent deformation model constraints, which are more consistent with actual conditions and improve the accuracy of the solution results.

[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 be more easily understood with reference to the accompanying drawings. Those skilled in the art will readily appreciate that these drawings are for illustrative purposes only and are not intended to limit the scope of protection of the present invention. Furthermore, similar numbers in the drawings represent similar components, wherein:

[0014] Figure 1 This is a flow chart of the 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. Those skilled in the art should understand that these embodiments are only used to explain the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0018] Example 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: Obtain the upward deformation observation of the landslide to be measured.

[0021] Step S2: Inputting the deformation observation amount of the landslide to be measured in the upward direction of the line 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 downslope direction, and the vertical upslope 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 downslope and vertical upslope deformations.

[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: the vertical and east-west deformations are constrained separately based on the fractal composite structure deformation constraint model, which can better consider the difference in vertical and east-west deformations, and can form constraints on the vertical and east-west deformations respectively. It also takes into account the difference in along-slope and vertical along-slope deformations, and constrains the along-slope and vertical along-slope deformations 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 includes at least 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 temporal 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 variation 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, and 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 changes of landslide deformation in the time dimension are more 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 acquired; t m is the mth moment, i.e., the moment when the mth SAR image is acquired; α U and α E are the vertical and east-west thermal expansion coefficients respectively (which will be used to exclude non-stress deformation components later); m Get 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 along-slope and perpendicular along-slope deformations corresponding to the mth moment, respectively; p0 to p3, H1 and H2 are the parameters of the along-slope deformation constraint model; q0 to q3, I1 and I2 are the parameters of the perpendicular along-slope 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 in the slope direction and perpendicular to the slope direction respectively (which will be used to exclude non-stress deformation components later); γ m Get 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 the line 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 downslope direction, and the vertical upslope direction, and the process 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 downslope direction and the vertical upslope 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 time series deformation of the landslide body in the vertical direction and the east-west direction; based on the second observation equation, solving the time series deformation of the downslope direction and the vertical upslope direction.

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

[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 temporal deformation of the sight line corresponding to the mth moment (m=0, 1, 2, ..., M) 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 equations 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. They are 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 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] Where 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 downslope and perpendicular downslope deformations. Obtaining only vertical and east-west time-series deformations is insufficient to characterize landslide motion. Downslope and perpendicular downslope deformations are the most intuitive indicators of dynamic changes. Existing technologies can only obtain deformation rates in the downslope and perpendicular downslope directions, but cannot capture deformation time series. This method cannot support analysis of landslide deformation patterns or dynamic risk assessment. This method draws on the observation geometry of ascending and descending SAR satellites, the three-dimensional surface geometry, and their relative relationship to the landslide sliding surface geometry to construct and solve two-dimensional time-series deformations in the downslope and perpendicular downslope directions.

[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 down-slope axis, the perpendicular down-slope axis and the normal axis, which are represented by OK, OT and OI respectively. The direction of the down-slope axis is the slope direction of the sliding surface, and the direction of the normal axis is the normal direction of the sliding surface. It is stipulated that downward movement along the down-slope axis is positive, right movement along the perpendicular down-slope axis is positive, and movement out of the sliding surface along the normal axis is positive. The deformation of the sliding body can also be represented by a "north-east-high" coordinate system composed of three directions: north-south (ON), east-west (OE) and vertical (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 high" coordinate system, D K 、D T and D Irepresent the temporal deformations 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 Represent the temporal deformation on the three axes of the “northeast-high” coordinate system, α and β represent the slope and direction of the sliding surface respectively. According to their geometric relationship, there is D in both the horizontal and vertical directions. 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 in 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 and north-south directions. From this, the projection relationship matrix of the deformation between the sliding surface coordinate system and the "northeast-high" coordinate system can be obtained, namely:

[0050]

[0051] It is stipulated that the displacement towards the satellite is positive and the displacement away from the satellite is negative. According to the geometry of radar satellite imaging, the deformation of the surface along the LOS direction is known to be D LOS In fact, it is the deformation of the earth's surface in the east-west direction. E , deformation in the north-south direction D N and vertical deformation D H The sum of the projections in the LOS direction is as follows:

[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 deformation along the slope, perpendicular to the slope, and normal, respectively.

[0057] In a 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 can be IIgnore. The above formula can be simplified into a two-dimensional estimation model of along-slope deformation and vertical along-slope deformation within 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 solution of the vertical and east-west two-dimensional deformation time series. The average downslope and vertical downslope deformation between two adjacent SAR images or the deformation increment between two moments are still used as the estimated parameters for modeling and solution. Here, "two adjacent SAR images" refer to the two SAR images that are temporally adjacent after the M+1 SAR images are arranged in chronological order after the two platforms are combined. 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 within the sliding surface, the basic observation equations for solving its time series two-dimensional deformation are constructed, expressed in matrix form as:

[0060]

[0061] Where Δd LOS is composed of all Δd i.k.LOS (ifg j ) is constructed by the Y-order LOS deformation observation column vector, and is 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 within 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 number k; "·*" represents the multiplication of the elements at the corresponding positions of the two matrices, and "·" represents the matrix multiplication. Assuming that the equation group (5) is solvable, when Δd K and Δd TAfter that, the time-dimensional integration of the internal elements of the two can be performed to obtain the time series deformation along the slope and vertically 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 vertical along-slope deformation. By combining (1), (4), (5) and we can get:

[0062]

[0063] Where 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 along-slope and perpendicular-slope 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.

[0064] In one embodiment, the process of inputting the sight-up deformation observations 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 downslope direction, and the vertical upslope direction further includes: based on the vertical and east-west time series deformation, obtaining the vertical and east-west deformation time series by integrating the time dimension; based on the downslope direction and the vertical upslope time series deformation, obtaining the downslope and vertical upslope deformation time series by integrating the time dimension; using the variance component estimation method to determine the weights of different platforms, and gradually refining the deformation time series by the weight selection iteration method.

[0065] In this embodiment, since the vertical and east-west deformations are constrained separately, it is not necessary to project them 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 angle values ​​can be solved by simply replacing them with a constant "1." Least squares or SVD methods are then used to calculate the vertical and east-west deformations within the time interval between adjacent SAR image acquisitions. By integrating the time dimension, the deformation time series in both directions can be obtained. Similarly, the above method can be used to obtain deformation time series in the downslope direction and vertically upslope direction.

[0066] It should be noted that the accuracy of line-of-sight deformation observations from different platforms varies. Therefore, we first perform a pre-adjustment using the standard deviation of the noise in the differential interferogram of each platform as the initial weight (the weight matrix estimated a priori). The residuals of the observations obtained after adjustment are used to estimate the variances of the observations from different platforms. Based on the estimated variances, the weights are re-determined to improve the initial values ​​of the weight matrix from the first adjustment. Adjustment is then performed again based on the re-determined weight matrix. This process is repeated until the variances of the different observations converge to a consistent value, ultimately yielding weighted adjusted estimates of the vertical and east-west deformation time series.

[0067] Thus far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art may make equivalent changes or substitutions to the original technical features, and the technical solutions after such changes or substitutions will fall within the scope of protection of the present invention.

Claims

1. A time-series InSAR method suitable for multi-dimensional deformation monitoring of landslides, characterized by: include: Obtaining the upward deformation observation of the landslide to be measured; Inputting the deformation observation amount of the landslide to be measured in the upward direction of sight into the monitoring model, obtaining the deformation time series of the landslide body in the vertical direction, the east-west direction, the downslope direction, and the vertical upslope direction; wherein the monitoring model at least includes 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 downslope and vertical upslope deformations; The fractal dimension 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 perpendicular-to-slope time-series deformation; The method comprises at least the following steps of constructing 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, specifically comprising: Acquire first parameters of a fractal composite structure deformation constraint model, the first parameters including: vertical and east-west deformations corresponding to the mth moment, parameters of the vertical deformation constraint model, parameters of the east-west deformation constraint model, the acquisition time of the first SAR image, the acquisition time of the mth SAR image, vertical and east-west thermal expansion deformation coefficients, and a temperature difference between the acquisition time of the mth SAR image and the starting time; and construct a first constraint model based on the first parameters: 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 acquired; 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; m Get time t for the mth SAR image m Temperature difference relative to the starting time t0; Acquire second parameters of the fractal composite structure deformation constraint model, the second parameters including: along-slope and perpendicular along-slope deformations corresponding to the m-th moment, parameters of the along-slope deformation constraint model, parameters of the perpendicular along-slope deformation constraint model, the acquisition time of the first SAR image, the acquisition time of the m-th SAR image, along-slope and perpendicular along-slope thermal expansion coefficients, and the temperature difference between the acquisition time of the m-th SAR image and the starting time; construct a second constraint model based on the second parameters: Among them, d m,K and d m,T are the along-slope and perpendicular along-slope deformations corresponding to the mth moment, respectively; p0 to p3, H1 and H2 are the parameters of the along-slope deformation constraint model; q0 to q3, I1 and I2 are the parameters of the perpendicular along-slope 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 in the slope direction and perpendicular to the slope direction respectively; m Get time t for the mth SAR image m Temperature difference relative to the starting time t0.

2. The method according to claim 1, characterized in that The monitoring model further includes a first observation equation and a second observation equation. The process of inputting the 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 downslope direction, and the vertical upslope direction includes at least: 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, constraints are formed on the along-slope and perpendicular along-slope deformations respectively, and then a second observation equation of the mutually independent deformation model constraint conditions is constructed; Calculating the vertical and east-west temporal deformation of the landslide body based on the first observation equation; Based on the second observation equation, the temporal deformation along the slope and vertically along the slope is calculated.

3. The method according to claim 2, characterized in that The process of inputting the sight-up 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 downslope direction, and the vertical upslope direction also includes: Based on the vertical and east-west temporal deformation, the vertical and east-west deformation time series are obtained by integrating the time dimension; Based on the temporal deformation along the slope and vertically along the slope, the time series of deformation 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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