InSAR Three-dimensional Surface Displacements Calculated By Considering The Spatiotemporal Characteristics Of Deformation

Interferometric synthetic aperture radar(In SAR)has been proven to measure ground surface displacements with the superiority of all weather,all day,large scale,high spatial resolution,and high precision compared with the traditional geodetic technologies(e.g.,leveling and GNSS),and has been widely used to obtain surface displacements caused by various geohazards(e.g.,earthquake and landslides).However,In SAR can only obtain the one-dimensional projection results of the real threedimensional(3-D)surface displacements along the line-of-sight(LOS)direction,making it difficult to accurately characterize the real surface deformations of geohazards,sometimes even resulting in misinterpretations of geohazards.Benefiting from the development of SAR(Synthetic Aperture Radar)satellites and data processing technology,heterogeneous SAR displacement observations can be obtained from multi-platforms,multi-orbits SAR data based on various data processing methods,and can be used to realize 3-D surface displacements measurement.However,the existing researches generally measure the 3-D surface displacements based on the pure geometric relationship between the SAR displacement observations and the 3-D displacements,which lacks the geophysical basis and is difficult to achieve the optimal fusion of heterogeneous SAR displacement observations.Besides,since the error signals contained in the heterogeneous SAR displacement observations are extremely complex,it is of great importance for measuring In SAR 3-D displacements to realize the accurate modeling and error correction for the heterogeneous SAR displacement observations.Generally,natural surface deformation is continuously and slowly changing within a certain temporal and spatial range(excluding temporal instantaneous deformation such as earthquakes and spatial jumps at earthquake faults,etc.).For example,under the assumption of the continuous stress field on the ground surface,the surface displacements within a certain small spatial range(such as several hundred meters)can be considered to be correlated.At the same time,in a short time scale(such as one month),the surface deformation can be regarded as a timedependent smooth process.In particular,with the launch of the new generation of SAR satellites,the temporal and spatial resolution of SAR data has been significantly improved,making the deformation signals in In SAR observations more consistent with the slowly and continuously changing spatiotemporal characteristics,therefore providing reliable prior information for the accurate In SAR 3-D surface displacements measurement.In this paper,aiming at the key technical problems in In SAR3-D surface displacements measurement,the prior information provided by the deformation’s spatiotemporal characteristics is fully studied.Based on the variance component estimation algorithm,iterative weighted least squares method,Kalman filter,etc.,this paper systematically studied the theory and method with respect to the In SAR 3-D surface displacements measurement by considering the spatiotemporal characteristics of deformations.This study enriches the theory and method system of In SAR surface displacement monitoring,and provides a reliable reference for high-precision In SAR 3-D surface displacements measurement.The main innovations/contributions lie in the following points:(1)Proposing an In SAR 3-D surface displacements measurement method based on the strain model and variance component estimation(SM-VCE),which establishes the geophysical and mechanical meaning function model for In SAR 3-D displacements measurement,realizes the posterior variance estimation of heterogeneous SAR displacement observations,and significantly improves the accuracy of In SAR 3-D surface displacements.The strain model represents the geophysical relationship between the 3-D surface displacements of the spatially adjacent points.This paper innovatively introduces the strain model to establish the function model for In SAR 3-D displacements measurement,which provides a large amount of redundant observations;on this basis,the variance component estimation algorithm is used to realize the posterior variance estimation and posterior weighting of heterogeneous SAR displacement observations,which not only significantly improves the accuracy of the obtained 3-D displacements,but also realizes the posteriori accuracy assessment of observations and unknowns without any variance’s prior information.Meanwhile,this paper proposes a method for selecting homogenous points of observations based on the strain model and an adaptive weighting method for the same type of observations within a window based on the iterative weighted least squares,which guarantees the robustness of the SM-VCE method in the displacement jump area or when the observations contain gross errors.This paper employs the SM-VCE method to calculate coseismic 3-D displacements of the 2007 Kilauea volcanic activity in Hawaii,the 2016 Kaikoura earthquake in New Zealand,and the 2019 Ridgecrest earthquake in the United States.Results indicate that the SM-VCE method can improve the accuracy of 3-D displacements with the accuracy improvement more than 20%.In particular,based on the case study of the2016 Kaikoura earthquake,this paper systematically analyzes the influence of different SAR observations combinations on the accuracy of 3-D displacements,and defines a term,the deformation dilution of precision(DDOP),to characterize the reliability of the 3-D displacements,which provides a reliable reference for In SAR 3-D surface displacements measurement.(2)Developing a strain-model based In SAR for geohazards’ monitoring approach(SIGMA)and constructing a joint model for decreasing the trend and DEM-related components in In SAR time series(Detrend In SAR),which can not only suppress the influence of decorrelation noise,but also reduce the effect of noise signals such as atmospheric delay and orbital error on In SAR displacement observations,and the accuracy and density of In SAR time series displacement observations are significantly improved.As one of the most important error sources in In SAR observations,decorrelation noise seriously hinders the accuracy and density of In SAR displacement phase time series.The SIGMA method proposed in this paper establishes the geophysical relationship between the In SAR phases at adjacent points based on the strain model,which provides effective geophysical constraints among the surrounding points for the phase optimization of the target point,thereby mitigating the effect of heterogeneous points/phases in the phase optimization process.Besides,the In SAR time series phase can be directly obtained from the original wrapped In SAR interferogram based on the iterative weighted least squares method,where the main procedures include the strain-model-based phase optimization,the phase time series calculation at arcs,and the spatial integration of arcs.The whole process of the SIGMA method is relatively simple and easy to understand.In addition to decorrelation noise,other noise signals such as atmospheric delay and orbital errors also seriously hinder the accuracy and reliability of In SAR displacement measurement.In general,the traditional method only analyzes and corrects one certain error signal under the premise that other error signals are effectively corrected,and its correction performance is bound to be affected by the existence of other signals.Based on the spatiotemporal characteristics of multi-source signals,this paper innovatively establishes a joint model of the displacement signal,atmospheric delay,orbital error and other components in the spatiotemporal dimensions,which effectively avoids the loss of displacement accuracy caused by the individual processing of multi-source error signals.Here,the local turbulent atmosphere and orbital errors can be modeled using spatially correlated polynomials(i.e.,the trend component),and the local stratified atmosphere can be correlated with DEM(i.e.,the DEM-related component).Taking the Geysers geothermal field in California as an example,the SIGMA and Detrend In SAR methods were subsequently used to successfully obtain the displacement time series from the 2007-2011 ALOS-1 data and the 2015-2020 Sentinel-1 data.Comparison with the open Sta MPS software and the GNSS data illuminates that the SIGMA and Detrend In SAR methods can significantly increase the density and accuracy of In SAR displacement measurements,therefore better revealing the spatiotemporal pattern of deformation over the study area.(3)Proposing a dynamic estimation method of three-dimensional displacement time series from In SAR based on Kalman filter and strain model(KFIn SAR),which constructs the 3-D displacements time series estimation model by considering the spatiotemporal characteristics of displacements,and effectively improves the accuracy and computational efficiency of In SAR 3-D displacements time series measurement.After obtaining multi-platform and multi-track highprecision In SAR one-dimensional displacement time series,how to efficiently integrate these data to achieve high-precision measurement of In SAR 3-D displacements time series is still an urgent problem to be solved.This paper systematically analyzes the key issues of In SAR 3-D displacements time series measurement.Under the framework of Kalman filter,this paper establishes the state transition functions of Kalman filter based on deformation’s temporal characteristics and the observation functions of Kalman filter based on the strain model,which provides an effective guarantee for high-precision and high-efficiency 3-D displacements time series measurement in the era of In SAR big data.At the same time,considering that the real surface deformation results may be non-smooth deformation,this paper further quantitatively analyzes the applicability of the KFIn SAR method when the deformation is non-smooth in both time and space;at the same time,since most of the existing SAR data can only be obtained with two distinctly different imaging geometries,this paper analyzes and deduces the influence on the east-west and vertical components when ignoring the north-south component.Simulation experiments and real experiments in the Geysers geothermal field in California show that,compared with the traditional method,the KFIn SAR method has significantly improved the accuracy and computational efficiency in In SAR 3-D surface displacements time series measurement.(4)This paper quickly obtained the first high-precision 3-D coseismic displacements of the 2021 Maduo earthquake,China based on the SM-VCE method,and the SIGMA method,the Detrend In SAR method and the KFIn SAR method were used to calculate the threedimensional postseismic displacements of the 2021 Maduo earthquake,which are of great significance and provide reliable datasets for the disaster assessment and mechanism interpretation of this earthquake.On May 22,2021,an Mw 7.4 earthquake occurred in Maduo County,Qinghai Province,China,which is the largest earthquake in our country since the 2008 Wenchuan earthquake.This earthquake located on the Jiangcuo fault in the northeast of the Bayankala block,and is important for the study of the active movement of the Bayankala block.Hence,after the earthquake,this paper quickly obtained the first high-precision 3-D surface displacements field of the earthquake based on the SM-VCE method and the ALOS-2/Sentinel-1 SAR data.Results show that the seismogenic fault of the 2021 Maduo earthquake is consistent with a left-lateral strike-slip fault,and the magnitude of the horizontal deformation on the north side of the fault is larger than that on the south side.The magnitude of east-west displacement component is larger than the north-south and vertical components,and the maximum westward and eastward displacements are2.4m and 1.7m;the vertical deformation shows a positive and negative alternation along the fault,indicating that the seismogenic fault plane of this earthquake is not a single simple vertical structure,but can be divided into multiple fault planes with different dip angles.Subsequently,in order to further reveal the movement of the earthquake fault,this paper used the SIGMA method,the Detrend In SAR method and the KFIn SAR method to obtain the high-precision east-west and vertical postseismic displacements time series by ignoring the north-south component.The results show that in the 6 months after the earthquake,there are still large and concentrated east-west surface displacements(6-8 cm)near the fault,while in the farfield area,the magnitude of displacement is small,but the spatial scale of displacement is large.In this paper,the relevant displacement results are made public and free of charge,which can provide reliable data support for disaster assessment and mechanism interpretation of the earthquake.