TWO-DIMENSIONAL LOESS LANDSLIDE DEFORMATION MONITORING WITH MULTIDIMENSIONAL SMALL BASELINE SUBSET ( MSBAS )-A CASE STUDY OF XINYUAN No . 2 LANDSLIDE , GANSU , CHINA

The deformation monitoring of active landslides is of great importance for the safety of human lives and properties. And twodimensional deformation result can give us more thoughts on the landslide type and deformation process. In this study, multidimensional small baseline subsets (MSBAS) technique is introduced and tested to compute two-dimensional deformation rate and time series for both east-west and vertical deformation of Xinyuan No.2 landslide by simultaneously processing ascending and descending TerraSAR-X data acquired from January 2016 to November 2016. Results show not only the spatiotemporal characteristics of this landslides, but the retrogressive loess landslide failure mode is revealed for the first time with the two-dimensional deformation.


INTRODUCTION
Loess occupies approximately 6.6% of the total area of China and exists in 12 provinces, of which 0.4 million square kilometers is loess plateau (Zhao et al., 2016).Loess plateau is an important base of energy sources and chemical industries in China, and it is also one of the regions with the most serious soil erosion and the most fragile ecological environment in the world.Loess plateau is prone to serious geo-hazard including collapse, landslide, earthflow, land subsidence and ground fissures (Qi et al., 2017), which seriously restrict the regional urban construction, economic development, and threaten the safety of transportation system and natural resource exploration.So, it is very important to identify in advance and monitor with high precision for these loess geo-hazards.Xinyuan No.2 landslide, located in the arid loess plateau, Gansu province, China is as small as 150m in length and 160m in width (Figure 1).People began to pump a large amount of water from the Yellow River for agricultural irrigation since the 1960s.Therefore, the longterm irrigation resulted in the groundwater level rising over 100cm in two years, the basal zone of loess is softened by saturation and readily to deform under overburden stress (Peng et al., 2017;Qi et al., 2017;Xu et al., 2011).As a result, a large number of loess landslides have occurred in this region (Figure 1) (Zhang et al., 2011).
In recent years, different InSAR technique have been widely used in landslide detection and monitoring (Zhao et al., 2012;Zhao et al., 2013;Zhao et al., 2016;Rosi et al., 2017).Usually, phase-based methods including differential SAR interferometry (D-InSAR), small baseline subset (SBAS), persistent scatterer InSAR (PSI) and their combination method are applied to measure landslide displacements in line-of-sight (LOS) direction.However, aiming to monitoring small scale and analyzing landslides mode, the following technical issues remain.It can only process one SAR dataset at once; it can only obtain onedimensional LOS deformation; and the temporal resolution defined by satellite revisit time is low.In what follows, twodimensional deformation monitoring method is introduced and high temporal resolution results are obtained.
To overcome the disadvantages of traditional one-dimensional multi-temporal InSAR methods, advanced multidimensional small baseline subsets (MSBAS) technique is introduced, with which two-dimensional deformation rate and time series deformation in both east-west and vertical directions are calculated.

METHODOLOGY
The MSBAS technique combines multiple D-InSAR datasets into a single solution, which has two kinds of improvement in terms of noise decreasing and temporal resolution increasing with almost uninterrupted temporal coverage (Tiampo et al., 2017).The MSBAS methodology is an extension of the original SBAS method that reconstructs two or three-dimensional deformation rate and time series from ascending and descending InSAR data acquired by different SAR sensors considering various characteristics including wavelength, temporal and spatial resolution, azimuth and incidence angles (Samsonov et al., 2014).The precision of MSBAS-derived results are affected by the quality of interferograms and some processing parameters including phase filtering strength, coherence threshold for unwrapping, location of reference point, techniques for the removal of spatially and temporally correlated atmospheric noise and residual orbital trend.
If a single set of SAR data acquired by a sensor with an incidence angle  and an azimuth  , the time series deformation can be reconstructed by applying the SBAS method (Berardino et al.,).
where A is an is the number of SAR images), Vlos is the LOS velocities,  obs is the observed phase.A  is a pseudo-inverse of matrix A calculated by Singular Value Decomposition (SVD), and d i los is the LOS displacement at the epoch t i .

When
K multiple SAR datasets are available with different incidence angles and azimuth, the Eq. ( 1) can be rewritten in the following form (Samsonov et al., 2013): where S is a unit vector of LOS with north, east and up components, and V is a velocity vector with components The MSBAS method that includes all K sets of independently acquired SAR data can be expressed in the following equation: where A ˆ is a new matrix with ˆis a new unknown velocity vector, and  ˆobs is a new observation vector.If only two ascending and descending SAR data, Eq. ( 4) can be further simplified, (Samsonov and d'Oreye, 2012).
Due to the inconsistence of acquisition dates of ascending and descending data, which results in rank deficiency of Eq. ( 4) and no unique solution.This problem can be solved under the leastsquare norm by applying SVD and the zero-, first-, or secondorder Tikhonov regularization.Once the unknown velocity vector for each pixel are solved, the time series deformation can be obtained easily by integrating the deformation in each neighbouring SAR acquisition dates.It is worth noting that the integration cannot be executed directly due to the inconsistency of ascending and descending data acquisition dates.Therefore, it is necessary to take boundary correction for both ascending and descending SAR images to make the first and the last ascending and descending images are corresponding to the same dates, respectively.

Test and results
In this test, twenty-three ascending and nineteen descending Xband Spot-mode TerraSAR-X data from January 2016 to topographic phase.The temporal baseline and spatial baseline thresholds are set to 60 days and 250m, respectively.And multilooking number two is set in range and azimuth directions, respectively.The interferograms are filtered using the Goldstein filter method (Goldstein and Werner, 1998), unwrapped using minimum cost flow (MCF) algorithm.Followed by a combined model comprising a biquadratic model for orbital phase errors and a linear model for the elevation dependent errors including stratified atmospheric delay and topography errors (Kang et al., 2017).Finally, 32 ascending and 27 descending pairs of high quality interferograms are selected to calculate two-dimensional deformation rate and time series deformation results.To this end, all ascending and descending interferograms are geocoded and resampled to a common longitude and latitude grid of three meters.
The one-dimensional LOS annual deformation rate maps for both ascending and descending data are shown in Figure 2. The maximum deformation rate of Xinyuan No.2 landslide in LOS of ascending and descending are about 60mm/ year and -40mm/y, respectively.Then MSBAS technique is used to produce vertical and horizontal east-west annual deformation rate maps (Figure 3) and time series results.The two-dimensional time series of point P1-P4 in Figure 1

Landslide mechanism analysis
It can be seen from Figure 3  3) The failure procedure is repeated to form retrogressive landslide ③ etc.

CONCLUSIONS
In this study, the two-dimensional deformation rate maps and time series results in both vertical and east-west direction is introduced and tested for Xinyuan No.2 landslide.The retrogressive characteristic of loess landslide is revealed successfully by MSBAS technique, which indicates that the MSBAS method is a promising technique in landslide monitoring and mechanism analysis.

Figure 1 .
Figure 1.(a) Location of study region; (b) a wide view of the landslides in study area; (c) zoom in Xinyuan No.2 landslide, where points P1-P4 will be analyzed in Figure 4.
November 2017 are acquired to monitor the deformation of Xinyuan No.2 landslide.The data processing is divided into two steps.Firstly, differential interferograms of ascending and descending are generated independently, where 3m resolution unmanned aerial vehicle (UAV) DEM is applied to remove the (c) are shown in Figure 4.The results show that annual deformation rate of Xinyuan No.2 landslide in east-west and vertical directions reached -60mm and 30mm from 2016 to 2017, respectively.

Figure 2 .Figure 4 .
Figure 2. Annual deformation rates in line-of-sight direction calculated with SBAS technique.(a) ascending TerraSAR data and (b) descending TerraSAR data Figure 5.A conceptual model of the multi-staged retrogressive failure of loess landslide.