Introduction

Effective monitoring urban subsidence is of great significance as to provide qualified data of urban geological disaster prevention and estimation. Underground resources such as underground water, coal, oil and natural gas are exploited with the development of economy, expansion of city development and population, as well as further industrialization. Meanwhile severe subsidence occurs in cities as underground water is exhausted. What's worse, subsidence becomes faster which was the consequence of the construction of a cluster of tall buildings and the underground rail. Subsidence renders the reduction of height. And the uneven deformation causes failure of urban drainage system and absence of flood control ability, destruction of linear engineering such as subways, railways and water pipelines, sinking or cracking of the foundations. So, urban subsidence, directly affecting urban sustainable development and the safety of citizens and their properties, is one of the most focused environment and geology problems of the city.

Traditional measuring tools including leveling, total station, GPS and wireless detection system which can obtain single point deformation with high temporal resolution and precision, but the results of these measurements are of low spatial resolution which fails efficiently to describe the spatial deformation field precisely. The data collected by traditional measuring tools give certain restriction to model construction based on data and other analysis, which cannot meet the requirements of geophysical research and geological disaster prediction.

Differential interferrometric synthetic aperture radar (DInSAR) is an effective technique for measuring surface displacement, which is widely applied on surface deformation (Gabriel et al. 1989; Liu et al. 2001; Ding et al. 2003; Wang et al. 2007), earthquake deformation (Massonnet et al. 1993; Li et al. 2011), glaciers movement (Goldstein et al. 1993), volcanic movement (Lu et al. 2002) and landslide (Gischig et al. 2009). While DInSAR is a proven, very effective technique for measuring deformation, almost any interferogram includes large areas where the signals decorrelate and no measurement is possible. Even though for the possible measurement, separating atmospheric delay phase from the interferometric phase is a difficult task.

Persistent Scatterer (PS) InSAR is an extension to the DInSAR technique (Ferretti and Rocca 2001; Ferretti et al. 2002, 2011), which addresses the problems of decorrelation and atmospheric delay. An important aspect of PS is that for point targets no spatial decorrelation occurs permitting interpretation of the interferometric phase of pairs with long baselines, even above the critical baseline. Obviously, a PS point must be remained stable over the time period of interest to permit analysis of the phase history. Based on these ideas one important objective of the PS is to achieve a more complete use of the available data. Through the use of point targets, interferometric pairs with long baselines can be employed. Consequently, more observations are available permitting reduction of errors resulting from the atmospheric path delay and leading to better temporal coverage. In the few years, Similar processing algorithm have been developed such as Coherent pixel technique (SPN) (Vander Kooij 2003), Interferometric point target analysis (IPTA) (Werner et al. 2003), stable points network (SPN) (Arnaud 2004) and small baseline subset (SBAS) (Berardino et al. 1999; Xu et al. 2012). These techniques can be categorized into those that rely on analysis of interferograms all with respect to the same master image, commonly known as persistent scatterer methods which are suitable for large SAR data stacks, and those that analyse interferograms formed with regarding to multiple masters, commonly known as small baseline methods for small SAR data stacks.

For small SAR data stacks, the temporal variability criteria to select point target candidates becomes unreliable for statistical reasons, which is not suitable for PSInSAR. The SBAS technique has already been successfully applied to small SAR data stacks; however, as it was originally designed to monitor deformations occurring at a relatively large spatial scale (pixel dimensions of the order of 100 × 100 m are typical), it is not appropriate to analyze local deformations which may affect, for example, single buildings or structures.

Therefore, in this paper, the muti-reference radar interferometry based on coherent targets is proposed to identify coherent targets and obtain deformation. This technique identifies coherent targets on account of sublook coherence of single SAR image without mutilook images and radiometric calibration. So, the coherent targets can be recognized even using single SAR image. Then, the spatial filter is used to obtain the spatial low frequency deformation and atmospheric phases by using the pairs with relatively short intervals based on differential interferrometric phase. Point height corrections are determined by using a 1-D regression on high frequency residual phase which is obtained by the subtraction of the spatially filtered phase contains the residual topographic phase, the phase noise, as well as the high frequency parts of the deformation and atmospheric phases. And conduct phase unwrapping for discrete CSs utilizing the minimum cost flow method (MCF). The unwrapped phase is decomposed using SVD method thus the deformation is obtained. An experiment of eight ALOS PALSAR SAR images over Zhengzhou urban area during 2007–2010 was being conducted in order to analyze the reliability of the proposed method.

Muti-reference Radar Interferometry Technique Based on Coherent Targets

Muti-reference radar interferometry technique which based on coherent targets consists of five parts: data preprocessing, identifying coherent targets, generating differential interferogram, unwrapping phase and estimating deformations.

Data Preprocessing

Image registration is among the most significant part of SAR data preprocessing. Some interferograms will have values of temporal, perpendicular and Doppler baseline that are higher than would be commonly chosen for conventional InSAR. This leads to high decorrelation and a correspondingly low coherence which makes coregistration routines based on cross-correlation of amplitude fail. Therefore, a modified image registration method is developed. This method includes two steps:

  1. (1)

    Selecting reference image. Choose reference image that maximizes the sum correlation of all the interferograms. This could make coregistration be easy (Zebker and Villasenor 1992).

  2. (2)

    Calculating image registration polynomial coefficients using weighted least squares. Due to the influence of the speckle noise, more than one extreme coherence value may appear in a small searching zone. So, some homonymy points with poor quality are determined by coherence. Directly using weighted least squares based on coherence shall exerts effect upon the final coregistration precision. In this paper, We use \( 1/{\delta}_{\varDelta \widehat{x}} \) as weighted factor where \( {\delta}_{\varDelta \widehat{x}} \) is the standard deviation of the offset estimates. The \( {\delta}_{\varDelta \widehat{x}} \) can be estimated by using the formula (1) derived by (Bamler 2000).

    $$ {\delta}_{\varDelta \widehat{x}}=\sqrt{\frac{3}{2N}}\frac{\sqrt{1-{\gamma}^2}}{\pi \gamma } os{f}^{3/2} $$
    (1)

    where N is the number of samples in the searching window, γ is the coherence of the interferometric pair, osf is oversampling factor of the data.

Identifying Coherent Targets

PSs are identified on a low temporal variability of the SAR intensity using the amplitude dispersion index. The reliability of PS candidate selection will strongly depend on the number of available SAR images (more than 25 images). So, from the perspective of statistics, it becomes unreliable for small SAR data stacks. What is often used for identifying PSs in small SAR data stacks is the method based on the coherent values of sequential interferometric pairs. The coherence of each point is determined by the size of coherent window. If the window is too large, the isolated PSs are easy to be affected by the surrounding low coherent targets and hard to be identified. On the contrary, the false PSs near real PSs will be wrongly identified, which will impact the final result. So, it is necessary to explore a new identifying coherent targets method for small SAR data stacks.

Compared with distributed scatterers such as farmland and forest, man-made objects can be seen as point targets (i.e., SAR image resolution cells for which the scattering is dominated by a target which is small in size as compared to the size of the resolution cell) do not exhibit the speckle observed for extended targets. For a point target almost the same backscattering intensity is found when observing from slightly different direction, which is widely unaffected by multiple scattering effects and geometrical distortions and keep high spectral correlation among sublook SAR images. While, for distributed scatterers, the coherent value is low (Arnaud 1999; Henry et al. 1999; Ouchi and Wang 2005). According to the above descriptions, the CSs identifying method based on sublook coherence is proposed here:

  1. (1)

    To conduct FFT transform for SLC data, and obtain the spectrum of the images. Then the spectrum is divided into two sublook ones using Hamming window without weight, which reduces the impact of system pulse sidelobes. And two sublook spectrums are shifted to the same central frequency in order to avoid any linear phase terms when forming the cross-product.

  2. (2)

    To process each sublook spectrum using Hamming weighted function respectively. Setting the length of weighted function to half of the original bandwidth, the size of sublook spectrograms are adjusted to the size of original one. Meanwhile, Hamming weighted function decreases the interference of side lobes, which runs quite well on urban areas with multiple scatterers.

  3. (3)

    To conduct inverse Fourier transform (IFFT) for both weighted sublook spectrums and obtain two sublook SLC data. And the normalized correlation coefficient obtained from two non-overlapping spectral halves is defined as (2):

    $$ \begin{array}{cc}\hfill \gamma =\frac{\left|<{X}_1{X}_2^{*}>\right|}{\sqrt{<{X}_1{X}_1^{*}><{X}_2{X}_2^{*}>}}\hfill & \hfill 0\le \gamma \le 1\hfill \end{array} $$
    (2)

    where X 1 and X 2 are two sublook images, * denotes complex conjugate operator, <> denotes ensemble averaging. Scatterers with a higher correlation than a given threshold value are then interpreted as CSs.

  4. (4)

    To determine coherent targets in time series with coherence dispersion index D r . The equation is:

    $$ \begin{array}{l}{D}_{\left(i,j\right)}=\frac{\delta_{\left(i,j\right)}}{m_{\left(i,j\right)}}\hfill \\ {}\begin{array}{cc}\hfill {m}_{\left(i,j\right)}=\frac{1}{M}{\displaystyle \sum_{ii=1}^M{\gamma}_{\left(i,j\right)}},\hfill & \hfill {\delta}_{\left(i,j\right)}=\sqrt{\frac{1}{M}{\displaystyle \sum_{ii=1}^M{\left({\gamma}_{\left(i,j\right)}-{m}_{\left(i,j\right)}\right)}^2}}\hfill \end{array}\hfill \end{array} $$
    (3)

    where M is the number of SAR imgaes, δ (i,j) and m (i,j) are respectively the standard deviation and mean of a series of coherent values. When recognizing coherent targets with formula (2), some moving targets such as cars or ships, which have strong sublook coherence in single SAR image especially in high resolution SAR image. But their coherences fluctuate in the time series. So, these targets should be removed in the time series analysis. Considering formula (2) and (3), setting double threshold to determine coherent targets with stable phase in time series.

Generating Differential Interferogram

On the basis of short temporal and spatial baseline principle, the application of combining muti-reference radar interferometric pairs is good for obtaining more precise deformation by increasing temporal sampling of interferometric pairs. The combination of short spatial and temporal baseline weakens height phase as well as avoids large displacement contained in differential interferogram. After confirming interferometry combination, the original differential interferometry value of CSs are received with two-pass difference method depending on coregistered SLC, DEM with the same geometry of SAR, and initial coherent targets. The differential interferometry phase is the sum of multiple terms, including the phase of reference surface, topographic phase, deformation phase, atmospheric phase and noise. It is denoted as:

$$ {\phi}_{dint,i}^k=\frac{4\pi {B}_{\perp}^k}{\lambda {R}_m \sin \theta}\varDelta {h}_i+\frac{4\pi }{\lambda}\varDelta {r}_i+{\phi}_{atm,i}^k+{\phi}_{orb,i}^k+{\phi}_{noi,i}^k $$
(4)

where i denotes the number of coherent targets, k is the serial number of interferometric pairs, λ is radar wave length, R m is the range distance between radar and the target, θ is incidence angle, B k⊥ is prependicular component of interferometer baseline, Δh i is residual height correction, Δr i is the displacement in line-of-sight (LOS) direction. In the Eq. (4), the first term is residual height phase, the second one is the deformation phase in LOS direction, the third is atmospheric phase, and the fourth is the orbital correction phase, the fifth is noisy phase and some possible nonlinear deformation phase.

Unwrapping Phase

If the unwrapped phase of initial differential interferogram of each coherent target is given, the deformation can be obtained directly using singular value decomposition (SVD). But in practice, it is hard to unwrap phase successfully for all interferometric pairs since initial differential interferometry value is a synthesis of multiple components and the phase gradient between adjacent coherent targets is large. Apart from residual height phase and noise with randomness, other parts of initial differential interferometry value have strong spatial correlation. So, the following unwrapping strategy is utilized in this paper.

  1. (1)

    Given that the candidate selection was adequate, For the interferometric pairs with short time intervals the phase noise should be small (<1 rad) for most scatterers, so spatial unwrapping was possible (Wegmuller et al. 2010). For the unwrapped interferometric pairs, based on the unwrapped phase, orbital phase corrections were estimated, considering only areas which were expected to be stable. The residual phase was then spatially filtered. The filtered phase contains the spatial low frequency deformation and atmospheric phases, and the high frequency residual phase which is obtained by the subtraction of the spatially filtered phase contains the residual topographic phase, the phase noise, as well as the high-frequency parts of the deformation and atmospheric phases. Link up discrete coherent targets with Delaunay triangulation network and calculate subtraction of each arc in high frequency phase part. A linear relation exists between residual height phase and prependicular baseline, so high frequency phase difference between adjacent points is:

    $$ {\phi}_{\varDelta h}^k\left(ar{c}_{i,j}\right)=\frac{4\pi {B}_{\perp}^k}{\lambda {R}_m \sin \theta}\varDelta {h}_{i,j}+{\phi}_n $$
    (5)

    where Δh i,j is residual height value difference between point i and j, ϕn is noise phase. Maximizing correlation coefficients method is utilized to cope with Eq. (5) (Colesanti et al. 2003; Chen et al. 2009, 2012). And the results are residual height difference between adjacent points and standard deviation of regression analysis in each point. Residual height of each point is calculated by integrating the whole triangulation network. Referring to standard deviation, the candidate CSs with low quality are removed.

  2. (2)

    Perform two-pass differential interferometry again after correcting initial height using residual height. Most of the residual height phases are removed, so the current differential interferometry phases only consist of low frequency phases and a few residual height phases. Therefore, most differential interferometry phases can be unwrapped in spatial domain. For unwrapped image pairs, high correction phases in differential interferometry phases would be removed according to the method mentioned in step (1). Final differential interferometry phases include deformation atmospheric, and a few high frequency parts. Assuming the deformation is a linear part, the phase difference between each is:

    $$ {\phi}^k\left(ar{c}_{i,j}\right)=\frac{4\pi {B}_{\perp}^k}{\lambda {R}_m \sin \theta}\overline{\varDelta {h}_{i,j}}+\frac{4\pi }{\lambda }{T}^k{v}_{i,j}+{\phi}_{atm}^k+{\phi}_n $$
    (6)

    where \( \overline{\varDelta {h}_{i,j}} \) the difference of height corrections between adjacent points, T k is the temporal baseline of interferometric pairs, v i,j is the difference of deformation velocities between adjacent points, ϕ k atm and ϕ n are atmospheric phase and noise phase of adjacent points respectively. Similarly, the deformation velocities and residual heights are calculated using the maximum correlation coefficients method. And height correction and displacement in each point are obtained by integrating the whole triangulation network. The corrected height and deformation velocity seen as initial values, iterating the above processes until all interferometric pairs are unwrapped correctly and determined phases of model are obtained. The residual height corrections and linear deformation phase obtained by using 2-D regression. The remaining phase contains the spatial low-frequency atmospheric phases and high-frequency noise phase and nonlinear deformation phases. Then spatially filter is utilized to separate atmospheric phase from the residual phases.

  3. (3)

    With known unwrapped differential interferometry phase, corrected height, precise baseline an atmospheric phase, the two-pass difference should be conducted again. The final unwrapped differential interferometry phase consists of deformation phase (linear and nonlinear deformation) and noise phase.

Estimating Deformations

Starting from the multi-reference stack, we derive a single-reference time series using SVD to obtain the least squares solution for the phase time series. A similar approach was proposed in (Berardino et al. 1999). A complete series is obtained for the times connected by the multi-reference pairs. Based on the ten pairs, namely, A-B, A-C, B-C, B-D, B-E, C-D, C-E, C-F, D-E, and E-F, we obtain for example, the time series for the six times, i.e., A, B, C, D, E, and F. Redundancy in the differential interferogram input data reduces uncorrelated errors in the time series. Uncorrelated errors include residual topographic phase errors and phase noise. Atmospheric phase, on the other hand, is not reduced by this estimation procedure. For a given acquisition date, there is a well-defined atmospheric phase delay pattern which is present in all the pairs including this date. The same applies for nonuniform deformation phase. Consequently, the obtained time series of unwrapped phases still includes the atmospheric phases as well as nonuniform deformation phase. Aiming at this issue, the linear displacement and residual phase (residual atmospheric phase and nonlinear deformation phase) are separated with linear regression method. And the regression equation is:

$$ {\phi}_{line- disp}=\frac{4\pi }{\lambda }{T}^kv $$
(7)

where ϕ line − disp is linear deformation phase, T k is temporal baseline, v is linear deformation velocity. Using the formula (7) on single-reference unwrapped phases permitted one to determine the linear deformation. The residual phase was then spatially filtered to obtain the nonlinear deformation. Thus, the nonlinear deformation phase was added to the linear deformation phase and interpreted as the final deformation result.

Experiment Data, Results and Analysis

Study Area and Data Acquisition

Zhengzhou city is located in east longitude 112°42′–114°14′ and north latitude 34°16′–34°58′. It is situated at the transitional zone among piedmont, torrential plain and the Yellow River alluvial plain. The general terrain trend is tilt from southwest to northeast. The city is bounded with Nanyang Road. West part of the road is the piedmont inclined plain with the height 100–130 m and surface lithology of Pleistocene series loess powder on the soil. And east part is the Yellow River alluvial plain with flat height 85–100 m and the surface lithology of Holocene alluvial silt (Q). Quaternary (Q) are widely distributed on the surface, sedimentary thickness is gradually increased from southwest to northeast, about 30–50 m thick in the west and 240 m in the east.

With the fast-growing urbanization, the construction of large infrastructure and a large number of long-term large foundation pit dewatering engineering lost shallow groundwater. Together with the decreasing water supplement of Yellow River and other rivers, large areas of urban subsidence appear in Zhengzhou. It is vital to tack action as early as possible to provide basis for decision-making of prevention and controlling. In this case, eight ALOS PALSAR images collected from January 2007 to April 2010 are utilized. The resolution is 4.7 m × 3.1 m and the polarization mode is HH. Height data is SRTM DEM.

Results and Analysis

According to the principle of maximizing overall correlation, the image of March 10, 2010, was selected as the reference image. Other images were precisely registered with the reference image on the basis of the image registration method mentioned in step 2.1, offsets determined in area for the coregistered SLCs showed very low standard deviations below 0.1 SLC pixel.

Calculate sublook coherent value of the image after precise registration. Setting sublook coherent value threshold 0.55 and the deviation threshold of sublook coherent value 0.1, 47047 CSs were selected with point density 122/km2. The location of the individual CSs in the park、bridge and the urbanized area, i.e., along walking promenades and on the corners/edges of buildings, indicates strongly their man-made character. As expected, the density of the CSs is high on the dense urbanized regions, and low on the forested and vegetated areas of the city. To verify the reliability of the method used to selecting targets, the amplitude deviation index and interferometry coherent average of selected targets are compared respectively. Figure 1 shows scatter plot of interferometry coherent average in abscissa axis and amplitude deviation index of coherent targets in vertical axis. In abscissa axis, all the interferometry coherent averages of coherent targets are larger than 0.5 and 81.5 % of them are larger than 0.8, which indicate that the phases of determined points are reliable enough. Amplitude deviation index cannot describe the noise situation of echo phase precisely for small dataset, which leads to the difference of amplitude deviation is larger than the fact, though it works effectively in identifying PSs for large dataset (more than 25 images). So in vertical axis in this case, 67.9 % of amplitude deviation indexes are lower than 0.25, also demonstrating that the coherent targets identified by proposed method are of stable phases.

Fig. 1
figure 1

Scatter plot of interferometry coherent average and amplitude deviation index of coherent targets

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In this case, 20 interferometric pairs are composed with setting spatial baseline threshold 2500 m and absence of temporal baseline threshold. The composed small baseline dataset and the differential interferometry results are illustrated in Figs. 2 and 3 respectively. Figure 3a and b indicate that clear phases still exist in interferometric pairs for long spatial prependicular baseline (2213 m) and long temporal baseline (1150 days), suggesting high coherence is kept by L band data of ALOS PALSAR. Since finite orbit precision of ALOS PALSAR and lack of highly precise orbits data, the initial differential interferogram still contains some orbital residual phases, which are more significant for long spatial prependicular baseline shown in Fig. 3b. In this paper, with the help of stable coherent targets on the ground (avoiding deformation areas), orbital residual phases are estimated by least squares method, and the result is shown in Fig. 3c.

Fig. 2
figure 2

Temporal baseline plot of the 8 ALOS PALSAR images

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Fig. 3
figure 3

The differential interferometry results a Differential interferogram of spatial baseline with 2213 m, b Differential interferogram of temporal baseline with 1150 days, c Differential interferogram without orbit error

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ALOS PALSAR images can keep significant coherence, so the density of selected CSs is large and intensive triangulation can be constructed. The first step is unwrapping differential interferometric pairs with spatial prependicular baseline smaller than 500 m and temporal baseline smaller than 150 days utilizing the minimizing cost flow method (MCF). Based on the unwrapped phases, height is optimized with initial height correction calculated with the method in step 2.4. Gradually expand the baseline thresholds until all the interferometric pairs unwrapped successfully.

Table 1 displays CSs height corrections statistics. 95.24 % (74.09 % + 21.15 %) of point height corrections are within ±10 m, verifying the precision of STRM DEM is 10 m. Meanwhile, measure 13 GPS height points (A1-A13) distributed on flat terrain and wide vision areas near coherent targets. These GPS height points are the white points distributed in Fig. 4. The largest difference, the smallest difference and the standard deviation of difference are −3.5, −0.15 and ±2.02 m respectively between calculated height and GPS ones. So, the above analysis verifies the proposed method runs well on calculating height. Also, it is obvious that ALOS PALSAR data reflects height precisely with small height ambiguity (long wavelength and long spatial perpendicular baseline).

Table 1 Table of the height corrections
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Fig. 4
figure 4

The deformation velocity obtained by InSAR between 2007 and 2010. Blue rectangles indicate typical deformation zones

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Quality checking of the unwrapped phase is very important. The quality of the individual CSs is checked by the consideration of the phase standard deviation in the regression used to estimate the CSs height correction. CSs with standard deviations above a certain threshold are discarded from the result. Furthermore, the spatial and temporal consistency of the phases is carefully checked to identify potential phase unwrapping errors. Errors identified are either corrected or the corresponding pair is discarded from the result.

After all interferometric pairs are unwrapped successfully, separate residual height corrections and linear deformation phases with 2-D linear regression analysis. Then spatial filter for residual phases were conducted. The size of filtering window is 50 pixels. Separating atmospheric phase, the final result only consists of deformation and noise phases. The absolute values of average atmospheric phases of all interferometric pairs are between 0.23 and 1.01, and corresponding deformation value is ranged from 4.31 to 18.92 mm. Therefore, it is difficult to monitor deformation with high precision without removing atmospheric phases.

The deformation rate map is shown in Fig. 4. Deformation areas are distributed in suburban and new urban region, yet old city regions are stable in Zhengzhou. The general trend of this area is sinking with the maximum subsidence rate −50.98 mm/a (negative value means sinking) and the average subsidence rate −8.65 mm/a. Figure 4 clearly shows that a significant deformation pattern is presented in four areas which can be easily identified: A region in the northern part of Zhengzhou, is a densely fabrication industries zone. Although it nears the Yellow River, Over-exploitation of groundwater causes declining underground water level and causes the ground subsidence. There are many urban villages with densely population in B region in the south of Zhengzhou. Excessive domestic water and irrigation cause ground subsidence. Subsidence is small in region C where located high-tech zone whose water necessity is limited in the west of Zhengzhou. Obvious subsidence funnel appears in region D owning to dense citizens living in mass high-rises buildings and large water demand. Figure 5 is the enlarged view of region E. Bounded by the blue line, the left side of the terrain is high and the right side is low with the height difference of 15 m. Left side is a stable region, but right side appears as obvious subsidence, which may be related to geologic activity for the absence of frequent human.

Fig. 5
figure 5

The enlarged image of region E in the Fig. 4

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To verify the result precision obtained by proposed method, two verification methods are applied in this paper. The first verification method is described as follows. After Estimating spatial statistics of final residuals for each date we find the absolute values of average residual phases between 0.14 and 0.65 rad. To calculate the error of deformation estimates, we consider that a deformation estimate requires two acquisitions and that the deformation estimate is related to a spatial reference point which is also affected by the same errors. The root sum square of the four error terms is consequently between 0.28 and 1.30 rad and corresponding deformation values between 5.25 and 24.36 mm. Given small dataset, the atmospheric phases cannot be removed completely. So, it is a conservative error estimation. Another verification method is comparing the result with CSs result with the leveling data with a root-mean-square accuracy of 2–3 mm/km for a loop line leveling. Leveling lines are shown Fig. 4. Table 2 displays the average deformation rate differences between them. The maximum value is −19.3 mm/a, mean value is 7 mm/a, and mean square error is 7.6 mm/a. It was known from comparative analysis that the proposed method for identifying CSs based on small SAR subsets is reliable and the data processing strategy is effective.

Table 2 Comparison between InSAR and leveling mean deformation velocities (Unit: mm/a)
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Conclusions

It is not reliable to obtain coherent targets using amplitude deviation index or interferometric coherent value threshold method for the small SAR subsets. The method of identifying coherent targets based on sublook coherent values and the corresponding data processing method are proposed to address the problem. CSs can be identified with a limited number of SAR, acquired with a short or even without temporal baseline in terms of spectral correlation properties. Through the experiment conducted with eight ALOS PALSAR images of Zhengzhou city, ranging from January 2007 to April 2010, we come to the conclusion that the identified coherent targets with high interferometric coherent values and small amplitude deviations are of great reliability. The density of the CSs is high on the dense urbanized regions, and low on the forested and vegetated areas of the city. Deformation areas of Zhengzhou city are distributed in suburban and new urban region. The maximum subsidence rate is −50.98 mm/a in the northern part of Zhengzhou. Comparative analysis with the leveling values was performed and two results which almost identical with mean square error is 7.6 mm/a, which prove the reliability of the proposed method of determining coherent targets and the data processing method, which provides new strategy for coping with the problem of small dataset and expands the application of InSAR technology. Still it is hard to remove atmospheric phases completely merely on temporal-spatial characteristics. Also, the monitoring precision of millimeter is hard to achieve since it is a long wavelength monitoring technique.