Effect of digital elevation models on monitoring slope displacements in open-pit mine by differential interferometry synthetic aperture radar

I Nyomn Sudi Prwt,Shinichiro Nkshim,Norikzu Shimizu,b,Tkhiro Osw

a Graduate School of Science and Engineering, Yamaguchi University, Tokiwadai, Ube, 755-8611, Japan

b Centre for Research and Application of Satellite Remote Sensing, Yamaguchi University, Tokiwadai, Ube, 755-8611, Japan

c Regional Satellite Applications Center for Disaster Management(RSCD),Satellite Applications and Operations Center(SAOC),Space Technology Directorate,Japan Aerospace Exploration Agency (JAXA), Industrial Technology Institute, Asutopia, Ube, 755-0195, Japan

d Centre for Remote Sensing and Ocean Sciences (CreSOS), Udayana University, Denpasar, Bali, 80232, Indonesia

Keywords:Open-pit mine Slope monitoring Digital elevation model (DEM)Interferometric synthetic aperture radar(InSAR)Differential interferometric synthetic aperture radar (DInSAR)

ABSTRACT Displacement monitoring in open-pit mines is one of the important tasks for safe management of mining processes. Differential interferometric synthetic aperture radar (DInSAR), mounted on an artificial satellite, has the potential to be a cost-effective method for monitoring surface displacements over extensive areas,such as open-pit mines.DInSAR requires the ground surface elevation data in the process of its analysis as a digital elevation model(DEM).However,since the topography of the ground surface in open-pit mines changes largely due to excavations, measurement errors can occur due to insufficient information on the elevation of mining areas. In this paper, effect of different elevation models on the accuracy of the displacement monitoring results by DInSAR is investigated at a limestone quarry. In addition, validity of the DInSAR results using an appropriate DEM is examined by comparing them with the results obtained by global positioning system(GPS)monitoring conducted for three years at the same limestone quarry. It is found that the uncertainty of DEMs induces large errors in the displacement monitoring results if the baseline length of the satellites between the master and the slave data is longer than a few hundred meters.Comparing the monitoring results of DInSAR and GPS,the root mean square error (RMSE) of the discrepancy between the two sets of results is less than 10 mm if an appropriate DEM, considering the excavation processes, is used. It is proven that DInSAR can be applied for monitoring the displacements of mine slopes with centimeter-level accuracy.

1. Introduction

Displacement monitoring plays an important role in assessing the stability of slopes. There are many useful instruments for monitoring displacements, for example, extensometers and inclinometers. The advantage of these instruments is that they provide displacements in real-time with high accuracy. On the other hand,these instruments measure the displacements only at certain points on the ground and can be applied only to limited areas of less than about 10,000 m2.Therefore,a large number of devices would be required if the displacements over the entire area of a large slope needed to be measured. In practice, this would lead to high costs and inefficiency. Although the global positioning system (GPS) is one of the solutions for monitoring displacements over extensive areas (Shimizu et al., 2014), it provides the displacements only at the points where sensors have been installed. In order to monitor the displacement distribution over an extensive area, many GPS sensors are needed, which are expensive and inefficient.

Synthetic aperture radar (SAR) has the potential to overcome the above difficulty, i.e. monitoring the distribution of displacements over an extensive area (Ferretti, 2014). Practically, differential interferometric SAR (DInSAR) can provide the displacement distribution of the Earth’s surface in a large area without installing any devices on the ground surface. Recently, the capability of DInSAR to measure the displacement of the Earth’s surface has been studied in various topics in rock and geotechnical engineering,such as land subsidence(Stramondo et al.,2008;Moghaddam et al.,2013; Chaussard et al., 2014; Yastika et al., 2019), landslides(Singhroy and Molch,2004;Rott and Nagler,2006;Zhu et al.,2014),and other ground movements (Liu et al., 2011; Woo et al., 2012;Eriksen et al., 2017; Klein et al., 2017; Wang et al., 2017). DInSAR has also been applied to open-pit mine slope monitoring(Paradella et al., 2015; Mura et al., 2016).

In the process of DInSAR,the elevation of the ground surface is required in order to obtain the displacements. Usually a public digital elevation model (DEM) (map) is used for this purpose.However, the topography of mine slopes often changes due to mining activities, and public DEMs do not include changes in the topography such as those of the local slopes of open-pit mines.This means that some errors are encountered when applying public DEMs for these specific cases.This is one of the fundamental issues in DInSAR (Massonnet and Feigl, 1998; Bürgmann, 2000), and several works related to this issue have been conducted by Tran et al. (2015), Gaber et al. (2017), and Tao et al. (2017). However,their studies addressed the application of DInSAR to the monitoring of the subsidence in flat areas, where the surface topography does not change much during monitoring. Therefore, the errors in the DEMs are not large and their effect is small. The effects of DEMs should be investigated before applying DInSAR to monitoring the displacements of excavated slopes. However, they have not been fully discussed in relation to open-pit mines.

This paper focuses on investigation of the influence of the errors in DEMs on the DInSAR results in their practical application to an open-pit mine slope.The excavation activities are seen to affect the changes in the topography of the mining area. Six different DEMs are used to clarify the effect of errors on the elevation, and an appropriate DEM is recommended.In order to verify the model,the DInSAR results are compared with the results of precise GPS displacement monitoring conducted for three years at the same limestone quarry.

2. Issue in application of DInSAR to slope in open-pit mine

SAR is a radar device mounted on an aircraft or artificial satellite that transmits microwaves to the Earth’s surface, observes the intensity and phase of the reflected waves from the surface, and generates high-resolution imagery (Hanssen, 2001). Interferometric SAR (InSAR) is a method for taking the signal phase difference from two scenes of SAR data (Massonnet and Feigl, 1998;Bürgmann, 2000), which are observed in the same area at different times. InSAR can be used to create a topography map of the ground under certain conditions (Graham, 1974; Massonnet and Feigl,1998; Bürgmann, 2000; Rocca et al., 2000). DInSAR can measure the changes in the distance between the radar and the ground surface after removing the topographic contribution from the interferograms(Ferretti et al.,2007). The advantage of DInSAR is that the distribution of the ground surface’s displacements in the direction of the microwave radiation can be observed over large areas with a spatial resolution of 3-30 m without the necessity for installing any devices on the ground.

In this section,outlines of InSAR and DInSAR are given to clarify the focus of this study.

2.1. InSAR technique to measure topography of Earth’s surface

Supposing a SAR satellite acquires two sets of SAR data over the same area at different times: the first SAR dataset comprises the master data and the second set comprises the slave data(Massonnet and Feigl,1998; Pepe and Calò, 2017). The phase difference φ between the reflection waves of the two sets of SAR data can be expressed considering the geometrical relation among the master and slave satellite positions and a point on the Earth’s surface (Fig.1) as follows (Pepe and Calò, 2017):

where φ is the phase difference observed by the master and slave satellite positions,whose value is between-π and π(Ferretti et al.,2007);λ is the wavelength of each microwave transmitted from the satellites; b is the baseline length (the distance between satellite positions M and S);r is the distance between a satellite and a point T on the ground surface; ?0indicates the side-looking angle for transmitting the microwaves from the satellites that corresponds to the case when the Earth’s surface is flat(i.e.the topographic height or elevation z=0);? is the side-looking angle that corresponds to the case when the Earth’s surface is not flat (i.e. z ≠0); α is the inclination angle of the baseline with respect to the horizontal direction; and b⊥is the perpendicular baseline length (Pepe and Calò, 2017).

The right side of Eq. (1) is formed by two phase forms, i.e. flat-Earth component φf(shuō)latand topographic phase component φtopo, as follows (Pepe and Calò, 2017):

From Eq. (1), the topographic height z can be estimated from observed phase difference φ by removing flat-Earth phase component φf(shuō)lat(Hanssen, 2001; Pepe and Calò, 2017):

The phase value of φ-φf(shuō)latis still between-π and π.In order to estimate topographic height z using Eq. (4), the phase φ-φf(shuō)latis integrated to obtain the absolute value.This process is called“phase unwrapping” (Ferretti et al., 2007).

This is the method using InSAR to generate a topographic map or DEM (Rabus et al., 2003; Zhou et al., 2005; Zink, 2015; Gao et al.,2017).

Fig.1. InSAR geometry (Pepe and Calò, 2017).

2.2. DInSAR technique to measure displacements of Earth’s surface

DInSAR is a technique for measuring the displacements of the Earth’s surface based on the process of InSAR. Removing topographic component φtopoand flat-Earth phase component φf(shuō)lat(Eqs.(2)and(3))from observed phase difference φ,the remaining phase can be expressed as follows (Pepe and Calò, 2017):

where Δφ = φ-φtopo-φf(shuō)latcan be computed by the observed φ and Eqs. (2) and (3); dLOSis the unknown ground surface displacement in the direction between a satellite and the Earth’s surface,which is called the line of sight(LOS)displacement;Δφtopois the residual phase due to the error in the topographic elevation of the Earth’s surface;Δφorbis the residual phase due to the use of the inaccurate satellite orbital position; Δφatmois the effect of the atmospheric phase delay; Δφscattindicates the phase scatter due to changes in the conditions on the ground surface;and Δφnoiseis the phase due to the noise contribution.The phase unwrapping process is applied to phase Δφ to compute the LOS displacement,dLOS,in a similar manner to that given in Section 2.1.

The displacement dLOSis obtained from Eq. (5), while Δφtopo，Δφorb， Δφatmo, Δφscattand Δφnoiseare included as errors. This is the fundamental procedure of DInSAR for measuring displacements of the Earth’s surface.

The procedures for InSAR and DInSAR are outlined in Fig.2a and b, respectively(Franceschetti and Lanari,1999; Hein, 2004).

2.3. Effect of topographic errors on application of DInSAR to openpit mine slope

In the process of DInSAR,the elevation of the ground surface is required to remove topographic component φtopo,as described in Section 2.2 (Fig. 2b). Usually, an appropriate public DEM, as mentioned in Section 3.2.1,is used to substitute elevation z of the model into Eq. (3) to compute φtopo(Fig. 2b). However, the topography of open-pit mine slopes often changes due to mining activities, e.g. excavations, and public DEMs do not include such local changes in the topography of open-pit mine slopes. This means that large errors can occur when applying public DEMs.An alternative method is for users of DInSAR to employ the topography of the target area to update the data themselves.The InSAR procedure represented by Eq. (4) (Fig. 2a) is one of the possible methods for updating the elevation of the topography of open-pit mine slopes.

If the errors from the third to the sixth terms on the right-hand side of Eq.(5)are ignored,and Δφtopoand dLOSare considered,the remaining phase difference can then be expressed as follows:

The second term on the right-hand side of Eq.(6),i.e.Δφtopo,is derived from Eq.(3),where Δz is the error in the height of the DEM.It is found that the error in the height Δz proportionally affects the displacement dLOSand its influence is proportional to b⊥,while λ,r,and ? are approximately constant.

Although the above consideration given to the elevation errors is based on the fundamental aspect of DInSAR (Franceschetti and Lanari,1999), the effect of the errors that occur with DEMs on the results of DInSAR does not seem to have been fully investigated in applications to open-pit mine slopes. Therefore,this study focuses on this issue in order to clarify the effect of DEMs on displacement monitoring by DInSAR and to discuss a better procedure for reducing the errors that occur.

Envi SARscape(version 5.4)by HARRIS is used for the InSAR and DInSAR data processing and analysis.ArcGIS(version 10.3)by ESRI is used for drawing the maps.

3. Effect of digital elevation models on results of DInSAR

3.1. Study area: Open-pit mine

A limestone quarry located in a northern prefecture of Japan is selected as the experimental site in this study, since continuous displacement monitoring by GPS has been conducted there for many years(Nakashima et al.,2012,2014)and the results of DInSAR can be compared with those of GPS.Fig.3 presents an outline of the site(Nakashima et al.,2012, 2014).

Fig. 4a and b shows the aerial photographs of the quarry taken on September 26,2002(GSI,2002)and April 5,2011(Google Earth,2011), respectively. As seen in Fig. 4b, the main quarry was excavated to the present bottom (-135 m from sea level) before 2006,and the mining area was expanded to the west and northwest areas of the quarry after 2006.In Fig.4a,the south part of the inside of the quarry and the west and northwest areas of the quarry were not excavated. The shape of the mining area has been changed.

3.2. SAR dataset

This context uses the SAR data observed by Advanced Land Observing Satellite using the Phased Array type L-band SAR(ALOSPALSAR) in operation from 2006 to 2011 by Japan Aerospace Exploration Agency(JAXA).The ALOS-PALSAR employs the L-band microwave with a frequency of 1270 MHz and a wavelength λ of 23.62 cm(JAXA-EORC,2008).Table 1 presents all the SAR data used in this study, which were observed for the study area during the operation of the ALOS-PALSAR.

3.3. Digital elevation model data

3.3.1. Public digital elevation models

There are several publicly available DEMs which can be used in DInSAR processing. This study uses five public DEMs:“SRTM-3 V2” and “SRTM-1 V3” by SRTM (Shuttle Radar Topography Mission), “GSI-DEM” by GSI (Geospatial Information Authority of Japan), “AW3D30-DEM” by ALOS-PRISM (Panchromatic Remotesensing Instrument for Stereo Mapping), and “ASTER-GDEM V2”by ASTER (Terra satellite using the Advanced Spaceborne Thermal Emission and Reflection Radiometer). The data acquisition date and the ground resolution are different for each DEM(Table 2).

The accuracies of the elevation in the five DEMs are as follows:5.6-9 m for SRTM-3 V2 and SRTM-1 V3 (Rodriguez et al., 2005),5 m for GSI-DEM(GSI,2016),5 m for AW3D30-DEM(Tadono et al.,2014; Takaku et al., 2014), and 6.1 m in flat areas and 15.1 m in mountainous areas for ASTER-GDEM V2 (Tachikawa et al., 2011).

3.3.2. Digital elevation models by InSAR

The InSAR procedure can provide DEMs (Fig. 2a). This study employs InSAR to generate an updated DEM using pairs of SAR data,as shown in Table 3. Three DEMs are generated, which are called InSAR-DEM 2007, InSAR-DEM 2009, and InSAR-DEM 2010.

3.3.3. Comparison of public and InSAR digital elevation models

Fig. 2. Outline of processing steps for InSAR and DInSAR: (a) InSAR for obtaining a digital elevation model and (b) DInSAR for obtaining surface displacements.

Fig.5 shows the five public DEMs for the study area.SRTM-3 V2,SRTM-1 V3 and GSI-DEM(Fig.5a,b and c)were created using data observed around 2000-2002.Comparing them with a photograph taken in 2002, as shown in Fig. 4a, the three models seem to represent the actual topography in 2002, while SRTM-3 V2 is of very low resolution. On the other hand, when comparing with a photograph taken in 2011, as shown in Fig. 4b, it is found that the models could not accurately represent the expanded (excavated)areas to the west near the surface,to the northwest or to the south of the inside of the quarry. The DEMs contain large errors for the areas excavated during 2006-2011.

AW3D30-DEM(Fig.5d)was developed using the data observed during 2006-2011 and seems to coincide well with the photograph taken in 2011 (Fig. 4b). The ASTER-GDEM V2 (Fig. 5e) is not adequate for the topography of the inside of the quarry in 2011,even though this model was developed in 2011. Fig. 6 shows the DEMs produced by the InSAR procedure in 2007, 2009 and 2010.Comparing Fig.6c with Fig.4b,InSAR-DEM 2010 seems to represent the actual topography.

Fig. 3. Experimental site: (a) Plan view, (b) Aerial view, (c) Vertical section, and (d) View of slope monitored by GPS (Nakashima et al., 2012, 2014).

Fig. 4. Changes in topography at experimental site: (a) Photo taken on September 26, 2002 (GSI, 2002) and (b) Photo taken on April 5, 2011 (Google Earth, 2011).

Table 1List of SAR data.

Therefore, some public DEMs may not be adequate for representing the present topography of the study area, because they were created during a certain period. The InSAR procedure can update the elevation model of the area.

3.4. Results of DInSAR using different digital elevation models

The DInSAR procedure is employed to estimate the surface displacement(Fig.2b)using the SAR data pairs as shown in Table 4.In order to investigate the effect of the DEMs on the DInSAR results,the DInSAR procedure is applied using all the public DEMs(Table 2)and three DEMs by InSAR (Table 3) in separate processes. Then,several LOS displacements are produced from the same SAR data pairs, but with different DEMs.

The LOS displacement distributions obtained by DInSAR are shown in Fig. 7. The contour lines in this figure represent the elevations of the DEMs. Fig. 7a, b and c shows the LOS displacement results obtained by DInSAR using the public DEMs and InSAR-DEM 2007,InSAR-DEM 2009,and InSAR-DEM 2010,respectively.The LOS displacements are represented by a color scale from -50 mm to 50 mm.The red color indicates the area moving far away from the satellite, the green color indicates almost no or only small displacement,and the blue color indicates the area moving toward the satellite.

The excavations of the main quarry were completed before 2006, as mentioned previously, and it has been confirmed that there have been no remarkable displacements at the slopes of the quarry since that time (Hirabayashi et al., 2009; Nakashima et al.,2014). Therefore, the displacement distribution should be green over the whole area,except for the newly expanded area.Any areas with non-green colors indicate different displacement results caused by the use of different DEMs.

Fig. 7 shows that the red color, representing large displacements,is found in the results acquired with the public DEMs,except for AW3D30-DEM,especially in Periods-1,2,5,6,8 and 10.They can be taken as errors in the LOS displacements brought about by the inaccuracy of the DEMs. In the case of using ASTER-GDEM V2, a large error is found in the center of the quarry because the topography of the whole quarry is incorrect(Fig.5e).In the cases of using SRTM-3 V2,SRTM-1 V3 and GSI-DEM,errors are found in the south and west areas of the quarry because the topography in those areas is also incorrect.

On the other hand, the results acquired with AW3D30-DEM and InSAR-DEMs are mainly green (displacements are within±10 mm), although there are no results (white area) for some of the northwest area during this period. This is because the excavation area was expanded to the northwest part of the quarry during the DInSAR measurement period,i.e.2007-2010;and thus,the ground surface conditions changed and no results could be obtained.

Table 2List of public digital elevation models for DInSAR processing.

Table 3SAR data pairs for generating digital elevation models by InSAR.

In order to understand the effect of the DEMs, the LOS displacement and the perpendicular baseline length for each case using different DEMs are presented in Fig.8.Four points,i.e.G1,G2,G3 and P,shown in Fig.8e,are selected as examples for comparison.G1,G2 and G3 are the GPS monitoring points,as shown in Fig.3,and point P is located at the bottom of the quarry. The LOS displacements are extracted from the DInSAR results during each period(Period-1 to Period-10),and they are plotted as the absolute values.Each error in the public digital elevation mode, Δz′, is defined by taking the differences in elevation between the public DEMs and InSAR-DEM 2010.

Fig. 5. Digital elevation models generated by other sources: (a) SRTM-3 V2, (b) SRTM-1 V3, (c) GSI-DEM, (d) AW3D30-DEM, and (e) ASTER GDEM V2. The vertical interval of the contour lines is 10 m.

Fig. 6. Digital elevation models generated by InSAR: (a) InSAR-DEM 2007, (b) InSAR-DEM 2009, and (c) InSAR-DEM 2010. The vertical interval of the contour lines is 10 m.

Table 4List of SAR data for DInSAR processing.

Almost all the absolute LOS displacements are within 10 mm at point G1(Fig.8a),because the value of Δz′is small(less than 30 m) for all the DEMs. At points G2 and G3, the LOS displacement in the case of using ASTER-GDEM V2 increases as the perpendicular baseline length increases, while the LOS displacement in the case of using the other DEMs is within about 10 mm. This is because that Δz′of ASTER-GDEM V2 is large at points G2(Δz′=63.26 m)and G3(Δz′=125.88 m),as observed in Fig. 8b and c, respectively.

At point P, since Δz′is large in the cases of using ASTER-GDEM V2 (Δz′= 154.06 m), SRTM-1 V3 (Δz′= 59.63 m), SRTM-3 V1(Δz′= 77.06 m), and GSI-DEM (Δz′= 89.54 m), the absolute LOS displacement increases as the perpendicular baseline length increases. AW3D30-DEM (Δz′= 5.54 m) and InSAR-DEMs are accurate; and thus, the absolute LOS displacements are within about 10-20 mm.

Fig. 7. Comparison of LOS displacement results obtained by DInSAR using public and InSAR digital elevation models: (a) Public digital elevation models and InSAR-DEM 2007, (b)Public digital elevation models and InSAR-DEM 2009, and (c) Public digital elevation models and InSAR-DEM 2010.

Fig.8. Relationship of absolute LOS displacement and perpendicular baseline(b⊥)from public and InSAR digital elevation models:(a)At point G1,(b)At point G2,(c)At point G3,(d) At point P, and (e) Locations of monitoring points. Δz′ is calculated by subtracting InSAR-DEM 2010 from the public digital elevation models.

Finally,it is found that if elevation error Δz′is large,the error in the LOS displacement increases. In some cases, the error becomes more than 100 mm. Such a tendency increases when the perpendicular baseline length is long.As long as the updated DEM is used,the errors in the displacement will remain within 10-20 mm in this quarry. The InSAR procedure is one of the effective solutions for updating the DEMs at this site; however, it is very important to check and update the DEMs before applying DInSAR to open-pit mine slope monitoring.

4. Validity of measured displacement by DInSAR using appropriate digital elevation model

In order to investigate the accuracy of the displacements measured by DInSAR, the LOS displacements are compared with the displacements measured by GPS in this section. The results acquired by DInSAR using InSAR-DEMs are used as the LOS displacements. Continuous displacement monitoring has been conducted with GPS at this site since November 18,2006.The accuracy(standard deviation)of this GPS monitoring system is within a few mm (Nakashima et al., 2014).

To make an appropriate comparison between GPS and DInSAR,the three-dimensional (3D) displacement components in the directions of latitude, longitude and height obtained by GPS should be transformed to the direction of the LOS displacements by the following equation (Fig. 9) (He et al., 2015):

Fig. 9. Projection of 3D displacement vectors onto dLOS vector in ascending SAR satellite direction.

where β is the azimuth angle of the SAR satellite orbit (flight direction); and GPSNS, GPSEWand GPSUDare the displacement components in the directions of latitude, longitude and height,respectively.

Fig. 10a-d shows the 3D displacements at point G1 continuously measured by GPS for four years(Nakashima et al.,2014),and the calculated LOS displacement is given in Fig.10d as an example.The GPS monitoring system has been measuring the displacements every hour since November 18, 2006. The monitoring results at the other points are similar to those at point G1.Therefore,it is found that there were no remarkable displacements during this period.

Fig.10. Measured displacements at point G1 by GPS and in the direction of LOS: (a) Displacement in the direction of latitude, (b) Displacement in the direction of longitude, (c)Displacement in the direction of height, (d) Displacement in the LOS direction,and (e)Extracted incremental LOS displacement of GPS in the period of the DInSAR measurement.

Fig.11. Comparison of LOS displacements by DInSAR and GPS: (a)-(i) Comparison at points G1-G9 and (j) Absolute perpendicular baseline length for each period.

In this context,the GPS data from November 18,2006 to October 28, 2010 were used. In order to compare the displacements obtained by DInSAR and GPS,the displacements measured hourly by GPS were averaged into daily data. Since DInSAR obtains the incremental displacements for each period based on the master and slave data (Table 4), the incremental displacements for the same period were calculated from the results of the GPS monitoring(Fig.10e).

Fig. 11a-i shows comparison of the LOS displacements obtained by DInSAR and GPS for all the GPS points (G1-G9). Thediscrepancy in the displacements by DInSAR and GPS is less than 10 mm, except at certain points and during certain periods. The root mean squared errors (RMSEs) in the measurement results for DInSAR and GPS are given in Tables 5 and 6. Table 5 shows the RMSE at each measurement point, while Table 6 shows the RSME for each period.

Table 5RMSEs of DInSAR and GPS for each measurement point.

Table 6RMSEs of DInSAR and GPS for each period.

Fig. 12. Scatter plot of displacements by DInSAR (vertical axis) and GPS (horizontal axis).

The RMSEs in the LOS displacements by DInSAR and GPS for each point are 3.9-8.8 mm and 1-2.2 mm, respectively (Table 5).The RMSE of the discrepancy between DInSAR and GPS is 4.1-8.6 mm. If the measurement accuracy is expressed by RMSE, it is seen that DInSAR can measure displacements with centimeterlevel accuracy at the slope of this quarry.

Fig.12 presents the correlation between the LOS displacements by DInSAR and GPS. It shows that the results of GPS are within±3 mm, while the DInSAR results are mostly within ±10 mm.

Fig.13a shows the relationship between the RMSEs in the DIn-SAR results and the elevation of the measurement points.It is found that the RMSE increases as the elevation becomes deeper. Points G3,G6 and G9 are located at deeper elevations than the other points(Fig.3).Points G8 and G9 are located near the corner of the quarry.The displacements at those points seem to have been influenced not only by the depth, but also by being near the corner of the slopes. The results at point G7 are generally good, because the RMSE is about 5 mm and only the results of Period-6 are scattered.This seems to have been caused by the length of the perpendicular baseline.

Fig. 13b shows the relationship between the RMSE of DInSAR and the length of the perpendicular baseline.As seen in Section 3.4,a long perpendicular baseline has a large influence on the results in terms of errors in the DEMs.From Fig.13b,the large discrepancies mostly appear during the periods of a long perpendicular baseline length.The RMSEs at Periods-2,5,6,8,9 and 10 are larger than the others. The perpendicular baseline lengths for those periods are larger than 200 m, except for Period-9. This means that the perpendicular baseline length is also an important parameter for obtaining better results by DInSAR.

It is found that DInSAR, using the updated DEM, can provide good results with RMSEs of less than 10 mm compared to the GPS results. To provide centimeter-level accuracy in the monitoring results, selection of SAR data with short perpendicular baselines(less than 200 m in this study) is recommended.

This study focuses on application of DInSAR to monitoring the slope of an open-pit mine with a slight vegetation cover.When DIn-SARis applied for monitoring a natural slope covered withvegetation,e.g.landslideslopes,the accuracy may below due tothe decorrelation phenomena of the radar(SAR)signal caused by changes in the surface condition of the vegetated area(Pepe and Calò,2017).

Fig.13. DInSAR RMSEs: (a) Relationship between RSMEs and elevation of measurement point, and (b) Relationship between RSMEs and perpendicular baseline length.

5. Conclusions

In this research, the effects of different DEMs on the displacement results by the DInSAR technique are examined, and the applicability of DInSAR to displacement monitoring at a limestone quarry is investigated. The following conclusions can be made:

(1) Public DEMs do not seem to be adequate for representing the topography of the open-pit mine in this study, because the DEMs are generated on certain dates and not regularly updated. On the other hand, the InSAR procedure can overcome such a problem by updating the DEM at the site.(2) Errors in public DEMs affect the measurement results of DInSAR.In some cases,the error becomes more than several hundred millimeters. Such a tendency increases when the perpendicular baseline length is long.As long as the updated DEM is used, errors in the displacement will remain within 10-20 mm in this quarry.

(3) DInSAR,using the updated DEM by InSAR,can provide good results with RMSEs of less than 10 mm compared to the GPS results.If the monitoring requires centimeter-level accuracy,selection of SAR data with short perpendicular baselines(less than 200 m in this study) is recommended.

(4) InSAR is one of the effective solutions for updating DEMs for open-pit mine slopes. It is very important to check and update the DEMs before applying DInSAR to open-pit mine slope monitoring.

Declaration of competing interest

The authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Acknowledgments

The authors express their gratitude to the Japan Aerospace Exploration Agency (JAXA) for providing the ALOS-PALSAR data.The authors also wish to express their sincere appreciation to Hachinohe Mining Co., Ltd. for their cooperation with the displacement monitoring by GPS.They also thank Emeritus Prof.T.Tanaka of Yamaguchi University and Prof. M. Shimada of Tokyo Denki University for their valuable suggestions. This research was partially supported by JSPS KAKENHI(Grant No.16H03153)and the Limestone Association of Japan. They also extend their thanks to Ms. H. Griswold for proofreading this paper.