anapproachforestimatingunderground-goafboundaries...

Research ArticleAn Approach for Estimating Underground-Goaf BoundariesBased on Combining DInSAR with a Graphical Method

Pu Bu12 Chaokui Li 2 Mengguang Liao2 Wentao Yang 2 Chuanguang Zhu3

and Jun Fang2

1School of Resource amp Environment and Safety Engineering Hunan University of Science and TechnologyXiangtan 411201 China2National-Local Joint Engineering Laboratory of Geo-Spatial Information TechnologyHunan University of Science and Technology Xiangtan 411201 China3Hunan Province Key Laboratory of Coal Resources Clean-utilization and Mine Environment ProtectionHunan University of Science and Technology Xiangtan 411201 China

Correspondence should be addressed to Chaokui Li chkl_hn163com and Wentao Yang 415709282qqcom

Received 21 November 2019 Accepted 1 May 2020 Published 29 May 2020

Academic Editor Roberto Nascimbene

Copyright copy 2020 Pu Bu et al 1is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

1e goaf left behind after mining has the potential to induce serious geological disasters due to the damaged internal structure ofthe rock Estimating the boundary of the underground goaf can effectively control the occurrence of such disasters Howevertraditional geophysical methods are inefficient and expensive and are particularly difficult to apply for a wide detection range1ispaper proposes a new method for estimating the boundary of underground goaf using the differential interference syntheticaperture radar technique (DInSAR) More specifically DInSAR is used to obtain the isoline of the subsidence basin above the goafand the direction of the two main sections of the goaf is then determined according to the basic law of mining subsidenceFollowing this the basic principles of the probability integral and the graphical methods are combined to determine the miningboundary of the strike section and the incline section of the goaf Finally six geometric parameters reflecting the boundary of thegoaf are obtained Experiments on simulated and measured data indicate that the proposed method is feasible with the averagerelative errors of the simulated and measured data reaching and maintained at 22 and 37 respectively

1 Introduction

1e presence of underground goaf generally results in thecollapse of the surrounding ground 1is causes damage tohouses and various types of ground-level transport routes aswell as polluting groundwater thus seriously affecting theecological environment of the mining area [1] In particularsubsidence may even cause secondary geological disasterssuch as mountain cracking the collapse of constructionslandslides mudslides and earthquakes [2] 1erefore un-derground goaf is currently an important issue that restrictsthe development of mines and the urbanization of miningareas Moreover the distribution range and spatial mor-phological characteristics of underground goaf are key forthe evaluation of the potential hazards and the establishment

of countermeasures 1us the determination of how toquantitatively evaluate the aforementioned range andcharacteristics of underground goaf is of crucial importance

Existing goaf detection methods can be divided intogeophysical and drilling technology Geophysical techniquesrefer to the detection of geological conditions such as li-thology and geological structures via the investigation ofchanges in various geophysical fields [3] Typical geophysicaltechniques include gravimetric electromagnetic and geo-thermal methods [4ndash7] Drilling technology refers to the useof drilling equipment to drill through rock formations at apredetermined location in order to extract physical samplesand other relevant data for experiments [8] Central drillingtechnology methods include the flushing fluid sonic ve-locity and ultrasonic imaging methods [9ndash11] Generally

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 9375056 13 pageshttpsdoiorg10115520209375056

speaking although these technologies are able to obtain therough location of the underground goaf along with its spatialdistribution they have several limitations For example suchtechnology is only suitable for small-scale detection whichcan be costly time-consuming and inefficient At the sametime the approximate geographical location of the goaf isrequired as prior information before detection Moreoverover the past few decades with the boomingmining industry(including legal and illegal mining) numerous unknownunderground goafs have emerged globally Traditionalgeophysical and drilling techniques are unable to meet thecurrent wide-ranging and time-sensitive goaf detectionneeds

1e interferometric synthetic aperture radar (InSAR)is a popular remote sensing technology that can surveylarge-scale surface deformation using two- or multi-viewsynthetic aperture radar (SAR) images Massonnet et alcombined two-scene ERS-1 images before and after anearthquake over the earthquake-prone area of LandersCalifornia with the DEM (Digital Elevation Model DEM)of the region to successfully observe the surface defor-mation caused by earthquakes Since then the differentialinterference synthetic aperture radar technique (DInSAR)has been widely used for the monitoring of surface de-formation caused by geological tectonic movements suchas seismic monitoring [12 13] glacial drift monitoring[14 15] volcanic eruption monitoring [16 17] landslidemonitoring [18 19] frozen soil degradation and ex-pansion monitoring [20ndash22] 1e use of DInSAR inmining subsidence is also a hot research topic and in-cludes applications in the detection of subsidence causedby mining [23 24] the prediction of mining-inducedgeological disasters [25 26] and the assessment of theimpact of mining on surface buildings [27 28]

Following the stabilization of the ground subsidencebasin caused by underground mining a close relationshipbetween the size and spatial distribution of the basin andgeological mining conditions can be observed 1is isdenoted as the subsidence rule More specifically thegeological mining conditions and the size of the goafdetermine the spatial distribution of the ground subsi-dence basin 1at is under specific geological miningconditions the spatial distribution characteristics of theground subsidence basin can also reflect the size of thegoaf DInSAR can not only survey the movement anddeformation of the subsidence area but also determine thedistribution state of the whole ground subsidence basin1us it can potentially be applied for the detection ofunderground goaf distributions

At present research on the detection of the geometricaldistribution of underground goaf using DInSAR is rare In2013 Zhe et al [29] proposed a method known as ldquoDInSAR-Based Illegal Gob Detection System (DIMDS)rdquo which uti-lizes the DInSAR to obtain the surface deformation valuealong the radar line-of-sight (LOS) direction 1e methodthen estimates the geodetic coordinates of the center of theground subsidence basin based on the mining subsidencetheory and subsequently determines the extent of under-ground goaf based on the ground subsidence basin

boundary However the DIMDS method has a key limita-tion It assumes that the center of the underground goaf is onthe same vertical line as the center of the ground subsidencebasin Yet for most cases this is not true as most coal seamsare not completely horizontal as long as the coal seam istilted the movement deformation caused by mining will notpropagate to the surface in the vertical direction 1is dis-crepancy seriously affects the accuracy of the boundary ofthe underground goaf estimated using the DIMDS method

In response to this problem Yang et al [30] definedthe geometrical distribution characteristics of the un-derground goaf using eight geometric parameters (lengthwidth height dip angle azimuth angle mining depth andtwo central geodetic coordinates) Based on the proba-bility integral method the relationship between thesegeometric parameters and the LOS deformation value ofthe ground subsidence basin is then established Fol-lowing this a mathematical model based on the simulatedannealing algorithm (SAGA) [31] is used to invert theeight geometric parameters from a large number of LOS-deformed observations obtained by DInSAR 1is methodconsiders the general law of mining subsidence and makesfull use of the surface information of the surface defor-mation obtained by DInSAR 1us prediction accuracy isgreatly improved compared to the DIMDS methodHowever due to the large number of inversion param-eters the stability of the mathematical model is low Inparticular the selection of the initial value of the modelwill have a great impact on the inversion results Yet inreal-world applications the initial value of a goaf is dif-ficult to determine Second due to the coherence losses ofthe echo signals from a SAR image pair a large number ofnull values are observed in the whole basin acquired byDInSAR 1is leads to errors in the inversion model so-lution process and subsequent incorrect results

At present most coalmines use long-arm coalmining andfull slumping to manage the roof Under the condition ofuniform mining thickness the main factors affecting thesubsidence rule are coal seam dip angle mining area size(length and width) and mining depth [32] 1ese parameterscan reflect the boundary range and basic shape of the goafHow to acquire these unknown parameters quickly and ef-fectively is of great significance to determine the boundariesof underground goaf 1erefore this paper proposes anunderground goaf boundary detection method by combiningDInSAR with a graphical method Our proposed method firstuses DInSAR to obtain the subsidence information of thewhole basin in the subsidence area and based on this thesubsidence contour map is generated 1e two main sections(the strike section and incline section) of the undergroundgoaf are determined according to the contour map and thesubsidence curve of these two sections is drawn Finally basedon the subsidence rule of coal mining the length coal seamdip angle mining area size and mining depth of the un-derground goaf are derived using a graphical methodMoreover after geocoding the size and location of the un-derground goaf the boundary is determined

1e paper is organized as follows In Section 2 we in-troduce the method used to estimate the boundary range of

2 Advances in Civil Engineering

the underground goaf based on DInSAR We then verify theproposed method using simulation and measured data inSection 3 Finally Section 4 concludes the study

2 Methods

After the underground ore body is mined out a cavity (ie agoaf) will be left inside the rock strata and the original stressequilibrium will be destroyed which will result in the stressredistribution in country-rock taking place to reach a newequilibrium1is is a very complex variation of physical andmechanical process causing movement and damage to theoverlying strata With the continuous progress of miningactivities the goaf has expanded to a certain extent and thenthe movement of rock strata will develop to the surface Formost coal mines the ratio of mining depth and thickness isusually large At this time the surface deformation iscontinuous in space and gradual in time and it has obviousregularity Because the geometry of the subsidence basin isclosely related to the spatial distribution of the goaf it can beobtained by measurement to infer the spatial distributioncharacteristics of the goaf

1e framework of the proposed method for the detectionof an underground goaf boundary based on DInSAR ispresented in Figure 1 First DInSAR is used to obtain thesubsidence information of the whole basin in the subsidencearea Based on this the subsidence contour map is createdSecond the strike and incline sections of the undergroundgoaf are determined from the contour map and the sub-sidence curves of these two sections are drawn Finally basedon the coal mining subsidence rule the length coal seam dipangle mining area size and mining depth of the under-ground goaf are calculated using a graphical method

21 Extracting Subsidence Data Using DInSAR Syntheticaperture radar differential interference (DInSAR) acquiressurface deformation information via the differential inter-ference processing of two SAR images of the same area indifferent phases If the spatial baseline between the SARimage pair is small enough the repeated deformation ob-servation can be used to survey surface deformation asshown in Figure 2 More specifically the surveyed defor-mation is the direction of the line-of-sight of the sensor Intheory it is possible to survey changes within the millimeterrange using DInSAR [33ndash36]

During the imaging of the two scenes the surface isdeformed According to the vector relationship these vectorsums are equal to zero 1erefore the following formula canbe obtained

R2rarr

R1rarr

+ ΔRmovrarr

minus Brarr

(1)

where Ri

rarris the line-of-sight vector ie the vector between

the ith subantenna and the ground point and ΔRmovrarr

is thedeformation vector of a ground point during the periodfrom t1 to t2 and B

rarris the distance vector between the

antennas of the two images1e interference phase ϕ of the two images can be

expressed as follows

ϕ 4πλ

ρ2 minus ρ1( 1113857

4πλlangR1

rarr+ D

rarrminus B

rarr R1rarr

+ Drarr

minus Brarrrang12 minus ρ11113874 1113875

(2)

where λ is the radar wavelength Drarr

is the displacementvector of the ground point during imaging ρi |Ri

rarr| is the

distance between the antenna and the ground point and lt gtindicates point multiplication

For a space-based SAR system the deformation of theground point and the spatial baseline of the two scene imagesis much smaller than the distance between the ground pointand the satellite 1us equation (3) can be expressed as

ϕ 4πλlangR1

rarr Drarrrang minuslangR1

rarr Brarrrang1113874 1113875

ϕdef + ϕtopo

(3)

where ϕdef is the surface deformation phase and ϕtopo is theterrain phase

1e phase derived from the differential interferenceconsists of two parts the terrain phase ϕtopo and the de-formation phase ϕdef 1e terrain phase determined viaDEM simulation can be applied to eliminate the influence ofterrain factors (known as the two-track method) and thusthe ground point deformation of the radar line of sight canbe obtained as follows

ΔRmov λ4π

ϕ minus ϕsim( 1113857 (4)

where ϕsim represents the terrain phase simulated by externalDEM

22 Estimating Underground-Goaf Boundaries Based on theGraphical Approach A total of four parameters namelylength (L1) width (L2) depth (H0) and dip angle (α) areneeded to characterize the goaf boundary where length andwidth are used to determine the size of the goaf and depthand dip angle are used to determine the position of the goaf1is paper aims to estimate these parameters based on thegraphical approach

1e subsidence data of the mining area used in this studywas obtained using DInSAR Preprocessing of the data in-cludes the geocoding and conversion to ArcGIS (100 ERSI)or CASS (90 SOUTHIS) readable formats 1e subsidencecontour map of the mining area is then obtained by ArcGISor CASS According to the distribution law of full-areamining subsidence [32] once the subsidence basin is stablethe subsidence contour is approximately elliptical 1esubsidence value peaks at the center of the ellipse while thefarther away from the center the smaller the subsidencevalue When the working surface is approximately rectan-gular the long semiaxis direction of the ellipse points to thestrike section of the working surface and the directionperpendicular to the strike section is taken as the inclinesection of this working surface So we can calibrate theposition of the maximum subsidence point on the subsi-dence contour map and then make two straight lines along

Advances in Civil Engineering 3

the major and minor semiaxes of the ellipse respectively1ese two lines are themain sections of the subsidence basin1e subsidence values at each point on the twomain sectionsare extracted and fitted based on the basic principle of theprobability integration method Following this the subsi-dence curves of the main section are drawn as shown inFigure 3

221 Strike Section Boundary Estimate Two points ofsubsidence values of 084Wm and 016Wm (where Wm isthe maximum subsidence value) are extracted from thestrike section and the horizontal distance between these twopoints is equal to 08r (r is the main influence radius and r0 isthe main influence radius of the strike section) If the r valuesobtained on both sides of the maximum subside point aredifferent the average of the two values is taken And then wecan calculate the depth (H) according to the definition of theparameter tan β (tangent of main effect angle) from the

probability integration method as shown in the followingequation

tan β H

r (5)

where H is mining depth 1us the mining depth of thestrike section (ie average depth) H0 can be calculated andused to create a horizontal plane below the strike sectionwith depth H0

Following this two inflection points at both ends of thestrike section are found on the subsidence curve 1ese twoinflection points are the computational boundary of theworking surface1e deviation of the inflection point (S) canbe calculated using the following equation

S kLH (6)

II II

IIprimeIIprime

IprimeI

I Iprime

60050040030020010010

Figure 3 Subsidence curve of the main section I-Iprime is the strikesection II-IIprime is the incline section the red line denotes the sub-sidence curve of the strike section and the green line is the sub-sidence curve of the incline section

External DEM

Differential interferogramgeneration

Subsidence contour

Probability integral method andgraphical method

Average depth(H0)length (L1) width(L2) dip angle (α)

Underground goaf boundary

Subsidence curve on two mainsections

Determining two main sectionsand selecting feature points

Settlement points extraction andtriangle interpolation

SAR image pair

Figure 1 Flow chart of the proposed method

y

B

H

P

x

R2

ΔRmov

R1

S1 t = t1 S2 t = t2

t = t2

t = t1

α

θ

Figure 2 DInSAR schematic


where kL is the coefficient of the inflection point offset 1emining boundary of the strike section presented in Figure 4is obtained by shifting the computational boundary outwardby S0 and the distance between these two boundary points isthe strike section length L1

222 Incline Section Boundary Estimate For this step fourpoints of the subsidence values of 084Wm and 016Wm areextracted in the rise and dip direction of the incline sectionrespectively 1e horizontal distance between these twopoints on the same side is equal to 08r (r1 and r2 are themaininfluence radii of the rise and dip directions respectively)1e mining depths H1 and H2 of the rise and dip directionsrespectively are then calculated according to r1 and r2 byequation (5) Following this two horizontal planes below theincline section with depths of H1 and H2 respectively aredetermined

Next two inflection points at both sides of the inclinesection on the subsidence curve are found Two vertical linesare drawn through these two points 1e vertical line of therise direction intersects the rise direction depth at point Nand the vertical line of the dip direction intersects the dipdirection depth at point M1ese two intersection points arethen connected whereby the angle between the intersectionline and the horizontal direction is the dip angle of the coalseam (α) (see Figure 5)

According to the definition of the probability integrationmethod the propagation angle is given as

θ 90∘ minus Kα (7)

where K is the propagation coefficient of extraction Anauxiliary line is then drawn in the depth direction throughthe inflection point such that the angle between the auxiliaryline and the horizontal direction is θ Moreover the in-tersection of the auxiliary and horizontal lines of the depth isthe calculated boundary of the goaf Following this the offsetdistances S1 and S2 of the dip and rise direction are thencalculated using the depthsH1 andH2 respectively based onthe geological conditions of the mining area 1e miningboundary is obtained by shifting the calculated boundaryoutwards by S1 and S2 and the distance between these twoboundary points is the incline section length L2 1e resultsare presented in Figure 6

Based on these results the boundary of the entire goafcan now be determined 1e determined geometric pa-rameters of the goaf are the average depth H0 dip directiondepth H1 rise direction depth H2 strike distance L1 slopelength L2 and dip angle α

3 Experimental Analysis

31 Simulation Experiment Assume that a coal face has thefollowing geometric parameters coal thickness m 22m

II II

IIprimeIIprime

IprimeI

I

08r0

H0

S0L1

S0

A B C D

Iprime

016Wm

084Wm

Figure 4 Estimate of the strike section boundary A and D are the actual boundaries of the goaf B and C are the calculated boundaries of thegoaf and the distance between the two points A and D is the strike section length L1


dip angle α 18deg strike length L1 240m inclined lengthL2 1385m dip section boundary depth H1 220m andrise direction boundary depth H2 187m Moreover theparameters of the probability integral method are as followssubsidence coefficient q 065 tan β 20 inflection pointoffset S 015 H and mining reflection coefficient kL 08Matlab (2015b MathWorks) is used to apply the probabilityintegral method to simulate the vertical displacement of thesurface as a result of mining After adding a random error tothe simulated value the subsidence contour of the area isobtained

In order to estimate the boundary range of the goaf thedirection of the two main sections is determined accordingto the subsidence contour 1e subsidence value of eachpoint on the main section is then extracted Following thisthe subsidence value is fitted using the probability integral

method and the subsidence and slope curves of the strikeand inclined sections are created

311 Strike Section Boundary Estimate Two inflectionpoints at both ends of the incline section are determined onthe subsidence curve ie the calculation boundary of theworking face 1e subsidence values 084Wm and 016Wmare extracted from the subsidence curve 1e distance be-tween these two points is 08r0 which is subsequently used tocalculate r0 According to the probability integral methodparameter tan β the strike depth is determined asH0 r0middottanβ 197m

1e inflection offset point of the simulated workingface is determined as S0 015H0 2955m 1us theactual boundary of the simulated working face can be

II II

IIprime

Aprime

Bprime

Cprime

Dprime

θ

θ

IIprime

IprimeI

I Iprime

08r2

08r1

H2

H1

S1

S2

L2

α

Figure 6 Estimate of the incline section boundary Aprime and Dprime denote the actual boundaries of the goaf in the dip and rise directionsrespectively while Cprime and Dprime are the calculated boundaries of the goaf in the dip and rise directions respectively 1e distance between Aprimeand Dprime is the length of the incline section of the face L2

II II

IIprimeIIprime

IprimeI

08r1

08r2

H2

N

α

H1

Figure 5 Derivation of the dip angle of the goaf N is the intersection of the vertical line of the rise direction depth M is the intersection ofvertical line of the dip direction depth and α is the dip angle of the coal seam


determined following an outward shift of the calculatedboundary by S0

312 Incline Section Boundary Estimate 1e subsidencevalues of 084Wm and 016Wm are extracted from thesubsidence curve 1e distance between these two points is08r which is then used to calculate the dip and rise di-rections of the main influence radii of r1 and r2 respectivelyFollowing this tan β is used to calculate the dip directiondepth of H1 2196m and the rise direction depth ofH2 1762m Next two inflection points at both ends of theincline section on the subsidence curve are determined Twovertical lines are drawn to the horizontal line through thesetwo points respectively1e vertical line of the rise directionintersects the rise direction depth while the other line in-tersects with the dip direction depth 1ese two intersectionpoints are connected to obtain the dip angle α ie the anglebetween the intersection line and the horizontal direction atα 183deg Based on the dip angle and mining reflectioncoefficients kL the propagation angle θ is determined andthe incline section boundary of the working face is thusidentified

Calculating the inflection offset points of the dip di-rection S1 and the rise direction S2 allows for the derivationof the actual boundary of the incline section working faceafter the calculated boundary is shifted outward by S1 and S2respectively

313 Experimental Results Using the estimated geometricparameters of the goaf the mining boundary can be de-termined 1e final estimate results are shown in Figure 7

314 Accuracy Assessment Next we can compare thepredicted boundary to the simulated boundary Figure 8shows the difference between the simulated and predictedboundary 1e predicted boundary (red rectangle) and thesimulated boundary (cyan rectangle) almost overlap and theobserved degree of coincidence is high 1is indicates thatthe boundary predicted by the proposed method is reliable

In order to quantitatively evaluate the accuracy of thepredicted boundary we calculate the deviation between thepredicted and simulated goaf geometric parameters (as re-ported in Table 1) as well as the relative error between thepredicted and simulated parameters 1e relative error K iscalculated as follows

K f

Gsim (8)

where f is the deviation between the predicted and simulatedparameters and Gsim is the simulated geometrical parameterof the goaf

1e results of the comparison are reported in Table 11e predicted geometric parameters are generally consistentwith the simulated geometric parameters with an averagerelative error of 22 1is again demonstrates the ability ofthe proposed method to accurately predict the boundaryrange of the underground goaf

32 Real Data Experiment

321 Study Area 1e Pangzhuang Coal mine is located inthe Jiuli District of Xuzhou City 13 km away from the centerof Xuzhou City 1e surface is mainly covered by vegetationand buildings (Figure 9) Over the years the coal mine hasproduced a large number of underground goafs causingserious problems in the area including damage to buildingsand roads and water inrush from mines In order tominimize the adverse effects of the underground goaf itsboundary must be identified We selected No 7503 workingface (represented in Figure 9 by a blue rectangular) of thePangzhuang 7 coal seam to test the proposed method 1eworking face adopts the fully mechanized long arm miningprocess and completely manages the roof 1e mining areabegan to operate in the 1980s and has a sufficient amount ofgeological and measured data of the underground goaf(Table 2) 1us this working face possesses the necessaryconditions required for the accuracy verification of theproposed method

322 Data Processing A total of 13 C-band ENVISATASAR images covering the Pangzhuang coal mining areawere selected with acquisition times from 2009-01-20 to2010-10-12 1e wavelength of the C-band is 56 cm theincident angle is 2278deg and the ground resolution is2012m1e image coverage area is shown in Figure 10 Dueto the time-space correlation only five images generatedinterference patterns taken on the following dates 2009-12-01 2010-01-5 2010-02-09 2010-03-16 and 2010-04-20 1eparameters of the interference pairs are reported in Table 3

ENVI SARscape (2014 sarmap) is used to implement theDInSAR processing First the SAR images are cut under theboundary of the study area and the size of the clipping datais 884times 4717 pixels After that based on the characteristics ofthe ASAR imagery the looks of azimuth and distance are setto 6 and 1 respectively in multi-looking processing to get acartographic resolution of 25m SARscape produces theinterference image pair and uses the 90m resolution SRTM-3 digital elevation data (V4) to remove the horizon effect ofthe interferogram Following this the Goldstein method isused to filter the deleveling interferogram to reduce coherentnoise 1e phase unwrapping process is then applied usingthe minimum cost flow method these pixels with low co-herence will be masked and the coherence threshold is set to02 1e GCPs (ground control points) are selected based ontheir suitability for most unwrapped phases 1ese GCPpoints are used to redefine the baseline parameters for or-bital refinement A polynomial model is then used to cal-culate the phase offset completing the releveling processFinally the residual phase is transformed into a shapevariable and geocoded to obtain the deformation result ofthe LOS direction 1e subsidence value can be obtained byprojecting the LOS deformation in the vertical directionwhich is equal to the LOS deformation divided by the cosineof the incident angle as shown in Figure 11

From Figure 11 it can be seen that several deformationabnormalities can be observed But only the area of 7503


working face (a black rectangular in Figure 11) presents acomplete subsidence process during the imaging period (iesubsidence begins subsidence development and subsidencestability) It indicates that underground mining operationsare present in the area during this period and the subsidencehas been stable 1erefore we can attempt to estimate the

boundary extent of an underground goaf in the area usingthe proposed method

323 Experimental Results 1e method proposed in thispaper aims to estimate the boundary of the undergroundgoaf in the study area1e time series surface subsidence canbe obtained by stacking the images (as in Figure 12) ArcGISis used to process the subsidence results obtained by InSARAt first load the subsidence data in ArcGIS After that selectthe ldquoRaster Surface-Contourrdquo tool from the ldquo3D Analystrdquomenu in the toolbox 1en allow for the generation of thesubsidence contour map after the tool finishing running1emaximum subsidence point in the subsidence basin is thenidentified Second according to the geometry of the contourthe direction of the main section of the underground goaf isdetermined and the two main sections are drawn throughthe maximum subsidence point Finally the subsidencevalues of various ground points are extracted from the mainsection and the subsidence curves of the two main sectionsare drawn (as in Figures 13)

II II

IIprime

DDprime

DAprime

ADprime

AAprime Aprime

Bprime

Cprime

Dprime

θ

θ

IIprime

IprimeI

I Iprime

08r2

08r1

08r0

H2

H1

S1

S2

L2

α

H0

S0L1

S0

A B C D

Figure 7 Estimate results A andD are the actual boundaries of the strike section C and B are the calculated boundaries of the strike sectionand the distance between A and D is the length of the strike section L1 Aprime is the actual boundary of the dip direction Bprime is the calculatedboundary of the dip direction Cprime is the actual boundary of the rise direction Drsquo is the calculated boundary of the rise direction and thedistance between Aprime and Dprime is the length of the incline section L2 1e final result is the rectangle AAprime-DAprime-DDprime-ADprime in the verticalprojection of the surface

300

200

200

100

100

X

Y

0

0

ndash100

ndash100ndash200

ndash200

Figure 8 Comparison of prediction results 1e red rectanglerepresents the predicted boundary and the cyan rectangle repre-sents the simulated boundary

Table 1 Comparison between the estimated and simulated pa-rameters of the underground goaf

Parameters L1 (m) L2 (m) H0 (m) H1 (m) H2 (m) α (deg)Simulation value 240 1385 2035 220 187 18Predictive value 2425 1383 197 2196 1762 183Difference minus25 +02 +65 +04 +108 minus03Relative error() 10 14 32 02 58 17


1e subsidence values of 084Wm and 016Wm areextracted from the strike and inline sections respectivelyNext the distance between the two points is measured tocalculate the average depth ofH0 3056m the dip directiondepth of H1 3189m and the rise direction depth ofH2 3002m 1en determine the position of an inflectionpoint on the subsidence curve According to the rockmotionreport (unpublished) of the mining area the coefficient ofthe inflection point offset is 013 (see from Table 2) thus wecan calculate the inflection point offset by formula (6) (ieS0 013 times H0 397m S1 013 times H1 415m S2

013 times H2 390m) 1e inflection point of the strike sec-tion is used to determine the calculated boundary of thestrike section and S0 is used to determine the miningboundary of the strike section 1e distance between thesetwo boundary points is the strike section length L1 7034Following this the inflection point of the incline section and thedepth of the dip and rise directions are used to determine thecoal seam inclination as α 43deg1en the propagation anglewascalculated by equation (7) And the calculated boundary of theincline section could be determined by the propagation angel

and the inflection point 1e mining boundary of the inclinesection is obtained by shifting the calculated boundary outwardsby S1 and S21e distance between these two boundary points isthe strike section length L21769 Finally the estimated resultsof the boundaries of the underground goaf can be obtained1eboundaries of the probe are marked with a red rectangle inFigure 14

324 Precision Evaluation In order to evaluate the accuracyof the estimate results we compared the boundary obtainedby standard geophysical techniques (blue) with that obtainedby the proposed method (red) as shown in Figure 15 1eboundary of the goaf predicted by DInSAR is consistent withthat predicted by the geophysical techniques indicating thatthe method proposed in this paper is reliable To quanti-tatively evaluate the reliability of the method we calculatethe difference between the geometric parameters of theunderground goaf estimated by our method and the actualgeometric parameters of the goaf (see Table 2) as well as the

34deg0prime0Prime

N35

deg0prime0Prime

N

117deg0prime0PrimeE 118deg0prime0PrimeE 117deg0prime0PrimeE 117V9prime0PrimeE

34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N

34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N

117deg0prime0PrimeE 117deg9prime0PrimeE

Working face

0 10 20 40 60 80 322416840kilometers kilometers

N

S

EWN

S

EW

Study areaRiver system

Figure 9 Geographic location of the Pangzhuang Coal Mine

Table 2 Geological and geometric parameters of No 7503 workingface of the Pangzhuang Coal Mine

Parameters Value Parameters ValueWorking face 7503 Strike length (m) 716

Subsidence coefficient (q) 085 Incline length(m) 188

Main influence angle tangent(tan β) 271 1ickness (m) 687

Inflection point offset (kL) 013 Dip angle (deg) 4

Propagation coefficient (K) 08 Average depth(m) 3155

Figure 10 Footprint of the ASAR imagery used in this experiment


relative error between the predicted and actual parameters(see Table 4)

As reported in Table 4 the relative errors of the fourpredicted geometric parameters are below 10 with anaverage value of 455 1e average relative error is ap-proximately 37 respectively Compared with the methodproposed by Yang et al [30] the relative errors of the fourgeometric parameters L1 L2 H0 and α are reduced by7375 suggesting that the method proposed in this paper ishighly accurate for estimating two-dimensional boundaries

Table 3 Parameters of the chosen interferometric pairs

No Master image Slave image Temporal baseline (day) Normal baseline (m) Incidence angle of master image1 2009-12-01 2010-01-5 35 minus3186 22816 42 2010-01-5 2010-02-09 35 36086 22802 03 2010-02-09 2010-03-16 35 minus33395 22795 14 2010-03-16 2010-04-20 35 23062 22817 2

20091201-20100105 20100105-201001209 20100209--20100316 20100316-20100420 N

E

S

W

ndash005003 ndash01 0 5 1 2 3 4kilometers

Figure 11 DInSAR-derived LOS deformation maps over four different time periods

Figure 12 DInSAR-derived LOS deformation maps

Figure 13 Contour generation the extraction of two main sec-tions and the plotting of the subsidence curves


4 Conclusion

1is paper reports an approach for estimating the boundaryrange of underground goaf using the DInSAR by combininga graphical method 1e proposed method fully considersthe spatial distribution relationship between surface de-formation obtained by DInSAR and the geometry of

A B

I3

I4

Aprime

Bprime

Cprime

Dprime

C D

I1

I2

Figure 14 Estimate result by DInSAR 1e red cuboids represent the estimated boundary of the underground goaf Points A D Aprime and Dprimeare the actual boundaries Points B C Bprime and Cprime are the calculated boundaries 1e distance between A and D is the length of the strikesection L1 And the distance between Aprime and Dprime is the width of the incline section L2

117035 11704 117045 11705 117055 11706117033433

34325

3432

34315

3431

3433

34325

3432

34315

3431117035

Geodetic L

Geo

detic

B

11704 117045 11705 117055 1170611703

Figure 15 Differences between the boundary of the goaf predictedby DInSAR and standard geophysical techniques1e red rectanglerepresents the boundary obtained by the proposed method and theblue rectangle represents the boundary obtained by the geophysicaltechniques

Table 4 Comparison between the estimated and actual geometricparameters of the underground goaf

Parameters L1 (m) L2 (m) H0 (m) α (deg)Actual value 716 188 3155 4Predictive value 7034 1769 3056 43Deviation +126 +111 +99 minus03Relative error () 17 59 31 75Relative error in Yang (2018) () 124 65 88 20


underground goaf and combines the relevant principles ofthe probability integral methodmodel Our results show thatthe predicted boundary of the underground goaf stronglyagrees with the measured boundary 1e average relativeerrors of the estimated andmeasured data are approximately22 and 37 respectively

However it is worth noting that DInSAR acquires thesurface deformation of the LOS direction thus the geometryof the generated contour will be deflected toward the radarline of sight leading to a deviation in the direction of themain section of the predicted goaf A higher deviation be-tween the predicted and measured data is observed com-pared to the simulated data In addition the strike sectionlength L1 the incline section length L2 and the depths H0H1 and H2 (predicted by the measured data) are allunderestimated 1is is because the deformation caused byunderground mining has not fully propagated to the surfacewhen SAR images are acquired resulting in the underes-timation of the boundary size Future research should focuson how to solve these problems in order to further improvethe prediction accuracy Considering the low cost and largespatial coverage of DInSAR it can be an effective tool for theestimate of the boundary range of underground goaf

Data Availability

1e data used to support the findings of this study are in-cluded in the article which is based on the SAR images andthe external DEM of the study area

Conflicts of Interest

1e authors declare no conflicts of interest regarding thepublication of this paper

Acknowledgments

1is work was supported by the following projects NationalNatural Science Foundation of China (41571374) NaturalScience Foundation of Hunan Province China(2019JJ50177) and Hunan Provincial Innovation Founda-tion for Postgraduate (CX2016B570)

References

[1] H Briggs Mining Subsidence E Arnold and CompanyLondon UK 1929

[2] H KratzschMining Subsidence Engineering Springer-VerlagBerlin Germany 1983

[3] S F Kelly ldquoGeophysical explorationrdquo Abstracts of ChineseGeological Literature vol 9 no 1 pp 39ndash56 2016

[4] D Lyness ldquo1e gravimetric detection of mining subsidencerdquoGeophysical Prospecting vol 33 no 4 pp 567ndash576 1985

[5] V Frid and K Vozoff ldquoElectromagnetic radiation induced bymining rock failurerdquo International Journal of Coal Geologyvol 64 no 1-2 pp 57ndash65 2005

[6] D W Brown Mining the Earthrsquos Heat Hot Dry Rock Geo-thermal Energy Springer Geography Berlin Germany 2012

[7] C Berthelot D Podborochynski T SaarenketoB Marjerison and C Prang ldquoGround-penetrating radarevaluation of moisture and frost across typical Saskatchewan

road soilsrdquoAdvances in Civil Engineering vol 2010 Article ID416190 9 pages 2010

[8] S P Singh ldquoNew trends in drilling and blasting technologyrdquoInternational Journal of Surface Mining Reclamation andEnvironment vol 14 no 4 pp 305ndash315 2000

[9] G Rossi ldquoHydrodynamics of flushing fluids in diamond wiresawing of hard rock theoretical treatmentrdquo Mining Tech-nology vol 115 no 4 pp 154ndash159 2006

[10] N Butel A Hossack and M S Kizil ldquoPrediction of in siturock strength using sonic velocityrdquo in Proceedings of the CoalAustralian Coal Operators Conference 2014 WollongongNSW Australia February 2014

[11] Y Sun Z Xu and Q Dong ldquoMonitoring and simulationresearch on development of water flowing fractures for coalmining under xiaolangdi reservoirrdquo Chinese Journal of RockMechanics amp Engineering vol 28 no 2 pp 238ndash245 2009

[12] J Fernandez R Romero D Carrasco et al ldquoInSAR volcanoand seismic monitoring in Spain results for the period1992ndash2000 and possible interpretationsrdquo Optics and Lasers inEngineering vol 37 no 2-3 pp 285ndash297 2002

[13] S Salvi F Sarti A Mouratidis A Coletta and S ZoffolildquoInSAR monitoring for seismic risk management the senti-nel-1 contributionrdquo in Proceedings of the EGU General As-sembly p 11278 Vienna Austria April 2012

[14] HWu Y Zhang J Zhang Z Lu andW Zhong ldquoMonitoringof glacial change in the head of the Yangtze river from 1997 to2007 using insar techniquerdquo ISPRSmdashInternational Archives ofthe Photogrammetry Remote Sensing and Spatial InformationSciences vol 39 no B7 pp 411ndash415 2012

[15] Y Sun L Jiang Q Sun L Liu Z Zhimin and S YonglingldquoGlacial surface topography and its changes in the westernQilian mountains derived from TanDEM-X Bi-static InSARrdquoin Proceedings of the 2016 IEEE International Geoscience andRemote Sensing Symposium (IGARSS) Beijing China July2016

[16] P Saranya and K Vani ldquoDeformation monitoring of volcaniceruption using DInSAR methodrdquo Computational Intelligencein Data Mining Springer Berlin Germany 2017

[17] I Alimuddin ldquoSurface deformation monitoring of Miyake-jima volcano using DInSAR technique of ALOS PALSARimagesrdquo in Proceedings of the IEEE International Geoscienceand Remote Sensing Symposium pp 1615ndash1618 VancouverBC Canada July 2011

[18] F Bozzano I Cipriani P Mazzanti and A PrestininzildquoDisplacement patterns of a landslide affected by humanactivities insights from ground-based InSAR monitoringrdquoNatural Hazards vol 59 no 3 pp 1377ndash1396 2011

[19] V Greif and J Vlcko ldquoMonitoring of post-failure landslidedeformation by the PS-InSAR technique at lubietova incentral Slovakiardquo Environmental Earth Sciences vol 66 no 6pp 1585ndash1595 2012

[20] A Elmzoughi R Abdelfattah and Z Belhadj ldquoSAR imageclassification using the InSAR coherence for soil degradationcartography in the south of Tunisiardquo in Proceedings of theIEEE International Conference on Image Processing HongKong September 2010

[21] H Bo W Hansheng J Lulu and W Ping ldquoUsing DInSAR tomonitor deformation of frozen ground inTibetan plateaurdquo Journalof Geodesy and Geodynamics vol 30 no 5 pp 53ndash56 2010

[22] L M Chen G Qiao and P Lu ldquoSurface deformationmonitoring in permafrost regions of Tibetan plateau based onalos palsar datardquo ISPRSmdashInternational Archives of the Pho-togrammetry Remote Sensing and Spatial Information Sci-ences vol 42 no W7 pp 1509ndash1512 2017


[23] Y Qin and D Perissin ldquoMonitoring underground miningsubsidence in South Indiana with C and L band InSARtechniquerdquo in Proceedings of the 2015 IEEE InternationalGeoscience and Remote Sensing Symposium (IGARSS) Hon-olulu HI USA July 2015

[24] Z W Li Z F Yang J J Zhu et al ldquoRetrieving three-di-mensional displacement fields of mining areas from a singleInSAR pairrdquo Journal of Geodesy vol 89 no 1 pp 17ndash32 2015

[25] X C Wang Y Zhang X G Jiang and P Zhang ldquoA dynamicprediction method of deep mining subsidence combinesDInSAR techniquerdquo Procedia Environmental Sciences vol 10pp 2533ndash2539 2011

[26] Z F Yang Z Li J Zhu et al ldquoAn InSAR-based temporalprobability integral method and its application for predictingmining-induced dynamic deformations and assessing pro-gressive damage to surface buildingsrdquo IEEE Journal of SelectedTopics in Applied Earth Observations amp Remote Sensingvol 11 no 2 pp 472ndash484 2018

[27] A Aditiya Y Aoki and R D Anugrah ldquoSurface deformationmonitoring of Sinabung volcano using multi temporal InSARmethod and GIS analysis for affected area assessmentrdquo IOPConference Series Materials Science and Engineering vol 344Article ID 012 2018

[28] D Peduto G Nicodemo J Maccabiani and S Ferlisi ldquoMulti-scale analysis of settlement-induced building damage usingdamage surveys and DInSAR data a case study in 1eNetherlandsrdquo Engineering Geology vol 218 pp 117ndash1332017

[29] H Zhe L Ge X Li K Zhang and Z Li ldquoAn underground-mining detection system based on DInSARrdquo IEEE Transac-tions on Geoscience and Remote Sensing vol 51 no 1pp 615ndash625 2013

[30] Z Yang Z Li J Zhu et al ldquoLocating and defining under-ground goaf caused by coal mining from space-borne SARinterferometryrdquo ISPRS Journal of Photogrammetry and Re-mote Sensing vol 135 pp 112ndash126 2018

[31] T W Leung C K Chan and M D Troutt ldquoApplication of amixed simulated annealing-genetic algorithm heuristic for thetwo-dimensional orthogonal packing problemrdquo EuropeanJournal of Operational Research vol 145 no 3 pp 530ndash5422003

[32] G He L Yang and G Lin Mining Subsidence EngineeringPress of China University of Mining amp Technology BeijingChina 1991

[33] F Casu M Manzo and R Lanari ldquoA quantitative assessmentof the SBAS algorithm performance for surface deformationretrieval from DInSAR datardquo Remote Sensing of Environmentvol 102 no 3-4 pp 195ndash210 2006

[34] G Nicodemo D Peduto S Ferlisi and J Maccabiani ldquoIn-vestigating building settlements via very high resolution SARsensors Life-cycle of engineering systems emphasis onsustainable civil infrastructurerdquo in Proceedings of the FifthInternational Symposium on Life-Cycle Civil Engineering(IALCCE 2016) pp 2256ndash2263 Delft Netherlands October2016

[35] D Peduto F Elia and R Montuori ldquoProbabilistic analysis ofsettlement-induced damage to bridges in the city ofAmsterdam (1e Netherlands)rdquo Transportation Geotechnicsvol 14 pp 169ndash182 2018

[36] D Peduto M Korff G Nicodemo A Marchese andS Ferlisi ldquoEmpirical fragility curves for settlement-affectedbuildings analysis of different intensity parameters for sevenhundred masonry buildings in 1e Netherlandsrdquo Soils andFoundations vol 59 no 2 pp 380ndash397 2019


speaking although these technologies are able to obtain therough location of the underground goaf along with its spatialdistribution they have several limitations For example suchtechnology is only suitable for small-scale detection whichcan be costly time-consuming and inefficient At the sametime the approximate geographical location of the goaf isrequired as prior information before detection Moreoverover the past few decades with the boomingmining industry(including legal and illegal mining) numerous unknownunderground goafs have emerged globally Traditionalgeophysical and drilling techniques are unable to meet thecurrent wide-ranging and time-sensitive goaf detectionneeds

1e interferometric synthetic aperture radar (InSAR)is a popular remote sensing technology that can surveylarge-scale surface deformation using two- or multi-viewsynthetic aperture radar (SAR) images Massonnet et alcombined two-scene ERS-1 images before and after anearthquake over the earthquake-prone area of LandersCalifornia with the DEM (Digital Elevation Model DEM)of the region to successfully observe the surface defor-mation caused by earthquakes Since then the differentialinterference synthetic aperture radar technique (DInSAR)has been widely used for the monitoring of surface de-formation caused by geological tectonic movements suchas seismic monitoring [12 13] glacial drift monitoring[14 15] volcanic eruption monitoring [16 17] landslidemonitoring [18 19] frozen soil degradation and ex-pansion monitoring [20ndash22] 1e use of DInSAR inmining subsidence is also a hot research topic and in-cludes applications in the detection of subsidence causedby mining [23 24] the prediction of mining-inducedgeological disasters [25 26] and the assessment of theimpact of mining on surface buildings [27 28]

Following the stabilization of the ground subsidencebasin caused by underground mining a close relationshipbetween the size and spatial distribution of the basin andgeological mining conditions can be observed 1is isdenoted as the subsidence rule More specifically thegeological mining conditions and the size of the goafdetermine the spatial distribution of the ground subsi-dence basin 1at is under specific geological miningconditions the spatial distribution characteristics of theground subsidence basin can also reflect the size of thegoaf DInSAR can not only survey the movement anddeformation of the subsidence area but also determine thedistribution state of the whole ground subsidence basin1us it can potentially be applied for the detection ofunderground goaf distributions

At present research on the detection of the geometricaldistribution of underground goaf using DInSAR is rare In2013 Zhe et al [29] proposed a method known as ldquoDInSAR-Based Illegal Gob Detection System (DIMDS)rdquo which uti-lizes the DInSAR to obtain the surface deformation valuealong the radar line-of-sight (LOS) direction 1e methodthen estimates the geodetic coordinates of the center of theground subsidence basin based on the mining subsidencetheory and subsequently determines the extent of under-ground goaf based on the ground subsidence basin

boundary However the DIMDS method has a key limita-tion It assumes that the center of the underground goaf is onthe same vertical line as the center of the ground subsidencebasin Yet for most cases this is not true as most coal seamsare not completely horizontal as long as the coal seam istilted the movement deformation caused by mining will notpropagate to the surface in the vertical direction 1is dis-crepancy seriously affects the accuracy of the boundary ofthe underground goaf estimated using the DIMDS method

In response to this problem Yang et al [30] definedthe geometrical distribution characteristics of the un-derground goaf using eight geometric parameters (lengthwidth height dip angle azimuth angle mining depth andtwo central geodetic coordinates) Based on the proba-bility integral method the relationship between thesegeometric parameters and the LOS deformation value ofthe ground subsidence basin is then established Fol-lowing this a mathematical model based on the simulatedannealing algorithm (SAGA) [31] is used to invert theeight geometric parameters from a large number of LOS-deformed observations obtained by DInSAR 1is methodconsiders the general law of mining subsidence and makesfull use of the surface information of the surface defor-mation obtained by DInSAR 1us prediction accuracy isgreatly improved compared to the DIMDS methodHowever due to the large number of inversion param-eters the stability of the mathematical model is low Inparticular the selection of the initial value of the modelwill have a great impact on the inversion results Yet inreal-world applications the initial value of a goaf is dif-ficult to determine Second due to the coherence losses ofthe echo signals from a SAR image pair a large number ofnull values are observed in the whole basin acquired byDInSAR 1is leads to errors in the inversion model so-lution process and subsequent incorrect results

At present most coalmines use long-arm coalmining andfull slumping to manage the roof Under the condition ofuniform mining thickness the main factors affecting thesubsidence rule are coal seam dip angle mining area size(length and width) and mining depth [32] 1ese parameterscan reflect the boundary range and basic shape of the goafHow to acquire these unknown parameters quickly and ef-fectively is of great significance to determine the boundariesof underground goaf 1erefore this paper proposes anunderground goaf boundary detection method by combiningDInSAR with a graphical method Our proposed method firstuses DInSAR to obtain the subsidence information of thewhole basin in the subsidence area and based on this thesubsidence contour map is generated 1e two main sections(the strike section and incline section) of the undergroundgoaf are determined according to the contour map and thesubsidence curve of these two sections is drawn Finally basedon the subsidence rule of coal mining the length coal seamdip angle mining area size and mining depth of the un-derground goaf are derived using a graphical methodMoreover after geocoding the size and location of the un-derground goaf the boundary is determined

1e paper is organized as follows In Section 2 we in-troduce the method used to estimate the boundary range of



2 Methods





R2rarr

R1rarr

+ ΔRmovrarr

minus Brarr

(1)

where Ri







ϕ 4πλ

ρ2 minus ρ1( 1113857

4πλlangR1

rarr+ D

rarrminus B

rarr R1rarr

+ Drarr


(2)



rarr| is the



ϕ 4πλlangR1



ϕdef + ϕtopo

(3)



ΔRmov λ4π









tan β H

r (5)



S kLH (6)

II II

IIprimeIIprime

IprimeI

I Iprime

60050040030020010010


External DEM


Subsidence contour







SAR image pair


y

B

H

P

x

R2

ΔRmov

R1

S1 t = t1 S2 t = t2

t = t2

t = t1

α

θ












II II

IIprimeIIprime

IprimeI

I

08r0

H0

S0L1

S0

A B C D

Iprime

016Wm

084Wm








II II

IIprime

Aprime

Bprime

Cprime

Dprime

θ

θ

IIprime

IprimeI

I Iprime

08r2

08r1

H2

H1

S1

S2

L2

α


II II

IIprimeIIprime

IprimeI

08r1

08r2

H2

N

α

H1









K f

Gsim (8)












II II

IIprime

DDprime

DAprime

ADprime

AAprime Aprime

Bprime

Cprime

Dprime

θ

θ

IIprime

IprimeI

I Iprime

08r2

08r1

08r0

H2

H1

S1

S2

L2

α

H0

S0L1

S0

A B C D


300

200

200

100

100

X

Y

0

0

ndash100

ndash100ndash200

ndash200









34deg0prime0Prime

N35

deg0prime0Prime

N


34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N

34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N


Working face


N

S

EWN

S

EW















20091201-20100105 20100105-201001209 20100209--20100316 20100316-20100420 N

E

S

W






4 Conclusion


A B

I3

I4

Aprime

Bprime

Cprime

Dprime

C D

I1

I2


117035 11704 117045 11705 117055 11706117033433

34325

3432

34315

3431

3433

34325

3432

34315

3431117035

Geodetic L

Geo

detic

B

11704 117045 11705 117055 1170611703







Data Availability




Acknowledgments


References









































2 Methods





R2rarr

R1rarr

+ ΔRmovrarr

minus Brarr

(1)

where Ri







ϕ 4πλ

ρ2 minus ρ1( 1113857

4πλlangR1

rarr+ D

rarrminus B

rarr R1rarr

+ Drarr


(2)



rarr| is the



ϕ 4πλlangR1



ϕdef + ϕtopo

(3)



ΔRmov λ4π









tan β H

r (5)



S kLH (6)

II II

IIprimeIIprime

IprimeI

I Iprime

60050040030020010010


External DEM


Subsidence contour







SAR image pair


y

B

H

P

x

R2

ΔRmov

R1

S1 t = t1 S2 t = t2

t = t2

t = t1

α

θ












II II

IIprimeIIprime

IprimeI

I

08r0

H0

S0L1

S0

A B C D

Iprime

016Wm

084Wm








II II

IIprime

Aprime

Bprime

Cprime

Dprime

θ

θ

IIprime

IprimeI

I Iprime

08r2

08r1

H2

H1

S1

S2

L2

α


II II

IIprimeIIprime

IprimeI

08r1

08r2

H2

N

α

H1









K f

Gsim (8)












II II

IIprime

DDprime

DAprime

ADprime

AAprime Aprime

Bprime

Cprime

Dprime

θ

θ

IIprime

IprimeI

I Iprime

08r2

08r1

08r0

H2

H1

S1

S2

L2

α

H0

S0L1

S0

A B C D


300

200

200

100

100

X

Y

0

0

ndash100

ndash100ndash200

ndash200









34deg0prime0Prime

N35

deg0prime0Prime

N


34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N

34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N


Working face


N

S

EWN

S

EW















20091201-20100105 20100105-201001209 20100209--20100316 20100316-20100420 N

E

S

W






4 Conclusion


A B

I3

I4

Aprime

Bprime

Cprime

Dprime

C D

I1

I2


117035 11704 117045 11705 117055 11706117033433

34325

3432

34315

3431

3433

34325

3432

34315

3431117035

Geodetic L

Geo

detic

B

11704 117045 11705 117055 1170611703







Data Availability




Acknowledgments


References











































tan β H

r (5)



S kLH (6)

II II

IIprimeIIprime

IprimeI

I Iprime

60050040030020010010


External DEM


Subsidence contour







SAR image pair


y

B

H

P

x

R2

ΔRmov

R1

S1 t = t1 S2 t = t2

t = t2

t = t1

α

θ












II II

IIprimeIIprime

IprimeI

I

08r0

H0

S0L1

S0

A B C D

Iprime

016Wm

084Wm








II II

IIprime

Aprime

Bprime

Cprime

Dprime

θ

θ

IIprime

IprimeI

I Iprime

08r2

08r1

H2

H1

S1

S2

L2

α


II II

IIprimeIIprime

IprimeI

08r1

08r2

H2

N

α

H1









K f

Gsim (8)












II II

IIprime

DDprime

DAprime

ADprime

AAprime Aprime

Bprime

Cprime

Dprime

θ

θ

IIprime

IprimeI

I Iprime

08r2

08r1

08r0

H2

H1

S1

S2

L2

α

H0

S0L1

S0

A B C D


300

200

200

100

100

X

Y

0

0

ndash100

ndash100ndash200

ndash200









34deg0prime0Prime

N35

deg0prime0Prime

N


34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N

34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N


Working face


N

S

EWN

S

EW















20091201-20100105 20100105-201001209 20100209--20100316 20100316-20100420 N

E

S

W






4 Conclusion


A B

I3

I4

Aprime

Bprime

Cprime

Dprime

C D

I1

I2


117035 11704 117045 11705 117055 11706117033433

34325

3432

34315

3431

3433

34325

3432

34315

3431117035

Geodetic L

Geo

detic

B

11704 117045 11705 117055 1170611703







Data Availability




Acknowledgments


References

















































II II

IIprimeIIprime

IprimeI

I

08r0

H0

S0L1

S0

A B C D

Iprime

016Wm

084Wm








II II

IIprime

Aprime

Bprime

Cprime

Dprime

θ

θ

IIprime

IprimeI

I Iprime

08r2

08r1

H2

H1

S1

S2

L2

α


II II

IIprimeIIprime

IprimeI

08r1

08r2

H2

N

α

H1









K f

Gsim (8)












II II

IIprime

DDprime

DAprime

ADprime

AAprime Aprime

Bprime

Cprime

Dprime

θ

θ

IIprime

IprimeI

I Iprime

08r2

08r1

08r0

H2

H1

S1

S2

L2

α

H0

S0L1

S0

A B C D


300

200

200

100

100

X

Y

0

0

ndash100

ndash100ndash200

ndash200









34deg0prime0Prime

N35

deg0prime0Prime

N


34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N

34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N


Working face


N

S

EWN

S

EW















20091201-20100105 20100105-201001209 20100209--20100316 20100316-20100420 N

E

S

W






4 Conclusion


A B

I3

I4

Aprime

Bprime

Cprime

Dprime

C D

I1

I2


117035 11704 117045 11705 117055 11706117033433

34325

3432

34315

3431

3433

34325

3432

34315

3431117035

Geodetic L

Geo

detic

B

11704 117045 11705 117055 1170611703







Data Availability




Acknowledgments


References













































II II

IIprime

Aprime

Bprime

Cprime

Dprime

θ

θ

IIprime

IprimeI

I Iprime

08r2

08r1

H2

H1

S1

S2

L2

α


II II

IIprimeIIprime

IprimeI

08r1

08r2

H2

N

α

H1









K f

Gsim (8)












II II

IIprime

DDprime

DAprime

ADprime

AAprime Aprime

Bprime

Cprime

Dprime

θ

θ

IIprime

IprimeI

I Iprime

08r2

08r1

08r0

H2

H1

S1

S2

L2

α

H0

S0L1

S0

A B C D


300

200

200

100

100

X

Y

0

0

ndash100

ndash100ndash200

ndash200









34deg0prime0Prime

N35

deg0prime0Prime

N


34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N

34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N


Working face


N

S

EWN

S

EW















20091201-20100105 20100105-201001209 20100209--20100316 20100316-20100420 N

E

S

W






4 Conclusion


A B

I3

I4

Aprime

Bprime

Cprime

Dprime

C D

I1

I2


117035 11704 117045 11705 117055 11706117033433

34325

3432

34315

3431

3433

34325

3432

34315

3431117035

Geodetic L

Geo

detic

B

11704 117045 11705 117055 1170611703







Data Availability




Acknowledgments


References














































K f

Gsim (8)












II II

IIprime

DDprime

DAprime

ADprime

AAprime Aprime

Bprime

Cprime

Dprime

θ

θ

IIprime

IprimeI

I Iprime

08r2

08r1

08r0

H2

H1

S1

S2

L2

α

H0

S0L1

S0

A B C D


300

200

200

100

100

X

Y

0

0

ndash100

ndash100ndash200

ndash200









34deg0prime0Prime

N35

deg0prime0Prime

N


34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N

34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N


Working face


N

S

EWN

S

EW















20091201-20100105 20100105-201001209 20100209--20100316 20100316-20100420 N

E

S

W






4 Conclusion


A B

I3

I4

Aprime

Bprime

Cprime

Dprime

C D

I1

I2


117035 11704 117045 11705 117055 11706117033433

34325

3432

34315

3431

3433

34325

3432

34315

3431117035

Geodetic L

Geo

detic

B

11704 117045 11705 117055 1170611703







Data Availability




Acknowledgments


References











































II II

IIprime

DDprime

DAprime

ADprime

AAprime Aprime

Bprime

Cprime

Dprime

θ

θ

IIprime

IprimeI

I Iprime

08r2

08r1

08r0

H2

H1

S1

S2

L2

α

H0

S0L1

S0

A B C D


300

200

200

100

100

X

Y

0

0

ndash100

ndash100ndash200

ndash200









34deg0prime0Prime

N35

deg0prime0Prime

N


34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N

34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N


Working face


N

S

EWN

S

EW















20091201-20100105 20100105-201001209 20100209--20100316 20100316-20100420 N

E

S

W






4 Conclusion


A B

I3

I4

Aprime

Bprime

Cprime

Dprime

C D

I1

I2


117035 11704 117045 11705 117055 11706117033433

34325

3432

34315

3431

3433

34325

3432

34315

3431117035

Geodetic L

Geo

detic

B

11704 117045 11705 117055 1170611703







Data Availability




Acknowledgments


References












































34deg0prime0Prime

N35

deg0prime0Prime

N


34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N

34deg1

5prime0Prime

N34

deg25prime

0PrimeN

34deg2

0prime0Prime

N


Working face


N

S

EWN

S

EW















20091201-20100105 20100105-201001209 20100209--20100316 20100316-20100420 N

E

S

W






4 Conclusion


A B

I3

I4

Aprime

Bprime

Cprime

Dprime

C D

I1

I2


117035 11704 117045 11705 117055 11706117033433

34325

3432

34315

3431

3433

34325

3432

34315

3431117035

Geodetic L

Geo

detic

B

11704 117045 11705 117055 1170611703







Data Availability




Acknowledgments


References












































20091201-20100105 20100105-201001209 20100209--20100316 20100316-20100420 N

E

S

W






4 Conclusion


A B

I3

I4

Aprime

Bprime

Cprime

Dprime

C D

I1

I2


117035 11704 117045 11705 117055 11706117033433

34325

3432

34315

3431

3433

34325

3432

34315

3431117035

Geodetic L

Geo

detic

B

11704 117045 11705 117055 1170611703







Data Availability




Acknowledgments


References








































4 Conclusion


A B

I3

I4

Aprime

Bprime

Cprime

Dprime

C D

I1

I2


117035 11704 117045 11705 117055 11706117033433

34325

3432

34315

3431

3433

34325

3432

34315

3431117035

Geodetic L

Geo

detic

B

11704 117045 11705 117055 1170611703







Data Availability




Acknowledgments


References










































Data Availability




Acknowledgments


References








































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