sustainability
Article Determination of GPS Session Duration in Ground Deformation Surveys in Mining Areas
Maciej Bazanowski 1, Anna Szostak-Chrzanowski 2,* and Adam Chrzanowski 1
1 Department of Geodesy and Geomatics Engineering, University of New Brunswick, P.O. Box 4400, Fredericton, N.B., E3B 5A3, N.B., Canada; [email protected] (M.B.); [email protected] (A.C.) 2 Faculty of Geoengineering, Mining and Geology, Wrocław University of Science and Technology„ul. Na Grobli 15, 50-421Wrocław, Poland * Correspondence: [email protected]
Received: 18 September 2019; Accepted: 25 October 2019; Published: 3 November 2019
Abstract: Extraction of underground minerals causes subsidence of the ground surface due to gravitational forces. The subsidence rate depends on the type of extracted ore, as well as its shape, thickness, and depth. Additionally, the embedding and overburden rock properties influence the time needed for the deformations to reach the surface. Using the results of geodetic deformation monitoring, which supply the information on pattern and magnitude of surface deformation, the performance of the mine may be evaluated. The monitoring can supply information on the actual rock mass behaviour during the operation and in many cases during the years after the mining operations have ceased. Geodetic methods of deformation monitoring supply information on the absolute and relative displacements (changes in position in a selected coordinate system) from which displacement and strain fields for the monitored object may be derived. Thus, geodetic measurements provide global information on absolute and relative displacements over large areas, either at discrete points or continuous in the space domain. The geodetic methods are affected by errors caused by atmospheric refraction and delay of electromagnetic signal. Since geodetic measurements allow for redundancy and statistical evaluation of the quality of the data, they generally provide reliable results. Usually, the designed accuracy of deformation measurements should allow for the detection of at least one third of the expected maximum deformations over the desired time span at the 95% probability level. In ground subsidence studies in mining areas, 10 mm accuracy at 95% level in both vertical and horizontal displacements is typically required. In the case of salt mines, the process of ground subsidence in viscous rock is slow; therefore, subsidence monitoring surveys may be performed once a year. In subsidence determination, two techniques are commonly used: leveling and satellite positioning. The satellite positioning technique is used to determine the 3D (horizontal coordinates and height) or 2D position of monitored points (only horizontal coordinates). When comparing the heights determined from satellite and leveling surveys, it has to be noted that the leveling heights are referred with respect to the geoid (orthometric heights), while heights determined from satellite surveys are referred with respect to the ellipsoid (ellipsoidal height). In the case of satellite surveys, the accuracy of horizontal position is typically 2–3 times better than vertical. The analysis of the optimal session duration lead to the conclusion that in order to achieve the sub-cm accuracy of horizontal coordinates at 95% confidence level, the satellite positioning session length using Global Positioning System (GPS) should be at least three hours long. In order to achieve the sub-cm accuracy of height coordinate at 95% confidence level in a single observation session, the GPS session length should be at least twelve hours long.
Keywords: GPS; mining; deformation monitoring
Sustainability 2019, 11, 6127; doi:10.3390/su11216127 www.mdpi.com/journal/sustainability Sustainability 2019, 11, 6127 2 of 12
1. Deformation Monitoring Requirements Geodetic methods of deformation monitoring supply information on the absolute and relative displacements (changes in position in a selected coordinate system), from which displacement and strain fields for the monitored object may be derived. Thus, geodetic measurements provide global information on absolute and relative displacements over large areas, either at discrete points or continuously in the spatial domain. The geodetic methods are affected by errors caused by atmospheric refraction and delay of electromagnetic signal. Since geodetic measurements allow for redundancy and statistical evaluation of the quality of the data, they generally provide reliable results. The design of the monitoring network should allow for a sufficient redundancy of measurements, as well as for the self-checking of the scheme through geometrical closures of loops of independent measurements. It is sufficient to say that usually, the designed accuracy of deformation measurements should allow for the detection of at least one third of the expected maximum deformations over the desired time span at the 95% probability level [1]. Among the currently available geodetic and remote sensing techniques that are applicable to ground deformation monitoring, one may consider the following techniques: geometric leveling, trigonometric leveling, traversing, global navigation satellite systems (GNSS), satellite-borne and ground-based radar interferometry, airborne LiDAR, and aerial photogrammetry. With the development of new monitoring technologies and new concepts concerning the integrated analysis of rock mass deformation in mining areas, the role of monitoring surveys has significantly increased over time to provide [2]: Verification that the behaviour of the structure follows the predicted pattern. • Better understanding of the structure’s deformation mechanism for improving the safety and • economy of mining production. Information for enhanced environmental protection. • Identification and separation of various causes of deformation. • Information for legal disputes concerning effects of mining on surface infrastructure. • The accuracy of the monitored surface deformations should allow for the detection of at least one third of the expected maximum deformations over the desired time span at the 95% probability level. In surface deformation studies in mining areas, typically 10 mm accuracy at 95% level in both vertical and horizontal displacements is required. To achieve a good reliability, the design of the monitoring system must have redundancy of observables and must be based on a good understanding of sources of errors and their mitigation. There is no single technique that can satisfy all of the listed ground deformation monitoring requirements as a stand-alone system—a combination of various monitoring methods which complement each other is recommended.
2. Use of GPS in Deformation Monitoring Pioneering use of GPS in ground subsidence studies dates back to the early 1980s. In 1987, in monitoring of oil fields in Venezuela, GPS was added to the monitoring leveling scheme to gain information on the horizontal movements and to connect the local leveling network to faraway reference points [3]. It was a pioneering and challenging application of GPS in surface deformation studies, with only eight GPS satellites available for civilian use at that time and with inadequate modeling of atmospheric effects. The GNSS technique in surface deformation surveys has been widely used [4–8], and it requires minimal user interaction (and therefore can be cost-effective). GPS makes it possible to obtain millimeter level position information for short baselines (<10 km). In order to achieve the desired sub-cm accuracy, the location of the GPS receiver should ensure full sky visibility. The main problems in GPS surveys are multipath error, tropospheric delay, and limited visibility to the satellites. The double-differenced (DD) ambiguity-fixed carrier-phase observation is the most commonly used GPS measurement for high -precision applications [9]. DD is the differencing between receivers followed by differencing between satellites or vice versa. This observation type allows for quick Sustainability 2019, 11, 6127 3 of 12 convergence on a solution once the ambiguity term has been resolved. However, the ambiguity term is always present, which leaves the possibility of false alarms caused by poorly handled cycle slips. The triple-differenced (TD) observable, despite introducing another level of differencing which increases the observation noise, offers several advantages over the DD [5]. After removing the error terms for receiver clocks and satellite clocks (which should be eliminated through DD processing when observation simultaneity criteria are met), the TD, carrier-phase observable between times t1 and t2 can be written as: ij ij f f ij f f δ∆AB (t12) = ∆AB ϕ + N + M c I + c T + eϕ + etrop ∆AB ϕ + N + M c I + c T + eϕ + etrop (1) ∇ ∇ − t2 − ∇ − t1 where: Sustainability 2019, 11, x FOR PEER REVIEW 3 of 12
ij single-diThefference triple-differenced (SD) operator (TD) observable, between despite satellites introducingi and anotherj level of differencing which ∇ ∆ SD operatorincreases between the observation receivers noise, Aoffers and several B advantages over the DD [5]. After removing the error AB terms for receiver clocks and satellite clocks (which should be eliminated through DD processing δ SD operatorwhen observation between simultaneity times t1 and criteria t2 are met), the TD, carrier-phase observable between times t1 ϕ carrier-phaseand t2 can observable be written as: (cycles)
푖푗 푖푗 푓 푓 N ambiguity (cycles) 훿∆퐴퐵∇ (푡12) = [∆퐴퐵∇ (휑 + 푁 + 푀 − 퐼 + 푇 + 푒휑) + 푒푡푟표푝] 푐 푐 푡2 M multipath (cycles) 푓 푓 (1) − [∆ ∇푖푗 (휑 + 푁 + 푀 − 퐼 + 푇 + 푒 ) + 푒 ] 퐴퐵 푐 푐 휑 푡푟표푝 I ionospheric delay of the L1 carrier phase (m) 푡1 T troposphericwhere: delay (m) ∇ij single-difference (SD) operator between satellites i and j f carrier waveΔAB SD frequencyoperator between (Hz) receivers A and B c speed of훿 lightSD oper in aator vacuum between (mtimes/s) t1 and t2 etrop residual휑 troposphericcarrier-phase obse delayrvable bias (cycles) (present over large height differences) N ambiguity (cycles) eϕ randomM carrier-phase multipath (cycles) measurement noise. I ionospheric delay of the L1 carrier phase (m) Errors andT biasestroposph sucheric delay as ionospheric(m) delay, satellite clock errors, and orbital errors are assumed to be mitigatedf throughcarrier wave di frequenfferencingcy (Hz) of the observables. Limitations of use and sources of errors in GPS surveysc arespeed presented of light in in a [vacuum8,10–12 (m]./s) The multipath effect can be mitigated by carefully selecting e residual tropospheric delay bias (present over large height differences) the antenna sitetrop to avoid reflective objects, using the receiver that filters multipath effects, using the 푒휑 random carrier-phase measurement noise. antenna that is multipath-resistant, masking signals from low-elevation satellites, or using longer Errors and biases such as ionospheric delay, satellite clock errors, and orbital errors are assumed session lengthsto be [ 6mitigated,13–15]. through differencing of the observables. Limitations of use and sources of errors in In surfaceGPS deformationsurveys are presented studies, in [8,10 the–12] satellite. The multipath positioning effect can be technique mitigated by cancarefully commonly selecting be used to determine thethe antenna 3D (horizontal site to avoid coordinatesreflective objects, and usingheight) the receiver or that 2D filters position multipath of effects, monitored using the points (only antenna that is multipath-resistant, masking signals from low-elevation satellites, or using longer horizontal coordinates).session lengths [6,13 When–15]. comparing the heights determined from satellite and leveling surveys, one has to keepIn in surface mind deformation that the leveling studies, the heights satellite are positioning referred technique with respect can commonly to the be geoid used to (orthometric height), whiledetermine heights the determined 3D (horizontal from coordinates satellite and height) surveys or 2D are position referred of monitored with respect points (only to the ellipsoid horizontal coordinates). When comparing the heights determined from satellite and leveling surveys, (ellipsoidal height).one has to The keep diinff minderence that betweenthe leveling the height ellipsoidals are referred and with orthometric respect to the geoid height (orthometric is called undulation (Figure1); theheight) relationship, while height betweens determined ellipsoidal from satellite and surveys orthometric are referred heights with respect can be to writtenthe ellipsoid as: (ellipsoidal height). The difference between the ellipsoidal and orthometric height is called undulation (Figure 1); the relationship betweenh = ellipsoidalH + N and orthometric heights can be written as: (2) ℎ = 퐻 + 푁 (2)
Figure 1. RelationFigure 1. betweenRelation between undulation, undulation orthometric, orthometric heights,heights, and and ellipsoidal ellipsoidal heights heights (after (after http: http://mathscinotes.com). //mathscinotes.com). Sustainability 2019, 11, 6127 4 of 12
In positioning surveys, in order to determine the orthometric height from GPS measurements, one has to know the value of undulation. In deformation surveys, one is interested in the height difference between consecutive monitoring campaigns. The orthometric height difference between the second and first monitoring epochs can be written as: ∆H = H H (3) 2 − 1 and ellipsoidal height difference can be expressed as:
∆h = h h (4) 2 − 1 If undulation is constant between campaigns:
∆h = H + N (H + N) (5) 2 − 1 ∆h = ∆H (6)
This means that in deformation surveys, the ellipsoidal and orthometric height differences between monitoring epochs are equal if the undulation stays constant.
3. Description of the Study Area Excavation of any underground deposit creates openings and disturbs equilibrium of forces in the surrounding rock mass. Due to gravitational forces, the rock strata surrounding the openings is deformed and starts moving towards the opening. The rock movement propagates to the surface and creates a subsidence bowl. The depth and horizontal dimensions of the subsidence bowl depend on the geometry and dimensions of the underground excavation, the mechanical properties and behaviour model of the rock mass, the depth of the mining operation, and the mining method. The time lapse between the time of underground excavation and full development of the subsidence on the surface may take from a few days to several months or even years (in the case of salt and potash mining), depending on the geology and properties of the rock strata. In an undisturbed state of stress, salt rock is under isotropic lithostatic conditions. Under loading conditions, the redistribution of stress causes the deformation in salt rock. The developed stresses σij can be divided into two parts: the hydrostatic and non-hydrostatic (deviatoric) stress. The hydrostatic part of stress results in elastic deformations. The deviatoric part of stress causes creep with time. Mining of a large deposit of high-grade sylvinite in New Brunswick has been carried out since the mid-1980s. Potash and salt mining takes place at depths between 400 and 700 m within a 25 km long dome-shaped salt pillow in which the potash is preserved in steeply dipping flanks. The potash deposit is structurally complex with a variable dip and width. A strong arch-shaped cap rock provides a natural support for the overlain brittle rocks. Salt mining is done using a multi-level room-and-pillar method with unsupported openings up to 25 m wide. Monitoring surveys are performed annually and consist of first-order leveling and static GPS observations in the 3 by 8 km area above the extraction. The leveling surveys are performed using a Leica DNA03 digital level to measure the subsidence, and GPS observations are performed using NovAtel dual frequency receivers to measure the horizontal displacement of survey monuments. The monitoring network consists of approximately 150 survey monuments. The leveling monitoring network with distances between leveling monuments of approximately 200–300 m has a necessary density to determine the surface subsidence. The aerial view of the investigated area is shown in Figure2. Sustainability 2019, 11, 6127 5 of 12 Sustainability 2019, 11, x FOR PEER REVIEW 5 of 12
Figure 2. AerialAerial view view of of the the investigated area.
Mining extraction ofof halitehalite was was done done at twoat two levels. levels. In 1996, In 1996 the extraction, the extraction of halite of inhalite the upperin the upperlevel was level completed. was completed. The mining The ofmining the lower of the level lower started level in 2013.started Locations in 2013. of Locations the GPS monumentsof the GPS monumentsselected for theselected analysis for ofthe session analysis duration of session were duration not affected were by not the affected extraction by the effects, extraction since theyeffects, are sincelocated they outside are located of the outsi deformationde of the zone. deformation zone.
4. GPS GPS Session Session Duration Duration GPS session session duration duration in in deformation deformation studies studies is isstill still underestimated underestimated and and is isusually usually too too short short in practice.in practice. The The optimal optimal session session duration duration improves improves the the economy economy of of the the deformation deformation surveys surveys while ensuring the re requiredquired accuracy. Over the last few decades decades,, the investigation of the influence influence of GPS session duration, baseline baseline length length,, and and seasonal variations on on the the accuracy of coordinates has been performed by by many many researche researchers;rs; examples examples can can be be found found in in [16 [16–19–19]. ].In In2005 2005,, a stud a studyy of ofevaluation evaluation of sessionof session duration duration was was performed performed in open in open pit mine pit miness by [20]. by [The20]. findings The findings of the ofstudy the studyshowed showed that a longerthat a longer session session length length improves improves the quality the quality of results, of results, especially especially for for the the baselines baselines with with height differencesdifferences larger than 100 m.m. The results results indicated indicated that the quality quality of of GPS GPS solutions solutions deteriorates deteriorates with the increase inin heightheight didifferencefferencebetween between the the baseline baseline stations stations and and that that the the tropospheric tropospheric delay delay is oneis one of ofthe the dominant dominant error error sources. sources. In In the the areas areas of openof open pit pit mines, mines, where where the the height height diff erencedifference between between the theGPS GPS reference reference station station and theand rover the rover receiver receiver can reach can upreach to severalup to several hundred hundred meters, meters, the main the limiting main limitingfactor of factor the accuracy of the accuracy of height of determination height determination is the tropospheric is the tropospheric delay [4]. delay [4]. In the presented results, in order to satisfy t thehe requirement of achieving an accuracy of 10 mm in the determination of horizontal displacements, the the optimal optimal duration duration of of GPS observation sessions sessions has been determined. The The main main concern concern in in the the choosing choosing of of the optimal session duration was the determination of the horizontal coordinates coordinates with accuracy accuracy better better than than 10 10 mm mm at at 95% 95% confidence confidence level. level. The evaluation has been performed on GPS sessions of differentdifferent durations,durations, ranging from two to twentytwenty-four-four hours, hours, in in the the area area affected affected by underground by underground extraction extraction of salt and of potash. salt and The potash. investigated The investigatedGPS site was GPS 3 km site wide was and 3 km 8 km wide long and in a8 ruralkm long area in with a rural a high area density with aof high forestation density ofof coniferforestation and ofleaf conifer trees (Figure and leaf2). trees The terrain (Figure in 2). the The investigated terrain in area the investigated was practically area flat was with practically maximum flat height with maximumelevation changes height elevation of approximately changes 40of app m. Theroximately GPS monitoring 40 m. The network GPS monitoring consisted network of 90 deformation consisted ofmonuments 90 deformation and 10 control monuments monuments. and 10 The control shortest monuments. GPS baseline The was shortest approximately GPS baseline 300 m long, was approximately 300 m long, while the longest baseline was 9000 m long. GPS baselines from the 2013 monitoring campaign are shown in Figure 3. Sustainability 2019, 11, 6127 6 of 12 while the longest baseline was 9000 m long. GPS baselines from the 2013 monitoring campaign are shownSustainability in Figure 2019, 311. , x FOR PEER REVIEW 6 of 12
FigureFigure 3.3. 20132013 GPS c controlontrol and and GPS GPS d deformationeformation networks. networks.
4.1.4.1. Determination Determination of of the the OptimalOptimal DurationDuration of GPS GPS S Sessionession TheThe analysis analysis of GPS of GPS session session duration duration for surface for deformationsurface deformation monitoring monitoring above the aboveunderground the saltunderground extraction wassalt extraction performed was using performed GPS sessions using GPS with sessions durations with ofdurations twenty-four of twenty hours-four on hours control networkon control monuments. network monuments. The GPS data The were GPS collected data were by collected Novatel DL-4 by Novatel and DLV3 DL-4 L1 and/L2 DLV3 receivers, L1/L2 with continuousreceivers, with data continuous acquisition data over acquisition the time over of 18 the days. time of The 18 days. observations The observations were collected were collected with 10 s intervals.with 10 s The intervals. height The diff erencesheight differences between receivers between werereceivers no greater were no than greater 40 m. than An 40 elevation m. An elevation mask of 15 degreesmask of was 15 degrees used. This was is used. a standard This is a elevation standard cuto elevationff commonly cutoff commonly used to avoid used multipathto avoid multipath errors and errorserrors caused and errors by poor caused satellite by poor geometry satellite [ 21geometry]. [21]. InIn order order to to determine determine the the optimaloptimal observation time time for for GPS GPS sessions, sessions, a baseline a baseline between between control control pointspoints HPN HPN and and ML4ML4 was selected selected for for the the analysis. analysis. The TheGPS GPSobservations observations on points on pointsHPN and HPN ML4 and were collected in sessions with durations of twenty-four hours. Point HPN serves as the main control ML4 were collected in sessions with durations of twenty-four hours. Point HPN serves as the main point, located outside the deformation zone. The twenty-four-hour sessions of the HPN-ML4 baseline control point, located outside the deformation zone. The twenty-four-hour sessions of the HPN-ML4 were divided into segments of two, three, four, six, eight, and twelve hours duration. In the two-hour baseline were divided into segments of two, three, four, six, eight, and twelve hours duration. In the segment, the spread of coordinates from 73 sessions was analyzed. In the three-hour segment, the two-hour segment, the spread of coordinates from 73 sessions was analyzed. In the three-hour segment, spread of coordinates from 58 sessions was analyzed. In the four-hour segment, the spread of the spread of coordinates from 58 sessions was analyzed. In the four-hour segment, the spread of coordinates from 29 sessions was analyzed. In the six-hour segment, the spread of coordinates from coordinates24 sessions from was 29analyzed. sessions In was the analyzed. twelve-hour Inthe segment six-hour, the segment, spread of the coordinates spread of coordinatesfrom 13 sessions from 24 sessionswas analyzed. was analyzed. In the twenty In the- twelve-hourfour-hour segment segment,, the the spread spread of of coordinates coordinates from from 18 13 sessions sessions was was analyzed.analyzed. In Figure the twenty-four-hour 3 shows the GPS segment,monitoring the network spread offor coordinates 2013. Baselines from marked 18 sessions in red was belong analyzed. to Figurethe GPS3 shows Control the Network. GPS monitoring Baselines network marked forin blue 2013. represent Baselines the marked observations in red from belong GPS to Control the GPS ControlNetwork Network. points to Baselines GPS Deformation marked inNetwork blue represent points. the observations from GPS Control Network pointsAll to GPS processed Deformation solutions Network have used points. the L1 and L2 frequency. The tropospheric model used was the Saastamoinen model [22] after Bond [4] findings that the Hopfield and Saastamoinen tropospheric models perform the best and are very similar. The Saastamonien model can be written as: 0.002277 1255 푑 = (푃 + ( + 0.05) 푒) (7) 푡푟표푝 sin(휀) 푇 where: Sustainability 2019, 11, 6127 7 of 12
All processed solutions have used the L1 and L2 frequency. The tropospheric model used was the Saastamoinen model [22] after Bond [4] findings that the Hopfield and Saastamoinen tropospheric models perform the best and are very similar. The Saastamonien model can be written as:
0.002277 1255 dtrop = P + + 0.05 e (7) sin(ε) T
where: ε—elevation angle, T—surface temperature (Kelvin), and e—partial water vapor pressure (millibars). Table1 shows the HPN-ML4 baseline characteristics.
Table 1. GPS baseline HPN-ML4.
Coordinate Differences Baseline GPS Baseline Length [m] DN [m] DE [m] DH [m] HPN-ML4 929.840 6136.808 20.325 6206.852 − − −
The Northing and Easting coordinates of point ML4 from the three-hour long sessions are shown in Figure4. In total, 58 three-hour long sessions were analyzed. The spread of Northing coordinates from the mean value is shown in Figure5. The spread of Easting coordinates from the mean value is shown in Figure6. The spread of Height coordinates from the mean value is shown in Figure7. The spread between the maximum and minimum Northing coordinates is 11 mm. The spread between the maximum and minimum Easting coordinates is 18 mm. The spread between the maximum and Sustainability 2019, 11, x FOR PEER REVIEW 8 of 12 minimum Height coordinates is 28 mm. The accuracies of coordinates at the 95% level are listed in Table2.
Figure 4. Coordinates of point ML4 ML4—three-hours—three-hours long sessions.
Figure 5. Point ML4—Spread of the Northing coordinates from the mean value—three-hour long sessions. Sustainability 2019, 11, x FOR PEER REVIEW 8 of 12
Sustainability 2019, 11, 6127 8 of 12 Figure 4. Coordinates of point ML4—three-hours long sessions.
Figure 5. 5. PointPoint ML4 ML4—Spread—Spread of ofthe the Northing Northing coordinate coordinatess from from the mean the mean value value—three-hour—three-hour long Sustainabilitysessions.long sessions. 2019 , 11, x FOR PEER REVIEW 9 of 12
0.012 0.010 0.008 0.006 0.004 0.002 0.000 -0.002 -0.004 -0.006
-0.008 Difference from the mean [m] mean Easting the Difference from -0.010 -0.012 0 2 4 6 8 10 12 14 16 18 20 22 24
Time [hour]
Figure 6. 6. PointPoint ML4—Spread ML4—Spread of the of the Easting Easting coordinates coordinate froms thefrom mean thevalue—three-hour mean value—three long-hour sessions. long sessions.
0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 -0.002 -0.004 -0.006 -0.008
-0.010 Difference from the mean mean Height [m] the Difference from -0.012 -0.014 -0.016 0 2 4 6 8 10 12 14 16 18 20 22 24
Time [hour]
Figure 7. Point ML4—Spread of the Height coordinates from the mean value—three-hour long sessions.
Table 2 shows the comparison of achievable accuracies of single point positioning of point ML4 using GPS surveys with respect to session length. The Northing, Easting, and Height accuracies are at 95% confidence level. Sustainability 2019, 11, x FOR PEER REVIEW 9 of 12
0.012 0.010 0.008 0.006 0.004 0.002 0.000 -0.002 -0.004 -0.006
-0.008 Difference from the mean [m] mean Easting the Difference from -0.010 -0.012 0 2 4 6 8 10 12 14 16 18 20 22 24
Time [hour]
Figure 6. Point ML4—Spread of the Easting coordinates from the mean value—three-hour long Sustainability 2019, 11, 6127 9 of 12 sessions.
0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 -0.002 -0.004 -0.006 -0.008
-0.010 Difference from the mean mean Height [m] the Difference from -0.012 -0.014 -0.016 0 2 4 6 8 10 12 14 16 18 20 22 24
Time [hour]
Figure 7. Figure 7. PointPoint ML4—Spread ML4—Spread of theof the Height Height coordinates coordinate froms thefrom mean the value—three-hour mean value—three long-hour sessions. long sessions. Table 2. Comparison of session lengths and respective accuracies at 95% level.
TableSession 2 shows Length the comparison Sample of Size achievable accuraciesεN [m] of singleεE [m]point positioningεH [m] of point ML4 using GPS surveys2 h with respect to 73 session length. 0.010The Northing, Easting 0.012, and Height 0.022 accuracies are at 95% confidence3 h level. 58 0.006 0.008 0.014 4 h 29 0.006 0.008 0.014 6 h 24 0.004 0.008 0.012 12 h 13 0.002 0.006 0.010 24 h 18 0.002 0.002 0.008
Table2 shows the comparison of achievable accuracies of single point positioning of point ML4 using GPS surveys with respect to session length. The Northing, Easting, and Height accuracies are at 95% confidence level. The analysis of the optimal session duration leads to the conclusion that in order to achieve the sub-cm accuracy of horizontal coordinates at 95% confidence level, the GPS session length should be at least three hours long. In order to achieve the sub-cm accuracy of the height coordinate at 95% confidence level, the GPS session length should be at least twelve hours long.
4.2. Verification of Session Duration In order to verify the GPS session duration, 29 GPS sessions of three-hour duration of baseline HPN-ML26 were analyzed, as seen in Figure8. Table3 shows the characteristics of the analyzed GPS baselines. Figure2 shows the HPN-ML26 baseline. Table4 shows the average coordinates of point ML26 from 29 observation sessions with the corresponding standard deviations. In conclusion, the three-hour long GPS session is long enough to determine the horizontal coordinates of points with an accuracy of 10 mm or better at 95% confidence level. Sustainability 2019, 11, x FOR PEER REVIEW 10 of 12
The analysis of the optimal session duration leads to the conclusion that in order to achieve the sub-cm accuracy of horizontal coordinates at 95% confidence level, the GPS session length should be at least three hours long. In order to achieve the sub-cm accuracy of the height coordinate at 95% confidence level, the GPS session length should be at least twelve hours long.
4.2. Verification of Session Duration In order to verify the GPS session duration, 29 GPS sessions of three-hour duration of baseline HPN-ML26 were analyzed, as seen in Figure 8. Table 3 shows the characteristics of the analyzed GPS baselines. Figure 2 shows the HPN-ML26 baseline. Table 4 shows the average coordinates of point SustainabilityML26 from2019 29, observation11, 6127 sessions with the corresponding standard deviations. In conclusion,10 ofthe 12 three-hour long G
Figure 8. HPN-ML4 and HPN-ML26 baselines.
Table 3. GPS baseline HPN-ML26. Table 3. GPS baseline HPN-ML26. Coordinate Differences Baseline Coordinate Differences GPS Baseline Length [m] DN [m] DE [m] DH [m] Baseline GPS Baseline Length [m] HPN-ML26DN 704.276 [m] DE [m] 2116.624 DH [m] 8.133 2230.731 −
HPN-ML26 Table704.276 4. Coordinates 2116.624 and respective accuracies−8.133 at 95% level of point2230.731 ML26.
Point ML26. Table 4. Coordinates and respective accuracies at 95% level of point ML26. N [m] E [m] H [m] Coordinates Point ML26. 5,073,117.231 316,340.765 40.845 N [m] E [m] H [m] Coordinates εN5,073[m],117.231 εE [m] 316,340.765 εH [m] 40.845 Error at 95% εN [m] εE [m] εH [m] Error at 95% 0.004 0.004 0.008 0.004 0.004 0.008 5. Conclusions 5. Conclusions The accuracy of the monitored surface deformations should allow for the detection of at least The accuracy of the monitored surface deformations should allow for the detection of at least one third of the expected maximum deformations over the desired time span at the 95% probability one third of the expected maximum deformations over the desired time span at the 95% probability level. In surface deformation studies in mining areas, 10 mm accuracy at 95% level in both vertical and horizontal displacements is typically required. The analysis of 58 three-hour long sessions of baseline HPN-ML4 indicated the accuracy of Northing and Easting coordinates of point ML4 as 6 and 8 mm, respectively. The achieved horizontal accuracy of Northings and Eastings of point ML26 after analysis of 29 three-hour long sessions of HPN-ML26 baseline was 4 and 4 mm, respectively. The accuracy of 8 mm for the height component of point ML4 was achieved in twelve-hour long GPS sessions of HPN-ML4 baseline. The analysis of the optimal session duration leads to the conclusion that in order to achieve the sub-cm accuracy of horizontal coordinates at 95% confidence level, the GPS session length should be at least three hours long. In order to achieve the sub-cm accuracy of the height coordinate at 95% confidence level in a single observation session, the GPS session length should be at least twelve hours long. Sustainability 2019, 11, 6127 11 of 12
Author Contributions: Equal contributions by all authors. Funding: Publication of this research is possible by grant nr 049u/0098/19 from the Faculty of Geoengineering, Mining and Geology, Wrocław University of Science and Technology, Wrocław, Poland Conflicts of Interest: The authors declare no conflict of interest.
References
1. Chrzanowski, A. Interdisciplinary Approach to Deformation Monitoring and Analysis. In Presented Papers of the Working Group Sessions, International Union of Surveying and Mapping; Int. Soc. for Photogrammetry and Remote Sensing: Washington, DC, USA, 1993; pp. 9–19. 2. Chrzanowski, A.; Bazanowski, M. Design and Implementation of Ground Monitoring Scheme at PCS Picadilly Mine in New Brunswick, Report submitted to Potash Corporation of Saskatchewan - New Brunswick Division. Internal report, unpublished. 2011. 3. Chrzanowski, A.; Chen, Y.Q.; Leeman, R.; Leal, J. Integration of the Global Positioning System with geodetic leveling surveys in ground subsidence studies. In Proceedings of the 5th International (FIG) Symposium on Deformation Measurements and 5th Canadian Symposium on Mining Surveying and Rock Deformation Measurements, Fredericton, NB, Canada, 6–9 June 1988; Chrzanowski, A., Wells, W., Eds.; pp. 142–155. 4. Bond, J. An Investigation on the Use of GPS for Deformation Monitoring in Open Pit Mines; Department of Geodesy and Geomatics Engineering Technical Report No. 222; University of New Brunswick: Fredericton, NB, Canada, 2004; p. 140. 5. Bond, D.J. Bringing GPS into Harsh Environments for Deformation Monitoring; Department of Geodesy and Geomatics Engineering Technical Report No. 253; University of New Brunswick: Fredericton, NB, Canada, 2007. 6. Rizos, C. Principles and Practice of GPS Surveying. 2001. Available online: http://www.gmat.unsw.edu.au/ snap/gps/gps_survey/principles_gps.htm (accessed on 20 February 2014). 7. Khan, F.A.; Rizos, C.; Dempster, A.G. Locata Performance Evaluation in the Presence of Wide-and Narrow-Band Interference. J. Navig. 2010, 63, 52. [CrossRef] 8. Teunissen, P.J.G.; Montenbruck, O. (Eds.) Springer Handbook of Global Navigation Satellite Systems; Springer: New York, NY, USA, 2017; ISBN 978-3-319-42926-7. 9. Bond, J.; Chrzanowski, A.; Kim, D. Bringing GPS into Harsh Environments for Deformation Monitoring. GPS Solut. 2008, 12, 1–11. [CrossRef] 10. Kleusberg, A.; Langley, R.B. The Limitations of GPS. GPS World, Vol.1, No.2. March/April 1990; 50–52. 11. Seeber, G. Satellite Geodesy, Foundations, Methods, and Applications; Walter de Gruyter: Berlin, Germany, 1993. 12. Hofmann-Wellenhof, B.; Lichtenegger, H.; Collins, J. Global Positioning System: Theory and Practice, 5th ed.; Springer: New York, NY, USA, 2001. 13. Satirapod, C.; Rizos, C. Multipath Mitigation by Wavelet Analysis of GPS Base Station Applications. Surv. Rev. 2005, 38, 2–10. [CrossRef] 14. Bazanowski, M.; Szostak-Chrzanowski, A. Salt Rock Deformations Caused by Mining Activity; Faculty of Geoengineering, Mining and Geology, Wrocław University of Science and Technology: Wrocław, Poland, 2016; p. 157. ISBN 978-83-942205-6-3. 15. Strode, P.R.R.; Groves, P.D. GNSS Multipath Detection using Three-frequency Signal-to-noise Measurements. GPS Solut. 2016, 20, 399–412. [CrossRef] 16. Eckl, M.C.; Snay, R.A.; Sole, T.; Cline, M.W.; Mader, G.L. Accuracy of GPS-derived Relative Positions as a Function of Interstation Distance and Observing-Session Duration. J Geod. 2001, 75, 633–640. [CrossRef] 17. Berber, M.; Ustun, A.; Yetkin, M. Comparison of Accuracy of GPS Techniques. Measurement 2012, 45, 1742–1746. [CrossRef] 18. Firuzabadi, D.; King, R.W. GPS Precision as a Function of Session Duration and Reference Frame Using Multi-Point Software. GPS Solut. 2012, 16, 191–196. [CrossRef] 19. Dogan, U.; Uludag, M.; Demir, D.O. Investigation of GPS Positioning Accuracy During the Seasonal Variation. Measurement 2014, 53, 91–100. [CrossRef] 20. Bond, J.; Chrzanowski, A.; Wilkins, R. Using GPS for Augmenting Deformation Monitoring System in Open Pit Mines–Problems and Solutions. Geomatica 2015, 59, 73–82. Sustainability 2019, 11, 6127 12 of 12
21. Wells, D.E.; Beck, N.; Delikaraoglou, D.; Kleusberg, A.; Krakiwsky, E.J.; Lachapelle, G.; Langley, R.B.; Nakiboglu, M.; Schwarz, K.P.; Tranquilla, J.M.; et al. Guide to GPS Positioning; Canadian GPS Associates: Fredericton, NB, Canada, 1987; ISBN 0-920-114-73-3. 22. Saastamoinen, J. Atmospheric correction for the troposphere and stratosphere in radio ranging of satellites. Use of artificial satellites for geodesy. In Geophysical Monograph 15; American Geophysical Union: Washington, DC, USA, 1972.
© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).