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DEM sourcing guidelines for computing 1 Eö accurate terrain corrections for airborne gravity gradiometry
Journal of Applied Geophysics 136 (2017) 335–342
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DEM sourcing guidelines for computing 1 Eö accurate terrain corrections for airborne gravity gradiometry Maria Annecchione ⁎, David Hatch, Shane W. Hefford Gedex Systems Inc, 407 Matheson Blvd East, Mississauga, Ontario L4Z 2H2, Canada
a r t i c l e
i n f o
Article history: Received 18 November 2015 Received in revised form 6 October 2016 Accepted 9 November 2016 Available online 22 November 2016 Keywords: Gravity gradiometry Terrain correction Eötvös LiDAR SRTM Satellite ranging
a b s t r a c t In this paper we investigate digital elevation model (DEM) sourcing requirements to compute gravity gradiometry terrain corrections accurate to 1 Eötvös (Eö) at observation heights of 80 m or more above ground. Such survey heights are typical in fixed-wing airborne surveying for resource exploration where the maximum signal-to-noise ratio is sought. We consider the accuracy of terrain corrections relevant for recent commercial airborne gravity gradiometry systems operating at the 10 Eö noise level and for future systems with a target noise level of 1 Eö. We focus on the requirements for the vertical gradient of the vertical component of gravity (Gdd) because this element of the gradient tensor is most commonly interpreted qualitatively and quantitatively. Terrain correction accuracy depends on the bare-earth DEM accuracy and spatial resolution. The bare-earth DEM accuracy and spatial resolution depends on its source. Two possible sources are considered: airborne LiDAR and Shuttle Radar Topography Mission (SRTM). The accuracy of an SRTM DEM is affected by vegetation height. The SRTM footprint is also larger and the DEM resolution is thus lower. However, resolution requirements relax as relief decreases. Publicly available LiDAR data and 1 arc-second and 3 arc-second SRTM data were selected over four study areas representing end member cases of vegetation cover and relief. The four study areas are presented as reference material for processing airborne gravity gradiometry data at the 1 Eö noise level with 50 m spatial resolution. From this investigation we find that to achieve 1 Eö accuracy in the terrain correction at 80 m height airborne LiDAR data are required even when terrain relief is a few tens of meters and the vegetation is sparse. However, as satellite ranging technologies progress bare-earth DEMs of sufficient accuracy and resolution may be sourced at lesser cost. We found that a bare-earth DEM of 10 m resolution and 2 m accuracy are sufficient for achieving 1 Eö accuracy in the terrain correction independent of relief or vegetation cover. For AGG systems operating at greater noise levels the 3 arc-second SRTM is adequate for areas having tens of meters of relief and sparse vegetation and even for areas of greater relief and sparse vegetation if a constant elevation survey is flown at 80 m above terrain peak. © 2016 Elsevier B.V. All rights reserved.
1. Introduction In mineral exploration, oil and gas exploration, groundwater applications and void detection, with some consultation with geologists, it is fairly easy to conceive of geological settings that produce gravity gradient responses of less than 10 Eötvös (Eö). This is the motivation behind the quest for the 1 Eö, high spatial resolution (50 m) airborne gravity gradiometer system. The gravity gradient response of the terrain, however, is easily several tens or even hundreds of Eö. The terrain is a part of the geological setting that geophysicists are not interested in interpreting but is closest to the sensor and has the greatest density contrast since its contact is with air. To interpret gravity gradiometry data for the underlying geology at the 1 Eö level it is important to get the terrain correction to better than 1 Eö accuracy. Software considerations ⁎ Corresponding author. E-mail address: [email protected] (M. Annecchione).
http://dx.doi.org/10.1016/j.jappgeo.2016.11.009 0926-9851/© 2016 Elsevier B.V. All rights reserved.
aside, this ultimately rests on the accuracy and spatial resolution at which the bare terrain elevation is known. To date, commercial airborne gravity gradiometry (AGG) systems are not capable of providing high spatial resolution gravity gradiometry data accurate to 1 Eö. As AGG system developers are working to drive data noise toward 1 Eö it is becoming increasingly relevant to have a high degree of confidence that the terrain correction is accurate to this level. Two common sources of terrain elevation data are airborne LiDAR and Shuttle Radar Topography Mission (SRTM). SRTM data are publically available globally at 1 arc-second (nominally 30 m) and 3 arc-second (nominally 90 m) resolution. The SRTM site (http://www2.jpl.nasa.gov/ srtm/statistics.html last accessed Oct. 3, 2016) states as an objective better than 16 m absolute vertical height accuracy for the 1 arc-second data. Over selected areas in the U.S. the U. S. Geological Survey (USGS) has made publically available airborne LiDAR data and airborne LiDAR-
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Table 1 Terrain elevation relief and standard deviation (σ) and vegetation cover in four study areas. Relief and σ are based on 3 arc-sec SRTM terrain models. Study area
Area (km2)
Relief (m)
σ (m)
Vegetation
Rogue River, Oregon Pine County, Minnesota Casper City, Wyoming Pima County, Arizona
1.5 8.4 2.4 2.7
620 20.4 243 65.5
140 3.8 55.8 14.8
Dense trees Dense varied Sparse trees Sparse trees
derived bare-earth digital elevation models (DEM) with 1/9 arc-second (nominally 3 m) resolution. The availability of terrain DEMs at various spatial resolutions and accuracies over the same area provides the opportunity to determine under what conditions of relief and vegetation cover 3 arc-second and 1 arc-second SRTM DEMs will produce terrain corrections good to 1 Eö and under what conditions a bare-earth LiDAR DEM is required to produce a terrain correction good to 1 Eö. The high pulse rate of airborne LiDAR systems enables high resolution bare-earth DEMs to be constructed from those pulses which have penetrated the vegetation. The wavelength of the SRTM pulse does not allow penetration of moderate to dense vegetation. As the vegetation becomes denser there is increasing discrepancy between the LiDAR DEM and the SRTM DEM. Also, as terrain relief becomes significant the spatial resolution of the DEM becomes increasingly important in calculating the terrain response. It is important to know under which conditions of relief and vegetation cover the SRTM DEMs are adequate because the cost of a standard airborne LiDAR survey over a typically-sized AGG survey block is in the hundreds of thousands of dollars. The cost of an airborne LiDAR survey increases as higher resolution and accuracy are required. Alternatively, commercial satellite ranging technologies are progressing to the point where bare-earth DEMs of sufficient accuracy and resolution will become available at much lesser cost. It is thus necessary to know the accuracy and resolution required of satellite ranging technologies to produce a terrain correction good to 1 Eö. Finally it is helpful to know under what conditions 3 arc-second SRTM DEMs are adequate to keep computational requirements at their lowest and to decide whether it is necessary to re-process archived AGG data previously processed utilizing a 3 arc-second SRTM DEM with a 1 arc-second SRTM DEM. We investigate requirements at heights typically flown in surveys for resource exploration. This means the minimum height above ground
allowable for safety reasons (80 m) to get the maximum signal-to-noise ratio. Dransfield and Zeng (2009) test a mathematical model for predicting terrain correction error. Their model relates terrain correction accuracy with terrain DEM error linearly, with observation elevation inversely to the power of α, and with terrain length scale inversely to power α-1. The exponent α relates to the geometry of the terrain features. They test their model utilizing four LiDAR-derived DEMs having 30 m, 50 m and 65 m spatial resolution. These tests allowed them to arrive at values of length scale and α that may be expected for different terrains. Grujic (2012) presents a graph relating survey height with terrain correction error when LiDAR-derived and SRTM-derived DEMs are utilized. However, DEM spatial resolutions and accuracies are not specified and questions of relief and vegetation cover are not addressed. From the graph we should expect uncertainties of 3 Eö with an SRTM-derived DEM and 0.07 Eö with a LiDAR-derived DEM at a height of 80 m. 2. Method The following methodology was applied to help answer the questions posed in the Introduction. First, four rectangular regions were selected: two with higher relief and two with lower relief. Of the two with higher relief, one has dense vegetation and the other has sparse vegetation. The same was done for the two regions with lower relief. Table 1 lists the four study areas selected and their attributes. The terrain attributes were computed from the 3 arc-second SRTM data. The SRTM acquired data in February 2000. The relief is defined here as the difference between the maximum and minimum terrain elevations within the study area. The Rogue River Study Area located in Oregon and the Casper City Study Area located in Wyoming are the two regions having greater relief. The former has dense tree cover while the latter has sparse tree cover. The Pine County Study Area located in Minnesota and the Pima County Study Area located in Arizona are the two regions having lower relief. The former has dense varied vegetation while the latter has sparse tree cover. The airborne LiDAR bare-earth DEM, the 1 arc-second SRTM DEM and the 3 arc-second SRTM DEM were then downloaded over each of the study areas. The bare-earth LiDAR DEMs were downloaded from the USGS The National Map site (Gesch, 2002; Gesch et al., 2007). The SRTM DEMs were downloaded from the USGS Earth Explorer site. The
Fig. 1. Rogue River Study Area, Oregon. (a) Google Earth image showing the dense tree cover. (b) The bare-earth LiDAR DEM. The white dots indicate hypothetical gravity gradiometer observation locations.
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Fig. 2. Rogue River Study Area, Oregon, point cloud LiDAR data and bare-earth LiDAR, 1 arc-sec SRTM and 3 arc-sec SRTM DEMs sampled to point cloud locations.
LiDAR point cloud data were also downloaded from this site. The SRTM DEMs are also available from the USGS The National Map site. The terrain gravity gradient response was then computed at observation points having constant 80 m height from the terrain. We focus our analysis on the vertical gradient of the vertical component of gravity (Gdd) because this element of the gradient tensor is most commonly interpreted qualitatively and quantitatively. A uniform density of 2.67 g/cm3 was assigned to the terrain. A variable density model may be considered. The problem has yet to be addressed, but will become more problematic as data resolution and noise level improve. We feel this task falls into the realm of data interpretation and is beyond the scope of this paper. The effects of increasing height (constant elevation and drape flying) and of terrain density are addressed in the Section 4.1. The gravity gradient terrain correction software, GGterrain, developed by Davis et al. (2010) was utilized. This software discretizes the terrain in right-rectangular prisms of varying size. Terrain that is flat and/or distant from the observation point is discretized more coarsely. The terrain mesh thus changes from one observation point to another. The user supplies the desired terrain correction error and the adaptive mesh is built with the local resolution required to keep the error within the specified tolerance. In this way all prism response calculations that collectively do not contribute meaningfully are eliminated. In this way the computation time is greatly reduced. This optimizing feature is particularly useful when computing the response of high resolution DEMs such as LiDAR DEMs. An independent check on this software is addressed in Section 4.2. Historical gravity gradient data, both public and private, have typically been processed utilizing similar code based on the rightrectangular prism model. We thus thought it appropriate to utilize this software and then assess whether the prismatic model might be introducing numerical inaccuracies. This would help determine whether it is necessary to re-process historical data utilizing a polygonal model approach. For each study area the terrain response was computed utilizing the airborne LiDAR bare-earth DEM, the 1 arc-second SRTM DEM and the 3 arc-second SRTM DEM with a tolerance of 0.1 Eö. This low tolerance ensured that the full resolution of the input DEM was utilized if necessary. The SRTM-based terrain corrections were then compared against the LiDAR-based terrain correction. If the difference is 1 Eö or less we conclude that for that study area the 1 arc-second or 3 arc-second SRTM data are adequate. The need to acquire LiDAR data over an AGG survey block can then be deduced by comparing its terrain attributes against the four study areas. Alternatively, a new study area with matching attributes can be selected and this methodology can be applied to it. Table 2 Standard deviation of the difference between LiDAR and SRTM terrain elevations for the Rogue River Study Area, Oregon. The DEMs were sampled at the LiDAR point cloud locations.
Point Cloud LiDAR Bare-earth LiDAR 1 arc-sec SRTM 3 arc-sec SRTM
Point Cloud LiDAR
Bare-earth LiDAR
1 arc-sec SRTM
0m 11.41 m 12.72 m 14.20 m
– 0m 11.29 m 12.21 m
– – 0m 4.64 m
To check whether a standard airborne LiDAR survey will provide a DEM of sufficient accuracy and resolution, vertical uncertainty is added to the airborne LiDAR DEM and the gravity gradient response is recomputed. If the difference is 1 Eö or less then the bare-earth DEM may be sourced from a standard airborne LiDAR survey. Airborne LiDAR systems provide point cloud densities ranging from 1 to 20 points/m2 and vertical accuracies ranging from 10 to 30 cm (Beaubouef et al. 2005). In standard fixed-wing LiDAR surveys, the point density for ground returns is sufficient to provide a 3 m resolution DEM with better than 50 cm accuracy. Normally-distributed noise of zero mean and 50 cm standard deviation is thus added to the airborne LiDAR DEMs. Finally, to answer the last question posed in the Introduction, the LiDAR DEMs are resampled to coarser resolution and vertical uncertainty is added. Satellite ranging technologies are evolving. Some organizations are claiming they will be able to provide bare-earth DEMs of 2 m accuracy at ~ 10 m resolution. The airborne LiDAR DEMs are thus resampled at 10 m cell size and vertical uncertainty of 2 m is added. The terrain response is recomputed and compared to the original response. This will help to assess whether satellite ranging systems built to these specifications may possibly out-perform more expensive airborne LiDAR surveys. 3. Results 3.1. Rogue River Study Area, Oregon Fig. 1 shows the vegetation cover and terrain elevation over the Rogue River Study Area, Oregon. The study area is in a mountainous region, the Rockies, and measures about 1.1 km by 1.4 km. The vegetation is dense with trees. The relief in the area is 620 m and the standard deviation of terrain elevation is 140 m. We expect this area to require LiDAR data for the terrain correction, but we would like to confirm this and also assess whether a standard fixed-wing LiDAR survey is adequate. These terrain correction calculations will also serve to validate the software in Section 4.2. Fig. 2 shows the discrepancy between terrain elevations according to the bare-earth LiDAR DEM and the SRTM DEMs for a grouping of points. The DEMs were sampled to the LiDAR point cloud locations. The LiDAR point cloud data include pulse returns from the vegetation and the ground. This raw data (acquired in the spring and summer of 2012) were processed by the USGS to obtain the bare-earth DEM. The bareearth point density is ~2 points/m2. The SRTM terrain elevations are systematically greater than the bare-earth LiDAR elevations demonstrating the wavelength of the SRTM pulse does not allow penetration of the vegetation. Table 2 summarizes the elevation differences between the different data sources. The standard deviation of the difference in terrain elevation between the bare-earth LiDAR DEM and the 1 arcsecond SRTM DEM is 11.29 m. Fig. 3a shows the Gdd response of the bare-earth LiDAR DEM. The response was computed at the locations indicated as white dots. As expected, the response is in the hundreds of Eö. Fig. 3b shows the difference in terrain response when the 1 arc-second SRTM DEM is utilized. The standard deviation of the difference at the observation point locations is 36 Eö. The standard deviation of the Gdd difference when
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Fig. 3. (a) Gdd response of bare-earth LiDAR DEM for the Rogue River Study Area, Oregon (Fig. 1). (b) Difference in Gdd response when the 1 arc-sec SRTM DEM is utilized. (c) Difference in Gdd response when 50 cm vertical uncertainty is added to the bare-earth LiDAR DEM. (d) Difference in Gdd response when bare-earth LiDAR DEM is resampled to 10 m and 2 m vertical uncertainty is added.
the 3 arc-second SRTM DEM is utilized (not shown) is about the same: 37 Eö. This indicates that the vegetation cover rather than the pixel size is driving the Gdd difference. We thus confirm that for an area of this level of vegetation cover and relief, SRTM data are not adequate if 1 Eö accuracy is sought in the terrain correction. Fig. 3c shows the difference in terrain response when 50 cm vertical uncertainty is added to the bare-earth LiDAR DEM. The standard deviation of the difference is 0.08 Eö. We conclude that a standard fixed-wing LiDAR survey is more than adequate in an area of significant relief if better than 1 Eö accuracy is sought in the terrain correction. Fig. 3d shows the difference in terrain response when the bare-earth LiDAR DEM is resampled to 10 m and 2 m vertical uncertainty is added. The standard deviation of the difference is 0.84 Eö. Commercial satellite ranging systems of this accuracy and resolution will thus be a good source of less expensive terrain DEMs for high resolution AGG systems operating at the 1 Eö noise level. 3.2. Pine County Study Area, Minnesota Fig. 4a and b show the vegetation cover and terrain elevation over the Pine County Study Area, Minnesota. The LiDAR data were acquired in the fall of 2006. The study area is in a relatively flat region and measures about 2.5 km by 3.5 km. The vegetation is dense and varied. The relief in the area is 20.4 m and the standard deviation of terrain elevation is
3.8 m. We expect the SRTM DEM to be adequate for the terrain correction in this area, but we want to verify this because the vegetation is dense and the discrepancy in terrain elevation relative to the bare-earth LiDAR DEM is not negligible. Table 3 summarizes the elevation differences between the data sources. The standard deviation of the difference in terrain elevation between the bare-earth DEM and the 1 arc-second SRTM DEM is 3 m. The bare-earth point density is ~1 point/m2. Fig. 4c shows the Gdd response of the bare-earth LiDAR DEM. The response was computed at the locations indicated as white dots. The response is in the tens of Eö. Fig. 4d shows the difference in terrain response when the 1 arc-second SRTM DEM is utilized. The standard deviation of the difference is 11.2 Eö. The standard deviation of the Gdd difference when the 3 arc-second SRTM DEM is utilized (not shown) is about the same: 10 Eö. We conclude that if 1 Eö accuracy is sought in the terrain correction, even in an area considered flat SRTM data are inadequate due to dense vegetation. The standard deviation of the difference in terrain response when 50 cm vertical uncertainty is added to the bare-earth LiDAR DEM is 0.06 Eö. A standard fixed-wing LiDAR survey is an excellent source of terrain data in an area of a few tens of meters of relief and dense vegetation if better than 1 Eö accuracy is sought in the terrain correction. When the bare-earth LiDAR DEM is resampled to 10 m and 2 m vertical uncertainty is added the standard deviation of the difference in terrain response is 0.83 Eö. Commercial satellite ranging systems of this
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Fig. 4. Pine County Study Area, Minnesota. (a) Google Earth image showing the dense vegetation. (b) The bare-earth LiDAR DEM. The white dots indicate hypothetical gravity gradiometer observation locations. (c) Gdd response of bare-earth LiDAR DEM. (d) Difference in Gdd response when the 1 arc-sec SRTM DEM is utilized.
accuracy and resolution will thus be a good source of less expensive terrain DEMs for high resolution AGG systems operating at the 1 Eö noise level. 3.3. Casper City Study Area, Wyoming Fig. 5a and b show the vegetation cover and terrain elevation over the Casper City Study Area, Wyoming. The LiDAR data were acquired in the spring of 2010. The study area is located on the edge of a mountainous region and measures about 1.5 km by 1.5 km. The vegetation is relatively sparse. There are some small patches of dense tree cover in the south-western part of the study area. The relief in the area is 243 m and the standard deviation of terrain elevation is 55.8 m.
Table 3 Standard deviation of the difference between LiDAR and SRTM terrain elevations for the Pine County Study Area, Minnesota. The DEMs were sampled at the LiDAR point cloud locations.
Point Cloud LiDAR Bare-earth LiDAR 1 arc-sec SRTM 3 arc-sec SRTM
Point Cloud LiDAR
Bare-earth LiDAR
1 arc-sec SRTM
0m 4.69 m 5.03 m 4.97 m
– 0m 3.01 m 2.74 m
– – 0m 0.85 m
Table 4 summarizes the elevation differences between the data sources. The standard deviation of the difference in terrain elevation between the bare-earth DEM and the 1 arc-second SRTM DEM is 3.3 m. In this case this discrepancy is more due to the larger SRTM footprint and the relief than the vegetation cover. Fig. 5c shows the Gdd response of the bare-earth DEM. The response was computed at the locations indicated as white dots. The response is a few hundred Eö. Fig. 5d shows the difference in terrain response when the 1 arc-second SRTM DEM is utilized. The standard deviation of the difference is 9.2 Eö. The standard deviation of the Gdd difference when the 3 arc-second SRTM DEM is utilized (not shown) is greater: 13.7 Eö. Since the vegetation is sparse in this case, the effect of a coarser DEM is more apparent. We conclude that if 1 Eö accuracy is sought in the terrain correction, even in an area with sparse vegetation SRTM data are inadequate if the relief is a few hundred meters. The standard deviation of the difference in terrain response when 50 cm vertical uncertainty is added to the bare-earth LiDAR DEM is 0.06 Eö. A standard fixed-wing LiDAR survey is an excellent source of terrain data in an area of sparse vegetation and high relief if better than 1 Eö accuracy is sought in the terrain correction. When the bareearth LiDAR DEM is resampled to 10 m and 2 m vertical uncertainty is added, the standard deviation of the difference in terrain response is 0.89 Eö. Again, commercial satellite ranging systems of this accuracy and resolution will be a good alternative.
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Fig. 5. Casper City Study Area, Wyoming. (a) Google Earth image showing the sparse vegetation. (b) The bare-earth LiDAR DEM. The white dots indicate hypothetical gravity gradiometer observation locations. (c) Gdd response of bare-earth LiDAR DEM. (d) Difference in Gdd response when the 1 arc-sec SRTM DEM is utilized.
3.4. Pima County Study Area, Arizona Fig. 6a and b show the vegetation cover and terrain elevation over the Pima County Study Area, Arizona. The LiDAR data were acquired in the spring of 2011. The study area is located in a flat to hilly region and measures about 1.6 km by 1.6 km. The vegetation is relatively sparse with trees throughout. The relief in the area is 65.5 m and the standard deviation of terrain elevation is 14.8 m. Table 5 summarizes the elevation differences between the data sources. The standard deviation of the difference in terrain elevation between the bare-earth DEM and the 1 arc-second SRTM DEM is 1.16 m. Fig. 6c shows the Gdd response of the bare-earth DEM. The response was computed at the locations indicated as white dots. The response is a few tens of Eö. Fig. 6d shows the difference in terrain response when the 1 arc-second SRTM DEM is utilized. The standard deviation of the difference is 4 Eö. The standard deviation of the Gdd difference when the 3 arc-second SRTM DEM is utilized (not shown) is about the same: 3.6 Eö. Since the vegetation is sparse and the relief is low in this case,
Table 4 Standard deviation of the difference between LiDAR and SRTM terrain elevations for the Casper City Study Area, Wyoming. The DEMs were sampled at the LiDAR point cloud locations.
Point Cloud LiDAR Bare-earth LiDAR 1 arc-sec SRTM 3 arc-sec SRTM
Point Cloud LiDAR
Bare-earth LiDAR
1 arc-sec SRTM
0m 1.64 m 3.27 m 4.63 m
– 0m 3.32 m 4.58 m
– – 0m 2.70 m
the effect of a coarser DEM is not apparent. We conclude that if 1 Eö accuracy is sought in the terrain correction, SRTM data are inadequate even if the vegetation is sparse and the relief is a few tens of meters. The standard deviation of the difference in terrain response when 50 cm vertical uncertainty is added to the bare-earth LiDAR DEM is 0.11 Eö. A standard fixed-wing LiDAR survey is an excellent source of terrain data in an area of sparse vegetation and low relief if better than 1 Eö accuracy is sought in the terrain correction. When the bareearth LiDAR DEM is resampled to 10 m and 2 m vertical uncertainty is added the standard deviation of the difference in terrain response is 0.90 Eö. Again, commercial satellite ranging systems of this accuracy and resolution will be a good alternative.
4. Discussion 4.1. The effect of observation point height and terrain density The case studies illustrate that the accuracy and resolution of 1 and 3 arc-second SRTM data would contribute unacceptable terrain correction error to airborne gravity gradiometer data of 1 Eö noise for practically any terrain relief or vegetation cover. The terrain correction is linearly dependent on density so the effect of varying the terrain density is easy to assess. For example, using a terrain density of 1.34 g/cm3 for the Pima County Study Area would reduce the Gdd difference to ~2 Eö. If this is acceptable to the geophysical data interpreter then the 3 arc-second SRTM DEM is good enough for any area with similar attributes. Using a terrain density of 2.2 g/cm3 for the Casper City Study Area would reduce the Gdd difference to 7.6 Eö. If this is acceptable given the
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Fig. 6. Pima County Study Area, Arizona. (a) Google Earth image showing the sparse vegetation. (b) The bare-earth LiDAR DEM. The white dots indicate hypothetical gravity gradiometer observation locations. (c) Gdd response of bare-earth DEM. (d) Difference in Gdd response when the 1 arc-sec SRTM DEM is utilized.
noise level of the AGG system then the 1 arc-second SRTM DEM is good enough for an area with similar attributes. The constant observation point height of 80 m represents the closest the AGG system may be flown to the terrain with a fixed-wing aircraft in resource applications, and therefore provides the most stringent requirements of DEM accuracy and resolution. In areas of moderate to high relief a loose drape would typically be flown to maintain safety and AGG performance, meaning that much of the data will be collected at heights greater than 80 m. The limiting case is a survey flown at constant elevation above sea-level, at a height 80 m above the highest peak. To assess the effect of increasing height on relaxing the requirement for LiDAR data, the Gdd difference grids were upward continued from “drape” to constant elevation 80 m above the terrain peak. The upward continued grids were then sampled at the observation point locations. Table 6 lists the adjusted Gdd differences. The original values at constant 80 m height are also listed for comparison in parentheses. In Table 7 the terrain density was reduced to 2.2 g/cm3. The Gdd difference is not reduced to 1 Eö or less for any of the cases evaluated.
For AGG systems operating at ~ 10 Eö noise level, the 3 arc-second SRTM is adequate for areas of low relief and sparse vegetation similar to the Pima County Study Area. Since the SRTM DEMs are somewhat coarser than the LiDAR DEM, we performed a noise check on the 1 arc-second and 3 arc-second SRTM for this study area. A vertical uncertainty of 1 m (Table 5) was added to the SRTM DEMs and the terrain responses were recomputed. For the 1 arc-second DEM the 1 m noise sensitivity is 1.2 Eö. For the 3 arc-second DEM the 1 m noise sensitivity is 3.2 Eö. This is acceptable for an AGG system operating at the ~10 Eö noise level. Note that for such AGG systems, if a constant elevation survey is flown, the 3 arc-second SRTM is also adequate for areas of greater relief and sparse vegetation similar to the Casper City Study Area. In this case the Gdd difference is a few Eö.
Table 5 Standard deviation of the difference between LiDAR and SRTM terrain elevations for the Pima County Study Area, Arizona. The DEMs were sampled at the LiDAR point cloud locations.
Table 6 Standard deviation of Gdd differences when the observation points are at constant elevation 80 m above terrain peak. The values in parentheses are Gdd differences when the observation points are at constant 80 m height above ground. Terrain density: 2.67 g/cm3.
Point Cloud LiDAR Bare-earth LiDAR 1 arc-sec SRTM 3 arc-sec SRTM
4.2. Software validation The elemental volume utilized to compute the terrain response in GGterrain is the right-rectangular prism. This type of discretization
Point Cloud LiDAR
Bare-earth LiDAR
1 arc-sec SRTM
Study area
1 arc-second SRTM DEM
3 arc-second SRTM DEM
0m 0.66 m 1.31 m 1.11 m
– 0m 1.16 m 0.93 m
– – 0m 0.70 m
Rogue River, Oregon Pine County, Minnesota Casper City, Wyoming Pima County, Arizona
22.9 Eö (36.1 Eö) 9.9 Eö (11.2 Eö) 2.9 Eö (9.2 Eö) 2.4 Eö (4 Eö)
19.4 Eö (36.8 Eö) 9.0 Eö (10 Eö) 3.7 Eö (13.7 Eö) 2.2 Eö (3.6 Eö)
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Table 7 Standard deviation of Gdd differences when the observation points are at constant elevation 80 m above terrain peak. The values in parentheses are Gdd differences when the observation points are at constant 80 m height above ground. Terrain density: 2.2 g/cm3. Study Area
1 arc-second SRTM DEM
3 arc-second SRTM DEM
Rogue River, Oregon Pine County, Minnesota Casper City, Wyoming Pima County, Arizona
18.9 Eö (29.7 Eö) 8.2 Eö (9.2 Eö) 2.4 Eö (7.6 Eö) 2 Eö (3.3 Eö)
16 Eö (30.3 Eö) 7.4 Eö (8.2 Eö) 3 Eö (11.3 Eö) 1.8 Eö (3 Eö)
results in steps across adjacent prisms. Given our stringent 1 Eö accuracy requirement for the terrain correction we want to verify that this type of discretization is not introducing non-negligible errors in our terrain correction and that our recommendations are not altered by these software considerations. To this end, terrain correction software based on the arbitrary polyhedron was developed. At its core is the code of Tsoulis (2012), polyhedron.f. In this representation of the terrain there are no discontinuities between the elemental volumes making up the terrain model. To validate the software the terrain corrections for the Rogue River Study Area (the area with greatest relief) were recomputed at 80 m constant height with 2.67 g/cm3 terrain density utilizing the polyhedrabased software. The outputs were then compared to the GGterrain outputs. When the LiDAR DEM is utilized the error is negligible. The standard deviation of the difference is 0.06 Eö. When the 1 arc-second SRTM DEM is utilized the error is acceptable (0.95 Eö). When the 3 arc-second SRTM DEM is utilized the error is unacceptable. The standard deviation of the difference is 10.52 Eö. Note that this does not affect our recommendation to source LiDAR data for areas of such relief and vegetation cover because the Gdd differences in Tables 6 and 7 are 1.5 times to 3.5 times greater than this for this study area. It is not advised to compute the terrain correction from the 3 arc-second SRTM DEM in this case anyway. Finally, the same software validation was performed for the area we might be considering utilizing the 3 arc-second SRTM DEM. For the Pima County Study Area the software-related Gdd difference is 0.59 Eö when the 3 arc-second SRTM DEM is utilized. Comparing this value with that in Table 6 (3.6 Eö), this is not enough to alter the recommendation to source LiDAR data if 1 Eö accuracy is sought. 5. Conclusions One of the more fundamental questions that should be addressed when attempting high resolution gravity gradiometry at 1 Eö accuracy is whether a bare-earth DEM of adequate resolution and accuracy to compute a terrain correction good to 1 Eö is available or can be acquired. We found that a bare-earth DEM of 10 m spatial resolution and 2 m vertical uncertainty is sufficient for generating a terrain correction of this accuracy at 80 m height. The terrain correction in this case is good to ~1 Eö regardless of terrain relief or vegetation cover. At present a standard fixed-wing LiDAR survey provides a terrain DEM with better
resolution and accuracy at considerable cost. Commercial satellite ranging systems are claiming to achieve this resolution and accuracy at moderate cost. A second question is whether we can forgo the expense of an airborne LiDAR survey or a satellite ranging mission if the terrain relief is low or the vegetation is sparse. The four area studies compared SRTMderived terrain corrections against LiDAR-derived terrain corrections for terrains having very different relief and vegetation cover. We found that the SRTM DEMs do not provide adequate spatial resolution and accuracy even when the terrain is relatively flat and the vegetation is sparse. This stringent requirement for commercially sourced DEMs quickly falls away however for AGG systems operating at the ~ 10 Eö noise level. We found that in an area of sparse vegetation and relatively low relief of a few tens of meters the 3 arc-second (~ 90 m) SRTM DEM will produce a terrain correction good to a few Eö. Areas of greater relief or vegetation cover should ideally be assessed on a case-by-case basis by selecting a study area with similar attributes for which LiDAR data are publically available and adjusting the terrain correction accuracy for terrain density and height. Acknowledgements The LiDAR and SRTM data utilized in this study are available from the U.S. Geological Survey. The terrain correction software GGterrain was developed by the Center for Gravity, Electrical, and Electromagnetic Studies (CGEM) for the sponsors of the Gravity and Magnetics Research Consortium (GMRC), Copyright 2010, The Colorado School of Mines. The Society of Exploration Geophysicists (SEG) owns worldwide copyright of the code polyhedron.f, (c) 2012. Polyhedron.f was downloaded at http://software.seg.org/2012/0001. References Beaubouef, T., Wagaman, M., Sfara, R., FitzMaurice, M., 2005. Use of airborne LiDAR in the full cycle of onshore hydrocarbon exploration: a legacy dataset. SEG Technical Program Expanded Abstracts. 2005:pp. 60–63. http://dx.doi.org/10.1190/1.2144396. Davis, K., Kass, M., Li, Y., 2010. Rapid gravity and gravity gradiometry terrain correction via adaptive quadtree mesh discretization. SEG Technical Program Expanded Abstracts. 2010:pp. 1789–1793. http://dx.doi.org/10.1190/1.3513189. Dransfield, M., Zeng, Y., 2009. Airborne gravity gradiometry: terrain corrections and elevation error. Geophysics 74 (5):I37–I42. http://dx.doi.org/10.1190/1.3170688. Gesch, D.B., 2007. The National Elevation Dataset. In: Maune, D. (Ed.), Digital Elevation Model Technologies and Applications: The DEM Users Manual, second ed. American Society for Photogrammetry and Remote Sensing, Bethesda, Maryland, pp. 99–118. Gesch, D., Oimoen, M., Greenlee, S., Nelson, C., Steuck, M., Tyler, D., 2002. The National Elevation Dataset. Photogramm. Eng. Remote. Sens. 68 (1), 5–11. Grujic, M., 2012. Data processing requirements for an 1 Eö/√Hz AGG system: ASEG Extended Abstracts 2012. 22nd Geophysical Conference. 1-4. http://dx.doi.org/10. 1071/ASEG2012ab075. Tsoulis, D., 2012. Analytical computation of the full gravity tensor of a homogeneous arbitrarily shaped polyhedral source using line integrals. Geophysics 77 (2):F1–F11. http://dx.doi.org/10.1190/GEO2010-0334.1.
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Journal of Applied Geophysics journal homepage: www.elsevier.com/locate/jappgeo
DEM sourcing guidelines for computing 1 Eö accurate terrain corrections for airborne gravity gradiometry Maria Annecchione ⁎, David Hatch, Shane W. Hefford Gedex Systems Inc, 407 Matheson Blvd East, Mississauga, Ontario L4Z 2H2, Canada
a r t i c l e
i n f o
Article history: Received 18 November 2015 Received in revised form 6 October 2016 Accepted 9 November 2016 Available online 22 November 2016 Keywords: Gravity gradiometry Terrain correction Eötvös LiDAR SRTM Satellite ranging
a b s t r a c t In this paper we investigate digital elevation model (DEM) sourcing requirements to compute gravity gradiometry terrain corrections accurate to 1 Eötvös (Eö) at observation heights of 80 m or more above ground. Such survey heights are typical in fixed-wing airborne surveying for resource exploration where the maximum signal-to-noise ratio is sought. We consider the accuracy of terrain corrections relevant for recent commercial airborne gravity gradiometry systems operating at the 10 Eö noise level and for future systems with a target noise level of 1 Eö. We focus on the requirements for the vertical gradient of the vertical component of gravity (Gdd) because this element of the gradient tensor is most commonly interpreted qualitatively and quantitatively. Terrain correction accuracy depends on the bare-earth DEM accuracy and spatial resolution. The bare-earth DEM accuracy and spatial resolution depends on its source. Two possible sources are considered: airborne LiDAR and Shuttle Radar Topography Mission (SRTM). The accuracy of an SRTM DEM is affected by vegetation height. The SRTM footprint is also larger and the DEM resolution is thus lower. However, resolution requirements relax as relief decreases. Publicly available LiDAR data and 1 arc-second and 3 arc-second SRTM data were selected over four study areas representing end member cases of vegetation cover and relief. The four study areas are presented as reference material for processing airborne gravity gradiometry data at the 1 Eö noise level with 50 m spatial resolution. From this investigation we find that to achieve 1 Eö accuracy in the terrain correction at 80 m height airborne LiDAR data are required even when terrain relief is a few tens of meters and the vegetation is sparse. However, as satellite ranging technologies progress bare-earth DEMs of sufficient accuracy and resolution may be sourced at lesser cost. We found that a bare-earth DEM of 10 m resolution and 2 m accuracy are sufficient for achieving 1 Eö accuracy in the terrain correction independent of relief or vegetation cover. For AGG systems operating at greater noise levels the 3 arc-second SRTM is adequate for areas having tens of meters of relief and sparse vegetation and even for areas of greater relief and sparse vegetation if a constant elevation survey is flown at 80 m above terrain peak. © 2016 Elsevier B.V. All rights reserved.
1. Introduction In mineral exploration, oil and gas exploration, groundwater applications and void detection, with some consultation with geologists, it is fairly easy to conceive of geological settings that produce gravity gradient responses of less than 10 Eötvös (Eö). This is the motivation behind the quest for the 1 Eö, high spatial resolution (50 m) airborne gravity gradiometer system. The gravity gradient response of the terrain, however, is easily several tens or even hundreds of Eö. The terrain is a part of the geological setting that geophysicists are not interested in interpreting but is closest to the sensor and has the greatest density contrast since its contact is with air. To interpret gravity gradiometry data for the underlying geology at the 1 Eö level it is important to get the terrain correction to better than 1 Eö accuracy. Software considerations ⁎ Corresponding author. E-mail address: [email protected] (M. Annecchione).
http://dx.doi.org/10.1016/j.jappgeo.2016.11.009 0926-9851/© 2016 Elsevier B.V. All rights reserved.
aside, this ultimately rests on the accuracy and spatial resolution at which the bare terrain elevation is known. To date, commercial airborne gravity gradiometry (AGG) systems are not capable of providing high spatial resolution gravity gradiometry data accurate to 1 Eö. As AGG system developers are working to drive data noise toward 1 Eö it is becoming increasingly relevant to have a high degree of confidence that the terrain correction is accurate to this level. Two common sources of terrain elevation data are airborne LiDAR and Shuttle Radar Topography Mission (SRTM). SRTM data are publically available globally at 1 arc-second (nominally 30 m) and 3 arc-second (nominally 90 m) resolution. The SRTM site (http://www2.jpl.nasa.gov/ srtm/statistics.html last accessed Oct. 3, 2016) states as an objective better than 16 m absolute vertical height accuracy for the 1 arc-second data. Over selected areas in the U.S. the U. S. Geological Survey (USGS) has made publically available airborne LiDAR data and airborne LiDAR-
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Table 1 Terrain elevation relief and standard deviation (σ) and vegetation cover in four study areas. Relief and σ are based on 3 arc-sec SRTM terrain models. Study area
Area (km2)
Relief (m)
σ (m)
Vegetation
Rogue River, Oregon Pine County, Minnesota Casper City, Wyoming Pima County, Arizona
1.5 8.4 2.4 2.7
620 20.4 243 65.5
140 3.8 55.8 14.8
Dense trees Dense varied Sparse trees Sparse trees
derived bare-earth digital elevation models (DEM) with 1/9 arc-second (nominally 3 m) resolution. The availability of terrain DEMs at various spatial resolutions and accuracies over the same area provides the opportunity to determine under what conditions of relief and vegetation cover 3 arc-second and 1 arc-second SRTM DEMs will produce terrain corrections good to 1 Eö and under what conditions a bare-earth LiDAR DEM is required to produce a terrain correction good to 1 Eö. The high pulse rate of airborne LiDAR systems enables high resolution bare-earth DEMs to be constructed from those pulses which have penetrated the vegetation. The wavelength of the SRTM pulse does not allow penetration of moderate to dense vegetation. As the vegetation becomes denser there is increasing discrepancy between the LiDAR DEM and the SRTM DEM. Also, as terrain relief becomes significant the spatial resolution of the DEM becomes increasingly important in calculating the terrain response. It is important to know under which conditions of relief and vegetation cover the SRTM DEMs are adequate because the cost of a standard airborne LiDAR survey over a typically-sized AGG survey block is in the hundreds of thousands of dollars. The cost of an airborne LiDAR survey increases as higher resolution and accuracy are required. Alternatively, commercial satellite ranging technologies are progressing to the point where bare-earth DEMs of sufficient accuracy and resolution will become available at much lesser cost. It is thus necessary to know the accuracy and resolution required of satellite ranging technologies to produce a terrain correction good to 1 Eö. Finally it is helpful to know under what conditions 3 arc-second SRTM DEMs are adequate to keep computational requirements at their lowest and to decide whether it is necessary to re-process archived AGG data previously processed utilizing a 3 arc-second SRTM DEM with a 1 arc-second SRTM DEM. We investigate requirements at heights typically flown in surveys for resource exploration. This means the minimum height above ground
allowable for safety reasons (80 m) to get the maximum signal-to-noise ratio. Dransfield and Zeng (2009) test a mathematical model for predicting terrain correction error. Their model relates terrain correction accuracy with terrain DEM error linearly, with observation elevation inversely to the power of α, and with terrain length scale inversely to power α-1. The exponent α relates to the geometry of the terrain features. They test their model utilizing four LiDAR-derived DEMs having 30 m, 50 m and 65 m spatial resolution. These tests allowed them to arrive at values of length scale and α that may be expected for different terrains. Grujic (2012) presents a graph relating survey height with terrain correction error when LiDAR-derived and SRTM-derived DEMs are utilized. However, DEM spatial resolutions and accuracies are not specified and questions of relief and vegetation cover are not addressed. From the graph we should expect uncertainties of 3 Eö with an SRTM-derived DEM and 0.07 Eö with a LiDAR-derived DEM at a height of 80 m. 2. Method The following methodology was applied to help answer the questions posed in the Introduction. First, four rectangular regions were selected: two with higher relief and two with lower relief. Of the two with higher relief, one has dense vegetation and the other has sparse vegetation. The same was done for the two regions with lower relief. Table 1 lists the four study areas selected and their attributes. The terrain attributes were computed from the 3 arc-second SRTM data. The SRTM acquired data in February 2000. The relief is defined here as the difference between the maximum and minimum terrain elevations within the study area. The Rogue River Study Area located in Oregon and the Casper City Study Area located in Wyoming are the two regions having greater relief. The former has dense tree cover while the latter has sparse tree cover. The Pine County Study Area located in Minnesota and the Pima County Study Area located in Arizona are the two regions having lower relief. The former has dense varied vegetation while the latter has sparse tree cover. The airborne LiDAR bare-earth DEM, the 1 arc-second SRTM DEM and the 3 arc-second SRTM DEM were then downloaded over each of the study areas. The bare-earth LiDAR DEMs were downloaded from the USGS The National Map site (Gesch, 2002; Gesch et al., 2007). The SRTM DEMs were downloaded from the USGS Earth Explorer site. The
Fig. 1. Rogue River Study Area, Oregon. (a) Google Earth image showing the dense tree cover. (b) The bare-earth LiDAR DEM. The white dots indicate hypothetical gravity gradiometer observation locations.
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Fig. 2. Rogue River Study Area, Oregon, point cloud LiDAR data and bare-earth LiDAR, 1 arc-sec SRTM and 3 arc-sec SRTM DEMs sampled to point cloud locations.
LiDAR point cloud data were also downloaded from this site. The SRTM DEMs are also available from the USGS The National Map site. The terrain gravity gradient response was then computed at observation points having constant 80 m height from the terrain. We focus our analysis on the vertical gradient of the vertical component of gravity (Gdd) because this element of the gradient tensor is most commonly interpreted qualitatively and quantitatively. A uniform density of 2.67 g/cm3 was assigned to the terrain. A variable density model may be considered. The problem has yet to be addressed, but will become more problematic as data resolution and noise level improve. We feel this task falls into the realm of data interpretation and is beyond the scope of this paper. The effects of increasing height (constant elevation and drape flying) and of terrain density are addressed in the Section 4.1. The gravity gradient terrain correction software, GGterrain, developed by Davis et al. (2010) was utilized. This software discretizes the terrain in right-rectangular prisms of varying size. Terrain that is flat and/or distant from the observation point is discretized more coarsely. The terrain mesh thus changes from one observation point to another. The user supplies the desired terrain correction error and the adaptive mesh is built with the local resolution required to keep the error within the specified tolerance. In this way all prism response calculations that collectively do not contribute meaningfully are eliminated. In this way the computation time is greatly reduced. This optimizing feature is particularly useful when computing the response of high resolution DEMs such as LiDAR DEMs. An independent check on this software is addressed in Section 4.2. Historical gravity gradient data, both public and private, have typically been processed utilizing similar code based on the rightrectangular prism model. We thus thought it appropriate to utilize this software and then assess whether the prismatic model might be introducing numerical inaccuracies. This would help determine whether it is necessary to re-process historical data utilizing a polygonal model approach. For each study area the terrain response was computed utilizing the airborne LiDAR bare-earth DEM, the 1 arc-second SRTM DEM and the 3 arc-second SRTM DEM with a tolerance of 0.1 Eö. This low tolerance ensured that the full resolution of the input DEM was utilized if necessary. The SRTM-based terrain corrections were then compared against the LiDAR-based terrain correction. If the difference is 1 Eö or less we conclude that for that study area the 1 arc-second or 3 arc-second SRTM data are adequate. The need to acquire LiDAR data over an AGG survey block can then be deduced by comparing its terrain attributes against the four study areas. Alternatively, a new study area with matching attributes can be selected and this methodology can be applied to it. Table 2 Standard deviation of the difference between LiDAR and SRTM terrain elevations for the Rogue River Study Area, Oregon. The DEMs were sampled at the LiDAR point cloud locations.
Point Cloud LiDAR Bare-earth LiDAR 1 arc-sec SRTM 3 arc-sec SRTM
Point Cloud LiDAR
Bare-earth LiDAR
1 arc-sec SRTM
0m 11.41 m 12.72 m 14.20 m
– 0m 11.29 m 12.21 m
– – 0m 4.64 m
To check whether a standard airborne LiDAR survey will provide a DEM of sufficient accuracy and resolution, vertical uncertainty is added to the airborne LiDAR DEM and the gravity gradient response is recomputed. If the difference is 1 Eö or less then the bare-earth DEM may be sourced from a standard airborne LiDAR survey. Airborne LiDAR systems provide point cloud densities ranging from 1 to 20 points/m2 and vertical accuracies ranging from 10 to 30 cm (Beaubouef et al. 2005). In standard fixed-wing LiDAR surveys, the point density for ground returns is sufficient to provide a 3 m resolution DEM with better than 50 cm accuracy. Normally-distributed noise of zero mean and 50 cm standard deviation is thus added to the airborne LiDAR DEMs. Finally, to answer the last question posed in the Introduction, the LiDAR DEMs are resampled to coarser resolution and vertical uncertainty is added. Satellite ranging technologies are evolving. Some organizations are claiming they will be able to provide bare-earth DEMs of 2 m accuracy at ~ 10 m resolution. The airborne LiDAR DEMs are thus resampled at 10 m cell size and vertical uncertainty of 2 m is added. The terrain response is recomputed and compared to the original response. This will help to assess whether satellite ranging systems built to these specifications may possibly out-perform more expensive airborne LiDAR surveys. 3. Results 3.1. Rogue River Study Area, Oregon Fig. 1 shows the vegetation cover and terrain elevation over the Rogue River Study Area, Oregon. The study area is in a mountainous region, the Rockies, and measures about 1.1 km by 1.4 km. The vegetation is dense with trees. The relief in the area is 620 m and the standard deviation of terrain elevation is 140 m. We expect this area to require LiDAR data for the terrain correction, but we would like to confirm this and also assess whether a standard fixed-wing LiDAR survey is adequate. These terrain correction calculations will also serve to validate the software in Section 4.2. Fig. 2 shows the discrepancy between terrain elevations according to the bare-earth LiDAR DEM and the SRTM DEMs for a grouping of points. The DEMs were sampled to the LiDAR point cloud locations. The LiDAR point cloud data include pulse returns from the vegetation and the ground. This raw data (acquired in the spring and summer of 2012) were processed by the USGS to obtain the bare-earth DEM. The bareearth point density is ~2 points/m2. The SRTM terrain elevations are systematically greater than the bare-earth LiDAR elevations demonstrating the wavelength of the SRTM pulse does not allow penetration of the vegetation. Table 2 summarizes the elevation differences between the different data sources. The standard deviation of the difference in terrain elevation between the bare-earth LiDAR DEM and the 1 arcsecond SRTM DEM is 11.29 m. Fig. 3a shows the Gdd response of the bare-earth LiDAR DEM. The response was computed at the locations indicated as white dots. As expected, the response is in the hundreds of Eö. Fig. 3b shows the difference in terrain response when the 1 arc-second SRTM DEM is utilized. The standard deviation of the difference at the observation point locations is 36 Eö. The standard deviation of the Gdd difference when
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Fig. 3. (a) Gdd response of bare-earth LiDAR DEM for the Rogue River Study Area, Oregon (Fig. 1). (b) Difference in Gdd response when the 1 arc-sec SRTM DEM is utilized. (c) Difference in Gdd response when 50 cm vertical uncertainty is added to the bare-earth LiDAR DEM. (d) Difference in Gdd response when bare-earth LiDAR DEM is resampled to 10 m and 2 m vertical uncertainty is added.
the 3 arc-second SRTM DEM is utilized (not shown) is about the same: 37 Eö. This indicates that the vegetation cover rather than the pixel size is driving the Gdd difference. We thus confirm that for an area of this level of vegetation cover and relief, SRTM data are not adequate if 1 Eö accuracy is sought in the terrain correction. Fig. 3c shows the difference in terrain response when 50 cm vertical uncertainty is added to the bare-earth LiDAR DEM. The standard deviation of the difference is 0.08 Eö. We conclude that a standard fixed-wing LiDAR survey is more than adequate in an area of significant relief if better than 1 Eö accuracy is sought in the terrain correction. Fig. 3d shows the difference in terrain response when the bare-earth LiDAR DEM is resampled to 10 m and 2 m vertical uncertainty is added. The standard deviation of the difference is 0.84 Eö. Commercial satellite ranging systems of this accuracy and resolution will thus be a good source of less expensive terrain DEMs for high resolution AGG systems operating at the 1 Eö noise level. 3.2. Pine County Study Area, Minnesota Fig. 4a and b show the vegetation cover and terrain elevation over the Pine County Study Area, Minnesota. The LiDAR data were acquired in the fall of 2006. The study area is in a relatively flat region and measures about 2.5 km by 3.5 km. The vegetation is dense and varied. The relief in the area is 20.4 m and the standard deviation of terrain elevation is
3.8 m. We expect the SRTM DEM to be adequate for the terrain correction in this area, but we want to verify this because the vegetation is dense and the discrepancy in terrain elevation relative to the bare-earth LiDAR DEM is not negligible. Table 3 summarizes the elevation differences between the data sources. The standard deviation of the difference in terrain elevation between the bare-earth DEM and the 1 arc-second SRTM DEM is 3 m. The bare-earth point density is ~1 point/m2. Fig. 4c shows the Gdd response of the bare-earth LiDAR DEM. The response was computed at the locations indicated as white dots. The response is in the tens of Eö. Fig. 4d shows the difference in terrain response when the 1 arc-second SRTM DEM is utilized. The standard deviation of the difference is 11.2 Eö. The standard deviation of the Gdd difference when the 3 arc-second SRTM DEM is utilized (not shown) is about the same: 10 Eö. We conclude that if 1 Eö accuracy is sought in the terrain correction, even in an area considered flat SRTM data are inadequate due to dense vegetation. The standard deviation of the difference in terrain response when 50 cm vertical uncertainty is added to the bare-earth LiDAR DEM is 0.06 Eö. A standard fixed-wing LiDAR survey is an excellent source of terrain data in an area of a few tens of meters of relief and dense vegetation if better than 1 Eö accuracy is sought in the terrain correction. When the bare-earth LiDAR DEM is resampled to 10 m and 2 m vertical uncertainty is added the standard deviation of the difference in terrain response is 0.83 Eö. Commercial satellite ranging systems of this
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Fig. 4. Pine County Study Area, Minnesota. (a) Google Earth image showing the dense vegetation. (b) The bare-earth LiDAR DEM. The white dots indicate hypothetical gravity gradiometer observation locations. (c) Gdd response of bare-earth LiDAR DEM. (d) Difference in Gdd response when the 1 arc-sec SRTM DEM is utilized.
accuracy and resolution will thus be a good source of less expensive terrain DEMs for high resolution AGG systems operating at the 1 Eö noise level. 3.3. Casper City Study Area, Wyoming Fig. 5a and b show the vegetation cover and terrain elevation over the Casper City Study Area, Wyoming. The LiDAR data were acquired in the spring of 2010. The study area is located on the edge of a mountainous region and measures about 1.5 km by 1.5 km. The vegetation is relatively sparse. There are some small patches of dense tree cover in the south-western part of the study area. The relief in the area is 243 m and the standard deviation of terrain elevation is 55.8 m.
Table 3 Standard deviation of the difference between LiDAR and SRTM terrain elevations for the Pine County Study Area, Minnesota. The DEMs were sampled at the LiDAR point cloud locations.
Point Cloud LiDAR Bare-earth LiDAR 1 arc-sec SRTM 3 arc-sec SRTM
Point Cloud LiDAR
Bare-earth LiDAR
1 arc-sec SRTM
0m 4.69 m 5.03 m 4.97 m
– 0m 3.01 m 2.74 m
– – 0m 0.85 m
Table 4 summarizes the elevation differences between the data sources. The standard deviation of the difference in terrain elevation between the bare-earth DEM and the 1 arc-second SRTM DEM is 3.3 m. In this case this discrepancy is more due to the larger SRTM footprint and the relief than the vegetation cover. Fig. 5c shows the Gdd response of the bare-earth DEM. The response was computed at the locations indicated as white dots. The response is a few hundred Eö. Fig. 5d shows the difference in terrain response when the 1 arc-second SRTM DEM is utilized. The standard deviation of the difference is 9.2 Eö. The standard deviation of the Gdd difference when the 3 arc-second SRTM DEM is utilized (not shown) is greater: 13.7 Eö. Since the vegetation is sparse in this case, the effect of a coarser DEM is more apparent. We conclude that if 1 Eö accuracy is sought in the terrain correction, even in an area with sparse vegetation SRTM data are inadequate if the relief is a few hundred meters. The standard deviation of the difference in terrain response when 50 cm vertical uncertainty is added to the bare-earth LiDAR DEM is 0.06 Eö. A standard fixed-wing LiDAR survey is an excellent source of terrain data in an area of sparse vegetation and high relief if better than 1 Eö accuracy is sought in the terrain correction. When the bareearth LiDAR DEM is resampled to 10 m and 2 m vertical uncertainty is added, the standard deviation of the difference in terrain response is 0.89 Eö. Again, commercial satellite ranging systems of this accuracy and resolution will be a good alternative.
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Fig. 5. Casper City Study Area, Wyoming. (a) Google Earth image showing the sparse vegetation. (b) The bare-earth LiDAR DEM. The white dots indicate hypothetical gravity gradiometer observation locations. (c) Gdd response of bare-earth LiDAR DEM. (d) Difference in Gdd response when the 1 arc-sec SRTM DEM is utilized.
3.4. Pima County Study Area, Arizona Fig. 6a and b show the vegetation cover and terrain elevation over the Pima County Study Area, Arizona. The LiDAR data were acquired in the spring of 2011. The study area is located in a flat to hilly region and measures about 1.6 km by 1.6 km. The vegetation is relatively sparse with trees throughout. The relief in the area is 65.5 m and the standard deviation of terrain elevation is 14.8 m. Table 5 summarizes the elevation differences between the data sources. The standard deviation of the difference in terrain elevation between the bare-earth DEM and the 1 arc-second SRTM DEM is 1.16 m. Fig. 6c shows the Gdd response of the bare-earth DEM. The response was computed at the locations indicated as white dots. The response is a few tens of Eö. Fig. 6d shows the difference in terrain response when the 1 arc-second SRTM DEM is utilized. The standard deviation of the difference is 4 Eö. The standard deviation of the Gdd difference when the 3 arc-second SRTM DEM is utilized (not shown) is about the same: 3.6 Eö. Since the vegetation is sparse and the relief is low in this case,
Table 4 Standard deviation of the difference between LiDAR and SRTM terrain elevations for the Casper City Study Area, Wyoming. The DEMs were sampled at the LiDAR point cloud locations.
Point Cloud LiDAR Bare-earth LiDAR 1 arc-sec SRTM 3 arc-sec SRTM
Point Cloud LiDAR
Bare-earth LiDAR
1 arc-sec SRTM
0m 1.64 m 3.27 m 4.63 m
– 0m 3.32 m 4.58 m
– – 0m 2.70 m
the effect of a coarser DEM is not apparent. We conclude that if 1 Eö accuracy is sought in the terrain correction, SRTM data are inadequate even if the vegetation is sparse and the relief is a few tens of meters. The standard deviation of the difference in terrain response when 50 cm vertical uncertainty is added to the bare-earth LiDAR DEM is 0.11 Eö. A standard fixed-wing LiDAR survey is an excellent source of terrain data in an area of sparse vegetation and low relief if better than 1 Eö accuracy is sought in the terrain correction. When the bareearth LiDAR DEM is resampled to 10 m and 2 m vertical uncertainty is added the standard deviation of the difference in terrain response is 0.90 Eö. Again, commercial satellite ranging systems of this accuracy and resolution will be a good alternative.
4. Discussion 4.1. The effect of observation point height and terrain density The case studies illustrate that the accuracy and resolution of 1 and 3 arc-second SRTM data would contribute unacceptable terrain correction error to airborne gravity gradiometer data of 1 Eö noise for practically any terrain relief or vegetation cover. The terrain correction is linearly dependent on density so the effect of varying the terrain density is easy to assess. For example, using a terrain density of 1.34 g/cm3 for the Pima County Study Area would reduce the Gdd difference to ~2 Eö. If this is acceptable to the geophysical data interpreter then the 3 arc-second SRTM DEM is good enough for any area with similar attributes. Using a terrain density of 2.2 g/cm3 for the Casper City Study Area would reduce the Gdd difference to 7.6 Eö. If this is acceptable given the
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Fig. 6. Pima County Study Area, Arizona. (a) Google Earth image showing the sparse vegetation. (b) The bare-earth LiDAR DEM. The white dots indicate hypothetical gravity gradiometer observation locations. (c) Gdd response of bare-earth DEM. (d) Difference in Gdd response when the 1 arc-sec SRTM DEM is utilized.
noise level of the AGG system then the 1 arc-second SRTM DEM is good enough for an area with similar attributes. The constant observation point height of 80 m represents the closest the AGG system may be flown to the terrain with a fixed-wing aircraft in resource applications, and therefore provides the most stringent requirements of DEM accuracy and resolution. In areas of moderate to high relief a loose drape would typically be flown to maintain safety and AGG performance, meaning that much of the data will be collected at heights greater than 80 m. The limiting case is a survey flown at constant elevation above sea-level, at a height 80 m above the highest peak. To assess the effect of increasing height on relaxing the requirement for LiDAR data, the Gdd difference grids were upward continued from “drape” to constant elevation 80 m above the terrain peak. The upward continued grids were then sampled at the observation point locations. Table 6 lists the adjusted Gdd differences. The original values at constant 80 m height are also listed for comparison in parentheses. In Table 7 the terrain density was reduced to 2.2 g/cm3. The Gdd difference is not reduced to 1 Eö or less for any of the cases evaluated.
For AGG systems operating at ~ 10 Eö noise level, the 3 arc-second SRTM is adequate for areas of low relief and sparse vegetation similar to the Pima County Study Area. Since the SRTM DEMs are somewhat coarser than the LiDAR DEM, we performed a noise check on the 1 arc-second and 3 arc-second SRTM for this study area. A vertical uncertainty of 1 m (Table 5) was added to the SRTM DEMs and the terrain responses were recomputed. For the 1 arc-second DEM the 1 m noise sensitivity is 1.2 Eö. For the 3 arc-second DEM the 1 m noise sensitivity is 3.2 Eö. This is acceptable for an AGG system operating at the ~10 Eö noise level. Note that for such AGG systems, if a constant elevation survey is flown, the 3 arc-second SRTM is also adequate for areas of greater relief and sparse vegetation similar to the Casper City Study Area. In this case the Gdd difference is a few Eö.
Table 5 Standard deviation of the difference between LiDAR and SRTM terrain elevations for the Pima County Study Area, Arizona. The DEMs were sampled at the LiDAR point cloud locations.
Table 6 Standard deviation of Gdd differences when the observation points are at constant elevation 80 m above terrain peak. The values in parentheses are Gdd differences when the observation points are at constant 80 m height above ground. Terrain density: 2.67 g/cm3.
Point Cloud LiDAR Bare-earth LiDAR 1 arc-sec SRTM 3 arc-sec SRTM
4.2. Software validation The elemental volume utilized to compute the terrain response in GGterrain is the right-rectangular prism. This type of discretization
Point Cloud LiDAR
Bare-earth LiDAR
1 arc-sec SRTM
Study area
1 arc-second SRTM DEM
3 arc-second SRTM DEM
0m 0.66 m 1.31 m 1.11 m
– 0m 1.16 m 0.93 m
– – 0m 0.70 m
Rogue River, Oregon Pine County, Minnesota Casper City, Wyoming Pima County, Arizona
22.9 Eö (36.1 Eö) 9.9 Eö (11.2 Eö) 2.9 Eö (9.2 Eö) 2.4 Eö (4 Eö)
19.4 Eö (36.8 Eö) 9.0 Eö (10 Eö) 3.7 Eö (13.7 Eö) 2.2 Eö (3.6 Eö)
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Table 7 Standard deviation of Gdd differences when the observation points are at constant elevation 80 m above terrain peak. The values in parentheses are Gdd differences when the observation points are at constant 80 m height above ground. Terrain density: 2.2 g/cm3. Study Area
1 arc-second SRTM DEM
3 arc-second SRTM DEM
Rogue River, Oregon Pine County, Minnesota Casper City, Wyoming Pima County, Arizona
18.9 Eö (29.7 Eö) 8.2 Eö (9.2 Eö) 2.4 Eö (7.6 Eö) 2 Eö (3.3 Eö)
16 Eö (30.3 Eö) 7.4 Eö (8.2 Eö) 3 Eö (11.3 Eö) 1.8 Eö (3 Eö)
results in steps across adjacent prisms. Given our stringent 1 Eö accuracy requirement for the terrain correction we want to verify that this type of discretization is not introducing non-negligible errors in our terrain correction and that our recommendations are not altered by these software considerations. To this end, terrain correction software based on the arbitrary polyhedron was developed. At its core is the code of Tsoulis (2012), polyhedron.f. In this representation of the terrain there are no discontinuities between the elemental volumes making up the terrain model. To validate the software the terrain corrections for the Rogue River Study Area (the area with greatest relief) were recomputed at 80 m constant height with 2.67 g/cm3 terrain density utilizing the polyhedrabased software. The outputs were then compared to the GGterrain outputs. When the LiDAR DEM is utilized the error is negligible. The standard deviation of the difference is 0.06 Eö. When the 1 arc-second SRTM DEM is utilized the error is acceptable (0.95 Eö). When the 3 arc-second SRTM DEM is utilized the error is unacceptable. The standard deviation of the difference is 10.52 Eö. Note that this does not affect our recommendation to source LiDAR data for areas of such relief and vegetation cover because the Gdd differences in Tables 6 and 7 are 1.5 times to 3.5 times greater than this for this study area. It is not advised to compute the terrain correction from the 3 arc-second SRTM DEM in this case anyway. Finally, the same software validation was performed for the area we might be considering utilizing the 3 arc-second SRTM DEM. For the Pima County Study Area the software-related Gdd difference is 0.59 Eö when the 3 arc-second SRTM DEM is utilized. Comparing this value with that in Table 6 (3.6 Eö), this is not enough to alter the recommendation to source LiDAR data if 1 Eö accuracy is sought. 5. Conclusions One of the more fundamental questions that should be addressed when attempting high resolution gravity gradiometry at 1 Eö accuracy is whether a bare-earth DEM of adequate resolution and accuracy to compute a terrain correction good to 1 Eö is available or can be acquired. We found that a bare-earth DEM of 10 m spatial resolution and 2 m vertical uncertainty is sufficient for generating a terrain correction of this accuracy at 80 m height. The terrain correction in this case is good to ~1 Eö regardless of terrain relief or vegetation cover. At present a standard fixed-wing LiDAR survey provides a terrain DEM with better
resolution and accuracy at considerable cost. Commercial satellite ranging systems are claiming to achieve this resolution and accuracy at moderate cost. A second question is whether we can forgo the expense of an airborne LiDAR survey or a satellite ranging mission if the terrain relief is low or the vegetation is sparse. The four area studies compared SRTMderived terrain corrections against LiDAR-derived terrain corrections for terrains having very different relief and vegetation cover. We found that the SRTM DEMs do not provide adequate spatial resolution and accuracy even when the terrain is relatively flat and the vegetation is sparse. This stringent requirement for commercially sourced DEMs quickly falls away however for AGG systems operating at the ~ 10 Eö noise level. We found that in an area of sparse vegetation and relatively low relief of a few tens of meters the 3 arc-second (~ 90 m) SRTM DEM will produce a terrain correction good to a few Eö. Areas of greater relief or vegetation cover should ideally be assessed on a case-by-case basis by selecting a study area with similar attributes for which LiDAR data are publically available and adjusting the terrain correction accuracy for terrain density and height. Acknowledgements The LiDAR and SRTM data utilized in this study are available from the U.S. Geological Survey. The terrain correction software GGterrain was developed by the Center for Gravity, Electrical, and Electromagnetic Studies (CGEM) for the sponsors of the Gravity and Magnetics Research Consortium (GMRC), Copyright 2010, The Colorado School of Mines. The Society of Exploration Geophysicists (SEG) owns worldwide copyright of the code polyhedron.f, (c) 2012. Polyhedron.f was downloaded at http://software.seg.org/2012/0001. References Beaubouef, T., Wagaman, M., Sfara, R., FitzMaurice, M., 2005. Use of airborne LiDAR in the full cycle of onshore hydrocarbon exploration: a legacy dataset. SEG Technical Program Expanded Abstracts. 2005:pp. 60–63. http://dx.doi.org/10.1190/1.2144396. Davis, K., Kass, M., Li, Y., 2010. Rapid gravity and gravity gradiometry terrain correction via adaptive quadtree mesh discretization. SEG Technical Program Expanded Abstracts. 2010:pp. 1789–1793. http://dx.doi.org/10.1190/1.3513189. Dransfield, M., Zeng, Y., 2009. Airborne gravity gradiometry: terrain corrections and elevation error. Geophysics 74 (5):I37–I42. http://dx.doi.org/10.1190/1.3170688. Gesch, D.B., 2007. The National Elevation Dataset. In: Maune, D. (Ed.), Digital Elevation Model Technologies and Applications: The DEM Users Manual, second ed. American Society for Photogrammetry and Remote Sensing, Bethesda, Maryland, pp. 99–118. Gesch, D., Oimoen, M., Greenlee, S., Nelson, C., Steuck, M., Tyler, D., 2002. The National Elevation Dataset. Photogramm. Eng. Remote. Sens. 68 (1), 5–11. Grujic, M., 2012. Data processing requirements for an 1 Eö/√Hz AGG system: ASEG Extended Abstracts 2012. 22nd Geophysical Conference. 1-4. http://dx.doi.org/10. 1071/ASEG2012ab075. Tsoulis, D., 2012. Analytical computation of the full gravity tensor of a homogeneous arbitrarily shaped polyhedral source using line integrals. Geophysics 77 (2):F1–F11. http://dx.doi.org/10.1190/GEO2010-0334.1.