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SRTM2gravity topographic gravity/terrain correction model - Readme file v5
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Contact:
Christian Hirt
Institute for Astronomical and Physical Geodesy
Technical University Munich
c.hirt(please use the at right here)tum(and here a dot)de
Michael Kuhn
School for Earth and Planetary Sciences
Curtin University
m.kuhn(please use the at right here)curtin(here a dot)edu(here a dot)au
Last edited 2019-04-24
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1. SUMMARY
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1.1 What is SRTM2gravity?
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SRTM2gravity is a global gravity map with 3" spatial resolution. It represents
the gravity field generated by the MERIT topography model and a mass-density
assumption of 2670 kg m^(-3). The model can be viewed as a topographic gravity
model and a modern model of gravimetric terrain corrections where the gravity
effect associated with terrain irregularities (valleys, summits), but also the
effect of a spherical Bouguer shell is represented by a single data set.
Different to "standard" terrain corrections, our model represents the total
gravitational signal of the Earth's global topography in spherical approximation.
It does not require separate modelling of Bouguer plates or Bouguer shells, and
is not limited to, e.g., 167 km zones, as is the case in classical terrain
corrections.
The SRTM2gravity model is an improved successor of the gravity component of the
ERTM2160 short-scale gravity model (Hirt et al. 2014 Comp. Geosc.), and a
precursor for a future update of the GGMplus gravity maps (Hirt et al. 2013,
GRL). The improvements of SRTM2gravity over previous efforts are threefold:
improved methodology, improved data and improved resolution (see Hirt et al. 2019
for details).
1.2 Citation:
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Hirt, C., M. Yang, M. Kuhn, B. Bucha, A. Kurzmann and R. Pail (2019),
SRTM2gravity: an ultra-high resolution global model of gravimetric terrain
corrections, Geophysical Research Letters 46, doi: 10.1029/2019GL082521.
1.3 Permanent link to the SRTM2gravity data sets and paper
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http://ddfe.curtin.edu.au/models/SRTM2gravity2018
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2. DATA and METHODS used for SRTM2gravity
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2.1 INPUT DATA
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SRTM2gravity is based on the MERIT (Multi-Error-Removed Improved-Terrain) DEM
(digital elevation model) data set Version v1.0.1 by Yamazaki et al.(2017).
MERIT primarily relies on SRTM elevations. It also uses Viewfinder Panorama
data for SRTM hole-filling and AW3D elevations in high latitudes (north of
60°). The SRTM tree-canopy signal and other error sources have been reduced by
Yamazaki et al. (2017), which is why MERIT represents the bare-ground in good
approximation. A total of 120 elevation outliers have been removed by Hirt (2018)
prior to our forward modelling.
2.2 PROCESSING PROCEDURES
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In brief, the SRTM2gravity model is a transformation of SRTM heights to implied
gravity effects via evaluation of Newton's integral. We combined state-of-the-art
spectral and spatial domain techniques for efficient yet accurate computation of
gravity effects. Important aspects:
- A uniform mass-density of 2670 kg/m3 was adopted in all computations.
- Any of the ~28 billion computation points resides at the surface of the MERIT
topography, that is, where gravity can be measured at the terrain surface.
More details are described in detail in Hirt et al. (2019). A pdf is available at
http://ddfe.curtin.edu.au/models/SRTM2gravity2018/Hirt2019_SRTM2gravity_GRL_av.pdf
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3. SRTM2gravity PRODUCTS, FILE FORMATS AND DIRECTORIES
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3.1 What's available?
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1) FullScaleGravity: Gravimetric terrain corrections reflecting the
gravitational attraction of Earth's global topography measured w.r.t. the geoid.
Technically, the "FullScaleGravity" product represents the negative
first-order radial derivative of the topography-implied gravitational potential.
It represents the linear effect of the topography on gravity (the Bouguer shell
of thickness h = DEM station height) together with the gravity effect of all
irregularities of the topography relative to the Bouguer shell. If you want to
remove the (total) topographic effect from gravity measurements, that's the
right product.
2) ResidualGravity: High-frequency gravity effects reflecting the gravitational
attraction of Earth's global topography residual to a degree-2160 spherical-
harmonic reference surface. If your application is the refinement of gravity
from GGMs such as EGM2008 at scales less than 10 km, then that's your product.
Note: The difference between both products is the gravitational attraction of
the degree-2160 MERIT topography in spectral band of degrees 0 to 2160,
evaluated at the 3" MERIT topography. In the FullScaleGravity product, these
long-wavelength signals are included, while removed from the ResidualGravity.
3.2 Accuracy
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The overall computational accuracy of the SRTM2gravity transformation has been
estimated to be at the level of 0.1 to 0.2 mGal. This estimate stems from a
comparison of SRTM2gravity full-scale gravity with gravity from global numerical
integration of topographic mass-density effects over test areas around the globe,
and assumption that the approximation errors are comparable over areas with similar
topography. Over extremely rugged terrain (Himalayas), the accuracy is reduced
to the level of ~1.0 mGal, and over Alpine terrain (such as European Alps or
Rocky Mountains), the accuracy level is ~0.5 mGal. Over rather gently undulating
terrain (such as the Australian Alps), the accuracy is ~0.1-0.2 mGal. For any
area with smoother topography than that of the Australian Alps, ~0.1 mGal
accuracy can be expected.
Note that these accuracy levels refer solely to the precision of our gravity
forward modelling procedure. In other words, they represent the accuracy of the
computational method, and are not a measure of how well the topography-implied
gravity signal approximates the real gravity field at short spatial scales.
The latter would require knowledge on mass-density anomalies or use of ground-
truth gravity data. Also see Sect. 5, point 1.
3.3 Directories
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The SRTM2gravity data is organised in directories as follows.
/data .. directory for all SRTM2gravity data files
|--> FullScaleGravity .. subdir with gravimetric terrain corrections
|--> N00E060 .. subdirs containing data files for 30 deg regions
|--> N00E090
... a total of 59 subdirs
|--> S60E120
|--> ResidualGravity .. subdir with high-frequency gravity values
|--> N00E060 .. subdirs containing data files for 30 deg regions
|--> N00E090
... a total of 59 subdirs
|--> S60E120
/software
s2g2018_v2.m .. Matlab skript for seamless extraction of gravity data
TestAccess_s2g.m .. Matlab test driver showing how to access data
s2g2018.mat .. Matlab index file for quicker data access
Each of the 57 30x30° regions contains up to 900 1° data files in binary
format and up to 900 png image files visualising the file content.
With a total of 19,402 1-deg data tiles and 5.625 MB/tile (see Table 2), there
are ~112 GB storage needed for all tiles of the full-scale gravity model and
another ~112 GB for the residual gravity model.
3.4 File formats
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Table 1: SRTM2gravity data files, exemplified for tile N27E086
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Product Filename Directory Filesize Unit Format (binary)
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Full-scale gravity N27E086_full.bin 1) 5.625 MB 0.01 mGal Int32, "ieee-be"
Residual gravity N27E086_res.bin 2) 5.625 MB 0.01 mGal Int32, "ieee-be"
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1) data\FullScaleGravity\N00E060
2) data\ResidualGravity\N00E060
The integer meridian and parallel located closest to the South-Westernmost data
point of each 1 deg x 1 deg determines the filename. Each binary file contains
1200 x 1200 values in cell-centred registration. For instance, the one-degree
tile N27E086 contains computation points with the geodetic (GRS80 ellipsoidal)
coordinates ranging from 27°+1.5" to 28°-1.5" latitude and 86°+1.5" to 87°-1.5"
longitude, with 3" being the constant step in both directions.
Records proceed along meridians from South to North and columns proceed from
West to East. The first record is the South-West corner (27°+1.5" deg latitude,
86°+1.5" deg longitude in the example), and the last record is the North-East
corner (28°-1.5" latitude, 87°-1.5" longitude).
Note that the gravity data is held in the unit 0.01 mGal in the binary files.
Accordingly, a conversion factor of 1/100 must be applied to scale the data to
basic unit mGal, and a factor of 1/10000000 for unit m/s^2. When extracting
SRTM2gravity data with the Matlab scripts provided, the conversion factors are
automatically taken into account.
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4. A simple How-to-use guide - two examples
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4.1 Terrain corrections
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Assuming you'd like to reduce a gravimetric survey covering the area -40 to -30°
latitude and 140 to 150° longitude (= parts of the Australian Alps).
Step 1: Find out the 30°x 30° region of this data set -> S60E120
Step 2: Go to SRTM2gravity/data/FullScaleGravity/S060E120 and choose all
1° tiles covered by your survey, or just download folder /S60E120
in its entirety.
Step 3: Download the access scripts s2g2018_v2.m and TestAccess_s2g.m
(from folder /software).
Step 4: Modify the TestAccess_s2g.m script with the geographical
coordinates of your test area and run the script in Matlab. The result
are three matrices, X containing the longitudes, Y the latitudes and
Z containing the extracted topographic gravity effects.
Step 5: Interpolate Z bicubically at the locations of your gravity stations
and subtract from the observed gravity disturbances, yielding
complete Bouguer gravity values.
Note that because the SRTM2gravity model contains the total gravitational effect
of the global topographic masses, the SRTM2gravity product "FullScaleGravity"
can be directly subtracted from observed gravity disturbances. There is no need
to model the gravity effect of a spherical Bouguer shell because it is
implicitly included in the "FullScaleGravity" product.
4.2 GGM augmentation
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Assuming you would like to enhance gravity from a degree-2160/2190 GGM (e.g.,
EGM2008) with topography-implied gravity information at scales of 10 km to
~90 m (same working area as above):
Step 1: Go to SRTM2gravity/data/ResidualGravity/S60E120 and choose all
1° tiles needed, or just download folder /S60E120 in its entirety.
Step 2: Download the access scripts s2g2018_v2.m and TestAccess_s2g.m
(from folder /software).
Step 3: Modify only the TestAccess_s2g.m script with the geographical
coordinates of your test area and run the script in Matlab. The result
are three matrices, X containing the longitudes, Y the latitudes and
Z containing the extracted residual gravity effects.
Step 4: Add a) gravity values (or disturbances) from a spherical harmonic
synthesis of EGM2008 over its complete band-width at the MERIT
topographic surface and b) residual gravity effects from step 3. The
result are gravity values (containing signals at scales down to ~90 m)
which will be in good agreement with measured gravity, e.g., at the
lower mGal-level over most EGM2008 good-data areas.
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5 KNOWN LIMITATIONS AND IMPERFECTIONS
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1) SRTM2gravity is a pure topography-implied gravity field model. It does not
contain any observed gravity values. At short spatial scales, our model
approximates the real gravity field, but it cannot be an exact description
of what can be measured with gravimetric techniques.
2) While due attempts have been made to remove spurious artefacts from the
topographic input model (Hirt 2018), we cannot exclude the presence of
further smaller artefacts in the topography data (e.g., steps or spikes),
and, in turn, in the forward-modelled gravity.
3) SRTM2gravity models the topographic gravity effect. Mass-density anomalies
(relative to the reference density of 2670 kg m^-3) have not been modelled:
Examples of unmodelled density anomalies include, but are not limited to,
the density contrasts associated with a) lake water, b) ocean water,
c) ice sheets, d) sediments. Users with mass density models at hand can
forward model and add/subtract the effect from the SRTM2gravity values.
4) The restrictions from 3) especially apply to all of Antarctica (not modelled)
Greenland (no ice-density contrast modelled) and to coastlines around the
world. Clearly an inclusion of ice-sheets and bathymetry in detailed
forward modelling is very desirable as it would better approximate Earth's
real gravity field. We note that this would require substantial resources
(money, time, computing power) for data cleaning, data homogenization,
forward modelling and validation. A good uptake of SRTM2gravity might help
us to justify such efforts in the future.
5) Over narrow and deep mountain valleys (e.g., 2 km height difference w.r.t.
surrounding summits), SRTM2gravity approximation errors will be largest.
This is a consequence of the harmonic correction approach applied in the
residual gravity forward modelling. As a rule of thumb, approximation
errors can be constrained not to exceed ~0.006 mGal/m, e.g., ~6 mGal for a
1 km deep very narrow valley relative to the summit topography. The
wider the valley, the smaller will be the maximum approximation errors.
6) The effect from 5) leads to worst-case RMS approximation errors of ~1.0mGal
(computed over 1200 x 1200 gravity values of a 1-deg tile) and maximum error
amplitudes of ~10 mGal for points located in very deep mountain valleys
found over parts of the Himalayas representing Earth's roughest topography.
By using SRTM2gravity products users agree to have read and understood the
model limitations and imperfections. If you encounter imperfections other than
those listed here, we would be pleased to receive your feedback. Thank you!
REFERENCES
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Hirt, C., M. Yang, M. Kuhn, B. Bucha, A. Kurzmann and R. Pail (2019),
SRTM2gravity: an ultra-high resolution global model of gravimetric terrain
corrections, Geophysical Research Letters 46, doi: 10.1029/2019GL082521.
Hirt, C., B. Bucha, M. Yang and M. Kuhn (2019), A numerical study of residual
terrain modelling (RTM) techniques and the harmonic correction using ultra-high
degree spectral gravity modelling, Journal of Geodesy, post-revision.
Hirt, C. (2018), Artefact detection in global digital elevation models (DEMs):
The Maximum Slope Approach and its application for complete screening of the
SRTM v4.1 and MERIT DEMs, Remote Sensing of Environment 207, 27-41,
doi:10.1016/j.rse.2017.12.037.
Hirt C., M. Kuhn, S.J. Claessens, R. Pail, K. Seitz, T. Gruber (2014), Study of
the Earth's short-scale gravity field using the ERTM2160 gravity model,
Computers & Geosciences, 73, 71-80. doi: 10.1016/j.cageo.2014.09.00.
Hirt, C., S.J. Claessens, T. Fecher, M. Kuhn, R. Pail, M. Rexer (2013), New
ultra-high resolution picture of Earth's gravity field, Geophysical Research
Letters, Vol 40, doi: 10.1002/grl.50838.
Rexer, M., C. Hirt, B. Bucha and S. Holmes (2018), Solution to the spectral
filter problem of residual terrain modelling (RTM), Journal of Geodesy 92(6),
675-690, doi:10.1007/s00190-017-1086-y.
Yamazaki, D., D. Ikeshima, R. Tawatari, T. Yamaguchi, F. O’Loughlin, J.C. Neal,
C.C. Sampson, S. Kanae, P.D. Bates (2017), A high accuracy map of global terrain
elevations, Geophysical Research Letters, Doi:10.1002/2017GL072874.
DISCLAIMER
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Neither Technical University Munich (TUM), Curtin University, nor any of its
staff accept any liability in connection with the use of data and models
provided here. Neither TUM, Curtin University nor any of its staff make any
warranty of fitness, completeness, usefulness and accuracy of the data and
models for any intended or unintended purpose. By using SRTM2gravity products
you agree to accept the disclaimer and you agree to have read Section 5 of the
Readme file.