This document summarizes the development of a new ultra-high resolution model of Earth's gravity field called GGMplus. Key points:
- GGMplus combines satellite gravity data from GOCE and GRACE with terrestrial gravity data and topography to achieve unprecedented 200m spatial resolution globally.
- It provides gridded estimates of gravity, horizontal and radial field components, and quasi-geoid heights at over 3 billion points covering 80% of the Earth's land.
- GGMplus reveals new details of small-scale gravity variations and identifies locations of minimum and maximum gravity, suggesting peak-to-peak variations are 40% larger than previous estimates. The model will benefit scientific and engineering applications.
Gravity anomaly across reagional structuresAmit K. Mishra
Gravity Anomaly across continents and ocean, gravity anomaly across mid-oceanic ridges, gravity anomaly across orogenic belts, and gravity anomaly across subduction zones.
The presentation comprises the Gravity Method, It's anomaly, reduction, and its applications. The Gravity method is commonly used in Geology specifically in Geophysics.
Definition
Geophysics is the application of method of physics to the
study of the earth.
On the other sense, it is a subject of natural science
concerned with the physical processes and the physical
properties of the earth and its surrounding space
environment and the use of co-ordinate methods for the
analysis.
It involves the application of physical theories and
measurements to discover the properties and processes of the
earth.
Gravity anomaly across reagional structuresAmit K. Mishra
Gravity Anomaly across continents and ocean, gravity anomaly across mid-oceanic ridges, gravity anomaly across orogenic belts, and gravity anomaly across subduction zones.
The presentation comprises the Gravity Method, It's anomaly, reduction, and its applications. The Gravity method is commonly used in Geology specifically in Geophysics.
Definition
Geophysics is the application of method of physics to the
study of the earth.
On the other sense, it is a subject of natural science
concerned with the physical processes and the physical
properties of the earth and its surrounding space
environment and the use of co-ordinate methods for the
analysis.
It involves the application of physical theories and
measurements to discover the properties and processes of the
earth.
Bouguer anomaly and free-air anomaly correlation signatures in parts of Benue...Premier Publishers
Topographic values in the study area range from 80m to 170m. The rock type comprises Basement Complex at the west bounded by River Niger, and sedimentary rock type in the east. Density measurements of various rocks were taken with the highest bulk density from the metamorphic schist (2.77gm/cm3), followed by igneous rock olivine gabbro (2.73gm/cm3), and sandstone (2.35gm/cm3). Results of gravity survey revealed a mean Bouguer anomaly of +12.15 mgals and a mean free air anomaly of +22.0 mgals. Interpretation of gravity measurements revealed the existence of a fracture at Gboloko NE-SW axis, a synclinal fold axis at about 5.5km west of Gboloko (between the Staurolite Schist and Cordierite-Tourmaline schist). The Basement-Sedimentary boundary is characterized by a drop in residual Bouguer anomaly from positive to negative at about 6km east of Gboloko. The thickness of the sediments is about 0.90km at the northern part of the Basement-Sedimentary boundary, and about 2.0km in the south, thus suggesting a progressive increase in sedimentary thickness at the western edge of the Benue trough. The Free-air anomaly ‘highs’ correspond to Bouguer anomaly ‘highs’ and tied to areas of high topography and bands of weathered, lateritized sediments. The Bouguer anomaly profiles exhibited reliable signature changes at the rock boundaries, thus a supportive tool for delineation of those border areas.
A Gravity survey is an indirect (surface) means of calculating the density pr...Shahid Hussain
A Gravity survey is an indirect (surface) means of calculating the density property of subsurface materials. The higher the gravity values, the denser the rock beneath.
Unstable/Astatic Gravimeters and Marine Gravity SurveyRaianIslamEvan
This is a descriptive article on stable and unstable gravimeters. The article is mainly focused on LaCoste-Romberg and Worden gravimeters. Also, it includes marine gravity survey shortly.
1980 öncesi deprem istasyon sayısı Türkiye'de herhalde 50'den azdı ve bu nedenle deprem istatistiği çalışmaları Türkiye boyunca çok büyük alanlara bölünerek yapılmış. Okla gösterdiğim yerlerde magnitüd aralığı çok yetersiz. Bu çalışmada, 4x4 şeklinde dilimleme yapılmış. 400kmx400 km olarak dilimlere ayrılarak yapılmış. Veri olmadığı zaman mecbur ALANI büyütmek zorunda kalıyorsunuz... bu nedenle Makro-İstatistik İnceleme yapılmış oluyor.a/b oranını çalışmalarımda hiç kullanmadım fakat bana kalırsa yararlı bir parametre olarak görünüyor. Bir yıl içinde olması beklenen en büyük deprem büyüklüğünü veriyor. Buna göre bu çalışmada, bir yıl içinde beklenen en büyük deprem M=5 bulunmuş ve alan 39 E ve 41 B arasında bir yere denk geliyor... muhtemelen Karlıova Üçlü Bileşimi çevresi olabilir.
Gravity and magnetic methods are an essential part of oil exploration. They do not replace seismic. Rather, they add to it. Despite being comparatively low-resolution, they have some very big advantages.
These geophysical methods passively measure natural variations in the earth’s gravity and magnetic fields over a map area and then try to relate these variations to geologic features in the subsurface. Lacking a controlled source, such surveys are usually environmentally unobjectionable.
Greetings all,
Nowadays, several datasets are -or will be- available in a near future to improve operational forecasting in most aspects, like the
ocean dynamics modeling, and the assimilation efficiency, that aims now to optimize the combination of temperature/salinity in
situ profiles, drifter's velocities, and sea surface height deduce from altimeter's data and GRACE or future Goce geoid. But also
strengthen forecasting system's applications, like the climate monitoring. For all these issues, an optimal use of ocean data,
always too sparse and not enough numerous, is mandatory.
Such studies are at the heart of this Newsletter issue. It begins with a Rio M.H. and Hernandez F. review of the Goce Mission,
dedicated to focus and document the shortest scales of the Earth's gravity field. Goce satellite is due to fly in December 2007.
With the next article Guinéhut S. and Larnicol G. investigate the influence of the in situ temperature profiles sampling on the
thermosteric sea level estimation. They show that the impact is not negligible, and can introduce large errors in the estimation. In
the second article, Benkiran M. and Greiner E. are evaluating the benefits of the drifter's velocities assimilation in the Mercator
Océan 1/3° Tropical and North Atlantic operational system. A description of the assimilation scheme upgrade to take into account
velocity control is given. Castruccio F. & al. describe in the third article the performance of an improved MDT reference for
altimetric data assimilation. They concentrate their study on the Tropical Pacific Ocean. Finally, the Newsletter comes to an end
with the Benkiran M. article. In his study, based on the 1/3° Mercator system, the impact of several altimeters data on the
assimilation performance is assessed
Have a good read
Bouguer anomaly and free-air anomaly correlation signatures in parts of Benue...Premier Publishers
Topographic values in the study area range from 80m to 170m. The rock type comprises Basement Complex at the west bounded by River Niger, and sedimentary rock type in the east. Density measurements of various rocks were taken with the highest bulk density from the metamorphic schist (2.77gm/cm3), followed by igneous rock olivine gabbro (2.73gm/cm3), and sandstone (2.35gm/cm3). Results of gravity survey revealed a mean Bouguer anomaly of +12.15 mgals and a mean free air anomaly of +22.0 mgals. Interpretation of gravity measurements revealed the existence of a fracture at Gboloko NE-SW axis, a synclinal fold axis at about 5.5km west of Gboloko (between the Staurolite Schist and Cordierite-Tourmaline schist). The Basement-Sedimentary boundary is characterized by a drop in residual Bouguer anomaly from positive to negative at about 6km east of Gboloko. The thickness of the sediments is about 0.90km at the northern part of the Basement-Sedimentary boundary, and about 2.0km in the south, thus suggesting a progressive increase in sedimentary thickness at the western edge of the Benue trough. The Free-air anomaly ‘highs’ correspond to Bouguer anomaly ‘highs’ and tied to areas of high topography and bands of weathered, lateritized sediments. The Bouguer anomaly profiles exhibited reliable signature changes at the rock boundaries, thus a supportive tool for delineation of those border areas.
A Gravity survey is an indirect (surface) means of calculating the density pr...Shahid Hussain
A Gravity survey is an indirect (surface) means of calculating the density property of subsurface materials. The higher the gravity values, the denser the rock beneath.
Unstable/Astatic Gravimeters and Marine Gravity SurveyRaianIslamEvan
This is a descriptive article on stable and unstable gravimeters. The article is mainly focused on LaCoste-Romberg and Worden gravimeters. Also, it includes marine gravity survey shortly.
1980 öncesi deprem istasyon sayısı Türkiye'de herhalde 50'den azdı ve bu nedenle deprem istatistiği çalışmaları Türkiye boyunca çok büyük alanlara bölünerek yapılmış. Okla gösterdiğim yerlerde magnitüd aralığı çok yetersiz. Bu çalışmada, 4x4 şeklinde dilimleme yapılmış. 400kmx400 km olarak dilimlere ayrılarak yapılmış. Veri olmadığı zaman mecbur ALANI büyütmek zorunda kalıyorsunuz... bu nedenle Makro-İstatistik İnceleme yapılmış oluyor.a/b oranını çalışmalarımda hiç kullanmadım fakat bana kalırsa yararlı bir parametre olarak görünüyor. Bir yıl içinde olması beklenen en büyük deprem büyüklüğünü veriyor. Buna göre bu çalışmada, bir yıl içinde beklenen en büyük deprem M=5 bulunmuş ve alan 39 E ve 41 B arasında bir yere denk geliyor... muhtemelen Karlıova Üçlü Bileşimi çevresi olabilir.
Gravity and magnetic methods are an essential part of oil exploration. They do not replace seismic. Rather, they add to it. Despite being comparatively low-resolution, they have some very big advantages.
These geophysical methods passively measure natural variations in the earth’s gravity and magnetic fields over a map area and then try to relate these variations to geologic features in the subsurface. Lacking a controlled source, such surveys are usually environmentally unobjectionable.
Greetings all,
Nowadays, several datasets are -or will be- available in a near future to improve operational forecasting in most aspects, like the
ocean dynamics modeling, and the assimilation efficiency, that aims now to optimize the combination of temperature/salinity in
situ profiles, drifter's velocities, and sea surface height deduce from altimeter's data and GRACE or future Goce geoid. But also
strengthen forecasting system's applications, like the climate monitoring. For all these issues, an optimal use of ocean data,
always too sparse and not enough numerous, is mandatory.
Such studies are at the heart of this Newsletter issue. It begins with a Rio M.H. and Hernandez F. review of the Goce Mission,
dedicated to focus and document the shortest scales of the Earth's gravity field. Goce satellite is due to fly in December 2007.
With the next article Guinéhut S. and Larnicol G. investigate the influence of the in situ temperature profiles sampling on the
thermosteric sea level estimation. They show that the impact is not negligible, and can introduce large errors in the estimation. In
the second article, Benkiran M. and Greiner E. are evaluating the benefits of the drifter's velocities assimilation in the Mercator
Océan 1/3° Tropical and North Atlantic operational system. A description of the assimilation scheme upgrade to take into account
velocity control is given. Castruccio F. & al. describe in the third article the performance of an improved MDT reference for
altimetric data assimilation. They concentrate their study on the Tropical Pacific Ocean. Finally, the Newsletter comes to an end
with the Benkiran M. article. In his study, based on the 1/3° Mercator system, the impact of several altimeters data on the
assimilation performance is assessed
Have a good read
On 17/10/2013 TU Delft Climate Institute organised the symposium The Greenland and Antarctic ice sheets: present, future, and unknowns. This is one of the four presentations given there.
http://www.tudelft.nl/nl/actueel/agenda/event/detail/symposium-tu-delft-climate-institute-17th-october-2013/
A global reference model of the lithosphere and upper mantle from joint inver...Sérgio Sacani
We present a new global model for the Earth’s lithosphere and upper mantle (LithoRef18) obtained
through a formal joint inversion of 3-D gravity anomalies, geoid height, satellite-derived
gravity gradients and absolute elevation complemented with seismic, thermal and petrological
prior information. The model includes crustal thickness, average crustal density, lithospheric
thickness, depth-dependent density of the lithospheric mantle, lithospheric geotherms, and average
density of the sublithospheric mantle down to 410 km depth with a surface discretization
of 2◦ × 2◦. Our results for lithospheric thickness and sublithospheric density structure are in
excellent agreement with estimates from recent seismic tomography models. A comparison
with higher resolution regional studies in a number of regions around the world indicates that
our values of crustal thickness and density are an improvement over a number of previous
global crustal models. Given the strong similarity with recent tomography models down to
410 km depth, LithoRef18 can be readily merged with these seismic models to include seismic
velocities as part of the reference model. We include several analyses of robustness and
reliability of input data, method and results. We also provide easy-to-use codes to interrogate
the model and use its predictions for the development of higher-resolution models.
Considering the model‘s features and data fitting statistics, LithoRef18 will be useful in
a wide range of geophysical and geochemical applications by serving as a reference or initial
lithospheric model for (i) higher-resolution gravity, seismological and/or integrated geophysical
studies of the lithosphere and upper mantle, (ii) including far-field effects in gravity-based
regional studies, (iii) global circulation/convection models that link the lithosphere with the
deep Earth, (iv) estimating residual, static and dynamic topography, (v) thermal modelling of
sedimentary basins and (vi) studying the links between the lithosphere and the deep Earth,
among others. Several avenues for improving the reliability of LithoRef18’s predictions are
also discussed. Finally, the inversion methodology presented in this work can be applied in
other planets for which potential field data sets are either the only or major constraints to their
internal structures (e.g. Moon, Venus, etc.).
Titan’s Topography and Shape at the Endof the Cassini MissionSérgio Sacani
With the conclusion of the Cassini mission, we present an updated topographic map of Titan,including all the available altimetry, SARtopo, and stereophotogrammetry topographic data sets availablefrom the mission. We use radial basis func tions to interpolate the sparse data set, which covers only ∼9%of Titan’s global area. The most notable updates to the topography include higher coverage of the polesof Titan, improved fits to the global shape, and a finer resolution of the global interpolation. We alsopresent a statistical analysis of the error in the derived products and perform a global minimization on aprofile-by-profile basis to account for observed biases in the input data set. We find a greater flattening ofTitan than measured, additional topographic rises in Titan’s southern hemisphere and better constrain thepossible locations of past and present liquids on Titan’s surface.
Towards the Implementation of the Sudan Interpolated Geoid Model Khartoum Sta...ijtsrd
The discussions between ellipsoid and geoid have invoked many researchers during the recent decades, especially during the GNSS technology era, which had witnessed a great deal of development but still geoid undulation requires more investigations. To figure out a solution for Sudans local geoid, this research has tried to intake the possibility of determining the geoid model by following two approaches, gravimetric and geometrical geoid model determination, by making use of GNSS leveling benchmarks at Khartoum state. The Benchmarks are well distributed in the study area, in which, the horizontal coordinates and the height above the ellipsoid have been observed by GNSS while orthometric heights were carried out using precise leveling. The Global Geopotential Model GGM represented in EGM2008 has been exploited to figure out the geoid undulation at the benchmarks in the study area. This is followed by a fitting process, that has been done to suit the geoid undulation data which has been computed using GNSS leveling data and geoid undulation inspired by the EGM2008. Two geoid surfaces were created after the fitting process to ensure that they are identical and both of them could be counted for getting the same geoid undulation with an acceptable accuracy. In this respect, statistical operation played an important role in ensuring the consistency and integrity of the model by applying cross validation techniques splitting the data into training and testing datasets for building the geoid model and testing its eligibility. The geometrical solution for geoid undulation computation has been utilized by applying straightforward equations that facilitate the calculation of the geoid undulation directly through applying statistical techniques for the GNSS leveling data of the study area to get the common equation parameters values that could be utilized to calculate geoid undulation of any position in the study area within the claimed accuracy. Both systems were checked and proved eligible to be used within the study area with acceptable accuracy which may contribute to solving the geoid undulation problem in the Khartoum area, and be further generalized to determine the geoid model over the entire country, and this could be considered in the future, for regional and continental geoid model. Ahmed M. A. Mohammed. | Kamal A. A. Sami "Towards the Implementation of the Sudan Interpolated Geoid Model (Khartoum State Case Study)" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd63483.pdf Paper Url: https://www.ijtsrd.com/engineering/civil-engineering/63483/towards-the-implementation-of-the-sudan-interpolated-geoid-model-khartoum-state-case-study/ahmed-m-a-mohammed
Mapping the Skies of Ultracool Worlds: Detecting Storms and Spots with Extrem...Sérgio Sacani
Extremely large telescopes (ELTs) present an unparalleled opportunity to study the magnetism,
atmospheric dynamics, and chemistry of very low mass stars (VLMs), brown dwarfs, and exoplanets.
Instruments such as the Giant Magellan Telescope - Consortium Large Earth Finder (GMT/GCLEF),
the Thirty Meter Telescope’s Multi-Objective Diffraction-limited High-Resolution Infrared Spectrograph
(TMT/MODHIS), and the European Southern Observatory’s Mid-Infrared ELT Imager and Spectrograph (ELT/METIS) provide the spectral resolution and signal-to-noise (S/N) necessary to Doppler
image ultracool targets’surfaces based on temporal spectral variations due to surface inhomogeneities.
Using our publicly-available code, Imber, developed and validated in Plummer & Wang (2022), we
evaluate these instruments’abilities to discern magnetic star spots and cloud systems on a VLM star
(TRAPPIST-1); two L/T transition ultracool dwarfs (VHS J1256−1257 b and SIMP J0136+0933); and
three exoplanets (Beta Pic b and HR 8799 d and e). We find that TMT/MODHIS and ELT/METIS are
suitable for Doppler imaging the ultracool dwarfs and Beta Pic b over a single rotation. Uncertainties
for longitude and radius are typically . 10◦
, and latitude uncertainties range from ∼ 10◦
to 30◦
.
TRAPPIST-1’s edge-on inclination and low υ sin i provide a challenge for all three instruments while
GMT/GCLEF and the HR 8799 planets may require observations over multiple rotations. We compare
the spectroscopic technique, photometry-only inference, and the combination of the two. We find
combining spectroscopic and photometric observations can lead to improved Bayesian inference of
surface inhomogeneities and offers insight into whether ultracool atmospheres are dominated by spotted
or banded features.
Gravimetri Dersi için aşağıda ki videoları izleyebilirsiniz.
Link 01: https://www.youtube.com/watch?v=HTyjVaVGx0k
Link 02: https://www.youtube.com/watch?v=fUkfgI8XaOE
Geopsy yaygın olarak kullanılan profesyonel bir program. Özellikle, profesyonel program deneyimi yeni mezunlarda çok aranan bir özellik. Bir öğrencim çalışmasında kullanmayı planlıyor.
M6.0 2004 Parkfield Earthquake : Seismic AttenuationAli Osman Öncel
HRSN isimli kuyu içi sismik istasyonlar kullanılarak, San Andreas fayı boyunca meydana gelen büyük depremler öncesi sismik azalımın varlığının olup olmadığı araştırılıyor.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Model Attribute Check Company Auto PropertyCeline George
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Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
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Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
2. 200 to 2190, leaving the main spectral range of transition
from GRACE/GOCE to EGM2008 in spectral band of de-
grees 181 to 200. The relative contributions of EGM2008
and GRACE/GOCE satellite gravity are shown in Figure 1.
[7] The spherical harmonic coefficients of the combined
GRACE/GOCE/EGM2008 (GGE) gravity model were used
in the spectral band of degrees 2 to 2190 to synthesize a range
of frequently used gravity field functionals at the Earth’s
surface. For accurate spherical harmonic synthesis at the
Earth’s surface, as represented through the Shuttle Radar
Topography Mission (SRTM) topography, the gradient
approach to fifth order [Hirt, 2012] was applied. This numer-
ically efficient evaluation technique takes into account the
effect of gravity attenuation with height. Applying the gradi-
ent approach as described in Hirt [2012] yielded numerical
estimates for radial derivatives (gravity disturbances) and
horizontal derivatives (deflections of the vertical) of the
disturbing potential and quasi-geoid heights from the GGE
data set at 7.2 arc sec resolution (about 3 billion surface
points) within the SRTM data coverage.
[8] For the Mount Everest region, Figure 2 exemplifies
the associated resolution of GOCE/GRACE satellite grav-
ity (a) and their combination with EGM2008 gravity (b).
The spatial resolution of the GGE gravity field functionals
is limited to about ~10 km (or harmonic degree of 2190)
which leaves the problem of modeling the field structures
at short scales, down to few 100 m resolution at any of
the surface points.
[9] Because ground gravity measurements at a spatial den-
sity commensurate with our model resolution do not exist over
most parts of Earth [e.g., Sansò and Sideris, 2013]—and will
not become available in the foreseeable future—alternative
solutions are required to estimate the gravity field signals at
scales shorter than 10 km. High-resolution topography data
is widely considered the key to ultrahigh-resolution gravity
modeling and used successfully as effective means to esti-
mate short-scale gravity effects [Sansò and Sideris, 2013;
Tziavos and Sideris, 2013; Pavlis et al., 2012; Forsberg and
Tscherning, 1981]. This is because the short-scale gravity field
is dominated by the constituents generated by the visible topo-
graphic masses [Forsberg and Tscherning, 1981]. However,
forward estimation of the short-scale gravity field constituents
from elevation models near-globally at ultrahigh (few 100
meters) resolution is computationally demanding. Yet we have
accomplished this challenge for the first time through ad-
vanced computational resources.
[10] Massive parallelization and the use of Western
Australia’s iVEC/Epic supercomputing facility allowed us to
convert topography from the Shuttle Radar Topography
Mission (SRTM) [cf. Jarvis et al., 2008]—along with bathy-
metric information along coastlines [Becker et al., 2009]—to
topographic gravity at 7.2 arc sec resolution everywhere on
Earth between ±60° latitude with SRTM data available.
Based on nonparallelized standard computation techniques,
the calculation of topographic gravity effects would have taken
an estimated 20 years, which is why previous efforts were re-
stricted to regional areas [Kuhn et al., 2009; Hirt, 2012].
[11] The conversion of topography to topographic gravity is
based on the residual terrain modeling technique [Forsberg,
1984], with the topography high-pass filtered through subtrac-
tion of a spherical harmonic reference surface (of degree and
order 2160) prior to the forward modeling. We treated the
ocean water masses and those of the major inland water bodies
(Great Lakes, Baikal, Caspian Sea) using a combination of
residual terrain modeling with the concept of rock-equivalent
topography [Hirt, 2013], whereby the water masses were
“compressed” to layers equivalent to topographic rock. These
procedures yield short-scale topographic gravity that is suit-
able for augmentation of degree 2190 spherical harmonic grav-
ity models beyond their associated 10 km resolution [cf. Hirt,
2010, 2013]. The topographic gravity is based on a mass-
Figure 1. Relative contribution of GOCE/GRACE data per
spherical harmonic coefficient in the combination with
EGM2008 data (in percent) for the degrees 0 to 250.
Figure 2. Gravity field at different levels of resolution over Mount Everest area. (a) Satellite-only (free-air) gravity from
GOCE and GRACE satellites, (b) GGE gravity (satellite gravity combined with EGM2008 gravity), and (c) GGMplus as
composite of satellite gravity, EGM2008, and topographic gravity. Shown is the radial component of the gravity field over a
~400 × 400 km area covering parts of the Southern Himalayas including the Mount Everest summit area (marked), units in
10 5
m s 2
. The spatial resolution of the gravity modeling increases from ~100 km, ~10 km to ultra-fine ~200 m spatial scales.
HIRT ET AL.: NEW PICTURE OF EARTH’S GRAVITY FIELD
4280
3. density assumption of 2670 kg m 3
and provides the spatial
scales of ~10 to ~250 m, which is complementary to the
GGE gravity (spatial scales from ~10,000 km to ~10 km).
3. Results
[12] Addition of both components (GGE and topographic
gravity) results in the ultrahigh-resolution model GGMplus
(Global Gravity Model, with plus indicating the leap in reso-
lution over previous 10 km resolution global gravity models).
The modeled gravity field components and their descriptive
statistics are reported in Table 1.
[13] This world’s first ultrahigh resolution modeling over
most of Earth’s land areas delivered us the expected gravity
signatures of small-scale topographic features—such as
mountain peaks and valleys—which are otherwise masked
in 10 km resolution models. This adds much local detail to
the gravity maps (compare Figures 2b and 2c) and yields a
spectrally more complete and accurate description of the
gravity field [e.g., Hirt, 2012].
[14] Our gridded estimates portray the subtle variations of
gravity (Figure 3) which are known to depend on factors such
as location, height, and presence of mass-density anomalies.
GGMplus reveals a candidate location for the minimum
gravity acceleration on Earth: the Nevado Huascarán summit
(Peru) with an estimated acceleration of 9.76392 m s 2
(Figures 3a and 3b and Table 2). A candidate location for
Earth’s maximum gravity acceleration was identified—outside
the SRTM area, based on GGE only—in the Arctic Sea with
an estimated 9.83366 m s 2
. This suggests a variation range
Table 1. Descriptive Statistics of the GGMplus Model Components Calculated at 3,062,677,383 Land and Near-Coastal Points Within
± 60° Geographic Latitudea
Gravity Model Component Min Max RMS Unit
Gravity Free-fall acceleration 976392 981974 980133 10
5
m s
2
Radial component 456 714 48.0 10
5
m s
2
Horizontal components North-south 108 94 6.9 arc sec
East-west 83 79 6.8 arc sec
Total (magnitude) 0 109 9.4 arc sec
Quasi-geoid 99.26 86.60 29.91 m
a
RMS is the root-mean-square of the component.
Figure 3. Candidate locations of some extreme signals in Earth’s gravity in the Andes and Himalaya regions. (a)
Topography and (b) free-fall gravity accelerations over the Huascarán region (Peru), where GGMplus gravity accelerations
are as small as ~9.764 m s 2
. (c) Topography and (d) GGMplus total horizontal field component over the Annapurna II region
(Nepal). The gravitational attraction of the Annapurna II masses is expected to cause an extreme slope of the quasi/geoid with
respect to the Earth ellipsoid of up to ~109 arc sec.
HIRT ET AL.: NEW PICTURE OF EARTH’S GRAVITY FIELD
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4. (peak-to-peak variation) for gravity accelerations on Earth of
about ~0.07 m s 2
, or 0.7%, which is about 40% larger than
the variation range of 0.5% implied by standard models
based on a rotating mass-ellipsoid (gravity accelerations are
9.7803 m s 2
(equator) and 9.8322 m s 2
(poles) on the
mass-ellipsoid [cf. Moritz, 2000]). So far, such a simplified
model is also used by the Committee on Data for Science
and Technology to estimate the variation range in free-fall
acceleration on Earth [Mohr and Taylor, 2005]. However,
due to the inhomogeneous structure of Earth, presence of
topographic masses and decay of gravity with height the ac-
tual variations in free-fall accelerations are ~40% larger at
the Earth’s surface (Table 2).
[15] GGMplus free-air gravity—the radial component of
Earth’s gravity field—varies within a range of ~0.011 m
s 2
(~0.1% of gravity accelerations) with its minimum value
of –456 × 10 5
m s 2
located in China and its maximum of
714 × 10 5
m s 2
located over the Pico Cristóbal Colón sum-
mit in Colombia. The higher variability of gravity accelera-
tions over free-air gravity reflects the well-known fact that
gravity accelerations include the gravitational attraction and
centrifugal effect due to Earth rotation.
[16] The horizontal components of the gravitational field
describe in approximation the north-south and east-west
inclination of the quasi/geoid with respect to the reference
ellipsoid. The variation range of the horizontal field
components (also known as deflections of the vertical) is about
~200 arc sec in north-south and ~160 arc sec in east-west, re-
spectively (Table 1). GGMplus reveals a candidate location
for Earth’s largest deflection of the vertical: about 10 km south
of Annapurna II, Nepal, the plumb line is expected to deviate
from the ellipsoid normal by an angle as large as ~109 arc sec
(Figure 3c and 3d). This translates into a most extreme quasi/
geoid slope of about 0.5 m over 1 km.
4. Model Evaluation
[17] We have comprehensively compared GGMplus gravity
field maps with in situ (direct) observations of Earth’s gravity
field from gravimetry, astronomy, and surveying (see
supporting information). Over well-surveyed areas of North
America, Europe, and Australia, the comparisons suggest an
accuracy level for free-air gravity and gravity accelerations
of ~5 × 10 5
m s 2
, for horizontal field components of about
1 arc sec, and for quasi-geoid heights of 0.1 m or better.
[18] Despite the improvements conferred by recent satellite
gravity to our model, the GGMplus accuracy deteriorates by
a factor of ~3 to ~5 over Asia, Africa, and South America,
which are regions with limited or very limited ground gravity
data availability. Comparisons suggest a decrease in accu-
racy down to ~20 × 10 5
m s 2
for gravity, ~5 arc sec for
horizontal field components, and ~0.3 m for quasi-geoid
heights. The reduced accuracy estimates mainly reflect the
limited availability of gravity observations at spatial scales
of ~100 to ~10 km. The accuracy of GGMplus gravity accel-
erations will always be lower than that of free-air gravity.
This is because accelerations are directly affected by errors
in the elevation data, with an elevation error of 10 m equiva-
lent to about 3 × 10 5
m s 2
.
[19] Given that any gravity field signals originating from
local mass-density variations are not represented by the topo-
graphic gravity, our gravity maps cannot provide information
on geological units at scales less than 10 km. This is akin to
EGM2008 at spatial scales of ~30 to ~10 km over many land
areas where gravity measurements are unavailable or of
proprietary nature [Pavlis et al., 2012]. Any global, regional,
or local gravity map or quasi/geoid model can only be
geologically interpreted down to a resolution commensurate
with the gravity observations used to construct the model.
Nevertheless, incorporation of topographic gravity to ap-
proximate gravity field features at spatial scales of ~10 km
to ~250 m significantly improves GGMplus gravity and
horizontal components when compared to 10 km resolution
maps. Depending on the terrain ruggedness, the observed
improvement rates mostly range between 40 and 90% for ra-
dial and horizontal field components (Tables S6 and S8),
while the quasi-geoid improvement is best observable over
rugged areas (up to 40 % improvement, Table S9).
5. Applications
[20] Apart from enhancing our knowledge of Earth’s grav-
ity and its variations, there are several scientific and engineer-
ing applications that require high-resolution and largely
complete gravity knowledge, which is now available through
GGMplus gravity maps.
[21] The quasi/geoid plays a crucial role in modern determi-
nation of topographic heights with Global Navigation Satellite
Systems (such as the Global Positioning System), allowing
the measurement of heights above mean sea level rather
than heights above the ellipsoid [e.g., Meyer et al., 2006;
Featherstone, 2008; Hirt et al., 2011]. While several
regional-size quasi/geoid models of good quality are available
at mostly ~2 km resolution over well-surveyed land areas
(e.g., Europe, U.S., Australia), GGMplus is capable of pro-
viding improved quasi/geoid information over those parts of
Asia, Africa, and South America, where no other source of
high-resolution gravity (e.g., from airborne gravity) is avail-
able. The GGMplus quasi-geoid can be suitable for water
flow modeling (e.g., as required in hydroengineering), and
height transfer with satellite systems, and can be of utility
for the determination of offsets among continental height
Table 2. Candidate Locations for Extreme Values of Earth’s Gravity Field
Gravity Component Minimum/Maximum Latitude/Longitude Geographic Feature/Location
Gravity acceleration 9.76392 m s
2
9.12°/ 77.60° Huascarán, Peru
9.83366 m s
2
86.71°/61.29° Arctic Seaa
Radial component 456 × 10
5
m s
2
29.71°/95.36° Gandengxiang, China
714 × 10
5
m s
2
10.83°/ 73.69° Pico Cristóbal Colón, Columbia
Horizontal componentb
109 arc sec 28.45°/84.13° ~10 km south of Annapurna II, Nepal
Quasi-geoid 106.59 m 4.71°/78.79° Laccadive Sea, south of Sri Lankaa
86.60 m 8.40°/147.35° Puncak Trikora, Papua, Indonesia
a
Offshore area, value estimated without topographic gravity using GGE-only (10 km resolution, also see supporting information).
b
Total component computed as magnitude from the north-south and east-west components.
HIRT ET AL.: NEW PICTURE OF EARTH’S GRAVITY FIELD
4282
5. systems (e.g., Australia and Europe) and their unification
[e.g., Flury and Rummel, 2005; Rummel, 2012]. This in turn
will allow for a more consistent comparison of sea level
observations at tide gauges across the oceans. Because of
incorporation of newer GOCE and GRACE satellite gravity,
the GGMplus quasi-geoid confers improvements at ~100
km spatial scales over parts of Asia, South America, and
Africa, while consideration of short-scale quasi-geoid
effects from topography data improves the resolution of
quasi-geoid heights over rugged terrain [Hirt et al., 2010].
[22] GGMplus gravity accelerations and free-air gravity are
a promising data source for screening and outlier-detection of
terrestrial gravity databases and aid in planning of local
precision gravimetric surveys. Gravity accelerations as
provided by our maps are required, e.g., as a correction in
the context of geodetic height systems [e.g., Meyer et al.,
2006], for accurate topographic mapping, in metrology for cal-
ibration of precision scales [Torge, 1989] and seismometers,
and in observational astronomy for meteorological corrections
(T. Corbard et al., On the importance of astronomical refrac-
tion for modern Solar astrometric measurements, submitted
to Astronomy and Astrophysics, 2013). For geophysics and
the exploration industry, GGMplus may prove beneficial as
novel data source for in situ reduction of detailed gravimetric
surveys, revealing locations of interest for mineral prospectivity
without the need to calculate and apply further and rather time-
consuming reductions [Jacoby and Smilde, 2009]. Finally, hor-
izontal field components are required to correct the impact of
the Earth’s irregular gravity field, e.g., for inertial navigation
at or near the Earth’s surface [Grejner-Brzezinska and Wang,
1998], or in the context of civil engineering (e.g., precision
surveys for tunnel alignment) [Featherstone and Rüeger,
2000]. All of these applications require spectrally most com-
plete information on the gravity field.
6. Conclusions
[23] GGMplus provides the most complete description of
Earth’s gravity at ultrahigh resolution and near-global
coverage to date. This confers immediate benefits to many
applications in engineering, exploration, astronomy, sur-
veying, and potential field geophysics. While GGMplus
provides moderate additional information (because of the
ultrahigh-resolution short-scale modeling) over areas with
dense coverage of gravity stations (e.g., North America,
Europe, Australia), significant improvements are provided
over areas with sparse ground gravity coverage (e.g., Asia,
Africa, South America). For the latter regions, GGMplus pro-
vides for the first time a complete coverage with gravity at
ultrahigh spatial resolution, thus providing scientific aid to
many developing countries. In addition, GGMplus provides
crucial information to revise current standards for the maxi-
mum range of free-fall gravity accelerations over the Earth’s
surface. The computerized GGMplus gravity field maps are
freely available for science, education, and industry via
and http://ddfe.curtin.edu.au/gravitymodels/GGMplus.
[24] Acknowledgments. We are grateful to the Australian Research
Council for funding (DP120102441). This work was made feasible through
using advanced computational resources of the iVEC/Epic supercomputing
facility (Perth, Western Australia). We thank all developers and providers of
data used in this study. Full methods and detailed evaluation results are avail-
able in the supporting information, and information on data access via the
project’s website http://geodesy.curtin.edu.au/research/models/GGMplus.
[25] The Editor thanks two anonymous reviewers for their assistance in
evaluating this paper.
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