G51B-0612
The use of ICAGM07 geoid model for vertical datum unification on Iberia and Macaronesian islands.
The vertical datum unification between two or more vertical datums separated by sea is one of the present day challenges of geodesy. In this paper, the first results of vertical datums unification between Iberia and Macaronesian islands (Azores, Madeira and Canary archipelagos) are presented. Such a vertical datums can be connected indirectly by the combination of precise geocentric coordinates of points on all datums determined by GNSS, their orthometric height (or potential) in the respective datum and the geoid height. For the later, ICAGM07 gravimetric geoid model was used. This geoid model incorporates updated terrestrial, airborne and shipborne free-air gravity anomalies, high resolution digital terrain models and the most recent geopotential model GGM02C. The main purpose of this geoid surface is to define a unified vertical datum for real time kinematics positioning within this geographic area. The geoid boundary value problem approach was used assuming that orthometric heights and gravity anomalies are refered to different height systems. The solution equation has k+1 parameters, where k is the number of local vertical datums considered. The first k parameters are the potential offsets relative to the global vertical datum and the last parameter is the difference in potential between the global vertical datum and the reference ellipsoid potential. The unknown off-sets between various datums were estimated in a least-squares adjustment with respect to a pre-defined W0=62636856.0m2s-2 using 1644 GPS/levelling points with geoid height given by ICAGM07 geoid model. The estimated vertical datum offsets ranging from - 1.17 m in Tenerife to 0.89 m on La Palma, on Canary, with an offset of -0.35m for Portugal mainland and - 0.49m for Spain mainland. The relative offset between Portugal and Spain (within Iberia) is close to the 16 cm obtained from the EUVN, revealing a very good precision of this geoid model for the vertical data unification.
G51B-0613
Current Geoid Studies in Turkey and the need for Local High-Precision Astrogeodetic Geoid Determination Using CCD/Zenith Cameras
During the last few years, the development of CCD image sensors at a reasonable price made the instruments of astrogeodetic observation possible to use for local high-precision astrogeodetic geoid and gravity field determination. Generally, the geoids of most European countries are in centimeter level accuracy except in mountainous regions. Turkish geoid also has accuracy problems in mountainous regions especially in the eastern parts of Anatolia and around boundaries of Marmara Sea. Studies performed in Europe in last decade indicate that, to reach the centimeter level accuracy in mountainous areas, astrogeodetic vertical deflections are more effective than gravimetric and other geoid determination methods. Turkey had started the geoid determination studies in 1976 with 13 absolute gravity points. Turkish National Fundamental Gravity Network (TNFGRN), densificated with 1st and 2nd order 66245 gravity points in Potsdam Gravity datum. TG03 has a final internal precision of 1 cm at the observation points and the external accuracy is within decimeter level. High precision in astrogeodetic geoid determination techniques are scarcely published by some universities around Europe using CCD/Zenith cameras. There are various zenith camera systems developed as state-of- art instrumentations using both CCD sensors for imaging stellar objects and GPS receivers for ellipsoidal coordinates, in order to determine the direction of the plumb line. These systems are designed and tested where conventional techniques are not sufficient. In this study, increasing accuracy of Turkish geoid is subjected to using CCD/Zenith cameras in the province of Istanbul. The planning test area is going to use the data available on the GPS/Leveling geoid of Istanbul and produce astrogeodetic data on a profile starting from the north shore of Marmara region, passing through the Marmara Sea to the south. The astrogeodetic instruments will be designed for engineering studies that are needed to determine vertical deflections to use ellipsoidal heights derived from GPS.
G51B-0614
A Local Geoid Model at South/East Part of Brazil
The south/east part of Brazil is the most important economic region of the country. It covers the important Paraná basin with a very thick layer of sediments. The gravity data coverage is quite complete in the area and that is the reason for a specific effort to derive a geoid model in this region. GRACE and EGM08 models have been used as a reference field restricted to degree and order 150. The model has been validated over GPS observations on Bench Marks of the spirit leveling network, where the geoidal height was derived from the association of the geodetic height and the orthomeric height. The height anomaly derived from EGM08 (order and degre 2160) has also been checked against the GPS points. The short wave length component of the geoid has been derived using the modified Stokes integral through the Canadian package SHGEO.
G51B-0615
An Experimental High Spatial Resolution Gravimetric Local Quasi-geoid Model for the Lake Tahoe Region, California-Nevada, USA - the Influence of Model Resolution, Topography, Bathymetry, Gravity, and Geologic Structure
The mountainous Lake Tahoe region is used to demonstrate and field test the computation of a high spatial resolution (400 m) local quasi-geoid model that also defines Lake Tahoe surface heights. For the preferred geologic model, the lake surface exhibits a concave, eastward-shifted asymmetric 50 cm height undulation with 35 cm variation expressed N-S along its eastern shoreline. Significant local features up to 20 cm over 10 km, and gradients of 13 cm/km are associated with major topographic changes. The computation method uses a synthetic gravity model which incorporates grid-interpolated complete Bouguer anomaly (CBA) gravity observations and theoretical free-air gravity based on a 400 m, volume- equivalent terrain model at 2.67g/cc density, with an MSL bottom. Terrain, crustal root, and mantle density variations are represented by the CBA observations. Two-dimensional Fourier wavenumber domain vertical integration of the synthetic gravity field is used to estimate the geopotential number anomaly on the synthetic terrain surface. The geopotential number anomaly is converted to a normal height anomaly, which is then related to a quasi-geoid. After its correction to helmert orthometric heights, low-order polynomials are removed from the quasi-geoid and replaced by polynomials derived from the gravitational geoid model NGS USGG 2003. The model approach effectively separates the terrain and CBA models and facilitates easy upgrades using only terrain or gravity difference grids. The effect of a hypothesized sedimentary basin under Lake Tahoe is investigated. Although, when positioned to approximate MSL, the local quasi-geoid is not an equal potential, when interpreted near the topographic surface, it is a scaled approximation to one. Hence, lateral change in the quasi-geoid will reflect change in the lake surface heights. Normalizing the geopotential number anomaly by the area's average surface gravity value, rather than the mean normal gravity value beneath each terrain cell will further improve relative height accuracy. As a test, three precision GPS ellipsoid height differences were measured along the shoreline; they diverged from the model by 6 cm in 25 km. Differences greater than 2 cm (GPS error) suggest the need to improve the gravity coverage in the adjacent mountains and over the lake using airborne gravity surveying.
G51B-0616
USGG08 – A new gravimetric geoid for the US
USGG08 is a new 1'x1' gravimetric geoid for the US. It is based on Analytical Downward Continuation using EGM08 to degree 2160 as a reference model. The new geoid is computed using the DNSC08 and SIO/NOAA altimetry-derived anomalies, some new Canadian and US surface gravity data and new airborne gravity in the Gulf of Mexico and Florida. USGG08 is the first US gravimetric geoid to use GRACE for determining the very long wavelength effects of the gravity field, rather than using terrestrial gravity data for those wavelengths. This paper will focus on the new data and their influences on the computed geoid, by comparison to GPS/Leveling and astro-geodetic control data. Also, the effect of the long wavelength content of the surface data versus that of GRACE is discussed.
G51B-0617
High Resolution DEM over Alaska and Its Application to Geoid Modeling
Many gravimetric quantities such as Terrain Corrections (TC), direct topographical effects on gravity, and indirect effects on geoid require accurate and high resolution Digital Elevation Models (DEM). Several DEM models, including the National Elevation Data (NED), the Shuttle Radar Topography Mission (SRTM) data, the Canadian data, and the ICESAT data are partially overlapped in Alaska. However, in addition to the different spatial resolutions, these DEMs refer to different datums, which may cause up-to half-kilometer horizontal differences. To establish a uniform DEM, first, we transformed these different coordinate systems into the same horizontal datum (WGS84 (G1150)), and the same vertical datum (the "mean sea level"). Then, the Cubic spline function is employed to resample and to filter the data in order to minimize artifacts and edge effects, as well as to fill the areas of missing data. Finally, a 3x3 arc-seconds DEM is obtained in Alaska and its neighboring areas. This high resolution DEM together with the gravity anomalies from surface data, airborne gravimetry, and altimetry, as well as the ArcGP will be more representative of the true gravity field. A new geoid for Alaska is determined by a Stokes type integral, whose kernel is modified to include the long wavelength components generated by the 5 arc-minute EGM08 model. Comprehensive comparisons will be conducted to analyze the effects of the DEM and the new gravity data as well as the methodology on the accuracy of the geoid.
G51B-0618
GRAV-D Part II : Examining Airborne Gravity Processing Assumptions With an Aim Towards Producing a Better Gravimetric Geoid
The primary objective of the GRAV-D (Gravity for the Redefinition of the American Vertical Datum) project is to redefine the American vertical datum by using an improved gravimetric geoid. This will be partially accomplished through an extensive airborne gravity measurement campaign, focusing first on the land/water interface (and later on interior areas) of the US and its holdings. This airborne campaign is designed specifically to capture intermediate wavelength gravity information by flying at high altitudes (35,000 ft, ~10 km) with a 10 km line spacing. The intermediate wavelengths captured by airborne gravity data are complementary to ground and satellite gravity data. Combining the GRAV-D airborne gravity data with the Gravity Recovery and Climate Experiment (GRACE) satellite gravity field will allow existing terrestrial data sets to be corrected for bias and trend problems. Ultimately, all three types of data can then be merged into a single accurate representation of the gravity field. Typically, the airborne gravity data reduction process is used to produce free-air anomalies for geological/geophysical applications that require more limited accuracy and precision than do geodetic applications. Thus we re-examine long-standing data reduction simplifications and assumptions with an aim toward improving both the accuracy and precision of airborne gravity data before their inclusion into a gravimetric geoid. The data reduction process is tested on a 400 km x 500 km airborne gravity survey in southern Alaska (in the vicinity of Anchorage) collected in the summer of 2008 as part of the GRAV-D project. Potential improvements in processing come from examining the impacts of various GPS processing schemes on free-air gravity results and re-considering all assumptions in standard airborne gravity processing methods, especially those that might introduce bias into absolute gravity levels.
G51B-0619
On the Use of the EGM08 Geopotential Model for Local Geoid Computations
Local geoid computations have been traditionally based on the Helmert condensation philosophy. The topography is condensed into a thin layer on the geoid while the direct effect corrected gravity anomaly is downward continued to the geoid. Numerically, this is done by replacing the surface free air gravity anomaly by the Faye anomaly. On the other hand, geopotential models (GPMs) have been developed by harmonic analysis of analytically downward continued surface free air gravity anomalies. Thus, the Faye anomaly is incompatible with free air anomaly synthesized using a GPM, since each of these anomalies describes a different gravity field. Yet, GPMs in the form of spherical harmonic coefficients of degree and order 360 or lower have been used in Helmert-condensation geoid computations in a simple remove-restore fashion. The fact that these models are incompatible with Helmert's condensation has been ignored since it used to cause only small long wavelength geoid errors. This situation has changed by EGM08, which is developed up to degree and order 2160. This model provides an unprecedented resolution and accuracy, exposing even the smallest of incompatibility errors. Achieving best results in local geoid computations using EGM08 will depend on how the topographic and gravity reductions are performed. As an example, when EGM08 to 2160 is used as a reference field in US geoid computations, the precision of the geoid (as compared to GPS/Leveling control) is 9.1 cm with Helmert's condensation and 7.28 cm using analytical downward continuation. This paper discusses the proper use of high resolution GPMs, such as EGM08, in combination with the Helmert and harmonically continued gravity anomalies in local geoid computations. Numerical results over the United States are presented.
G51B-0620
Combination of Earth Gravity Model EGM08, Local Gravity Data and GNSS Observations for Determination of Normal Heights
The Earth Gravity Model EGM08 is very suitable as reference gravity field for physical height determination. The EGM08 model, local gravity data and GNSS observations are used for normal height determinations. The normal heights are tested using classical leveling/gravity method. The paper presents the practical solution of normal height determination using second modified boundary value problem in the area of Slovakia.
G51B-0621
Sub-surface Models of Long- and Short-wavelength Gravity Anomalies in Pennsylvania
Over the past several years we have been collecting and compiling gravity data in various areas in
Pennsylvania to complement existing data previously compiled by the National Image and Mapping Agency
and GeoNet. Supported by the Pennsylvania Geological Survey, the aim of this project is to generate a
gravity map for the state. This has involved the collection of approximately 4000 new observations and
identification of previously acquired data from other sources that had not been included in the above listed
data bases. While we are still in the process of cleaning up the data set, it is now possible to use the data to
model subsurface density changes for both short and long-wavelength anomalies.
An intriguing feature of the gravity map of Pennsylvania is the long-wavelength NE-SW-trending positive and
negative anomalies that have little direct correlation with the observed surface geology. The negative
anomalies range in amplitude from -12 to - 40 mgals, with wavelengths from 80 to 150 km, while the positive
anomalies have amplitudes from 11 to 54 mgals and wavelengths between 100 and 135 km. We have
modeled several of these using both wavelength analysis and simple two-dimensional modeling. The results
suggest that, unlike previous interpretations that suggested shallow basins or intrusions, part of the cause of
these anomalies may be as deep as topographic variations at the crust-mantle boundary.
With well-constrained regional trends we have also been able to use these data to isolate and model short-
wavelength anomalies. Within the Newark Basin in southeastern Pennsylvania one focus has been on the
diabase intrusions. The gravity data demonstrate a remarkable special coincidence of 5 to 10 mgal positive
anomalies with the known outcrop pattern of the sills, however there are also some areas where the sill is
observed to outcrop, but where the gravity signature is minimal or does not exist. The density models of the
sills range in thickness from .3 km to almost 1 km and generally increase in structural thickness from east to
west, suggesting a possible source towards the west-central portion of the basin, or conversely greater
removal of material (and uplift) towards the east.
http://ww2.lafayette.edu/~malincol/GravityProject.html
G51B-0622
The Combined Effect Model: A New Isostatic Compensation Technique
Processes controlling the relative timing and overall relationship between extension and magmatism are not well understood. Because buoyancy is the force that propels magma toward the earth's surface, the density contrast between the magma and the surrounding rock is a major control on magma ascent. Therefore, crustal density may be a primary control on the location and timing of volcanism, especially mafic eruptions. Isostatic gravity anomaly data are used to infer upper crustal density, and the method used for the isostatic correction should be considered as a possible source of error in gravity models. The isostatic gravity anomaly reflects density heterogeneities within the upper crust and is useful for interpreting structural features, tectonic evolution, and inferring the location of both magma bodies and dense deposits. The long wavelength isostatic correction is meant to remove from the gravity data set the effect of rock masses supporting high topography. Errors in the isostatic correction produce errors in the isostatic anomaly and therefore in the interpretation of the crustal density. The two most commonly used methods of isostatic correction, the Airy-Heiskanen and Pratt-Hayford correction techniques, were developed in the early to mid twentieth century when the nature of the lower crust and upper mantle and the interface between the two was largely unknown. Increased understanding of the true crust and mantle boundary makes a new comparison of isostatic correction methods appropriate. A comparison of Airy-Heiskanen and Pratt-Hayford correction techniques was conducted to assess the impact the differences in correction technique have on isostatic gravity anomaly values, and thus on the results of gravity modeling. A difference of as much as 30 mgal over 36 km in areas of rapidly changing elevation was indicated by the comparison. A new isostatic compensation technique, the Combined Effect Model, uses both Airy and Pratt type isostatic compensation and the increased understanding of the depth to Moho. The model uses constant density crust, depth to Moho values obtained from seismic data, and assumes isostatic equilibrium to calculate upper mantle density. The isostatic support is then calculated from contributions provided by both the laterally varying density in the upper mantle and the crustal root.
G51B-0623
Determination of the geopotential difference based on gravity frequency shift equation
Based on general relativity theory (GRT), an atomic clock at a position with higher gravity potential (geopotential) runs faster (with a higher frequency) than a clock at a position with lower geopotential. The geopotential difference between two arbitrary points P and Q is related with the difference (shift) between the frequencies of the clocks located at P and Q by an equation, which is referred to as the gravity frequency shift equation. Conventionally, the geopotential difference between two points P and Q located on the Earth's surface are determined by gravimetry and leveling, the drawback of which is that it is almost impossible to connect these two points in the case that they are located on two continents or islands separated by ocean. In the present paper the basic idea and realization for determining the geopotential difference between two points on ground or in space based on the gravity frequency shift equation are provided. On an arbitrary equigeopotential surface, there does not exist the frequency shift of an electromagnetic wave signal. However, between two different equi-geopotential surfaces, there exists the frequency shift of an electromagnetic wave signal. Then, after measuring the frequency shifts of electromagnetic wave signals, especially the GPS signals, between the two points P and Q, one can determine the geopotential difference between these two points. The approach is stated as follows. GPS signals are emitted and two receivers at P and Q receive the signals coming from the GPS satellite simultaneously. The signals are recorded by receivers at P and Q with different frequencies, and consequently the frequency difference (shift) between the frequencies received by the receivers located at P and Q is determined. Then, the geopotential difference between these two points is determined. Using a data series (GPS signals) covered 24 hours at a station we calculated the frequency shift between the atomic clocks located at the station and a satellite. From the calculated results two conclusions have been drawn out: 1) the frequency shift equation based on GRT is correct at least to the accuracy level of 10-3; 2) it is necessary to use time-keeping system (atomic clock) with the accuracy level of about 10-15 to determine the geopotential difference at the accuracy level of 1 m2s-2. This study is supported by National 863 Program of China (grant No. 2006AA12Z211) and the National Natural Science Foundation of China (grant No. 40637034).
G51B-0624
Global Map of the Ice and Sediment Stripped BT Gravity Disturbances
We compile a global map of the gravity disturbances corrected for the effects of the topography of average crustal density and of density contrasts of oceans, sediments, and ice using techniques for a spherical harmonic analysis of the gravity field. The gravity disturbances are computed from the coefficients of a global geopotential model (GGM) with a spectral resolution complete to degree 180 of spherical harmonics. The same spectral resolution is used to compute the topographical correction and the bathymetric stripping correction to the gravity disturbances. The coefficients of a global elevation model (GEM) are used to compute the gravitational attraction due to the topography, adopting the average crustal density 2670 kg/m3. The coefficients of a global bathymetric model (GBM) are used to compute the gravitational attraction due to the ocean density contrast, adopting the mean ocean saltwater density 1030 kg/m3. The ice and sediment stripping corrections involve the forward modelling of the gravitational attraction of ice and (marine and continental) sediment density contrasts. The coefficients of a global ice thickness model (GITM) complete to degree and order 90 (generated from the 2×2 arc-deg geographical grid of ice thickness data) are used to compute the gravitational attraction due to the ice density contrast, adopting the mean ice density 913 kg/m3. The global data of sediment thickness and density with the 2×2 arc-deg geographical resolution are used to compute the gravitational attraction due to the sediment density contrast. The results reveal that the minima of the ice and sediment stripped BT gravity disturbances are located in the mountainous regions where the negative values reach several hundreds milligals; from our numerical estimation the extreme minima is -382.8 mGal. Over the flat continental regions, the ice and sediment stripped BT gravity disturbances are mostly within the interval from 100 to 200 mGal. The convergent ocean to continent tectonic plate boundaries represents the regions with the largest variations of the ice and sediment stripped BT gravity disturbances. The maxima are located over the areas of the open ocean where they reach several hundreds milligals; the extreme maxima is 748.3 mGal. Since we use the spherical representation up to degree 180, it is expected that the signal due to the residual anomalous density within the topography is highly suppressed and our global map unveils the signal of density anomalies from deeper in the crust and the upper mantle. However, the map is expected to be dominated by the signal due to the isostatic compensation, as well as (offshore) by the relief of the ocean floor. The signature of the lithospheric plates is also identifiable.