Integral formulas for geopotential coefficient determination from gravity anomalies versus gravity disturbances

1989 ◽  
Vol 63 (2) ◽  
pp. 213-221 ◽  
Author(s):  
Lars E. Sjöberg
Keyword(s):  
Gravity Anomalies ◽  
Integral Formulas ◽  
Geopotential Coefficient ◽  
Gravity Disturbances

Towards an updated, enhanced regional gravity field solution for Antarctica

2021 ◽  
Author(s):  
Mirko Scheinert ◽  
Philipp Zingerle ◽  
Theresa Schaller ◽  
Roland Pail ◽  
Martin Willberg
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Data Set ◽  
Gravity Field Model ◽  
Terrestrial Gravity ◽  
Field Solution ◽  
Gravity Disturbances ◽  
Regional Gravity

<p>In the frame of the IAG Subcommission 2.4f “Gravity and Geoid in Antarctica” (AntGG) a first Antarctic-wide grid of ground-based gravity anomalies was released in 2016 (Scheinert et al. 2016). That data set was provided with a grid space of 10 km and covered about 73% of the Antarctic continent. Since then a considerably amount of new data has been made available, mainly collected by means of airborne gravimetry. Regions which were formerly void of any terrestrial gravity observations and have now been surveyed include especially the polar data gap originating from GOCE satellite gravimetry. Thus, it is timely to come up with an updated and enhanced regional gravity field solution for Antarctica. For this, we aim to improve further aspects in comparison to the AntGG 2016 solution: The grid spacing will be enhanced to 5 km. Instead of providing gravity anomalies only for parts of Antarctica, now the entire continent should be covered. In addition to the gravity anomaly also a regional geoid solution should be provided along with further desirable functionals (e.g. gravity anomaly vs. disturbance, different height levels).</p><p>We will discuss the expanded AntGG data base which now includes terrestrial gravity data from Antarctic surveys conducted over the past 40 years. The methodology applied in the analysis is based on the remove-compute-restore technique. Here we utilize the newly developed combined spherical-harmonic gravity field model SATOP1 (Zingerle et al. 2019) which is based on the global satellite-only model GOCO05s and the high-resolution topographic model EARTH2014. We will demonstrate the feasibility to adequately reduce the original gravity data and, thus, to also cross-validate and evaluate the accuracy of the data especially where different data set overlap. For the compute step the recently developed partition-enhanced least-squares collocation (PE-LSC) has been used (Zingerle et al. 2021, in review; cf. the contribution of Zingerle et al. in the same session). This method allows to treat all data available in Antarctica in one single computation step in an efficient and fast way. Thus, it becomes feasible to iterate the computations within short time once any input data or parameters are changed, and to easily predict the desirable functionals also in regions void of terrestrial measurements as well as at any height level (e.g. gravity anomalies at the surface or gravity disturbances at constant height).</p><p>We will discuss the results and give an outlook on the data products which shall be finally provided to present the new regional gravity field solution for Antarctica. Furthermore, implications for further applications will be discussed e.g. with respect to geophysical modelling of the Earth’s interior (cf. the contribution of Schaller et al. in session G4.3).</p>

scholarly journals Global atmospheric effects on the gravity field quantities

2009 ◽  
Vol 39 (3) ◽  
pp. 221-236 ◽  
Author(s):  
Robert Tenzer ◽  
Peter Vajda ◽  
Keyword(s):  
Density Distribution ◽  
Gravity Field ◽  
Gravity Anomalies ◽  
The United States ◽  
Lower Atmosphere ◽  
Atmospheric Effects ◽  
Atmospheric Density ◽  
Standard Atmosphere ◽  
Gravity Disturbances ◽  
United States Standard

Global atmospheric effects on the gravity field quantitiesWe compile the global maps of atmospheric effects on the gravity field quantities using the spherical harmonic representation of the gravitational field. A simple atmospheric density distribution is assumed within a lower atmosphere (< 6 km). Disregarding temporal and lateral atmospheric density variations, the radial atmospheric density model is defined as a function of the nominal atmospheric density at the sea level and the height. For elevations above 6 km, the atmospheric density distribution from the United States Standard Atmosphere 1976 is adopted. The 5 × 5 arc-min global elevation data from the ETOPO5 are used to generate the global elevation model coefficients. These coefficients (which represent the geometry of the lower bound of atmospheric masses) are utilized to compute the atmospheric effects with a spectral resolution complete to degree and order 180. The atmospheric effects on gravity disturbances, gravity anomalies and geoid undulations are evaluated globally on a 1 × 1 arc-deg grid.

scholarly journals Harmonica and Boule: Modern Python tools for geophysical gravimetry

2021 ◽  
Author(s):  
Leonardo Uieda ◽  
Santiago R. Soler ◽  
Agustina Pesce ◽  
Lorenzo Perozzi ◽  
Mark A. Wieczorek
Keyword(s):  
Community Involvement ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Point Sources ◽  
Magnetic Data ◽  
Spherical Coordinates ◽  
Forward Modelling ◽  
Free Air ◽  
Gravity Disturbances ◽  
Gravity And Magnetic Data

&lt;p&gt;Gravimetry is a routine part of the geophysicists toolset, historically used in geophysics following the geodetic definitions of gravity anomalies and their related &amp;#8220;reductions&amp;#8221;. Several authors have shown that the geodetic concept of a gravity anomaly does not align with goals of gravimetry in geophysics (the investigation of anomalous density distributions). Much of this confusion likely stems from the lack of widely available tools for performing the corrections needed to arrive at a geophysically meaningful gravity disturbance. For example, free-air corrections are completely unnecessary since analytical expressions for theoretical gravity at any point have existed for over a decade. Since this is not easily done in a spreadsheet or short script, modern tools for processing and modelling gravity data for geophysics are needed. These tools must be trustworthy (i.e., extensively tested) and designed with software development and geophysical best practices in mind.&lt;/p&gt;&lt;p&gt;We present the Python libraries Harmonica and Boule, which are part of the Fatiando a Terra project (https://www.fatiando.org). Both tools are open-source under the permissive BSD license and are developed in the open by a community of geoscientists and programmers.&lt;/p&gt;&lt;p&gt;Harmonica provides tools for processing, forward modelling, and inversion of gravity and magnetic data. The first release of Harmonica was focused on implementing methods for processing and interpolation with the equivalent source technique, as well as forward modelling with right-rectangular prisms, point sources, and tesseroids. Current work is directed towards implementing a processing pipeline for gravity data, including topographic corrections in Cartesian and spherical coordinates, atmospheric corrections, and more. The software is still in early stages of development and design and would benefit greatly from community involvement and feedback.&lt;/p&gt;&lt;p&gt;Boule implements reference ellipsoids (including oblate ellipsoids, spheres, and soon triaxial ellipsoids), conversions between ellipsoidal and geocentric spherical coordinates, and normal gravity calculations using analytical solutions for gravity fields at any point outside of the ellipsoid. It includes ellipsoids for the Earth as well as other planetary bodies in the solar system, like Mars, the Moon, Venus, and Mercury. This enables the calculation of gravity disturbances for Earth and planetary data without the need for free-air corrections. Boule was created out of the shared needs of Harmonica, SHTools (https://github.com/SHTOOLS), and pygeoid (https://github.com/ioshchepkov/pygeoid) and is developed with input from developers of these projects.&lt;/p&gt;&lt;p&gt;We welcome participation from the wider geophysical community, irrespective of programming skill level and experience, and are actively searching for interested developers and users to get involved in shaping the future of these projects.&lt;/p&gt;

scholarly journals COMPUTATION OF GRAVITY FIELD FUNCTIONALS WITH A LOCALIZED LEVEL ELLIPSOID

2021 ◽  
Vol 6 (24) ◽  
pp. 226-242
Author(s):  
Chivatsi Jonathan Nyoka ◽  
Ami Hassan Md Din ◽  
Muhammad Faiz Pa’suya
Keyword(s):  
Gravity Field ◽  
Spherical Harmonic ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Earth’S Gravity Field ◽  
Geopotential Models ◽  
Gravity Disturbances ◽  
Zero Degree ◽  
Equipotential Surfaces ◽  
Best Fit

The description of the earth’s gravity field is usually expressed in terms of spherical harmonic coefficients, derived from global geopotential models. These coefficients may be used to evaluate such quantities as geoid undulations, gravity anomalies, gravity disturbances, deflection of the vertical, etc. To accomplish this, a global reference normal ellipsoid, such as WGS84 and GRS80, is required to provide the computing reference surface. These global ellipsoids, however, may not always provide the best fit of the local geoid and may provide results that are aliased. In this study, a regional or localized geocentric level ellipsoid is used alongside the EGM2008 to compute gravity field functionals in the state of Johor. Residual gravity field quantities are then computed using GNSS-levelled and raw gravity data, and the results are compared with both the WGS84 and the GRS80 equipotential surfaces. It is demonstrated that regional level ellipsoids may be used to compute gravity field functionals with a better fit, provided the zero-degree spherical harmonic is considered. The resulting residual quantities are smaller when compared with those obtained with global ellipsoids. It is expected that when the remove-compute-restore method is employed with such residuals, the numerical quadrature of the Stoke’s integral may be evaluated on reduced gravity anomalies that are smoother compared to when global equipotential surfaces are used

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