GMT322 – GEODESY-1

1. GMT322 – GEODESY-1 Lecture5 Dr. Kamil Teke

2. Geoid types (IERS Conventions) • Observed (instantaneous) geoid (at epoch t): W = W0 = Vgeo + Vcentrifugal + Vtidalpermanent + Vtidalperiodic + Vdeformationpermanent + Vdeformationperiodic • Meantide geoid (≈mean ocean surface): W = W0 = Vgeo + Vcentrifugal + Vtidalpermanent+ Vdeformationpermanent • Zero-tide geoid: W = W0 = Vgeopotential + Vcentrifugal + Vdeformationpermanent • Tide-free geoid: (Tide-free crust : e.g., ITRF2014, VTRF2008, ...) W = W0 = Vgeo + Vcentrifugal Nominal love numbers Petit G., and Luzum B. (2010). IERS Conventions 2010, IERS Technical Note ; 36, Frankfurt am Main: Verlag des BundesamtsfürKartographie und Geodäsie, ISBN 3-89888-989-6.

3. Height anomaly and Telluroid (Hirvonen, 1960, 1961) • The surface whose normal potential U at every point Q is equal to the actual potential W at the corresponding topography point P on the same ellipsoid normal. UQ = WP • Her P topografya noktasındaki gerçek gravite potansiyeline (Wp) eşit olan normal gravite potansiyeline (UQ) sahip bir Q noktası vardır. Q noktalarının oluşturduğu yüzeye Telluroid denir. Ellipsoid height = normal height + height anomaly

4. Geoid height (geoid undulation), height anomaly, telluroid geoid and ellipsoid topography and telluroid Molodensky et al. 1962 Franz Barthelmas (2009). Definition of functionals of the geopotential and their calculation from spherical harmonic models. Scientific Technical Report STR09/02. Deutsches Geoforschunszentrum, Potsdam.

5. Gravity Anomaly (), Disturbing gravity () Classic Definiton of gravity anomaly Gravity anomaly definition by Molodensky vd. 1962

6. Deflections of vertical • The direction of the gravity anomaly (geoid undulation) vector is called as the deflection of vertical. In other words, the deflection of gravity vector direction at the geoid from the corresponding normal gravity vector direction. • The direction of the gravity disturbance vector is also called as the deflection of vertical. Because, the directions of and coincide virtually. north-south component east-west component Bernhard Hofmann-Wellenhof ve Helmut Moritz (2006) Physical Geodesy, Second Edition, Springer, Wien, NewYork, ISBN-10 3-211-33544-7.

7. Deflections of vertical The relation between geoid undulation (N) and deflection of vertical ()

8. Gravity reduction • The objective of the Bouguer reduction of gravity is the complete removal of the topographic masses, that is, the masses outside the geoid. G = 6.67428*10^(-11); % Newtonian gravitational constant (m3*kg-1*s-2) Bouguer plate Spherical shell approximation • Due to the assumption of no masses above the geoid may be interpreted in the sense that such masses have been mathematically reduced beforehand, e.g. using Bouguer plate, the free-air reduction of gravity should be carried out to reduce the gravity from the height of the topography to the geoid surface.

9. Gravity reduction – Bouguer gravity and Bouguer anomaly • Combined process of removing the topographic masses (Bouguer plate) and applying the free-air reduction is called complete Bouguer reduction. Its result is Bouguer gravity at the geoid. • now refers to the geoid, then we can derive the gravity anomalies by subtracting the normal gravity referred to the ellipsoid by the following equation. are called as Bouguer anomalies.

10. Gravity reduction – Terrain correction • The deviation of the actual topography over the geoid can be reduced directly (instead of Bouguer plate or a shell) and then a free-air reduction can be introduced to the observed gravity at the topography. For example: EGM2008 used SRTM 3’’(Digital elevation/terrain model: Shuttle Radar Topography Mission) IDEMS (IGFS), DEM products : SRTM, ACE, ACE2, ASTER, GLOBE, GTOPO30,

11. Poincare and Prey gravity reduction • The reduction of Poincare and Prey, abbreviated as Prey reduction yields the actual gravity which would be measured inside the Earth if it were possible. Its purpose is, thus, completely different from the purpose of the other gravity reductions which give boundary values at the geoid. • W=WQ üzerindeki tüm kitleleri kaldır. P noktasında ölçülen g’den çıkar. • P noktasından Q noktasına g’ ye serbest hava indirgemesi yap. • Kaldırdığın kitleleri yerine koy. gP P noktasında ölçülen gravite 1- Bouguer plakasını kaldır....................................................... – 0.1119(HP – HQ) 2- P den Q ya serbest hava indirgemesi yap............................ + 0.3086 (HP – HQ) 3- Bouguer plakasını ekle......................................................... – 0.1119(HP – HQ) Q daki gravite ............... gQ= gP + 0.0848 gal km-1 x (HP – HQ) km

12. Calculation of geoid undulation from Bruns equation Bruns equation (iterative approach) • Homework2 • Q1: At a control point of which geodetic (ellipsoid) latitude is 30 degrees, the gravity is measured as gT = 979,8532 gal. The orthometric height of this point is known as 763 meters. • Calculate the Bouguer gravity (gb) of the corresponding geoid point P. • (Ab = 85.4, F = 235.5, gb = gT - Ab + F = 980003.2 mgal) • Calculate the Bouger anomaly (gp) of P with respect to the normal gravity of the WGS84 ellipsoid (). (=979324.7 mgal, gp= gp= 678.5 mgal • Calculate the gravity disturbunce (gT) of the the same control point with respect to the normal gravity of the WGS84 ellipsoid (). (gT= gT= 979853.2 - 979089.3 = 763.9 mgal) • Calculate the actual gravity which would be measured inside the Earth for a point Q of which orthometric height is 189 meters and located in the same plumb line of the gravity observed control point. • (Ab = 64.3, F = 177.1 , gprey= gT - Ab + F - Ab= 979901.7 mgal

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