CE 414 Physical Geodesy For Civil Engineering

Credit Structure: (2-2)3

Catalog Description:
Geodetic displacement measurements to evaluate the displacement coordinate and their differences and the time and displacement vector and its speed. Measurement of precise elevation data and levelling differences. Evaluation of 1st and 2nd order vertical derivatives in order to calculate the density contrasts to Bouguer anomaly map density, map vector of the anomolg surface and its depth differences and also static time.

Course Objectives:
Geoid, which is the equipotential surface of the earthís gravity potential, constitutes the fundamental reference surface for mapping as all survey operations and reductions refer to the gravity vector. This course is designed to provide the necessary theoretical background as well as computational skills which will enable the students to perform gravity observations, do all relevant reductions, and to compute a local or a regional geoid using gravity and/or satellite data.

Prerequisites:
None

Textbook(s):
Vanicek and Krakiwsky, “Geodesy: The Concepts”, North Holland Publications, 1987.

Reference(s):
Heiskenen and Moritz, “Physical Geodesy”, Freeman Publications, 1967.

Syllabus:
1. Singly, doubly and triply scalar vector fields, gradient, divergence, curl and Laplace operator, Gauss theorem, Green’s identities
2. Orthogonal curvilinear coordinate systems, scale factors, line, area, volume elements. Spherical, polar and ellipsoidal coordinate systems
3. Boundary value problems for a nearly spherical boundary, Dirichletís principle, boundary value problems of Dirichlet, Neumann and mixed types
4. Newtonian attraction, gravitational and gravity potentials, neutral coordinates, astronomical latitude, longitude and orthometric height
5. Ellipsoidal reference frame, solution of the boundary value problem for the normal field
6. Disturbing potential, gravity anomalies, deflection of vertical, orthometric and normal heights. Spherical harmonic series expansion of these quantities
7. Solution of geodetic boundary value problem, Stokeís and Vening-Meinesz's integrals
8. Terrestrial and satellite methods of gravity observations, gravity reductions, free air, Bouguer and isostatic gravity anomalies
9. Practical methods of geoid computation using Rice rings and gridded data
10. Combination of gravimetric and satellite data, Fourier transform techniques

Homeworks, Quizzes, Projects:
None

Computer Usage:
1. Computation of gravity reductions, Construction of grid and ring data from unequally spaced observations.
2. Computation of associated Legendre functions of the first kind and surface spherical harmonics up to the degree and order 180.
3. Quadrature methods of geogid and deflection computations.
4. Geoid computation for planar earth using fast Fourier transforms and convolutions.

Laboratory Work:
There will be a field project with the aim of establishing and adjusting a small gravity network using a LaCost Romberg gravimeter supplied by the eneral Command of Mapping.

Category Content:
Mathematics and Basic Scineces: None
Engineering Design: None
Engineering Sciences: 3 credits
Humanities & Social Sciences: None
Departmental: None

Instructors:
S. Mete Nakiboglu