HR: 1330h
AN: G32A-0739    [PDF]
TI: Constrained 3-D Linear Inversion of Geoid Anomalies
AU: * Leite, E P
EM: emilson@iag.usp.br
AF: Department of Geophysics, Astronomical and Geophysical Institute, University of Sao Paulo., Rua do Matao, 1226, Sao Paulo, SP 05508-900 Brazil
AU: Ussami, N
EM: naomi@iag.usp.br
AF: Department of Geophysics, Astronomical and Geophysical Institute, University of Sao Paulo., Rua do Matao, 1226, Sao Paulo, SP 05508-900 Brazil
AU: Pagiatakis, S
EM: spiros@yorku.ca
AF: Department of Earth and Atmospheric Science, Faculty of Pure and Applied Science, York University., 4700 Keele Street, Toronto, ON M3J 1P3 Canada
AB: Lithospheric-scale geoid anomalies with wavelength of $<$ 1000 km may provide independent geophysical evidence of mantle thermal state. In order to estimate the density distribution within the lithosphere from geoid anomalies, a constrained linear inversion technique is proposed for an arbitrarily shaped 3-D body by approximating it by a set of right-rectangular prisms. The forward problem is expressed by the gravitational potential given by Nagy et al. (2000). The geoid anomaly at each point on the surface of the Earth is the sum of the gravitational potential of all prisms, divided by the normal gravity. We take the first derivative of the gravitational potential with respect to density in order to compute the system sensitivity matrix (G), which is used in the inversion procedure. Non-uniqueness and instability problems are solved by minimizing two functionals that represent absolute and relative constraints, so that the absolute value of the difference between observed and calculated geoid anomalies is minimum in the least-squares sense. Inequality constraints are also introduced to represent lower and upper bounds for the densities. This method with the current computing capability allows us to invert large data sets with a sizable model space. Other advantages of this approach include: 1) geological and geophysical information can be incorporated to constrain the solution 2) it avoids problems related to wavenumber domain transforms, and 3) it is possible to analyse the solution in terms of resolution and variance. The algorithm was tested on synthetic models and a discussion of the potentialities of the method to solve real problems are also presented using as an example the case of a 8-meter amplitude positive geoid anomaly observed along the Eastern Brazilian continental margin.
DE: 1212 Earth's interior--composition and state (8105)
DE: 1234 Regional and global gravity anomalies and Earth structure
DE: 3210 Modeling
DE: 3260 Inverse theory
SC: Geodesy [G]
MN: 2003 Fall Meeting