Regional Gravity Field Modelling using Adjausted Spherical Cap Harmonic Analysis

In this study, the problem of local gravity field modeling is investigated with thw aid of spherical cap harmonic analysis. To do so, the Dirikhlet boundary value problem for Laplace equation is solved for boundary condition prescribed on the surface of a spherical cap. In this case, the solution of Laplace equation is represented based on linear combinations of associated Legendre function of non-integer degree and integer order. To evaluate the performance of the model, a spherical cap zone located in northwest of Iran with a half-angle of one degree is selected and the local gravity data in the form airborn observations are simulated over the cap region using global geopotential model. Morover the simulated data are contaminated with random noise in order to better adapt with actual airborn observations. Using thses observation in series representation by pherical cap harmonic analysis, then, the geopotential coefficients for local gravity field are computed. Since the govering equations for determination of the cofficients suffer from an ill-condition problem, it is necessary that some regularization schemes are applied. Here, the Tikhonov regularization method is utilized to obtaine the regular solution. To validate the accuracy of proposed model over the cap region, results are compared with observation of gravity at some control points distribute both within the cap and on its margin.