الفهرس 
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Abstract
In accordance with the main objectives of the thesis, this PhD dissertation investigated the inversion-based Fourier transformation method on synthetic and in-situ measured datasets (western central part of Sinai Peninsula, Egypt) in three distinct categories; 1) reducing the outlier sensitivity by applying the inversion method to the synthetic 1D wavelet and 2D magnetic and gravity datasets, 2) analyzing the inversion approach in processing the non-regularly sampled complete datasets in 1D and 2D, 3) analyzing the incomplete sampling problem at various degrees of missing data. In the framework of this inversion method, the continuous Fourier spectrum is discretized using the series expansion method to solve our over-determined inverse problem in the form of the expansion coefficients. Moreover, for quick and accurate determination of the elements of the Jacobian matrix, the Hermite functions are constructed as basis functions making use of the favor that they are eigenfunctions of the Fourier transformation. To make the inversion algorithm more robust and resistant, the most frequent value (MFV) method is used to handle the problem of scale parameters by iteratively calculating the Cauchy-Steiner weights with the least amount of data loss. The results demonstrated that inversion-based 1D and 2D Fourier transformation approach is highly effective, robust, and applicable for reducing the outlier sensitivity regardless the data are taken over regular or non-regular sampling grids. In addition, the newly developed inversion method is applicable for processing the regularly, non-regularly, and randomly sampled incomplete datasets even when 50% of the measuring data points are missing. At higher ratios (when the over-determination rate is below 1.3) the results are highly distorted where the inverse problem is marginally over-determined.