Testing The Noise Rejection Capability Of The Inversion Based Fourier Transformation Algorithm Applied To 2d Synthetic Geomagnetic Datasets

Abdelaziz, Mahmoud Ibrahim and Dobróka, Mihály (2020) Testing The Noise Rejection Capability Of The Inversion Based Fourier Transformation Algorithm Applied To 2d Synthetic Geomagnetic Datasets. GEOSCIENCES AND ENGINEERING: A PUBLICATION OF THE UNIVERSITY OF MISKOLC, 8 (13). pp. 70-82. ISSN 2063-6997

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Abstract

For signal processing, different algorithms can be applied to enhance the quality of measured datasets that contain simple or complex noises during the field survey. Treating these noisy data can be done using the discrete Fourier transform (DFT based noise filtering) which converts the data from time to a frequency domain but in some cases is not preferable due to its low noise suppression capability. Therefore, a robust and effective 2D inversion called the iteratively reweighted least-squares Fourier transformation (IRLS-FT) method is applied. In the framework of this inversion, the continuous Fourier spectrum is discretized using the series expansion to solve our inverse problem in the form of the expansion coefficients. Moreover, the Hermite functions are used as basis functions with the distinguishing feature of the Fourier transform eigenfunctions to facilitate and speed up the calculation of the Jacobian matrix without complex integration. In the robust inversion studied in the article, the Steiner weights are calculated through an internal iteration loop instead of Cauchy weights to overcome the problem of scale parameters. In this paper, the 2D IRLS-FT inversion method is applied to synthetic magnetic datasets and their reduction to the pole. The results demonstrated that the method is very stable during the procedures as well as its robustness, resistance, and effectiveness in the process of noise rejection.

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