Application of a modified fou rier transformation for modeling variations in the gravity field

Introduction. The analysis and processing of signals with complex structures — particularly those exhibiting frequency and phase modulation — remains a relevant challenge, especially in cases where traditional methods fail to provide sufficient accuracy. This study considers a modified Fourier transformation suitable for processing signals with modulated frequency and phase, referred to in the article as frequency-phase modulated (FPM) signals.

Objective. To develop and apply a modified Fourier transformation for obtaining the amplitude-frequency characteristics (AFC) of FPM signals, aiming to improve the accuracy of signal fitting and to address problems related to modeling the responses of complex systems.

Materials and methods. The proposed transformation is applied directly to FPM signals and, due to its strictly periodic structure, enables the accurate determination of their AFC. The method was tested on gravimetric data acquired using the GNU-KB and CG-6 gravimeters. These data represent detrended temporal fluctuations of the gravity field, which are typically difficult to describe and interpret using conventional methods.

Results. It has been demonstrated that the proposed transformation effectively addresses the problem of determining the AFC of FPM signals, including those embedded within the transformation itself. The results show a high degree of fitting accuracy, thereby offering new opportunities for analyzing the responses of complex systems without the need for detailed physical modeling.

Conclusion. The modified Fourier transformation may serve as a valuable tool for constructing fitting functions in the form of AFCs when studying complex systems. In gravimetry, this approach opens new prospects for both fundamental research and the solution of applied geological and geophysical problems.

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