Ali Ahmed Mohieldain Ali, PhD

Ali A. Mohieldain¹, N.P. Szabó¹ 

¹Department of Geophysics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary

Geophysical inversion is widely used to estimate subsurface properties and better understand geological structures. In this study, a three-dimensional gravity inversion was carried out to determine subsurface density variations using a series expansion–based inversion approach. The method is built on a linearized inversion framework in which the density model is represented as a weighted combination of orthogonal basis functions. This allows the subsurface to be described using a limited number of expansion coefficients rather than a large set of individual density values. Reducing the number of unknown parameters makes this approach particularly suitable when gravity data are sparse, as it improves the stability and solvability of the inverse problem. For comparison, both the conventional Gaussian least-squares method and the proposed series expansion–based inversion were applied independently. Their performance was evaluated using synthetic gravity data, including cases with significantly different initial models to test the ability of each method to recover the true subsurface structure. Additional tests were conducted using noisy synthetic data to examine the robustness of the inversion under realistic measurement conditions. The results show that both inversion approaches perform well and reliably minimize the misfit between observed and calculated gravity data when the inverse problem is overdetermined. However, in underdetermined situations—which are common in practical gravity surveys—the Gaussian least-squares solution becomes unstable unless extra constraints are introduced. In contrast, the series expansion–based method naturally reformulates the problem into a reduced parameter space, producing an overdetermined system and improving stability without the need for external constraints. The proposed method was also applied to field gravity data from the Shendi–Atbara Basin in Sudan. Although the application involves simplifying assumptions, such as representing the subsurface as a single vertical layer rather than a fully discretized 3D model, this choice was made to focus on assessing the feasibility and stability of the approach. Overall, the results demonstrate that the series expansion–based inversion method is a robust and effective alternative to the Gaussian least-squares approach, especially when gravity measurements are limited and sparsely distributed.