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Mathematics, Vol. 12, Pages 3953: On a Numerical Solution to an Inverse Structural Density Problem with a Method of Local Corrections
Mathematics doi: 10.3390/math12243953
Authors: Alexander Tsidaev Igor Ladovskii
The structural gravimetry problem, which involves determining the geometry of a contact surface between two homogeneous layers based on observed gravity fields, is addressed in this paper. The method of local corrections is presented in a generalized form to improve its applicability to a broader range of problems. This study introduces several improvements to the local corrections method, including the use of a finite element approach for more accurate field calculations, particularly for near-surface boundaries. Additionally, the method incorporates prior knowledge of the boundary geometry, which serves as an initial approximation to enhance convergence and avoid potential divergence issues. Demonstrations on several synthetic examples are performed, which show the advantages of the generalized form of the method. For the territory of the Middle Urals, Russia, the refinement of two crustal boundaries is performed (the Moho boundary and middle crust boundary).
