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Approximate Solution of Inverse Problems of Gravity Exploration on Fractals
Chaotic Modeling and Simulation International Conference
CHAOS 2021: 14th Chaotic Modeling and Simulation International Conference pp 97–108Cite as
Approximate Solution of Inverse Problems of Gravity Exploration on Fractals
- Conference paper
- First Online: 14 June 2022
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138 Accesses
Part of the Springer Proceedings in Complexity book series (SPCOM)
Abstract
The work is devoted to the approximate methods for solution direct and inverse problems of gravity exploration on bodies with a fractal structure. It is known that in order to construct mathematical models adequate to the geological reality, it is necessary to take into account the orderliness inherent in geological environments. One of the manifestations of orderliness is self-similarity, which remains during the transition from the microlevel to the macrolevel. Scaling of geological media can be traced in petrophysical data and in anomalous fields. It should be noted that in real structures there is no infinite self-similarity and scaling must be considered in a certain range. The work investigates analytical and numerical methods for solving inverse contact problems of the logarithmic and Newtonian potential in the generalized setting. In the case of a Newtonian potential, the problem is formulated as follows. It is required, having three independent functionals of the gravity field above the Earth's surface and additional information on the self-similarity of the disturbing body, to determine the depth, the density and the surface of the perturbing body.