2015/08/18 by V. S. Sizikov, Sizikov, Valery
Earth and Planetary Sciences · Mathematics · #41A29 #65C20 #65F22 #86A22 #FOS: Mathematics #FOS: Physical sciences #G.1 #Geophysical and Geoelectrical Methods #Geophysics (physics.geo-ph) #Geophysics and Gravity Measurements #I.6 #J.2 #Numerical Analysis (math.NA) #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.1508.04410
openalex publication_date 2015/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The direct gravimetry problem is solved using the subdivision of each body of a deposit into a set of vertical adjoining bars, and in the inverse problem each body of a deposit is modeled by a uniform ellipsoid of revolution (spheroid). Well-known formulas for z-component of gravitational intensity of a spheroid are transformed to a convenient form. Parameters of a spheroid are determined by minimizing the Tikhonov smoothing functional using constraints on the parameters. This makes the ill-posed inverse problem by unique and stable. The Bulakh algorithm for initial estimating the depth and mass of a deposit is modified. The technique is illustrated by numerical model examples of deposits in the form of two and five bodies. The inverse gravimetry problem is interpreted as a gravitational tomography problem or the intravision of the Earth's crust and mantle.