Anomalies of the external and internal gravitational fields of the Earth’s isostatically balanced crust in the quadratic approximation

Nasonova, L. P.; Chuikova, N. A.

doi:10.3103/s0027134907060148

Cited by 4 publications

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“…The distribution histogram for the relative quadratic contribution to the Stokes constants (the ratio of the quadratic terms to linear) reaches its maximum (22% of coefficients) for the relative square contribution equal 0.4 (for the Earth, these figures are 16% and 0.01, respectively [7]).…”

Section: Results and Disscussionmentioning

confidence: 99%

“…(1) In this study, we used algorithms and formulae that express the expansion coefficients in the spherical functions of the square of some function of (x = sin ϕ, λ), given initially in the form of a similar expansion into spherical harmonics, through the coefficients of this initial expansion [7]. Algorithm developed by us allows to receive these formulae for arbitrary degree N max of initial expansion.…”

Section: Results and Disscussionmentioning

confidence: 99%

“…This problem was solved in the linear approximation. However, our similar studies of density structure of the Earth' crust showed that the linear approximation is insufficient for the accurate accounting of the contribution of the crust boundaries in the internal and external gravitaty fields, it is necessary to take into account the quadratic members [2,7,8]. Thus, the account of quadratic members from the relief' expansion of the degree N brings the additional contribution to harmonics of potential of degree n=0-2N, with this contribution increasing with the growth of n. Especially the account the quadratic terms is essential in dipole (by depth) distribution of anomalous masses.…”

Section: Introductionmentioning

confidence: 99%

“…where the terms in braces {} 1 , {} 2 , and {} 3 with the subscripts 1, 2, and 3 correspond to the expansion coefficients of the functions h s , (h s ) 2 , and h s P2 (sin ϕ) respectively. The formulas expressing the coefficients {a nm , b nm } 2 and {a nm , b nm } 3 , in terms of the linear terms {a nm , b nm } 1 , have been derived by mathematically simulating symbolic computations in computer algebra systems [7].…”

Section: Introductionmentioning

confidence: 99%

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Depths of the Relief Compensation and the Anomalous Structure of Crust and Mantle of Mars

Chuikova,

Nasonova,

Maximova

2012

Preprint

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The contribution to the gravity from the Mars' relief (topography) and the density jump at the Mohorovicic discontinuity (M) in the quadratic approximation have been derived. The problem of determination of possible depths of compensation for relief's harmonics of different degree and order have been solved. It is shown, that almost all compensation of a relief is carried out in a range of depths of 0-1400 km. For various relief's inhomogeneities the compensation is most probable at the depths corresponding to the upper crust ( d = 4.5 ± 3.7 km), to crust-mantle transition layer ( d = 78 ± 24 km); to lithospheric boundary ( d = 200 ± 34 km); to upper-mean mantle transition layer ( d = 400 ± 70 km); to mean-lower mantle transition layer ( d = 1120 ± 180 km). The lateral distribution of compensation masses is determined of this depths, and maps are constructed. The possible stresses in crust and mantle of Mars are evaluated. They reach 10 8 Pa. It is shown that relief' anomalies of volcanic plateau Tharsis and symmetric formation in east hemisphere could arise and be supported dynamically by two plumes of melted mantle substance, enriched by fluids. The plumes have their origins on the boundary depths of lower mantle.

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Section: Results and Disscussionmentioning

confidence: 99%

Section: Results and Disscussionmentioning

confidence: 99%