NDLI: Estimation of the gravitational potential energy of the earth based on different density models

Content Provider	Springer Nature Link
Author	Marchenko, Alexander N. Zayats, Alexander S.
Copyright Year	2011
Abstract	The estimation of the Earth’s gravitational potential energy E was obtained for different density distributions and rests on the expression E = − (W$_{min}$ + ΔW) derived from the conventional relationship for E. The first component W$_{min}$ expresses minimum amount of the work W and the second component ΔW represents a deviation from W$_{min}$ interpreted in terms of Dirichlet’s integral applied on the internal potential. Relationships between the internal potential and E were developed for continuous and piecewise continuous density distributions. The global 3D density model inside an ellipsoid of revolution was chosen as a combined solution of the 3D continuous distribution and the reference PREM radial piecewise continuous profile. All the estimates of E were obtained for the spherical Earth since the estimated (from error propagation rule) accuracy σ$_{E}$ of the energy E is at least two orders greater than the ellipsoidal reduction and the contribution of lateral density inhomogeneities of the 3D global density model. The energy E contained in the 2nd degree Stokes coefficients was determined. A good agreement between E = E$_{Gauss}$ derived from Gaussian distribution and other E, in particular for E = E$_{PREM}$ based on the PREM piecewise continuous density model and E-estimates derived from simplest Legendre-Laplace, Roche, Bullard and Gauss models separated into core and mantle only, suggests the Gaussian distribution as a basic radial model when information about density jumps is absent or incomplete.
Starting Page	35
Ending Page	54
Page Count	20
File Format	PDF
ISSN	00393169
Journal	Studia Geophysica et Geodaetica
Volume Number	55
Issue Number	1
e-ISSN	15731626
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-02-12
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	gravitational potential energy of the Earth internal potential density distribution Meteorology/Climatology Structural Geology Geophysics/Geodesy
Content Type	Text
Resource Type	Article
Subject	Geochemistry and Petrology Geophysics

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