One option of constructing three-dimensional distribution of the mass and its derivatives for a spherical planet Earth
Journal Title: Геодинаміка - Year 2016, Vol 21, Issue 2
Abstract
Purpose. To build a three-dimensional function of the mass distribution of the Earth's interior according to the parameters (Stokes constant to the second order inclusive) of the external gravitational field of the Earth without considering the minimum deviation from its known density models in geophysics. Methodology. The classic methods of constructing mass distribution use only the Stoke’s constants zero and second orders. In iterative methods of determining the distribution models the reference model of density is taken for zero approximation which is agreed upon by Stoke’s constants up to the second order inclusive. Further, the coefficients of potential expansion to a certain order are taken into account, but their contribution to the function of mass density does not investigate. This research provides an attempt to obtain such an estimation. The proposed method is approximate, but in the iterative process a function of the density is not only used, but also its derivatives. Bringing the order moments of density toward the controlled values (values that are defined on the surface of a sphere) makes it possible to analyze the process of successive approximations. Results. In contrast to the second-order model, which describes the global gross irregularities, the obtained distribution function gives a detailed picture of the placement density anomalies (deviation of three-dimensional functions from the average on the sphere – “izoden”). Analysis of maps at different depths (2891 km core-mantle, 5,150 km of the inner-outer core) allow making preliminary conclusions about global redistribution of mass due to the rotating component of gravity across the radius: its dilution along the axis of rotation and accumulation of rejecting it. This is particularly evident for the equatorial regions. On the contrary, there is minimum deviation in the polar regions of the Earth, which also have their own justification since the value of the rotation force decreases when moving away from the equator. The function of mass distribution, which is constructed using the proposed method, describes the mass distribution better. Originality. This research is in contrast to the classical results which have been obtained from the Adams-William’s equations for the derivatives of the density of one variable (depth), and make attempted to obtain derivatives using Cartesian coordinates. Using the gravitational field parameters up to second order increases the order of approximation of the distribution function of the masses of three variables from two to four through the possibility of restoring the planet's mass distribution by its derivatives. At the same time, in contrast to previous research, geophysical information accumulated in the reference PREM model is used, therefore, features of the internal structure are taken into account. Practical significance. The received function of mass distribution of the Earth can be used as a zero-order approximation when used in the presented algorithm Stokes constant of higher order. Their applications give the possibility to interpretate of the global anomalies of the gravitational field, and explore the geodynamic processes deep inside the Earth.
Authors and Affiliations
М Fys, М. Yurkiv, А. Brydun, V. Lozynskyi
Keywords
Related Articles
- EP ID EP195186
- DOI -
- Views 91
- Downloads 0
Modeling of vertical movements of tectonic blocks, according to tide gauge observations
Purpose. The purpose of this study: to reconstruct the vertical movements of the earth crust in northern parts of Europe, according to long-term tide gauge observations; to investigate the change of kinematic parameters...
Analysis of the results of vertical crust movement velocities of the European coastline per the tide gauge and GNSS-observation data
Purpose. The purpose of the study is to detect and investigate the differences in determining vertical crust movement velocities (VCMV) in Europe applying two independent methods: tide gauge and GNSS-observations. Method...
Research of daily movement of BRGN reference station
Purpose. Investigation of daily movement of GNSS station BRGN of GeoTerrace reference network of Institute of geodesy Lviv Polytechnic National University, by the results of GNSS and linear-angular measurements in order...
Modeling elastic-dynamic effects of the crust under nuclear power plant (on the example of Chornobyl NPP)
Purpose. The aim of study is to create the method of seismic wave fields modeling for a broad class of vertically and horizontally inhomogeneous layered media. Simulation will make it possible to more precisely assess th...
Spatial correlations of pelite silt rocks in the sedimentary cover of the Novogradskiy block (Volin megablock of the Ukrainian shield)
Purpose. The goal of the research is to identify spatial trends and patterns in concordant bedding of sedimentary rocks, first of all pelite silt rocks of the sedimentary cover of the Ukrainian shield, using the Novograd...