On the gradient of curvature of the plumblines of the Earth's normal gravity field and its isocurvature lines

Manoussakis, G; Delikaraoglou, D

dc.contributor.author	Manoussakis, G	en
dc.contributor.author	Delikaraoglou, D	en
dc.date.accessioned	2014-03-01T01:36:33Z
dc.date.available	2014-03-01T01:36:33Z
dc.date.issued	2011	en
dc.identifier.issn	0039-3169	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/21337
dc.subject	curvature	en
dc.subject	isocurvature lines	en
dc.subject	isocurvature surface	en
dc.subject	normal gravity field	en
dc.subject	plumblines	en
dc.subject.classification	Geochemistry & Geophysics	en
dc.subject.other	curvature	en
dc.subject.other	gravity field	en
dc.subject.other	gravity survey	en
dc.title	On the gradient of curvature of the plumblines of the Earth's normal gravity field and its isocurvature lines	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s11200-011-0030-5	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s11200-011-0030-5	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	This paper presents an approach to determine the gradient of curvature of the normal plumblines at a point P above the ellipsoid and introduces a new geometrical object which is the isocurvature line. The assumed facts are the coordinates of the point P and the formula for the normal gravity potential U. For the determination of the gradient of the normal plumbline curvature k at the point P we define a small circle on the meridian plane of P whose center is at the point P. The circle has the radius of one meter and interior D. In this circle we construct a curvature replacement function to approximate the curvature function k. This replacement function is a quotient of polynomials hence it is easy to find its partial derivatives at the point P. For the construction of replacement function we make the assumption that in the interior of the circle D the first order partial derivatives of U behave linearly and the second order partial derivatives have constant values which equal their value at the point P. Then we set the gradient of the curvature function to be equal with the gradient of the aforementioned replacement function at P. An isocurvature line of the normal gravity field passing through a point P is a curve such that the value of the function of the plumblines' curvature k is constant and equals k(P). We give a formula to find the direction of the isocurvature line on the meridian plane and we prove that there are infinitely many isocurvature lines passing through the point P and they all lie on a special surface, the isocurvature surface. © 2011 Institute of Geophysics of the ASCR, v.v.i.	en
heal.publisher	SPRINGER	en
heal.journalName	Studia Geophysica et Geodaetica	en
dc.identifier.doi	10.1007/s11200-011-0030-5	en
dc.identifier.isi	ISI:000293643000008	en
dc.identifier.volume	55	en
dc.identifier.issue	3	en
dc.identifier.spage	501	en
dc.identifier.epage	514	en