Graphical Terrane Correction for Gravity Gradient Page: 2
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2 GRAPHICAL TERRANE CORRECTION FOR GRAVITY GRADIENT
subsurface mass Nikiforov 8 devised a graphic method which can be
adapted to the calculation of the terrane effects in places of rugged
relief; the writer, as yet, has been able to see only the brief English
digest appended to a short discussion of the Russian original in a
communication from Capt. H. Shaw.
The present paper gives a graphical method that is as accurate as
possible under the conditions of ordinary field surveying with the
torsion balance, that is rapid, simple, and elastic, and that allows
the observer to visualize readily the extent to which rugged to-
pography will affect the gradient at his station. This graphical
method is not meant to supersede the Edtv6s or older Schweydar
methods of calculating the terrane correction for the gradient but to
supplement them where the terrane around the station has a relief
of more than one-half meter above the level of the base of the instru-
ment or more than several meters below it. The method given does
not take into account the distinction made by Eotvas, Heiland,
and others between the terrane correction for the zone within 100
meters and the cartographic correction for the topography further
than 100 meters from the instrument; it can be used with ease to ob-
tain the gradient terrane correction for all the topography further
than 5 meters (5 feet if used with the Lancaster-Jones Shaw terrane
BASIS OF EOTVOS AND SCHWEYDAR METHODS OF CALCULATING TERRANE
CORRECTIONS FOR THE GRADIENT
The Eotvos and the Schweydar methods of calculating the terrane
correction for the gradient are based on approximate integrations of
the following fundamental formula:
bv C2C2 z rzlI p2 (cos a) (h- z) dadpdz
=3 KSj J (1)
b z o [p2 + (h - z) 2]'
where the base of the instrument is the origin of a system of cylin-
drical coordinates with the linear axis vertical, where a equals the
azimuth of any point; p, the horizontal distance of the point from
the origin; A, the height of the center of gravity of the instrument
above the ground; z, the elevation of the point above the level of
the base of the instrument; K, the gravity constant; and 8, the
specific gravity of the soil. In areas of flat terrane where z is small
the quantity (h-z) differs only slightly from A in value, but in
areas of rougher terrane, as z approaches h in value (h-z), and with
it the whole expression approaches zero, and as z approaches 2A in
value, (1i-z) approaches -A in value. The value of the integral of
8 Nikiforov, P., : Institute of Practical Geophysics of the Supreme Council
of Public Economy, U. S. S. R., Bull. 1, Leningrad, 1926, pp. 153-242.
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Barton, Donald C. Graphical Terrane Correction for Gravity Gradient, report, 1929; [Washington D.C.]. (digital.library.unt.edu/ark:/67531/metadc66454/m1/4/: accessed May 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.