Graphical Terrane Correction for Gravity Gradient Page: 3
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DERIVATION OF THE WRITER'S GRAPHICAL METHOD
(1) taken z=0 to z= z is at a maximum when z,=h and becomes
zero when zn becomes greater than 2h. In both the E6tvis and the
older Schweydar methods the gradient effect, C, produced by any
one of the zones in any sector is considered to be
where M is a constant; that is, C is assumed to increase linearly
with the increase of the value of ez, although as a matter of fact C
reaches a maximum at z,= h and decreases indefinitely algebraically
through zero at z,= 2h for increasing values of z,, if za>h. The
relation of (2) is accurate enough for small values of zs, and when
that assumption is valid the assumption also holds valid that
Ca- Ca+, = M (z - za+,~). (3)
In general, however, where the relation of (2) is not valid the
relation of (3) likewise does not hold, and if z, and za+, differ by
a moderately small amount it makes considerable difference whether
their value is in the neighborhood of 0, h, or > h.
DERIVATION OF THE WRITER'S GRAPHICAL METHOD FOR CALCULA-
TION OF THE GRADIENT TERRANE EFFECT
The terrane around the instrument is divided into the N., NE., E.,
SE., S., SW., W., NW. octants as in the EotvSs and Schweydar
methods and into zones bounded by circles of 5, 10, 20, 40, 80, 160, 320,
640 -------640 x 2. Each zone is divided into subzones delim-
ited by circles of radius differing by /p.
For each subzone of each octant a curvilinear prism -is used; its
front and back faces are the vertical surfaces through the 5, 5 x ,
5 X 2, 5 42~3 10 ---------- or 5 X meter circles; its lateral
faces are vertical radial planes.
In the original construction of the author's charts rectangular
prisms were used as an approximation for the curvilinear prisms,
and the gradient effects were calculated by the ordinary simple
formula for the gradient produced by a horizontal rectangular block
perpendicular to the axis of reference and bisected by it; that is,
baxU (x +y2 + )y ( + y2 ) - y
(1/x2 + y2 zzi) - y (/x 2 2 z) (4)
(4x +y 22 :2
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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/m1/5/: accessed September 19, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.