Graphical Terrane Correction for Gravity Gradient Page: 7
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FLEXIBILITY OF METHOD
produced by each one-half or one-fourth octant is calculated as for
the whole octant, but the effect produced by 0.1 E block of the chart
in the first case is 0.05 E and in the second case 0.025 E and the total
effect for the one-half or one-fourth octant as read from the chart
must be divided by two or by four.
(b) If the irregularity of the topography is confined to one or two
subzones of one or more octants, one-half octants, or one-fourth
octants, it is necessary to apply the procedure only to those subzones
within those octants, one-half or one-fourth octants.
2. A high degree of complexity in the variation of the specific
gravity can be handled. If necessary, each 0.1 E block of each sub-
zone, or even each 0.05 E or 0.025 E block of the one-half or one-
fourth octants, respectively, could be assumed to have a different
specific gravity. Such detail would be more exact than the exigencies
of the actual situation in the field would warrant, and in most prac-
tical work it is necessary only to divide the hills along the division
lines of the zones and subzones, along one-fourth, one-half, or whole
octants, and along horizontal planes of equal elevation into large-
step rectangular blocks, each of which is assumed to have some defi-
nite uniform specific gravity. The number of 0.1, 0.05, or 0.025 E
blocks included within each of those large blocks can be counted and
multiplied by the specific gravity of the block. As a matter of fact,
a fairly irregular distribution of specific gravity can be handled if
one-fourth octants are used.
Where the gradient correction is calculated for a valley or other
depression and where the distribution of specific gravity is irregular,
the effect of each zone or subzone for each one-fourth, one-half, or
whole octant must be calculated for the same depth as for the cor-
responding symmetrically opposite zone or subzone, and instead of
using the effect from the line of zero elevation to the top of the
ground, according to the directions of a preceding paragraph, the
effect must be calculated from the surface to that depth. If a sub-
zone is divided into upper and lower zones of different specific
gravities, if E, is the chart reading in E for the common contact
of the two zones, E and ED are the chart readings for the surface
and the depth to which the correction is carried, if 8 and a, are
the respective specific gravities, and if C is the effect for the subzone:
0= - [3, (E,- E_,) + 62(E- E,)] (8)
The quantities (EE - E,) and (ED - EE) are always positive.
3. To carry the calculation of the gradient correction beyond a
distance of 640 meters from the instrument, it is necessary by the
law of similar bodies similarly placed in projection of each other
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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/m1/9/: accessed May 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.