Graphical Terrane Correction for Gravity Gradient Page: 10
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10 GRAPHICAL TERRANE CORRECTION FOR GRAVITY GRADIENT
of gravity of the instrument. The Eoitvis and Schweydar methods
of calculating the terrane correction for the differential curvature
give fully as accurate and easily obtained results as the chart of
Figure 5. The advantage of this chart, however, is that it allows a
ready visualization of the very serious effect of rugged topography
on the differential curvature and a visualization of the fact that, on
account of the difficulty of making an accurate calculation of the
effect of the terrane, the differential curvature, much more than the
gradient, becomes increasingly unreliable with increasing rugged-
ness of the topography.
EXAMPLE OF APPLICATION OF CHART
A station is taken at the foot of the northwest-southeast fault-line
scarp facing southwest. The surface trace of the fault lies about 80
meters northeast of the station. The fault plane dips about 60 to the
northeast. More or less horizontal limestone on the northeast of the
fault has been faulted down against shales on the southwest. The
specific gravity of the limestone is 2.8 and of the shales, 2.3.
To illustrate the use of the charts, the terrane effect is calculated
for the northeast octant. A topographic map covering the northeast
octant is given in Figure 6. The elevations at 80, 160, 320, 640, and
beyond, for use in the calculations, can be taken from the map. The
average elevation of the northeast octant at 80 meters can be seen to
be about 70 feet plus or minus a foot and a half or about 21 meters.
As a variation of 1 meter in elevation produces a difference in
effect of (sp. gr. x 0.08) E at 80 meters distance and 20 meters
elevation, it is about a toss-up whether or not to run the instru-
mental leveling out to 80 meters. At 160, 320, and 640 meters dis-
tance the average elevation for the octant, respectively, is 85, 103,
106 plus or minus about a foot in each case, or about 26, 31, and 32
meters, respectively. At those elevations and distances a difference
in elevation of 1 meter produces a negligible difference in the terrane
effect, so that it is unnecessary to carry the instrumental leveling to
160 meters or beyond. As the elevation beyond 640 meters is about
constant or shows an indication of decreasing, it is not necessary to ob-
tain the elevation at 1,280 meters, for the chart shows that a mass ex-
tending out infinitely from 640 meters and not rising above 35 meters
has a practically negligible effect.
Elevations are taken with an alidade, transit, or level at distances
of 5, 10, 20, 40, and, if desired, 80 meters along the central axis
of the octant. The rod positions are shifted slightly, however, to get
the best average value of the elevation of the octant at the various
distances. The elevations determined in this case are 0.32, 2.0, 3.5,
11.0, and 21.1 meters.
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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/m1/14/: accessed June 28, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.