Frontiers and Opportunities in Antarctic Geosciences * Certosa di Pontignano * 29-31 July 2004
Modular Conversion Method for Regional Comparison of
Structural Data in Antarctica
C. SMITH SIDDOWAY & M.F. SIDDOWAY
Colorado College, Colorado Springs, U.S.A.
Comparison of regional structural and geophysical datasets is hindered, in Antarctica, by the convergence of meridians
of longitude at high latitude. Measured orientations of geological structures and geophysical lineaments (strike; trend)
are ordinarily reported with respect to geographic North, but the North reference direction varies with longitude
position due to proximity to South Pole. This is of consequence for regional tectonic interpretations that incorporate
geometrical and kinematic information from faults, dike arrays, or geophysical lineaments. To make a legitimate
comparison of structural data from 76°S, 160°E in the Transantarctic Mountains with data collected at 76°S, 215°E
longitude in Marie Byrd Land (MBL), for example, requires a normalization to a common reference orientation.
Difficulties also arise for regional synthesis of structural data collected within MBL, from outcrops distributed across
30° of longitude (205 to 235°E). This poster presentation proposes a simple modular arithmetic conversion as a means
of normalization of geological orientation data to a common reference direction. An underlying assumption is that the
geological features to be compared are correlatable from the standpoint of age or origin, and that tectonic rotations can
be ruled out. The poster’s objective is to stimulate discussion, obtain input, and develop a protocol that will allow
regional synthesis and comparison of structural/geophysical data between geographically separated study regions in
Antarctica.
For air navigation in Antarctica, the convergence problem is solved through use of a rectilinear grid constructed parallel
and orthogonal to the Prime Meridian, referred to as the Antarctic Navigational Grid (ANG). Converting compass
bearings from geographic to grid coordinates amounts to a modular arithmetic conversion using the function: ANG
bearing =MOD [(longitude position + bearing with respect to true north), 360]. Modular arithmetic is commonly used in
number theory as a means of partitioning integers and dealing with remainders (Burton, 2001). A reasonable way to
normalize structural data can be to convert strike to “ANG strike,” or, the angle with respect to the Prime Meridian. In
the function given here, strike would be substituted in to the “bearing” term.
Not limited to use for ANG conversion, the modular function is versatile and can be used to normalize structural data to
any specified longitude reference direction. For example, MBL data measured with respect to geographic north at
scattered outcrops between 205° to 230°E can be normalized to a single MBL reference such as 215°E, or converted to
the coordinates of a “comparison region” outside MBL, such as the Transantarctic Mountains along longitude 160°E.
The general expression becomes SC = MOD [(S + L), 360], where SC = converted strike; S = measured strike; L =
angle in degrees longitude between study site and reference site, measured counterclockwise; and 360 = the divisor. The
expression does not account for the small effects of curvature of the Earth or distance from South Pole.
Two applications of the function are presented here, for brittle fault data and dike orientations from MBL. In the first
example, brittle fault data from the Ford Ranges on the east side of the Ross Sea at ~76°S are normalized to southern
Victoria Land coordinates (~76°S, western Ross Sea), for comparison with prevalent structural trends described by
Wilson (1992, 1995). The exercise tests for parallelism between post-Jurassic brittle arrays that record dextral- and
oblique shear. The second example compares orientations of Cretaceous dolerite dykes forming a regional array at
215°E in the Ford Ranges (Siddoway et al., 2004) versus a dyke swarm to the east at 230°E, Hobbs Coast, MBL. Hobbs
Coast dykes have been interpreted to record breakup of the Gondwana active margin, potentially influenced by a mantle
plume (Storey et al., 1999). The conversion allows a test of geometrical and kinematic compatibility between the dike
arrays, and clarifies the spatial configuration of the arrays with respect to the proposed plume.
Opportunities to apply this normalization technique will increase as detailed structural investigations continue (e.g.
Rossetti et al., 2002, 2003; Läufer & Phillips, 2004) and geophysical coverage of central East Antarctica improves,
providing a means to correlate bedrock structures and geophysical lineaments. The modular conversion is generally
applicable as a means to convert structural data recorded in terms of strike to polar stereographic coordinates, for direct
comparison with aeromagnetic and other geophysical trends in polar projection. Consequently, the modular arithmetic
conversion method may become increasingly valuable for regional comparison of multiple data sets.
REFERENCES
Läufer & Phillips, G., 2004, Abstracts 73: Geological Society of Australia [AGC 2004, Hobart, Tasmania], p. 171.
Rossetti et al., 2002, J.Geol.Soc.London, v. 159, p. 159-173. --- 2003, Tectonics, v. 22, doi:10.1029/2002TC001416.
Siddoway, C. et al., 2004, in Whitney, D. et al., eds.; Gneiss domes and orogeny, GSA Spec.Paper 380, p. 267–294.
Storey, B.C. et al., 1999, Journal of the Geological Society, London, v. 156, p. 659-671.
Wilson T.J., 1992, in Yoshida et al., eds., Recent Progress in Antarctic Earth Science, TerraPub, Japan. p. 295-301
Wilson, T.J., 1995, Tectonics, v. 14, p. 531-545.