How perfect is the Himalayan arc?: Comment
COMMENT
Ebbe H. Hartz*
Geological Survey of Norway, PB 5348 Majorstua, N-0304 Oslo,
Norway
Viggo Hartz
Stålhøjen 11, 8240 Risskov, Denmark
In a recent paper, Bendick and Bilham (2001) neatly show that
the Himalayan arc (Fig. 1A) forms a small circle with a radius of 1696
6 55 km centered at long 91.6 6 1.68E and lat 42.4 6 2.18N regardless
of whether orogen-perpendicular earthquakes, topography, drainage
pattern, stress state, maximum horizontal strain rate, or a peak in the
vertical velocity field define the arc. This newly calculated small circle
is well within error of previous calculations (e.g., Klootwijk et al.,
1985), but nicely illustrates that the small circle can be calculated both
from features directly caused by the collision (reverse seismicity in the
crust) as well as by secondary orogenic expressions (e.g., uplift, topography, stress state).
Bendick and Bilham (2001) propose a new model that they suggest is preferable to previous models of oroclinal bending because it
‘‘produces a small circle without special starting conditions or boundary conditions.’’ Without further description we cannot discuss this
new model in detail, but instead point out that collisional zones always
initiate as small circles (volcanic arcs), and that this should not be a
surprise because all applicable simple geometric forms (e.g., segments
of cylinders, cones, spheres, ellipsoids, and planes), as well as many
far more complex shapes, cut a sphere along a small circle.
The fundamental question is defining the third dimension of the
seismic thrusts (i.e., the cutting surface), since these both define the
Himalayan arc and control secondary features (e.g., topography). Perhaps the simplest three-dimensional solution to the Himalayan arc is a
flat surface cutting the sphere (Earth) normal to the small circle axis.
Since Earth curves ;10.88 from the Himalayan arc and to the small
circle axis, a flat surface normal to the axis will cut into Earth, along
the Himalayas, with a dip of 10.88. To test this simple threedimensional model we examined a profile across the orogen (Owens
and Zandt, 1997) (Fig. 1B). The profile shows an apparent curved
(listric) shape of the main thrust faults; this, however, is primarily an
effect of Earth being presented as flat (Fig. 1B). When the same profile
is bent to follow the curvature of Earth, the thrust faults show a rampflat geometry, which over several hundred kilometers averages as a
plane with listric splays of the Main Frontal, Main Boundary, or the
Main Central thrust merging into the deeper Main Himalayan fault
(Fig. 1C). Using the same databases as Bendick and Bilham (2001) we
note that segments of the Main Boundary, Central, and Himalayan
thrust (thick lines on Fig. 1C) overlap with the zone of reverse siesmicity. On average, these faults are normal to the small-circle axis, and
occur within 15 km of a circular plane with a diameter and normal
(axis) similar to the Himalayan small circle, as defined from seismic
thrust faults and other criteria (Fig. 1C).
Modelling collisions of lithospheric spherical shells is obviously
not trivial, and we do not question that Bendick and Bilham’s (2001)
new model generates applicable small circles. We nevertheless note
that small circles always form when planar or upward-concave surfaces
*E-mail: ebbe.hartz@ngu.no.
GEOLOGY, March 2003
Figure 1. A: Indian peninsula and surrounding areas as seen from
space (http://antwrp.gsfc.nasa.gov/apod/image/0011/earthlightspdmsp.
jpg). Himalayan small circle controls topography, and is thus outlined
by contrast between human lightening of night sky of India and Pakistan, and darkness of Himalayas, Nepal, and Tibet. B and C: Profiles
across Himalayas and Tibet modified from deep seismic studies compiled by Owens and Zandt (1997). Profiles show main Himalayan structures: MFT—Main Frontal thrust, MBT—Main Boundary thrust, MCT—
Main Central thrust, STD—South Tibetan detachment, and MHT—Main
Himalayan thrust. In B structures are normalized to a flat Earth and in
C they are normalized to the curved surface of Earth. The high Himalayas are situated between the MCT and the STD, and are marked by
black square showing height of Mount Everest. Thick line marks where
thrusts within crust overlap with seismic small circle defined (6100 km)
by orogen-normal reverse seismic events (Bendick and Bilham, 2001).
Grey line marks a plane normal to small circle axis, which cuts Earth’s
surface along Himalayan arc. Plane is within error of seismic faults
(thick lines). Earth is not a perfect sphere, so we have used diameter
of 12,740 km as approximation.
incise a sphere (easily illustrated with a knife, spoon, and apple). This
is also the case with the Himalayan small circle tracing near planar or
slightly ellipsoidal (listric) thrusts within the near-spherical Earth. Any
model of the arc, and its variation over time, thus should focus on the
geometry of the small circle-controlling thrusts.
REFERENCES CITED
Bendick, R., and Bilham, R., 2001, How perfect is the Himalayan arc?: Geology, v. 29, p. 791–794.
Klootwijk, C.T., Conaghan, P.J., and Powell, C.McA., 1985, The Himalayan
arc: Large-scale continental subduction, oroclinal bending and back arc
spreading: Earth and Planetary Science Letters, v. 75, p. 167–183.
Owens, T.J., and Zandt, G., 1997, Implications of crustal property variations
for models of Tibetan Plateau evolution: Nature, v. 387, p. 37–43.