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How Perfect Is the Himalayan Arc?

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How Perfect Is the Himalayan Arc? How perfect is the Himalayan arc? R. Bendick Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado, Boulder, R. Bilham Colorado 80309-0399, USA ABSTRACT range. Relief depends on the interaction of up- The Himalayan plate boundary, because it is entirely subaerial, is both the most dra- lift and ¯uvial incision, such that locations matic and the most accessible to direct observation of all active convergent boundaries where uplift rates are high also have increased on Earth. The shape of this boundary can be described as a small circle of radius 1696 relief. This depends on the concomitant as- 6 55 km, centered at long 91.6861.68E and lat 42.4862.18N for the extent of the arc sumption that incision rates are approximately between long 77.28 and 92.18E. The pole of this small circle is consistent whether seis- constant in arc-normal sections, such that in- micity, topography, or stress state is used to de®ne the position of the tectonic boundary. cision is not the cause of variation in relief. The de®ned small circle also coincides with a peak in microseismicity, the maximum In the one location where quantitative mea- horizontal strain rate, and a peak in the vertical velocity ®eld. This quantitative de®- surements of uplift rates from leveling exist, nition of a stable, curved tectonic boundary is a prerequisite to modeling the dynamics we con®rm that the maximum relief and max- of curvature in convergent arcs and applying appropriate boundary conditions to other imum vertical velocity are coincident (Bilham regional models. et al., 1997) (Fig. 1). ArcInfo (ESRI, 1998) was used to convert Keywords: convergence, arcs, tectonics, geomorphology, Himalaya. the 309 digital elevation model for Asia into a map of regional relief by application of ®lters INTRODUCTION proximations of the plate boundary. In the at two wavelengths, 50 and 25 km. Trans- One of the common characteristics of con- second, additional data with incomplete along- Himalayan arc-normal sections were then ap- vergent boundaries worldwide is a curved arc coverage are analyzed for agreement with proximated by a Gaussian curve derived from shape. Such curvature has been included in the previously estimated small circle. We then a least-squares ®t to the data. From these the analyses of the Aleutian arc (AveÂ-Lalle- discuss the implications of a geometrically co- Gaussian curves, we were able to specify the mant, 1996), South America (Judge and Mc- herent boundary on the regional dynamics. form of relief in terms of four parameters: am- Nutt, 1991), and the Himalaya (Royden and The data used for the curve-®tting analysis plitude, wavelength, arc-normal location of Burch®el, 1987), among others (e.g., Mc- include the world 309 data set (GTOPO30; maximum relief, and an elevation offset. The Caffrey, 1996), but has not been explicitly Eros Data Center, 1996), seismicity from the position of the Gaussian maximum was then quanti®ed for these locations. The Himalayan Engdahl±van der Hilst±Buland catalog (Eng- used as the position of maximum relief for arc appears to be in a steady-state equilibrium dahl et al., 1998) and from Molnar and Lyon- ®tting a small circle (Fig. 2A). condition with respect to shape in map view, Caen (1989), ¯uvial geomorphology (Seeber Fits to subsegments of the arc were also independent of topographic steady state dis- and Gornitz, 1983), and change in stress state made to search for scaling effects and along- cussed for mountain ranges elsewhere (e.g., due to topographic loading (e.g., Mercier et arc shape variations. From these ®ts, we cal- Dahlen, 1990). Such equilibrium requires a al., 1987; Armijo and Tapponnier, 1989). Sup- culate that the line of maximum relief deviates mechanism. We propose a formal analogy porting but incomplete data include horizontal by more than 2 s from the small-circle ap- with the interfacial forces of surface thermo- and vertical velocity measurements from the proximation west of 74.98E and east of dynamics, the further development of which global positioning system (GPS), fault kine- 90.18E. The length of the arc that conforms to requires the rigorous de®nition of a geometric matics, and leveling. a small-circle approximation is thus more than and physical interface. Thus, although several Additional qualitative data demonstrate that 1800 km. In the east, the divergence from the attempts have been made to describe the dy- the rheologies of the Indian subcontinent and model arc seems to coincide with the Shillong namics of curvature at collisions (e.g., Buck the Tibetan Plateau differ and that the transi- Plateau, which may be accommodating large and Sokoutis, 1994; Bevis, 1986; Frank, 1968; tion between the two occurs across the narrow amounts of shortening south of the Himalaya Tanimoto, 1998), we consider it necessary to arcuate zone of the Himalaya. Principal stress (Bilham and England, 2001). ®rst demonstrate that: (1) at least one colli- directions inferred from seismicity and bore- For circles ®tted to varying arc lengths, all sional boundary is curved, according to a sim- hole measurements (Zoback, 1992) appear to convergent solutions for the 50 km ®lter (Fig. ple geometrical rule, (2) the curvature is con- rotate to remain arc normal within the arc, and 2A) range between lat 40.458N and 42.38N, sistent among several independent types of the minimum compressive stress changes between long 89.58E and 90.98E, and between data used to delineate tectonic boundaries, and from vertical on the Indian craton to horizon- radii of 1444 and 1688 km. This result sug- therefore (3) a simple, coherent tectonic inter- tal in Tibet. Temperature from heat-¯ow mea- gests a real pole solution of u541.686 face may be described. The India-Asia colli- surements (Francheteau et al., 1984; Gupta 0.88N, w590.3860.88E, and r 5 1588 6 sion is especially suited to such an investiga- and Yamano, 1995) and rigidity from seismic 100 km for the long-wavelength relief (Fig. tion because topographic and velocity data are tomography (Brown et al., 1996) suggest a 3). For the calculations using a ®lter with a distributed throughout the deforming region cold, rigid India and a soft, hot Tibet. radius of 25 km, the same methods give u5 such that description of the shape is not in¯u- 44.8860.458N, w592.3860.678E, and r enced by the spatial distributions of measure- REGIONAL OBSERVATIONS 5 1955 6 66 km (Fig. 3). It is clear that there ments, as might be the case for arcs where Topography are aliasing effects due to the sampling wave- most of the deforming region is submarine. The analysis of relief in this section is pred- length, but the results are remarkably consis- This paper is divided into three parts. In the icated on the assumption that maximum relief tent within the arc region. ®rst, data with broad distribution along the Hi- in the Himalaya corresponds to maximum ver- All model small circles between long malayan arc are used to de®ne small-circle ap- tical velocity of particles in the deforming 74.98E and 90.18E are within a region with an q 2001 Geological Society of America. For permission to copy, contact Copyright Clearance Center at www.copyright.com or (978) 750-8400. Geology; September 2001; v. 29; no. 9; p. 791±794; 4 ®gures; 1 table. 791 Seismicity All events in the catalog of Engdahl et al. (1998) within the box between 258N and 428N and 708E and 1008E and with focal mecha- nisms either in the Harvard CMT catalog (Centroid Moment Tensor Project, 2000) or in Molnar and Lyon-Caen (1989) were used in this analysis. Only 221 reverse events and 110 normal events had published mechanisms (Fig. 2B). The focal mechanisms were used to classify the fault motions; the epicenters from Engdahl et al. (1998) were used to map events. A small circle was then ®t to all of the shallow, arc-normal thrust events. For circles ®tted to varying arc lengths, all convergent solutions range between lat 40.68N and 42.58N, between long 92.18E and 93.88E, and Figure 1. Plots of mean elevation, mean relief, vertical velocity with 1 s error envelope, and microseismicity cross sections in arc-normal direction. All data used to construct these between radii of 1557 and 1757 km. This re- pro®les were ®rst straightened by projection, so that mathematical operations could com- sult suggests a pole solution of u541.686 bine cross sections throughout region. Peaks in vertical velocity and relief are coincident, 18N, w592.78618E, and r 5 1672 6 100 suggesting that maximum relief elsewhere in arc may be used as proxy for position of km (Fig. 3). maximum vertical velocity (modi®ed from Bilham et al., 1997). Geomorphology arc-normal width of only 18 km (Table 1; Fig. ers such as the Sutlej and the Karnali, where Seeber and Gornitz (1983) used digitized 3). The maximum deviation of maximum re- the quality of the Gaussian ®ts to trans- 1:1 000 000 and 1:250 000 topographic maps lief from the small-circle ®t to the arc is only Himalayan relief is poor. If these data are of the Himalayan arc to calculate arc-normal 48 km for the central 1800 km of the arc. omitted, maximum relief deviates from a river-long pro®les, the elevation of points Maximum mis®ts to the arc occur near the small circle by less than 5 km in the central along the main channel of the largest trans- drainage basins of large trans-Himalayan riv- 1500 km of the Himalayan arc.
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