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- km, centered at long 91.6؇؎1.6؇E and lat 42.4؇؎2.1؇N for the extent of the arc sumption that incision rates are approximately 55 ؎ -between long 77.2؇ and 92.1؇E. 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 30Ј 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 30Ј 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 ␴ from the small-circle ap- with the interfacial forces of surface thermo- and vertical velocity measurements from the proximation west of 74.9ЊE and east of dynamics, the further development of which global positioning system (GPS), fault kine- 90.1ЊE. 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 40.45ЊN and 42.3ЊN, sistent among several independent types of the minimum compressive stress changes between long 89.5ЊE and 90.9ЊE, 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 ␪ϭ41.6ЊϮ face may be described. The India-Asia colli- surements (Francheteau et al., 1984; Gupta 0.8ЊN, ␸ϭ90.3ЊϮ0.8ЊE, and r ϭ 1588 Ϯ 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 ␪ϭ such that description of the shape is not in¯u- 44.8ЊϮ0.45ЊN, ␸ϭ92.3ЊϮ0.67ЊE, and r enced by the spatial distributions of measure- REGIONAL OBSERVATIONS ϭ 1955 Ϯ 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 74.9ЊE and 90.1ЊE are within a region with an

᭧ 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 25ЊN and 42ЊN and 70ЊE and 100ЊE 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 40.6ЊN and 42.5ЊN, between long 92.1ЊE and 93.8ЊE, and Figure 1. Plots of mean elevation, mean relief, vertical velocity with 1 ␴ 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 ␪ϭ41.6ЊϮ bine cross sections throughout region. Peaks in vertical velocity and relief are coincident, 1ЊN, ␸ϭ92.7ЊϮ1ЊE, and r ϭ 1672 Ϯ 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. Himalayan rivers. They argued that knick-

Figure 2. Input data for circle-®tting experiments. See text for discussion. A: Figure 3. Best-®t small circles and poles with error ellipses. Locations of maxima of Gaussian approximations of relief with 50-km-radius For central Himalaya, all small circles are statistically iden- (light blue) and 25-km-radius (dark green) ®lter. B: Locations of 221 reverse tical. We consider this result to demonstrate that (1) Hima- seismic events with published hypocenters and focal mechanisms (Engdahl layan boundary may be approximated as small circle with -et al., 1998; Centroid Moment Tensor Project, 2000; Molnar and Lyon-Caen, center of long 91.6؇E, lat 42.4؇N, and radius of 1696 km (com 1989). C: Locations of reaches where Seeber and Gornitz (1983) estimated bined solution), and (2) location of boundary is not sensitive that river-long pro®les are 10 times steeper than predicted. D: Location of to data type. 4000 m contour, approximate position of change in regional stress state. Fig- ures 2±4 show topography projected onto best-®t pole to Himalaya.

792 GEOLOGY, September 2001 TABLE 1. RESULTS FROM FITTING A SMALL CIRCLE (IN A LEAST-SQUARES SENSE) TO DATA that this transition occurs near the edge of the DESCRIBING THE HIMALAYAN ARC Tibetan Plateau, as approximated by the 4000 Data set Min. long. Max. long. r ␪␸␹2 m contour (Fig. 2D). A small-circle ®t to the ( E) ( E) (km) Њ Њ smoothed 4000 m contour gives a pole very Reverse* 75.315 92.761 1695.7 41.749 92.412 0.027 close to the pole from the maximum-relief cal- Reverse* 73.780 93.744 1555.6 40.556 92.074 0.058 Reverse* 73.320 94.278 1763.3 42.472 93.770 0.106 culations, but with a smaller radius. For circles 50 km ␭² 74.478 85.942 1453.5 40.455 89.525 0.060 ®tted to varying arc lengths, all convergent so- ² 50 km ␭ 71.390 85.942 1713.3 42.499 91.140 0.112 lutions range between lat 37.67ЊN and 45.64ЊN, 50 km ␭² 71.390 88.806 1663.9 42.269 90.585 0.225 25 km ␭§ 70.002 94.506 2000.5 45.080 93.215 3.703 between long 87.98ЊE and 93.56ЊE, and be- 25 km ␭§ 74.490 90.786 1994.0 45.202 92.040 0.846 tween radii of 1124 and 2110 km. This result 25 km ␭§ 78.594 88.802 1933.2 44.549 91.633 0.099 Fluvial# ÐÐ ÐÐ 1695.3 42.450 91.100 ÐÐ suggests a pole solution of ␪ϭ40.46ЊϮ3ЊN, 4000 m** 76.249 86.087 1124.3 37.672 87.978 0.372 ␸ϭ89.98ЊϮ2ЊE, and r ϭ 1470 Ϯ 333 km 4000 m** 78.002 84.958 2109.8 45.635 93.565 0.114 (Fig. 3). 4000 m** 76.404 86.700 1174.7 38.065 88.398 0.419 Note: Subsegments of the data are ®tted to test for scaling effects in the analysis. *Reverse data are geographic positions of reverse seismic events with published hypocenters and focal Velocity mechanisms (Engdahl et al., 1998; Molnar and Lyon-Caen, 1989; Centroid Moment Tensor Project, 2000). The vertical motion of the collision zone is ²50 km ␭ data are geographic positions of Gaussian maxima of topography ®ltered with a 50-km-radius relief ®lter. estimated in an analysis of leveling data from §25 km ␭ data are Gaussian maxima of topography ®ltered with a 25-km-radius ®lter. 1977 and 1995 by Jackson and Bilham (1994). #Fluvial data are positions of oversteepened river reaches reported in Seeber and Gornitz (1983). At long 86ЊE, they identi®ed a 40-km-wave- **4000 m data are geographic positions of the 4000-m-elevation contour. length region with a peak uplift of 7 Ϯ 3 mm/ yr relative to the India border. The point of maximum vertical velocity is centered at lat points, convex reaches in otherwise concave because the minimum stress direction (␴3)is ¯uvial pro®les, represent the location of active vertical. In the plateau, however, because of the 27.9ЊN (Fig. 1). This direct measurement of uplift at rates exceeding the erosive power of gravitational potential of the elevated mass, the maximum vertical velocity is coincident with the stream. These locations therefore represent maximum compressive stress is vertical, and the band of maximum vertical velocity esti- maxima in the vertical velocity ®eld (Fig. 2C). the minimum stress direction is approximately mated according to maximum relief. They ®t a small circle centered at 42.45ЊN and east-west. Thus, south of the plateau edge, the Figure 4 summarizes values for horizontal- 91.10ЊE with a radius of 1695 km (Fig. 3) to regime is dominantly north-south compression; velocity vectors in the India-Asia collision these oversteepened reaches. within the southern plateau, the regime is dom- zone as reported in the literature. GPS veloc- inantly east-west extension. The absolute mag- ities are shown (e.g., Larson et al., 1999; Stress State nitude of the compressive stress between India Jouanne et al., 1999), as well as ground-based Several arguments have been made to dem- and Asia is not known, so the location at which analysis of fault offsets and velocities (Armijo onstrate that India and Tibet have different the maximum vertical stress (which may be and Tapponnier, 1989; Armijo et al., 1986; Wesnousky et al., 1999). The salient feature stress regimes, notably that ␴1 and ␴3 swap di- calculated simply as ␳gh, where ␳ is the aver- rections across the High Himalaya (e.g., Mer- age density of a column of crust, g is the ac- of these point-velocity measurements is that cier et al., 1987). South of the Tibetan Plateau, celeration of gravity, and h is the height of the they are not parallel to each other or to the total relative plate motion between India and the maximum compressive stress (␴1) is par- crustal column) exceeds the compressive stress allel to India-Asia convergence. Thrusting and is not known. However, earthquake focal mech- Eurasia (DeMets et al., 1994). Rather, vertical deformation are energetically favorable anisms (Molnar and Lyon-Caen, 1989) suggest throughout the Himalayan boundary region, the horizontal-velocity vectors are rotated to arc normal (Fig. 4). This ®nding allows two conclusions: (1) one can begin to estimate a pole for these velocities, and (2) the pole rep- Figure 4. Regional veloc- resents an apparent pole of extrusion of the ity vectors have radial components. Estimates arc, such that there is an along-arc component of arc-parallel stretching of extension. Estimates of the magnitude of range from 4.5 ؎ 3.5 mm/ this along-arc extension range from 4.5 Ϯ 3.5 yr (Jouanne et al., 1999) mm/yr (Jouanne et al., 1999) to 14 Ϯ 2 mm/ to 14 ؎ 2 mm/yr (Chen et al., 2000). Global posi- yr (Chen et al., 2000). tioning system (GPS) Because velocity measurements within the vectors are modi®ed Himalaya are concentrated in the center for the from Jouanne et al. arc, the pole is poorly determined at this time. (1999), Chen et al. (2000), A small-circle approximation for the velocity- and Larson et al. (1999). Vectors from offset ter- de®ned plate boundary, from the assumption races and moraines are that the convergence direction is arc normal and from Wesnousky et al. the extension direction is tangential, gives a cen- (1999), Armijo and Tap- ter at lat 57ЊϮ19ЊN and long 98ЊϮ23ЊE. ponnier (1989), and Ar- mijo et al. (1986). NUVEL- 1A vector is from DeMets Summary et al. (1994). Table 1 summarizes the results of modeling the shape of the boundary from relief, topo- graphically derived stress, geomorphic, and seis-

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794 GEOLOGY, September 2001