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Mathematic Modelling of Non-Equilibrium Suspended Load

Mathematic Modelling of Non-Equilibrium Suspended Load

By Robert Sanders, Media Relations | 5 October 2009 BERKELEY —Sinuous, meandering streams produce diverse and wildlife-rich habitats and are the aim of many river restoration efforts, but until now, the bank, water flow and sediment conditions required to form and maintain meanders have been largely a matter of speculation. No one has been able to experimentally create self-sustaining meanders in the lab, and numerous restored meanders have straightened out or turned into multi-channel "braided" rivers after the first flood.Now, a University of California, Berkeley, study reports the first experimental creation of meanders in a flume – a scaled down representation of a natural channel using alfalfa sprouts to represent vegetated stream banks. These experiments reveal some of the necessary conditions for formation of meanders on Earth and throughout the solar system."The money spent nationally on stream restoration is expanding exponentially, yet we're fixing things faster than we can tell whether it's doing any good," said UC Berkeley graduate student Christian Braudrick, a former environmental consultant. "Our flume model will now let us do investigations that we can't do in the field but, until now, haven't been able to do in the lab, finally linking experiment with the geomorphology we see in nature."Braudrick and William Dietrich, UC Berkeley professor of earth and planetary science, along with colleagues at San Francisco State University and Berkeley-based Stillwater Sciences, reported their results last week in the online early edition of the journal Proceedings of the National Academy of Sciences.Snaking meanders like those characteristic of the lower Mississippi River are common along rivers and streams on Earth, as well as along now-dry channels on Mars and even on the frozen surface of Saturn's moon Titan. On Earth, they typically form in low-sloping valleys where, over the years, they wander across their floodplain, creating new floodplain deposits and leaving behind tree-lined sloughs, chutes and oxbow lakes that team with fish, birds, mammals and reptiles. The gravel bars, called point bars, at the inner bank of a meander also provide new surfaces that are critical for the establishment of riparian trees. Yet, understanding how these channels form has relied until now on limited field measurements or theoretical ysis based on known physics and hydraulics – no one has been able to experimentally create meanders in a laboratory that don't eventually turn into straight channels or braided streams, Braudrick said. An effort to restore Uvas Creek in Gilroy, Calif., for example, ended in failure when a five-year flood stripped away the sinuous meanders leaving a braided channel, similar to the channel prior to the restoration.Braudrick created a successful laboratory model of a gravel-bed stream by finding the right material to reinforce the banks – alfalfa sprouts – and the right material to represent fine sediment – 0.25-0.42-millimeter lightweight plastic particles. He used sand to represent gravel. Working in a gently-sloping, 6.1x17-meter (20x56-foot) box filled with sand and planted with alfalfa sprouts, he carved a 40-cm (16-inch) wide channel with a single bend at the top, turned on the water, introduced plastic and sand and let the sproutscape rearrange itself over a total of 136 hours."We found that you need enough vegetation on the outer bank to slow down erosion and let the bars grow on the inner bank; otherwise, the stream cuts through the point bars and creates a braided river," Braudrick said. During the experiments, as the channel migrated into chutes or the sinuosity increased, individual bends cut off as the channel took a shorter path. Over the course of the experiment, which took a year to complete and was equivalent to about 5-7 years of high stream flow, the stream formed five new bends that moved downstream as they grew, cut off and re-formed, all the while migrating laterally across the flume's floodplain.One key to letting real-world bars grow, he said, is fine sediment, about the size of sand, that keeps point bars from being undermined or cut through before they can grow to the elevation of the floodplain, and that plugs holes in bars before the chutes becomes cutoffs. Sand and fine sediment are today considered detrimental when restoring streams for fish spawning because of fears the sediment will cover the gravel in which fish lay their eggs. "Eliminating fine sediment is probably not a good idea if you want to maintain a single-thread, meandering river that migrates," Braudrick said. A naturally migrating meander, however, constantly brings new sediment in from eroded banks upstream, while also providing wood and debris for animal habitat.Interestingly, the researchers found that mixing high flows of various heights was not essential to creating meanders, as suggested by other studies. A steady flood flow was sufficient to provide the sediment needed to maintain and build bars and erode banks.Key to their success was the use of alfalfa sprouts, which was suggested by related experiments at the University of Minnesota, headquarters of the National Center for Earth-Surface Dynamics, of which UC Berkeley is a member. As with trees and other vegetation along natural rivers, the roots of the alfalfa sprouts provide strength to the soil and, when exposed, protect the banks from the force of the water, preventing banks from washing away too quickly.The downside of sprouts, Braudrick said, is that they rot when repeatedly wet and take time to grow. Every three days, the experiment had to be halted for more than a week to allow the sprouts to die and be replanted. The search is on for hardier plants or other materials that will allow longer trials that should more precisely reproduce natural, long-term processes.Also key to the success was finding a way to scale-model the fine sediment common in rivers and streams. While sand adequately models gravel, the substances used previously to represent sand did not stay suspended in the water like sand and silt. Plastic materials like those used in sand-blasting were the right size and density to remain suspended and demonstrate the importance of fine sediment in stabilizing point bars.  “This work has taken extraordinary patience and considerable trial and error by Christian to perfect the methods, but now, for the first time, we know how to make dynamic, self-maintaining meanders in the lab, and this opens up many new areas of research," Dietrich said.Dietrich, Braudrick and their colleagues plan to investigate the role of various factors in determining the shape and migration rate of streams and how variables associated with climate change and land use might be expected to affect river form. In addition, they hope to determine the conditions that allow meanders to form in permafrost absent vegetation, and on the lifeless surface of Mars."What's cool is that meandering channels are all over Mars, and there's no vegetation, so clearly the bank strength is coming from somewhere else, probably ice," Braudrick said. "And the frozen surface of Titan has meanders. All these are vexing problems."



The ysis of crustal deformation by tectonic processes has gained much from the clues offered by drainage geometry and river behaviour, while the interpretation of channel patterns and sequences benefits from information on Earth movements before or during their development. The interplay between the two strands operates at many scales: themes which have already benefited from it include the possible role of mantle plumes in the breakup of Gondwana, the Cenozoic development of drainage systems in Africa and Australia, Himalayan uplift in response to erosion, alternating episodes of uplift and subsidence in the Mississippi delta, buckling of the Indian lithospheric plate, and changes in stream pattern and sinuosity along individual alluvial channels subject to localized deformation. Developments in remote sensing, isotopic dating and numerical modelling are starting to yield quantitative yses of such effects, to the benefit of geodymamics as well as fluvial hydrology.Active tectonism affects the characteristics of river channels, and fluvial activity influences the geometry and tempo of fold and fault development and even the gross behaviour of continental land masses. Both concepts have long been grasped but they are gaining in scope and specificity from recent conceptual and technical developments in Earth science and a variety of fields.Some of the most thought-provoking large-scale studies of river history hinge on simplistic views of channel morphology just as early studies of continental drift drew inspiration from rudimentary cartography. But fluvial ysis, in the field as well as in the laboratory and underpinned by refined dating and computing techniques, is starting to help resolve issues—such as the consequences of the collision between India and Asia—which have hitherto focused on kinematic narratives. The outcome sheds light on processes in the Earth's mantle as well as in the crust.The examples discussed here can be grouped into three. The first two yse the adaptation of rivers to existing geological structures and their response to tectonic change: broadly equivalent to the passive and active tectonic controls of Summerfield [1]. The categories evidently overlap, as when erosion of a growing anticline comes to expose alternating resistant and weak strata to which the stream has to adapt, and they are complicated by climatic and other factors. The third group of studies focus on how far fluvial action drives or at least modifies tectonic processes nearby and far afield. Again the distinction is mainly one of convenience, as river behaviour may be enhanced or damped by the deformation it promotes.In reviewing the field of fluvial tectonics we begin by considering channels in plan view. To be sure, there is no such thing as a two-dimensional watercourse, but many of the pioneering studies in the 1950s and 1960s that put fluvial geomorphology on a quantitative basis concentrated on mappable features including stream order, sinuosity and channel width. What is more, river patterns at regional and continental scale played a part in the elaboration of plate tectonics and mantle plume models.Plate tectonics, like its precursor continental drift, initially involved tracing the breakup of land masses by fitting together the resulting fragments. The centuries-old recognition of the match between the west African and South American Atlantic coasts was eventually confirmed and improved by a computer-based fit of the 500 fathom margins by Bullard et al. [2]. Here, and at other reconstituted margins, river channels played a useful role in establishing or explaining the extent of misfit. The apparent 120 km overlap between the two continents near the Niger delta, for example, could be explained by delta growth following final separation in Albian (Cretaceous) times [3].The cause of continental breakup remained a secondary consideration until its reality could finally be taken for granted, contrary to Harold Jeffreys' [4] standpoint that drift was untenable because it was mechanically unfeasible. One candidate which remains in contention is the action of mantle plumes, upwellings which nucleate at the boundary between the Earth's core and its mantle and which rise through the mantle and the crust to drive volcanic activity and other symptoms of anomalous heat. Plumes are suspected of promoting the disruption of the supercontinent of Gondwana during the last 200 Myr (figure 1). The associated updoming appeared to account for the present drainage pattern of a number of continental basalt provinces, although dome-flank patterns are likely to be complicated by the effects of secondary rifting (figure 1c). In southeast Africa the Orange River system dates in its essentials from the Jurassic, say 190 Ma when activity in the Karoo flood basalt province was at its peak [5]; the ensuing deformation would then explain why the east-flowing rivers apart from the Limpopo are much shorter than those flowing west [7]. On the other hand, the plume-head model for the Deccan of peninsular India conflicts with stratigraphic evidence, which shows that easterly drainage of the peninsula predates the uplift [8]. (a) Location of mantle plumes (circled) thought to have contributed to the breakup of Gondwand approximately 200 Ma. Based on Cox [5]. (b) Pattern of separation between South America (SA), Africa (AF) and Antarctica (AN) (a, proto Atlantic; b, proto Indian Ocean). After www.wits.ac.za/. (c) Domal drainage disrupted by rifting. Adapted from Cox [5] and Moore & Blenkinsop [6]. (Online version in colour.)The survival of radial drainage systems for 60 Myr or more seems barely plausible even if the dome continues to rise buoyantly in response to surface erosion or to the addition of magma (‘underplating’) to its base; and the pattern would also be equally consistent with late deformation of ancient rock formations, as in the Lake District of northwest England where Palaeozoic rocks were raised into a dome in Tertiary times. But even if South African drainage systems since Gondwana times have been disrupted by structural effects, the exposure of buried topographies and river capture, it may be possible to recognize the ‘first-order imprint’ imposed on the drainage by successive plumes. The Paraná plume pattern, which was superimposed on the earlier Karoo pattern, would thus be responsible for a dominant eastward drainage orientation since the early Cretaceous [6].The search for corroboration has been taken into the subsurface. Regional rather than radial drainage was identified in space-borne imaging radar (SIR-C) data in the Selima sand sheet of southwest Egypt [9]. The imagery revealed large flood features, which to judge from fault alignments were to some extent structurally controlled and provisionally dated to the Tertiary and on which were superimposed a variety of drainage channels thought to date from the Quaternary. A similar story has emerged in southeast Australia. Two major rivers draining to the Murray Basin, the Lachlan and Macquarie, may represent superimposition from sediments dating from the Mesozoic whose direction was determined by uplift and tilting about 95 Ma [10].Rivers also played an important part in tracing the regional deformation resulting from convergence between India and Asia: ‘long linear valleys and adjacent ridges characteristic of active strike-slip faulting’ were boldly displayed, particularly in China and Mongolia, in the images used in the classic study by Tapponnier & Molnar [11]. Total shortening was estimated at 1500 km at least and wholly in continental lithosphere. An estimated 300–700 km of this displacement was taken up by crustal shortening and underthrusting; the remainder was relegated to lateral extrusion, a mechanism which had been previously proposed for Turkey and Iran and modelled by the deformation of a plastic body subject to indentation by a flat rigid die [12]. Comparison with imagery of the San Andreas fault in California encouraged the estimate of 500–1000 km of eastward displacement of southeast China on the major faults that originate in central China (figure 2). (a) Major drainage systems implicated in the indentation of Asia by India. RR, Red River fault; KL, Kunlun fault. (b) Streams dislocated 15–72 m by left-lateral slip on portion of Kunlun fault (ASTER image dated 20 July 2000, courtesy of NASA). The dark area shows vegetation where groundwater has been dammed by the fault. (Online version in colour.)The work has proved to be inspirational, in the Mediterranean and in The Philippines no less than in Tibet, but also controversial. A telling illustration is provided by the Ailao Shan or Red River, which occupies a shear zone running from southeast Tibet to the south China Sea and which in the extrusion model took up 500–1000 km of movement by Indo-China in response to Indian penetration. Yet slip along the Red River fault is right-lateral, with offsets of 25–54 km at most [13]. Moreover, the faulting should have cut through the entire lithosphere and not just the crust; the heat produced by shearing should have resulted in partial melting and metamorphism of crustal rocks; and the shearing itself should have affected granites along the fault. None of these criteria applies, and any extrusion must have happened at least 29 Myr after India collided with Asia [14].Again, river terraces and other geomorphological indicators along the Kunlun fault (figure 2) at millennial scale (rather than short-term seismological data) show that, along the easternmost 150 km of the fault, slip rates fall from over 10 mm yr−1 to less than 2 mm yr−1 within thickened crust, suggesting that slip is absorbed within the plateau rather than manifested as eastward extrusion [15]. In southeast Tibet river patterns which appear to indicate extensive tectonic shear have been otherwise explained by surface uplift accompanied or followed by river capture and flow reversal in streams which once drained to the China Sea by way of a single system [16].Despite the inclusion of field sites in California and other tectonically lively areas, ‘tectonism’ is sometimes seen simply as a more plausible source of channel steepening than aggradation or degradation [17]. But the search for laws governing channel equilibrium yielded relationships between geometry and discharge which would allow disequilibrium (including that due to tectonics) to be identified [18]. These inferences are increasingly complemented by instrumentation for more direct assessment of the tectonic factor. In the Long Valley caldera, for example, streams, springs, water wells and other components of the hydrological system are monitored continuously so that the effect of extension in the resurgent dome within the caldera can be evaluated.Experiments using flumes [19,20] suggest that, in meandering channels within alluvium, aggradation tends to follow uplift both above and below the axis of deformation while near the axis itself degradation is accompanied by increased sinuosity. Subsidence sees degradation upstream and downstream, with aggradation near the axis [21] (figure 3). The relationship will be complicated by associated changes in slope, width and other variables, and obscured once its effects propagate upstream or downstream though perhaps not if the deformation—as where a stream crosses a growing anticline—is persistent. And it is increasingly clear that rooted plants (alfalfa sprouts in one flume study) favour the development in alluvium of single-thread meandering channels. Effect of experimental deformation on channel form [21]. The axis of uplift or subsidence is marked by filled triangle; stream flow left to right. (a,b) Subsidence in a meandering channel after 4 and 48 h, respectively, showing increased sinuosity upstream; (c,d) uplift on a meandering channel after 16 and 40 h, respectively, showing increased sinuosity downstream. Photographs taken at Engineering Research Center, Colorado State University, Fort Collins (courtesy of Prof. Ouchi). (Online version in colour.)More generally, such relationships are constantly adjusting in a state of quasi-equilibrium to variations in discharge and are governed by a tendency towards minimum work and the uniform distribution of energy utilization [22]. It therefore seems mistaken to equate any one channel characteristic, such as the presence of braiding, or the average wavelength of a train of meanders, with a single controlling factor, such as discharge, sediment calibre or slope.Yet that kind of oversimplification has on occasion proved fruitful. Three intraplate earthquakes with magnitudes of 7.5 or above struck at New Madrid (Missouri) in 1911–1912. At least one of them was produced by the Reelfoot thrust fault (figure 4). Trenching across the fault scarp revealed three slip events dated to AD 900, 1450 and 1812. An earlier event at about AD 300 left traces in the region but not at the fault, and the 900 and later events account for only 8–9 m of the cumulative 15 m of displacement represented by deposits at the scarp [24]. Active and fossil meanders on the Mississippi near New Madrid (Missouri) and location of Reelfoot fault (toothed line), Reelfoot lake and one of the three main events of 1811–1812 (7.4 on 7 February 1812). Google Earth image. Inset lower left: three successive flood plains near latitude 36° implying that the zone of unloading shifted eastwards. Adapted from Calais et al. [23]. (Online version in colour.)Intraplate earthquakes are among the most destructive and least understood, in part because they recur at intervals that may measure centuries or millennia, and it is therefore essential to extend the scanty instrumental and historical record as far back as possible in order to identify any pattern in their behaviour. Two additional earthquakes were identified in the local valley deposits by mapping abandoned meander loops over a 100 km reach and identifying meandering-straightening events in pervasively meandering reaches upstream of the fault. Dating by radiocarbon (14C) and optically stimulated luminescence indicated ages of approximately 2200–1600 BC and AD 900 for two such episodes [24]. Channel straightening can result from changes other than a reduction in gradient, such as an increase in discharge or bed load or perhaps a spontaneous meander cutoff, but the AD 900 straightening episode is reasonably ascribed to a change in slope caused by the faulting event of the same date, with an estimated slip of 1 m, especially as straightening was confined to a 30 km reach immediately upstream of the fault. This was taken as endorsement of a tectonic interpretation for the 2200–1600 BC straightening episode, which saw several centuries of low river sinuosity with a strong similarity to the ‘New Madrid’ series of faulting events that was launched by the AD 900 earthquakes.If correct, this comparison suggests that the Reelfoot fault displays earthquake clusters separated in time by prolonged quiescence. More generally, it shows that fluvial tectonics is an effective device for investigating deforming structures which would escape detection even by prolonged and expensive monitoring by geodetic and levelling survey because their development may span centuries and millennia and elude ysis in sections however neatly excavated and richly endowed with numerical ages.Entire drainage systems may respond to structural controls such as tilting, doming, faulting and jointing by developing appropriate dendritic, parallel, radial, trellis, rectangular, annular and centripetal drainage geometries. The association generally takes time to develop by successive approximations that embody some kind of natural selection and it has been argued that river patterns, especially if carved in rock (rather than fickle alluvium), ought therefore to be long-lasting [25].In his discussion of channel slope Leopold [22] emphasized that the familiar moderately concave longitudinal profile (like other aspects of channel morphology) represented a compromise between uniformity of energy loss and minimum work. Yet longitudinal profiles and sharp breaks in their gradients (or knickpoints) remain enduringly enticing to students of tectonics and not solely because the requisite small-scale profiles can be constructed from topographic maps or digital elevation models (DEMs). The major attractions are that the method can be applied to bedrock as well as alluvial rivers, can integrate records spanning millions of years, and will record major tectonic events.Presumably with such aims in mind the profiles of the major trans-Himalayan rivers were investigated in the context of current seismic activity [26]. All but one (the Subansiri) were found to display low gradients within the high plateau north of the High Himalayas, within the Sub-Himalayas and the Lesser Himalayas, and in the alluvial plains to the south, whereas within the High Himalayas their gradients were two (or more) times steeper than the theoretical profile of a graded river. The poor correlation between lithology and steep river gradients suggests that tectonic movement rather than differential erosion plays the main role in shaping the profiles; uplift is balanced by erosion, and topography is ‘invariant’ in a steady-state setting. This ysis is supported by the correspondence between the steep reaches and the basement thrust front, which is marked by thrust earthquakes, and the presence of the highest terraces above river level in the gorges through the high range.Profile ysis therefore revealed large-scale tectonic activity which, as at New Madrid, seismology had failed to detect because the instrumental record was short and patchy. As the investigators put it, in the Himalayas topography may be a better indicator of active sub-surface tectonics than surface structures. The argument is especially convincing if changes in channel long profile are associated with datable sediments. The classic study of this kind was conducted in Pallett Creek, an ephemeral stream in California which flows from the San Gabriel Mountains into the Mojave Desert and crosses the San Andreas fault 55 km northeast of Los Angeles. In order to uncover any evidence for earthquakes other than the great 1906 and 1857 events the valley deposits were trenched over a distance which ultimately amounted to 50 m and a depth of 5 m. The evidence that was sought consisted of sandblows (or sand volcanoes), fissures and offsets [27]. The study yielded evidence of 12 large earthquakes between AD 260 and 1857 separated by intervals of about 145–200 years [28]. The original 14C ages had errors of 50–100 years at the 95 per cent confidence level. Progress in dating methodology reduced these errors to less than 23 years for 10 of the events; the interval between events now ranged from 45 years to 330 years but the past 10 earthquakes were found to have occurred in four clusters of 2 or 3 events separated by gaps of 200–250 years.The question of chronology is worth pursuing for two main reasons. First, there may be some kind of pattern in the local earthquake sequence, such as the clustering we have already encountered at New Madrid, as it would colour (and perhaps even discourage) any attempt to forecast earthquakes. Second, if events of the same age have been reported elsewhere in the region it should be possible to estimate earthquake size; event V of AD 1480±15 at Pallett Creek, for instance, appears to have ruptured the entire southern half of the San Andreas fault over a distance of about 300 km. Yet the earthquake history of Wallace Creek, also crossed by the San Andreas fault 300 km to the northwest, is surprisingly different. The channel has been offset horizontally by a total of 128 m; the interval between the last three great earthquakes was 240–450 years, twice as long as at Pallett Creek [29].Pallett Creek and Wallace Creek illustrate stream sequences which reveal local seismic history and contribute to wider assessment of earthquake chronology if only by complicating it. They also bear on regional tectonics by showing how far movement over recent centuries compares with the expectations of plate tectonics. At Wallace Creek the average rate of slip—both during earthquakes and by creep between them—is about 34 mm yr−1 over the last 13 000 years, close to the rate obtained by geodetic methods for 1977–1981 of about 30 mm yr−1, a measure of agreement which is sometimes taken to show that strain (i.e. the capacity to generate an earthquake) is not building up on this stretch of the fault. Yet the average motion between the North American and Pacific plates over the last 3.16 Myr points to motion at about 50.2 mm yr−1 along the San Andreas fault [30].The deficit is arguably being taken up by other fault systems near the Californian coast and in the Basin Range, but there remains the interesting alternative that plate motion is not necessarily steady; as it happens, GPS measurements for relative movement between the Pacific and North American plates persistently differ significantly from the geological rates. For 1996–1998, for example, they indicate a rate of about 49.4 mm yr−1 [31]. Various explanations for the discrepancy have been proposed, including a real change in the direction of plate motion over the past 3.2 Myr [30]. Any information on this count is to be treasured for what it might say about the mechanisms of plate tectonics, and valley history is uniquely placed to bridge the large gap in the time intervals used by geodetic and geological approaches and also to provide near-continuous records rather than average rates.The Pallett and Wallace fault systems added detail to the San Andreas system; a growing number of fractures are being revealed in novel locations by surface folds. Perhaps the first of these ‘blind’ faults was revealed in Algeria in 1980 when the El Asnam earthquake (Ms=7.3) of 10 October nucleated on a segment of the Oued Fodda fault (figure 5) [35]. The middle segment of the fault is aligned transversely to Wadi Chelif. Reverse slip was marked by a number of topographic effects indicating both elastic and brittle deformation. A temporary lake on the Chelif was initially ascribed to blockage by the fault but was soon found to represent downbuckling of the channel. Exposures (and, later, excavations) into the lake bed revealed eight large events marked by temporary ponding which antedated 1980. Organic material in the deposits yielded 14C ages sufficient to identify six earthquakes similar to that of 1980. Although the interval between large earthquakes ranged between 300 and 500 years, those with magnitudes greater than 7 clustered around 4000 years ago and also within the last 1000 years [36]. Upwarping was vividly recorded by deformation of an alluvial terrace dating from medieval times, as shown by its burial of a Roman site and 14C dating of charcoal in the alluvium. The terrace could be traced into a gorge cut by the Chelif, where it had risen by 5 m above its normal level. (a) Hypothetical pattern of buckling of the Indian plate (dashed lines) in response to collision with Asia [32] (Nuvel 1A after [33]). The model gains support from field evidence including (b) channel pattern and (c) displacement away from the major watershed (dashed line) at lineament III [34]. 1 and 2 show successive channels of rivers Gurupur and Nethravarthi. (Online version in colour.)Soon after the El Asnam earthquake, on 2 May 1983, there occurred the Coalinga (Mw 6.5) earthquake in the San Joaquin valley of California [37]. Here too a blind reverse fault had created a surface fold; levelling showed 40 cm of uplift and 25 cm of subsidence along a survey line crossing the anticline. The Los Gatos river also crosses the anticline and a terrace dated to 2550 years rises from an elevation of 1–3 m to 10 m above the river. The recurrence interval for events comparable to that of 1983 was therefore put at approximately 100 years.El Asnam and Coalinga prompted a search for active, possibly seismogenic, structures in areas where geologists had previously focused on surface faults. In California itself buried faults are now seen to pose as serious a threat as the blatantly exposed San Andreas fault. The Northridge (Mw 6.7) earthquake of 17 January 1994, in the San Fernando valley, is a case in point. With associated ground acceleration as high as 1.7 g it proved an unexpected hazard in an area which had been thoroughly investigated for active structures. The year 2003 saw what was perhaps the first precautionary study of a blind thrust, when tilted river deposits beneath what is now central Los Angeles were interpreted as evidence of four major (Mw 7.2–7.5) events during the last 11 000 years [38].The search for quantitative tectonic signals from sediments and landforms continues to gain impetus from such stark findings [39]. Active folding is of course of more general interest as a symptom of deformation in progress, and it may lead to the regional syntheses required for refining tectonic models. In Central Otago, New Zealand, a peneplain has been deformed by folds driven by buried reverse faults, and drainage ysis shows (for example) how separate fold segments can coalesce into ridges [40]. In the Manawatu region anticlinal ridges have also developed above buried reverse faults, this time in a mid-Quaternary marine surface. The drainage systems are consequent on the growing folds but are no longer perpendicular to the structural contours on the flanks of the anticlines, presumably because of regional tilting [41]. The estimated rate of tilting is similar to that from river terraces in the Rangitikei River, an interesting endorsement of such indirect methods for tracing crustal movements. In Epirus (northwest Greece) a compressional component of motion has long been identified from the topography and from limited seismological data. Field studies, including ysis of river long profiles, revealed features which combined dip-slip with a strike-slip component of motion [42]. The observed deformation could be reproduced by applying a slip vector of approximately 260–280° across Epirus as a whole.Such patterns become especially interesting where they are discordant, as their history can help to resolve the role of stream antecedence. The issue has long occupied students of drainage in the Zagros Mountains of Iran. The debate was shortcircuited by studies which showed how river capture too could create transverse drainage systems [43] and more recently by evidence that fold segments some 20–40 km long may coalesce into chains of over 100 km. This process distorts any throughgoing drainage but, as in Otago, the pattern of tributary streams records the progress of fold propagation [44] and it may help to distinguish between fault-bend folds, with lengths determined by the driving reverse fault, and detachment folds, which undergo lateral propagation at the fault tips [45].The detachment folds exhibit serial folding, the principle that folds have grown in sequence rather than simultaneously [46]. The idea was given prominence in a series of simple laboratory experiments in which stratified materials over a detachment surface were compressed by a piston [47]. The implication for the Zagros was that folding began at the rear of the fold belt and is currently in progress at the deformation front on the Gulf. A river section close to the coast showed that part of the shortening was taken up by reverse faulting (the Chah Shirin thrust); ysis of uplifted marine terraces had shown that Holocene shortening was indeed concentrated in the frontal fold to the tune of 19 mm yr−1, close to the average approximately 20 mm yr−1 opening rate for the Red Sea during the last 3–4 Myr. There are obvious implications for seismic hazard assessment, in the sense that, as many of the Zagros folds are driven by concealed reverse faults, the zones most prone to shallow earthquakes and ground deformation can be provisionally identified from the topography. More important, the force required to sustain the locked and developing folds against gravity yields a value (less than 1 kbar) which can be compared with competing models for the convergence between Arabia and Eurasia [48], making gravity glide resulting from Red Sea opening a plausible mechanism for compressing the Zagros.Inland the vertical component of valley deformation could be measured only by laborious levelling until the development of space geodesy. On the coast sea level provides a convenient datum, as in the Musandam peninsula of northeast Oman, which links Arabia to the Zagros. A strongly indented coastline betrays the submergence of a valley network. The onshore valleys are floored with a calichefied gravel unit. It is stratigraphically and petrographically related to the Tehran Alluvium of north and west Iran, whose accumulation had ceased by about 6000 years ago. The Musandam valleys can be traced offshore by plotting the cemented river gravels by geophysical means and are seen to extend to their greatest depths towards the northeast. After allowing for sea-level rise over the last 6000 years the age/depth data yield a maximum average subsidence rate of 8.5 mm [49]. There is good agreement with the results of satellite measurements (by differential synthetic aperture radar interferometry), which indicate a seismic subsidence at 10 mm yr−1 at Ras al-Khaimah, southwest of the peninsula, and 5 mm at Khor Fakkan, southeast of the peninsula, the latter possibly associated with earthquake activity [50].Geologists working in the region have long recognized that Musandam was subsiding in contrast with the Oman Mountains further south, which were known to be rising. The process could not previously be quantified even though the tectonics of Musandam were known to be in response to extension of the Red Sea. We now see that Arabia is transmitting this extension from the Red Sea to Iran without deforming significantly. In short, by allowing subsidence to be quantified the valleys of Musandam helped to demonstrate the truth of an axiom of plate tectonics, namely that deformation is strongly concentrated at plate margins.The residual strain acting at plate interiors to marginal compression can be lethal as it gives rise to large earthquakes which, as at New Madrid, are too infrequent to stimulate adequate building codes or evacuation procedures. Peninsular India is a case in point, as its interior has been struck by a number of very violent earthquakes at locations which are not self-evidently seismic. Consider, for example, the Coimbatore (M 6.0) earthquake of 28 February 1900, the Kilari/Latur (Mw 6.1) earthquake of 24 August 1993 and the Koyna (Mw 6.5) earthquake of 10 December 1967.It has been suggested that collision between India and Eurasia has given rise to a major downfold south of the Himalayas and that, as the Indian plate traverses this topographic low, successive parts of the plate are subjected to compression which from time to time is sufficient to trigger earthquakes [51]. An alternative view is that the plate develops a number of buckles which undergo progressive compression. Evidence for two such upwarps began to accumulate in the 1980s and 1990s, the first of them running east from Cochin (I on figure 5) [52] and the second between Mangalore and Madras (II). Along the latter there was evidence for a thin crust and anomalously positive values for gravity, both of them consistent with extension and the presence of mantle rocks relatively close to the surface, microseismicity associated with pervasive rock fracturing, and above all the displacement of river channels away from the proposed axis of uplift [34].Four more buckles were later proposed on the basis of compressional earthquakes, rather than surface deformation, with a spacing of approximately 400–800 km and some anticlockwise rotation in the north in response to the irregular margin of the deforming plate [32]. The Indian plate extends south into the Indian Ocean, and the submerged portion displays a series of undulations with a wavelength of about 200 km which are widely seen to represent plate compression. Modelling on the basis of an elastic thickness of 35 km—for oceanic crust—yields buckles with a wavelength of approximately 150–200 km [53]; a greater wavelength would be expected in the emergent part of the plate with a thickness of 65–79 km.The ysis will eventually shed light on the force required to drive the plate and hence the relative importance of gravity, ridge push and basal drag in its displacement. Buckling would require a force of about 1013 N m−1; sustaining the Tibetan Plateau against gravity requires between 4×1012 and 1013 N m−1 [54]. In short, there is broad equivalence in the force expended by two major crustal processes at work in the region.The possibility that fluvial erosion and deposition could influence tectonic processes has long been recognized and indeed quantified. Fridtjof Nansen [55] was among the first to postulate isostatic adjustment to loading and unloading; he understandably focused on ice as the primary agency, and deglaciation has remained an important topic of research into mantle properties because both the history of ice retreat and the progress of land uplift and deformation at high latitudes can be traced in sufficient detail for such matters as mantle viscosity to be evaluated. Glacial lakes, notably Bonneville, offer similar advantages including a built-in horizontal datum.Isostatic adjustment in the world's major deltas has also long been recognized. Despite the difficulties that arise in evaluating the relative contribution of fault movement, sediment compaction, fluid and gas extraction and other sources of subsidence, isostatic modelling for the Mississippi delta (figure 6) suggests that channel incision during glacial episodes of low sea level and channel filling during the ensuing rises suffice to induce alternating episodes of uplift and subsidence amounting to almost 8 m over a distance of some 150 km along the Gulf coast [56]. An elastic model was used to estimate the effects of a load 40 m thick and 80 km wide with density 1800 kg km−3 and a lithosphere with an elastic thickness Te of 30 km. Load removal would lead to an elastic uplift of approximately 12 m in the valley centre and 9.7 m at the margins. The field evidence indicates six such episodes of channel-belt deposition between 54 000 and 12 000 years ago separated by periods of valley cutting. The Mississippi delta (Multi-angle Imaging SpectroRadiometer image, courtesy of NASA); inset shows surface deflection over time at different longitudes at 30° N based on a three-dimensional viscoelastic model. Note uplift followed by susbsidence with dissipation of the signal with distance along the shoreline. Adapted from Blum et al. [56]. (Online version in colour.)The study suggests that other large deltas have probably undergone repeated uplift and subsidence, especially where glacial meltwaters have provided enhanced erosion at times of low sea level. More important in the present context, the detail with which delta deposits can be traced and dated offers scope for refined tests of competing mechanisms, a kind of gravitational titration. Evidently this holds only for deltas riddled with boreholes and for which distortion by the human factor is well documented. In the Mississippi delta regional subsidence can be shown to be locally compounded by fault reactivation induced by hydrocarbon extraction [57,58].In deciding whether erosion alone can trigger an isostatic response the key issue is the stress level required to exceed crustal resistance. Faulting can set in motion buoyancy forces which either reduce or accentuate the effects of the original displacement provided the structure is substantial enough for the resulting imbalance to exceed the elastic strength of the lithosphere. Fluvial activity may have an ogous effect and allow crustal strain originating in plate motions and other regional sources to be identified. At New Madrid, GPS data show that any motions across the seismic zone measure less than 0.2 mm yr−1, which suggests that strain is not accumulating at a steady rate and that existing faults have been reactivated by a local process. A plausible explanation is that upward flexure of the lithosphere consequent on river erosion reduced normal stresses in the upper crust sufficiently to unclamp faults close to failure [23], ogous to the mechanism that has been proposed for locations at high latitudes where fault movement followed unloading by glacial melting and glacial erosion.The fluvial record for the central and lower Mississippi shows that some 6 m of sediments were removed over a zone 60 km wide between 16 000 and 12 000 years, BP and a further 6 m over a zone 30 km wide between 12 000 and 10 000 years, BP (figure 4). Finite-element modelling, on the assumption that unloading was linear between 16 000 and 10 000 years BP, suggests that with a strong mantle (little viscous relaxation) the unclamping stress increases linearly with load removal and is then constant. With a weak mantle, stresses continue to build up long after unloading is over. In either case faults in the New Madrid fault zone continue being unclamped as much as 10 000 years after significant alluvial erosion came to an end. In brief, existing faults here are reactivated by small stress changes resulting from flexure that has been induced by erosion, so that seismicity migrates from fault to fault ‘drawing elastic energy from the long-lived strain reservoir’ [23, p. 610].Note that interaction between fluvial activity and deformation can be traced away from faults and alluvium and without the assistance of isostatic rebound. The effect on fold development lends itself well to ysis at scales smaller than 200 km provided surface processes are rapid relative to the rate at which deformation can operate. If the crust is already stressed to the failure limit, erosion and deposition can accentuate buckling rate and increase buckling wavelengths: if the topography is increased it is because the dynamic folding instability is amplified through a change in the distribution of gravitational loads and changes in the thickness—and hence the strength—of the deforming elastic–plastic layer [59]. A fine illustration of this process is the Oxaya antiform in northern Chile (figure 7), a structure which displayed its greatest rate of growth between 6.7 and 2.7 Ma when transverse stream incision attained up to 1500 m and coincided with plastic deformation of the crust under regional compression [61]. (a) Deflection and topography resulting from deformation (37% shortening) in the presence of (i) relatively efficient and (ii) relatively inefficient surface processes. Heights and distances normalized for comparison. Dashed line, topography; full line, deflection. Based on Simpson [59]. (b,c) Buckling amplified by river incision: the Oxaya antiform, north Chile (thick dashed line). Adapted from Zeilinger et al. [60]. (Online version in colour.)Uplift resulting from erosional unloading is evidently not confined to major deltas at times of low sea level and enhanced stream flow. It is at its most spectacular in some of the loftiest mountain ranges. In an ysis of stream antecedence in the Himalayas, Wager [62] argued that a stream may maintain its course while a mountain rises in its path, citing the Yo Ri gorge reach of the Arun as evidence: like other streams in the region the Arun runs parallel to the Himalayan range for hundreds of miles and suddenly turns south to run across the High Himalaya between Mt Everest and Kanchenjunga. The notion that isostatic rebound contributes to mountain uplift dates back at least to Clarence Dutton, who argued in 1899 that the effect of erosion in the mountains was abetted by the counterflow of material displaced by deposition near the coasts.Some have argued that transverse courses in the region often owe more to capture and superimposition than antecedence. As often happens the battle lines eventually become blurred. Many rivers cross the Himalayan axis at bends or at points where headward erosion was easy and perhaps where it subsequently led to localized isostatic uplift; at some of the crossings the stream is in effect superimposed on a discordant structure.For a quantitative ysis it may therefore be simpler to deal with river systems and rock masses in bulk. The positive feedback between erosion and uplift can be viewed as a special case of the interaction between tectonics and climate where removal of a thickness ΔT of crust of density ρc compensated with a crustal root in mantle of density ρm leads to surface lowering by about ΔT/6: a ‘gentle highland’ of mean elevation h incised by rivers nearly to sea level would fall in mean elevation to about 0.83 h but the peaks would rise to 1.8 h or higher [63].Nevertheless, detailed case studies show that the influence of erosion on mountain building is complex and often subject to feedback. An example in the eastern Himalaya which has parallels with the Oxaya antiform is the Namche Barwa-Gyala Peri massif, also antiformal, where high relief and rapid erosion by what is deemed the most powerful river in the Himalaya, the Brahmaputra, point to a balance between rock uplift and river incision at least for the last 1 Myr [64]. Such observations have led to the suggestion that river anticlines represent the most recent phase of Himalayan deformation. The Arun river also crosses an anticline which coincides with a local rainfall maximum, and it may be that the coupling between tectonics and erosion is manifested to different degrees within an active orogen in response to climatic variations and their effect on erosion [65].More generally, deep valleys may indicate isostatic response to incision rather than the massive post-Pliocene net uplift that has been widely proposed for the Alps and Rockies. Accelerated sedimentation could give an equally misleading impression of enhanced tectonics: a fourfold increase in deposition rate over the last 2 Myr in the Gulf of Mexico, for example, has been equated with rapid uplift of the Rockies whereas the onset of widespread glaciations in the Northern Hemisphere may be responsible for the necessary increase in erosion at source [66].Assuming periodically spaced, uniform, long, parallel, V-shaped valleys, and crust and mantle densities, respectively, of 2800 and 3300 kg m−3, the rate of mountain uplift will be 42 per cent of the rate of valley incision. Measured incision averaging 172 m in the Sierra Nevada would account for only 9 per cent of the uplift that has been estimated for the last 10 Myr, whereas as much as 1500 m (20–30%) of the present elevation of the Himalayan peaks may be an isostatic effect [67]. Valley incision by trans-Himalayan rivers at the margins of the Tibetan Plateau in the late Cenozoic, possibly accelerated by climate changes, could have accomplished the requisite unloading.Of course the extent to which compensation is realized depends on the flexural rigidity of the lithosphere and the wavelength of the topography. It can be estimated using a formulation by Turcotte & Schubert [68], which is applicable to topographic wavelengths of 102–103 km and flexural rigidities of 1020–1025 N m and encompasses many mountain ranges. An important result is that at topographic wavelengths of less than about 100 km even low flexural rigidity will suppress local compensation: valley incision influences mountain peak elevation where the mountain range is large or the lithosphere is weak or thin. Flexural rigidity of the lithosphere is in the region of 1023–1024 N m beneath the Sierra Nevada, which is 200–400 km wide; compensation is 1–5%; for the Himalayas (400–500 km wide) the rigidity is estimated to be 1022–1023 N m and the compensation could be as much as 45–95% [67]. The answer may embody both isostasy and climate change: in the Sierra Nevada any uplift must be primarily due to tectonic factors, while—assuming a plateau 250 km wide and 6 km high falling to 0 km 300 km from the watershed—stream incision at the margin of the Tibetan Plateau indirectly accounts for the great height of Himalayan peaks.The drainage pattern of rivers contains ‘unique information about the past and present tectonic regime. The longitudinal profile of a river is sensitive to the ongoing process of uplift and can be used to recognize active structures’ [26, p. 343]. This distinction is at its most valid where the network is incised in bedrock and the river flows in alluvium; for, as we have seen, stream networks can be disrupted by seismicity at a stroke and individual profiles may embody traits inherited from a very different tectonic past. What is more, solitary channels as much as river systems can trigger disproportionate tectonic reactions.Perhaps more instructive today would be a distinction between historical and geodynamic case studies. An important function of research on fluvial tectonics is explanatory. ysis of Neogene strata, for example, shows that uplift of the eastern Cordillera of South America diverted the Orinoco drainage from Lake Maracaibo to the Atlantic [69]. There is even dedicated computer software (e.g. [70]) to facilitate such tasks as determining flow direction, knickpoint selection and stream profile generation from DEMs. But the way forward surely lies in applying the results to the dynamics of deformation and thence to the geophysical mechanisms that are at work. Buckling of continental lithosphere, as in India, leads to some understanding of the forces at work where plates converge. The pattern of movement along a major strike-slip fault, such as the Red River fault, mentioned earlier, or the Altyn Tagh fault on the Tibetan Plateau [71], may show that a region deforms internally by a network of faults in the shallow brittle crust rather than by slip on a transform fault cutting through the entire lithosphere and separating two relatively rigid blocks. Isostatic processes in major mountain rivers could conceivably promote ‘channel flow’ of low viscosity in the mid-crust [72] whereupon ‘rivers may be the authors not only of their own valleys, but in some circumstances the structural geology of the surrounding mountains as well’ [65, p. 14].This amounts to using the data of river history experimentally, much as has long been possible with changing ice loads in glaciated areas, to assess the properties of the crust and mantle. Although many of the processes at issue are nonlinear (e.g. [73]), and topographic ysis remains at best a qualitative tool for neotectonic ysis [74], advances in fluvial chronology continue to increase its value to the experiment.I thank Eric Force for his comments on a draft of this paper, Shunji Ouchi for discussion and photographs of his experimental studies, Ray Weldon II for preprints, NASA for images, and Tom Blenkinsop, Mike Blum, Eric Calais, Mustapha Meghraoui, Andy Moore, Guy Simpson, K. R. Subrahmanya, Graham Yielding and Gerold Zeilinger for illustrations.One contribution of 10 to a Theme Issue ‘River history’.Thank you for your interest in spreading the word on Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences.NOTE: We only request your email address so that the person you are recommending the page to knows that you wanted them to see it, and that it is not junk mail. We do not capture any email address.Please log in to add an alert for this article.Article reuseCelebrating 350 years of Philosophical TransactionsAnniversary issue with free commentaries, archive material, videos and blogs.Copyright © 2017 The Royal Society





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