II. Methods in Morphotectonics 1- Identification of Active Faults 2- Determination of slip-rate on strike-slip faults 3- Determination of fold growth and shortening rates across a thrust fault. 4- Determination of vertical deformation and extension rate across a rift system Appendix A : Dating techniques

References Avouac, J. P. (2003), Mountain building, erosion and the seismic cycle in the Nepal Himalaya., in Advances in Geophysics., edited by R. Dmowska, pp. 1-79, Elsevier, Amsterdam. Bull, W. (1991), Geomorphic response to climatic change, 326 pp., Oxford University Press. Lavé, J., and J. P. Avouac, Active folding of fluvial terraces across the Siwaliks Hills, Himalayas of central Nepal, Journal of Geophysical Research, 105, , Lavé, J., and J. P. Avouac, Fluvial incision and tectonic uplift across the Himalayas of central Nepal, Journal of Geophysical Research, 106, , Suppe, J., Geometry and kinematics of fault-bend folding, American Journal of Science, 283, , Suppe, J. (1985), Principles of Structural Geology, 537 pp., Prentice-Hall, Inc, Englewood cliffs, N.J. Thompson, S. C., R. J. Weldon, C. M. Rubin, K. Abdrakhmatov, P. Molnar, and G. W. Berger, Late Quaternary slip rates across the central Tien Shan, Kyrgyzstan, central Asia, Journal of Geophysical Research-Solid Earth, 107, art. no.-2203, 2002.

Mosaique 3-D + section

Abandoned Terraces along Trisuli river On the use of fluvial terraces

Consistency between Structural Section and Indepth Seismic Profile

Structural Section Across Central Nepal Himalaya All thrust faults seem to root into some mid-crustal decollement

The Siwalik Fold Belt along the Himalayan piedmont 10 km Main Frontal Thrust Main Boundary Thrust

Structural Section Along Bagmati River. A Simple Fault Bend Fold.

Uplifted Fluvial Terrace along Bagmati River. Strath surface Top of terrace tread

This terrace corresponds to a 9 cal. kyr old river bed. It overhangs present river bed by about 100m, indicating 11mm/yr incision rate on average over the Holocene Overbank deposits Fluvial gravel

Inferring paleo-river bed from terrace remnants 9.2 kaBP6.2 kaBP2.2 kaBP

River incision and terrace formation across an active fold

Folded abandoned terraces along Bagmati river Only the MFT is active along that section Incision rate correlates with the fold geometry suggesting that it reflects primarily tectonic uplift.

The two major terrace T0 (9.2ka) and T3(2.2ka) show similar pattern of incision although their ratio is not exactly constant nor exactly equal to the ratio of their ages (0.19 vs 0.24). Should incision be stationary if the fold is growing at a constant rate?

What is the initial geometry of a river terrace? - Valley confinement favor complex geometry of terrace tread (due to diachronous aggradation, lateral input from affluent or colluvium from valley flanks). >> It is important to measure the strath. - River sinuosity might have changed >> It is important to evaluate the possible influence of sinosity changes on river incision (ex Meander cutoff) - The stream gradient might have changed - The ‘base-level’ might have changed In general, we have discontinuous terrace remnants. We can then derive local incision rates at the best. >> What can we do with this information only?

Converting Incision into Uplift u(x,t): uplift relative to the undeformed footwall i(x,t) : river incision b(t) : sedimentation at front of the fold (local base level change) u(x,t)= i(x,t) + b Assuming no change of sinusosity or stream gradient

In the previous slide it is assumed here that the initial terrace profile was parallel to the present river bed (in projection). In reality the initial terrace profile may not be parallel to the present river bed because of: –Sinuosity changes –Change of stream gradient –Change of base level hence b(x,t) = D(x,t) + P(x,t) If stream gradient is assumed constant, D(x,t). is independent of x: b(x,t) = D 0 +P(x,t) Horizontal advection needs also to be compensated for. This terms contribute to a base level change (it can be absorbed in D(x,t)

Inferring paleo-river bed from terrace remnants 9.2 kaBP6.2 kaBP2.2 kaBP

River incision : T-R (T is terrace elevation, R is present river bed elevation), Contribution of sinusosity changes : P Base level changes : D Uplift : U

Comparison of Uplift and Incision profiles The various terraces yield very similar uplift profiles. (base level change from sedimentation rate in the foreland)

How do we convert that information into horizontal shortening of slip rate on the thrust fault? Uplift relative to footwall basement

is the slip on the fault if ‘backshear’ is neglected (d is independent of depth). is the horizontal shortening across the fold if the decollement is horizontal. If the section is parallel to the direction of transport, then:

The excess area method in structural geology This method (Chamberlin, 1910) is used in structural geology to estimate cumulative shortening.

- For a ‘flexural’ detachment fold… curvimetric shortening = planimetric shortening - For a ‘pure-shear’ detachment fold… curvimetric shortening ≠ planimetric shortening Curvimetric shortening = s-x Planimetric shortening Δ s = Δ V/z Laubscher 1962

Determination of shortening from conservation of area

It is assumed here that: - area is preserved during deformation (no compaction nor dilatancy) - deformation is plane (no displacement out of plane) Determination of shortening from conservation of area

Note that the ‘excess area’ is a linear function of depth only if there is no backshear. (Bernard et al, 2006)

This approach is often not applicable because terrace treads (or growth strata) cannot be traced continuously across the fold, also it generally yields quite large uncertainties. Alternative approach: use structural model of folding to relate incremental and cumulative deformation

Constant bed length v1=v2 No backshearv1 constant with depth Constant bed thickness u(x) = v1.sinθ(x) Fault-bend folding

The hanging wall deforms by ‘bedding slip’ (syn. ‘flexural slip folding’, ‘bed parallel shear’) If d does not vary with depth then: U/sinθ should be constant along the profile Fault-bend folding

Folded abandoned terraces along Bagmati river Is the uplift pattern consistent with Fault-bend Folding as has been assumed to construct the section?

Comparing uplift derived from river incision with uplift predicted by fault-bend folding It is possible to estimate the cumulative shortening since the abandonment of each terrace. The uplift pattern is consistent with fold-bend folding with no back-shear. (Lave and Avouac, 2000)

Comparing uplift derived from river incision with uplift predicted by fault-bend folding The shortening rate across the fold is estimated to 21 +/- 1.5 mm/yr (taking into account the fact that slip is probably stick slip) (Lave and Avouac, 2000)

Incision rate and tectonic uplift (Lave and Avouac, 2001)

Appendix : Modeling River Incision Can we use a physical fluvial incision law to estimate rate of river incision along a particular reach? Ref: Lavé, J., and J. P. Avouac, Fluvial incision and tectonic uplift across the Himalayas of central Nepal, Journal of Geophysical Research, 106, , 2001.

Fluvial incision probably depends on shear stress as defined by  =  gR Se where R is Hydraulic radius (which might be taken equal to water depth) and which can be related to Q using some hydologic equation such as the Manning equation (see Lave and Avouac, 2001, for details) >> Shear stress might then be estimated from channel geometry, and water discharge:  = k (QS/W) 2/3

Shields Stress Incision rate is approximately a linear function of Shields stress : I = K (  *-  *c) where K depends on lithology,  * =  /(  s –  ) D 50, and  *c is a critical Shields stress (here about 0.03)

Conclusion Bedrock fluvial incision is to the first order a linear function of Shields stress I = K (  *-  * c ) (1) with,  *  (QS/W) 2/3 Provided it has been calibrated equation (1) might be used to infer rate of river incision along a bedrock channel.

Introduction of the ‘stream power law’ In the case a river would follow the scaling law, W  Q   (where  is about 0.5) and if Q is some power law function of A: Q  A  (where  is about 0.9) The erosion law might be simplified to a ‘stream power law’ (Howard, 1994). E = K (A m S n -Ec) (2) Generally ‘stream power laws’ neglect Ec E = K A m S n (3)