GSA Data Repository Item DR Topographic advection on fault-bend folds: Inheritance of valley positions and the formation of wind gaps

Transcription

1 GSA Data Repository Item DR Topograpic advection on fault-bend folds: Ineritance of valley positions and te formation of wind gaps S.R. Miller and R.L. Slingerland Department of Geosciences, Pennsylvania State University, University Park, Pennsylvania 1680, USA;

2 Miller - APPENDIX DR1. Topograpic cross-correlation Swat topograpic profiles of mean elevation measured te lengt of ridge flanks eiter te proximal or distal side as defined in te paper demarcate te general positions of transversely oriented valleys and interfluves along linear ridge segments. For tis, we used 3 arc-second SRTM digital elevation models projected into te local UTM projection and resampled at a 90 m resolution. Swat profiles were produced by averaging elevation data sampled parallel to te direction of anging-wall motion, extending from crest to base of eac ridge. Averaging was done parallel to tis direction, rater tan perpendicular to te ridge trend or trust fault strike, because slip on tese faults is locally oblique (Mugnier et al., 1999). Study areas and te exact regions from wic profiles were extracted are sown in Figure DR1. Averaging in te direction of anging-wall motion yielded approximately strike-wise topograpic swat profiles were lows and igs represent transverse valleys and ridges, respectively (Fig. DR). Wind gaps and peaks are evident in te ridge-line profile and commonly correspond spatially wit valleys and ridges on te proximal and distal ridge flanks. For better comparison against model results (e.g., te null ypotesis simulation cross-correlation results in Fig. DR3), profiles were smooted wit a 500 m-wide moving averaging window. Topograpic profiles from te two opposing ridge flanks were ten crosscorrelated witout a lag across te principal drainage divide, yielding a Pearson productmoment correlation coefficient, r (Davis, 1973; Borradaile, 003). Range widt and drainage divide position depend on parameters N e and α. Because simulated steady-state topograpy is sensitive to initial conditions and strict comparisons of correlation coefficient among individual simulations wit different input

3 Miller - 3 parameters is not meaningful, we used a Monte Carlo approac to constrain model uncertainty and terefore better assess comparisons among model results (Borradaile, 003). For eac set of parameters, multiple realizations of eac model (n = depending on computational cost) were created using different orizontal initial surfaces of randomly perturbed node elevations. In our study, we intended not to determine if a given correlation coefficient was significant suc as by using a t-test (Davis, 1973), but rater to determine if te correlation coefficient associated wit certain model parameters was significantly different from te null ypotesis (i.e., r for simulations wit no orizontal bedrock motion).

4 Miller - 4 APPENDIX DR. Model description Bedrock streamlines are controlled in te landscape evolution model by simple kinematic rules following Suppe (1983). Rock streamlines parallel te fault everywere and bedrock as a velocity of V. Tis rate is equivalent to te fault-slip rate. Velocities cange direction, but not magnitude, across axial surfaces. Te dips of te detacments or flats are 0 ; α is ramp dip and β is te axial surface dip, were β = (180-α))/. Above te fault ramp, te orizontal component, v, is defined as v = V cosα (A1) Te vertical component, u, is defined as u = V sinα (A) Note tat tis notation goes against te convention in pysics were u is te x-directed velocity but conforms wit common geologic usage were u is uplift rate. Te rate of fluvial erosion in bedrock cannels is assumed to be proportional to unit stream power (Howard et al., 1994). Erosion rate, E, as units of m yr -1 and is defined as Q E = kb S (A3) W

5 Miller - 5 were k b is te intrinsic erodibility (m -1 ), Q is total water discarge (m 3 yr -1 ), W is stream widt (m), and S is stream slope (unitless). We rewrite te stream power law in terms of upstream drainage area in order to allow simpler comparison wit sites were area is readily measurable from DEMs but Q is not. Hydrologic and ydraulic variables are taken to be time-averaged quantities suc tat tey can be more simply related to area. First, we solve for Q using a simple relation for conservation of mass, Q = PA (A4) were P is a spatially and temporally constant precipitation rate (m yr -1 ) and A is upstream drainage area (m ). Tis relation also assumes tere is no effective subsurface water storage or input and no evapotranspiration. Second, we use an empirical relation for ydraulic geometry, b W = k w Q (A5) were b 0.5. Tis equation as been found to be an appropriate relation for bot alluvial and bedrock streams (Leopold and Maddock, 1953; Montgomery and Gran, 001; Wipple, 004). Combining equations (A3), (A4), and (A5), fluvial erosion rate is recast as E = KA m S n (A6)

6 Miller - 6 were w b k P k K 1 =, m = 1/, and n = 1. Hillslope erosion is simulated wit an equation for linear diffusion in two orizontal dimensions (Culling, 1965): = y x E κ (A7) were κ is a spatially constant diffusivity (m yr -1 ). Combining equations (A6) and (A7) and a tectonic velocity field in a continuity equation for landscape evolution yields: S KA y x x v u t 1 = κ (A8) To furter simplify analysis, we nondimensionalize equation (A8): S A V KT y x TV x v u t 1 = κ (A9) wic is furter simplified as S A N y x D x t e 1 cos sin = α α (A10)

7 Miller - 7 Definitions of te nondimensional variables and parameters are given in Appendix DR3. In our model, te average nondimensional orizontal node spacing is 0.5, simulation space is 8 units long in te y-direction and its widt varies as a function of N e and D. All four model boundaries are open, except in model 1f, in wic case te lateral boundaries are reflected. In contrast to all of te oter simulations, wic use te landscape evolution model CHILD (Tucker et al., 001), for model 1f we use te landscape evolution model GOLEM, wic is based on a regular grid (Tucker and Slingerland, 1994).

8 Miller - 8 APPENDIX DR3. Equations for nondimensional variables and parameters x Spatial variables: x =, T y y =, T A =, A = T T Velocity: u u =, V v = v V Time: tv t = T Erosional parameters: D = κ, TV N e = KT V m Rv Rw Relief: R v =, R 0 w = 0 R R v Flux: φ = v R w = cosα R w w

9 Miller - 9 APPENDIX DR4. Estimation of erosion number in Siwalik Hills Fluvial erosion number, N e, was estimated for te Siwalik Hills using available constraints on its component parameters and constants (K, T, V, and m). In te region of study in te Siwalik Hills, anging wall velocity ranges from 4 1 mm/yr based on te records of deformed Holocene river terraces above te Main Frontal Trust and Main Dun Trust (Lavé and Avouac, 000; Mugnier et al., 004). Hanging-wall tickness ranges from ~4 6 km (Mugnier et al., 1999; Lavé and Avouac, 000). In te eastern region, near te Bakeya and Bagmati Rivers, estimates of K fall in te range m 0.08 /yr wen m = 0.46 (Kirby and Wipple, 001). Mean annual precipitation varies substantially across soutern Nepal by a factor of ~4, indicating tat te above value of K sould also vary spatially, ignoring oter factors suc as litology (Bookagen et al., 005). Te eastern study area lies in a region of ig precipitation rates relative to muc of soutern Nepal. Given tat K scales wit precipitation rate to a power of ~1/ following te simplified formulation in Appendix DR (for a more complete derivation and formulation, see Wipple and Tucker, 1999), we migt expect tat K sould vary due to precipitation by a factor of ~. Bearing in mind tat V and K are probably te least well-constrained parameters among our tree sites, N e likely falls between approximately 5 and 15.

10 Miller - 10 APPENDIX DR5. Notation x, y orizontal dimensions, m t elevation of land surface, m time, yr v orizontal component of bedrock velocity, m yr -1 u vertical component of bedrock velocity, m yr -1 A drainage area, m Q water discarge, m 3 yr -1 W S m T stream widt, m stream cannel gradient, unitless area exponent in te stream-power erosion equation tickness of anging wall, m V bedrock velocity or slip rate above fault, m yr -1 α ramp dip, β axial surface dip, κ diffusivity, m yr -1 k b intrinsic bedrock incision coefficient, m -1 k w cannel widt coefficient, yr 1/ m -1/ b cannel widt exponent, unitless K stream power coefficient, yr -1 D N e r diffusion number, unitless erosion number, unitless Pearson product-moment correlation coefficient, unitless

11 Miller - 11 R w R v 0 R w mean wind-gap relief, m mean cross-valley relief, m mean wind-gap relief formed wen ramp dip is 90, m 0 R v mean cross-valley relief formed wen ramp dip is 90. m R w R v nondimensional wind-gap relief, unitless nondimensional cross-valley relief, unitless φ nondimensional lateral advection rate of relief across a ridge crest, unitless

12 Miller - 1 TABLE DR1. CROSS-CORRELATION RESULTS FROM THE SIWALIK HILLS, NEPAL Location Coordinates Convergence azimut Lat. ( N) Long. ( E) α T r ( ) (km) Lengt (km) ( ) Sout (km) Maximum widt Eastern A ~ B ~ C ~ D ~ E ~ Central F ~ G ~ Western H ~ I ~ J ~ Mean 0.36 ± 0. # Based on Lavé and Avouac (000) and Mugnier et al. (1999). Pearson product-moment correlation coefficient (r) is calculated from paired vectors of mean elevations of opposing, wole ridge flanks. # Te distribution of r passes te Lilliefors goodness-of-fit test for a normal distribution (5% significance level). Te reported confidence interval is 95%. Nort (km)

13 Miller - 13 TABLE DR. LIST OF MODEL PARAMETERS AND CROSS-CORRELATION RESULTS Model code N e D α T r ( ) (km) mean 95% confidence interval Vertical uplift simulations 1a (null ypotesis) b c d e f # Fault-bend fold simulations a b c d e f g a b c d e f g a b c d e f g a b c d e f g Correlation coefficient is calculated for mean elevations of entire ridge flanks. Te distribution is not normal as determined by te Lilliefors test at te 5% significance level. Te p-value of tis individual test is # Model 1f differs from 1a in tat 1a as lateral boundaries at fixed elevations and model 1f as reflected boundaries, wic wrap around and are continuous wit te opposite edge. In contrast to all oter model runs, tis was conducted using te landscape evolution model GOLEM, wic is based on a regular grid (Tucker and Slingerland, 1994). n

14 Miller - 14 REFERENCES CITED Bookagen, B., Tiede, R.C., and Strecker, M.R., 005, Abnormal monsoon years and teir control on erosion and sediment flux in te ig, arid Nortwest Himalaya: Eart and Planetary Science Letters, v. 31, p Borradaile, G., 003, Statistics of Eart Science Data: Berlin, Springer-Verlag, 351 p. Culling, W.E.H., 1965, Teory of erosion on soil-covered slopes: Journal of Geology, v. 73, p Davis, J.C., 1973, Statistics and Data Analysis in Geology: New York, Jon Wiley and Sons, 550 p. Howard, A.D., Dietric, W.E., and Seidl, M.A., 1994, Modeling fluvial erosion on regional to continental scales: Journal of Geopysical Researc, v. 99, p. 13,971-13,986. Kirby, E., and Wipple, K., 001, Quantifying differential rock-uplift rates via stream profile analysis: Geology, v. 9, p Lavé, J., and Avouac, J.P., 000, Active folding of fluvial terraces across te Siwaliks Hills, Himalayas of central Nepal: Journal of Geopysical Researc, v. 105, p Leopold, L.B., and Maddock, T., Jr., 1953, Te ydraulic geometry of stream cannels and pysiograpic implications: U. S. Geological Survey Professional Paper 5, p. 57. Montgomery, D.R., and Gran, K.B., 001, Downstream variations in te widt of bedrock cannels: Water Resources Researc, v. 37, p Mugnier, J.-L., Huyge, P., Leturmy, P., and Jouanne, F., 004, Episodicity and rates of trust-seet motion in te Himalayas (western Nepal), in McClay, K.R., ed., AAPG Memoir, v. 8, p Mugnier, J.L., Leturmy, P., Mascle, G., Huyge, P., Husson, L., Calaron, E., Vidal, G., and Delcaillau, B., 1999, Te Siwaliks of western Nepal; I, Geometry and kinematics: Journal of Asian Eart Sciences, v. 17, p Suppe, J., 1983, Geometry and kinematics of fault-bend folding: American Journal of Science, v. 83, p Tucker, G.E., Lancaster, S.T., Gasparini, N.M., Bras, R.L., and Rybarczyk, S.M., 001, An object-oriented framework for distributed ydrologic and geomorpic modeling using triangulated irregular networks: Computers & Geosciences, v. 7, p Tucker, G.E., and Slingerland, R.L., 1994, Erosional dynamics, flexural isostasy, and long-lived escarpments; a numerical modeling study: Journal of Geopysical Researc, v. 99, p. 1,9-1,43. Wipple, K.X., 004, Bedrock rivers and te geomorpology of active orogens: Annual Review of Eart and Planetary Sciences, v. 3, p Wipple, K.X., and Tucker, G.E., 1999, Dynamics of te stream-power river incision model; implications for eigt limits of mountain ranges, landscape response timescales, and researc needs: Journal of Geopysical Researc, v. 104, p. 17,661-17,674.

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