Morphologies of knickpoints in submarine

Neil C. Mitchell† School of Earth, Ocean and Planetary Sciences, Cardiff University, Cardiff CF10 3YE, Wales

ABSTRACT scour associated with a hydraulic jump, for rise and abyssal plains. In the new sonar data example), the upstream profi les can be repro- becoming available, continental slope canyons The question of how turbidity currents duced solely by diffusion. In these channels, are indeed morphologically similar to subaerial erode their beds is important for under- the threshold stress for transport or is erosional systems in both visual and quantitative standing how submarine canyons develop, probably small relative to stress imposed by senses (McGregor et al., 1982; Mitchell, 2004, how they maintain continuity in tectonically the currents, because modeling shows that a 2005; Pratson and Ryan, 1996). Recent attempts active margins to ensure bypass, threshold sharpens the knickpoint lip rather have been made to model slope morphol- and for knowing how knickpoints (reaches of than rounds it. For the other, mostly smaller, ogy by adapting -power erosion laws now anomalously steep gradient) record tectonic knickpoints studied, however, the lip varies popular in fl uvial to submarine information. The problem is potentially more from sharp to rounded. This varied morphol- erosion (Mitchell, 2004, 2005). Although such complex than fl uvial erosion, because fl ow ogy could arise from a number of infl uences: models can explain aspects of canyon morphol- vigor is also affected by the fl ow entraining effects of fl ow acceleration, differing thresh- ogy, such as the concave-upward long profi les of ambient water and incorporating or depos- old stress, differing sediment fl ux affect- U.S. Atlantic canyons, they rely on assumptions iting , which can signifi cantly ing fl ow power, or depth-varying substrate of how sedimentary fl ows originate (e.g., from affect its excess density. However, in canyon resistance to erosion. Despite the diversity of slope failure in canyon walls) that are diffi cult to sections where the total sedimentary mass forms, upstream migrations imply that ero- verify quantitatively. In contrast, canyons with passing through the canyon is much larger sion can be enhanced where fl ow is more vig- large through-put compared with their eroded than the locally excavated mass, the solid orous on steep gradients, implying that the mass, such as the sections of canyons studied loads of eroding currents change little during body rather than the head of turbidity cur- here (Fig. 1), suffer less from this complication passage down-canyon. Canyon morphology rents is responsible for erosion in those cases. and present an alternative way to isolate param- can then potentially reveal how gradient and Also discussed is how bed failure, quarrying, eters controlling erosion rate. In particular, the other factors affect erosion rate. Simple bed and abrasive scour lead to knickpoint evolu- geometry of knickpoints can potentially reveal erosion models are presented herein, which tion in submarine channels that is analogous the extent to which the style of erosion is detach- are analogous to the detachment- and trans- to that in fl uvial channels, but also likely dif- ment-limited or transport-limited, depending on port-limited erosion models of fl uvial geo- ferences are noted. whether they advect or smooth out, respectively morphology, which predict that the (e.g., Whipple and Tucker, 2002). topography should advect or diffuse (smooth Keywords: accretionary prisms, tectonically out), respectively. Data sets from continen- active continental slopes, submarine canyon tal slopes off Alaska, New Jersey, Oregon, morphology, erosion. Chile, the Barbados accretionary prism, and published maps from other areas show these INTRODUCTION tendencies. Although knickpoints may arise 60˚N from spatially varied resistance to erosion, Since the speculations of Daly (1936), tur- Alaskan some of those described here lie upstream bidity currents (in which suspended sediment slope of faults or anticlines and within uniform is carried downslope by a turbulent fl ow driven NJ turbidites, implying that they can advect by the fl uid bulk density excess caused by the Oregon 30˚N slope upstream. A forward numerical model is sediment) have been considered the submarine developed for knickpoints in the southern equivalents of in carving out continental Barbados accretionary prism, which appear slope canyons. Just as bed erosion and asso- to have been created in a simple manner by ciated control the relief of 0˚ the frontmost thrusts. If the erosion rules are tectonic landscapes and sedimentary fl uxes (e.g., Barbados prism applied continuously, the channel profi les are Whipple and Tucker, 2002), erosion by turbidity well represented with both advective and dif- currents, along with debris fl ows (denser fl ows 30˚S fusive components. If a boundary condition in which particles are held in suspension by a Chile of nondeposition/erosion is imposed on the viscous matrix), mass movements (landslides), 150˚W 120˚W 90˚W 60˚W base of the knickpoint slope (representing and effects of oceanographic currents (Shepard, 1981), dictate the incised relief of continental Figure 1. Locations of the studied data sets. †E-mail: [email protected]. slopes and sediment transfer to the continental NJ—New Jersey.

GSA Bulletin; May/June 2006; v. 118; no. 5/6; p. 589–605; doi: 10.1130/B25772.1; 12 fi gures; Data Repository item 2006065.

For permission to copy, contact [email protected] 589 © 2006 Geological Society of America N.C. MITCHELL

These studies have implications for the al., 1990), in which case scour depth should also bank and Anderson, 2001) would be desirable to details of stratigraphy and mass transfer within be related to fl ow vigor, amongst other factors. demonstrate migration less equivocally. Further, accretionary prisms. Whereas isolated prisms Scours can occur in the lee of obstacles (Hughes as induration and compaction typically increase typically have only veneers of slope sediment, Clarke et al., 1990), presumably created by the with burial depth in trench turbidites, aside from those close to continents can have signifi cant kinetic energy of suspended particles where local overpressure effects (e.g., Bray and Karig, thicknesses (e.g., 30% off Costa Rica; Shipley detached fl owlines reattached to the bed, which 1986; Screaton et al., 2002), knickpoint relief is et al., 1990). Whether turbidity currents deposit is similar to the spatial concentration of unlikely to be controlled by resistant caps (Hol- sediment in piggyback basins on the prism or observed in the lee of river boulders (Hancock land and Pickup, 1976). Knickpoint interpreta- whether they bypass to the trench depends in et al., 1998). Furrows are also common (Piper et tion is also complicated, because no data set yet part on whether channels maintain continuous al., 1999, 1985), which Farre and Ryan (1985) exists to constrain fully the history of tectonic downgradient profi les. Localized tectonic uplift likened to the effect of snow avalanche furrows motion and of the through-canyon sediment can block channels and lead to abandonment and which are thought to be caused by relatively fl ux and properties of the fl ows. Nevertheless, (Huyghe et al., 2004). Continuity or abandon- coherent fl ows (debris fl ows or slides). by compiling a large body of data, we can get a ment likely depends on many factors, such as In fl uvial geomorphology, reach-scale sense of the diversity of knickpoint morphology fl ow frequency, vigor, duration, and occurrence bed erosion rate is often modeled as a simple and can discuss possible causes. The survey pre- relative to tectonic uplift history, whether the function of either bed gradient or curvature, sented herein provides evidence that the lips of transported particles are abrasive, and on the depending on whether the erosion is detach- small knickpoints vary from sharp to rounded, substrate’s susceptibility to erosion. The differ- ment-limited or transport-limited, respectively. a result that implies the varied infl uence of a ent styles of knickpoint evolution implied by In detachment-limited models, the rate at which number of factors, whereas the largest knick- the detachment- and transport-limited models particles are removed from the bed is related to points studied (from the Barbados prism) have described in the following sections could lead the fl ow shear stress (Howard, 1994) or power rounded lips, suggesting at least a component of to geometrically different drawdown of topog- (Seidl et al., 1994). Erosion rate is then related diffusion. raphy around the exit channels of piggyback to bed gradient, which dictates the vigor of basins, potentially affecting the stratigraphy the fl ow, and can be shown to lead to advec- CHANNEL BED EROSION MODELS within basins and hence tectonic signals that can tion (migration) of knickpoints (Whipple and be inferred from stratigraphy. These issues also Tucker, 2002). In transport-limited models (e.g., Although submarine channels can appear apply to slope basins created by salt or shale tec- Tucker and Whipple, 2002), material is easily similar to stream networks, the dynamics of tur- tonics (Adeogba et al., 2005; Prather, 2003). An detached from the bed, and erosion rate is then bidity currents are likely to differ in a number indication of the likely mathematical form of the governed by variations in transport fl ux of the of respects from (Peakall et al., 2000), erosion law would be further useful for incor- stream, which lead to diffusive-like bed changes which complicates the study of how fl ow and porating erosion into numerical models for how (related to the degree of long-profi le curvature, substrate properties determine bed erosion rate stratigraphy develops at continental margins with downward and upward curvature leading to and also the ability to discriminate between (e.g., Pirmez et al., 1998; Steckler et al., 1999). erosion and , respectively). detachment- and transport-limited models from The schemes considered here for modeling In this study, similar models are presented for morphologic data. The excess density of the morphology are similar to those used in fl u- submarine erosion, and their results are com- fl ow with ambient water is much smaller than vial geomorphology, because smooth abraded pared against the morphologies of canyon fl oor for river water with air, so relatively minor surfaces and blocks quarried along joint planes knickpoints created by faulting or folding. Apart changes in solid load arising from erosion or observed in some submarine canyons (McHugh from deposition due to converging bedload, the deposition can signifi cantly change fl ow veloc- et al., 1993; Robb et al., 1983; Shepard, 1981) models do not allow for deposition; they are ity, leading to feedbacks with erosion (Parker et suggest that erosion by turbidity currents and intended only to represent erosion (“accumu- al., 1986). Some numerical models (Fukushima debris fl ows can involve similar abrasion, pluck- lative fl ow”; Kneller, 1995). To simplify them, et al., 1985; Pantin, 1979; Parker et al., 1986) ing, and quarrying such as occurs in river beds fl ow is assumed to be locally at equilibrium (not represent how changes in velocity arise from (Hancock et al., 1998; Whipple et al., 2000). accelerating), because this allows fl ow prop- pickup of loose, unconsolidated bed material. Furthermore, observations in many subma- erties to be related to local bed gradient. The Their complexity illustrates that fl ow velocity rine channels have revealed large-scale erosive smaller knickpoints studied here are affected by near source regions will be diffi cult to recon- scours, fl utes, and trenches (Farre and Ryan, backwater (nonequilibrium) effects that are not struct, for example because sediment entrain- 1985; Gee et al., 2001; Hughes Clarke et al., well represented by such models, but compiling ment rates are sensitive functions of grain size 1990; Klaucke and Cochonat, 1999; Klaucke et knickpoints with a range of scales may provide a and other properties that are poorly known for al., 2000; Malinverno et al., 1988; Normark and sense of the transition to equilibrium conditions. the prehistoric fl ows responsible for erosion. Piper, 1991; Piper et al., 1999; Robb et al., 1983; A further diffi culty is that knickpoints could Turbidity currents can originate from dilution of Ryan, 1982; Shor et al., 1990). Some appear to potentially arise during simple entrenchment debris fl ows (Mohrig and Marr, 2003), hyper- be the result of bed shear failure under the infl u- because of varied resistance of the substrate to pycnal outfl ow of muddy river water (Mulder ence of fl ow stress (e.g., Klaucke and Cochonat, erosion (Miller, 1991). As detailed ground-truth and Syvitski, 1995), or storm agitation (Wright 1999), a process not unlike that of quarrying in data are generally lacking, such a possibility et al., 2001), also adding uncertainty to recon- which river fl ow stress works against friction on cannot be ruled out for individual knickpoints, struction of fl ow properties near the source. Fur- joints (Hancock et al., 1998). Shear failure is also but some occur in channels eroded through thermore, fl ows produced by failure of canyon implied by sheets of material removed leaving trench and piggyback basin fi ll turbidites, where wall deposits are likely to lead to a progressive peripheral bedding planes exposed (Piper et al., an explanation in terms of isolated resistant sub- increase in frequency and erosive effects down- 1999). Alternatively, scours may be excavated strates seems unlikely. A time progression in the canyon (Mitchell, 2004). Deriving information by concentrated abrasion by particles (Shor et abandonment of or other terraces (Bur- on how erosion rate is controlled by substrate

590 Geological Society of America Bulletin, May/June 2006 SUBMARINE CANYON KNICKPOINTS or fl ow properties from morphology is there- slope, the fl ow velocity U can be calculated from the sensitivity of U to local gradient and will be fore problematic for proximal regions. In this equation 2 by expanding the fi rst derivative and a small effect if Cd > ew, as usually is assumed. study, fi eld examples were sought far from fl ow setting ∂U/∂x = 0 and ∂Ch2/∂x = 0 so that: If the fl ow is not at equilibrium, variations in h sources, where relative changes in sediment load from entrainment can affect other parts of the 2 2∂ ∂ over the short sections studied were expected to u* + U h/ x = RgChS, (3) fl ow because of the pressure term in equation 2. be minor, so that an assumption of conserva- Ignoring temporarily the threshold of ero- 2∂ ∂ tive sediment fl ux could be adopted. Relative retaining the entrainment part U h/ x of the sion, and incorporating g, Qs, Cd, and ew into Ka, ∂ 2 ∂ 2 2 changes in frequency of fl ows arising from can- total acceleration U h/ x. As u* = CdU , where equations 1 and 5 suggest that: yon wall failures (Mitchell, 2004) should also Cd is a friction coeffi cient, and at quasi-equilib- ∂ ∂ be minor. rium, the entrainment rate ew = h/ x (Pirmez E = Ka(S/W)2n/3. (7) et al., 2000) equation 3 can be rearranged to a

Detachment-Limited Erosion Models form similar to the familiar Darcy-Weisbach or Ka also encompasses factors representing bed Chezy formula (e.g., Komar, 1969): erodibility and other rate factors, such as turbid- In these models, erosion is constrained by ity current frequencies, durations, and the nature the rate at which material is removed from the 12 of solid load if eroding by abrasion. If E is pro- ⎛ RgChS ⎞ bed, while the resulting sediment is effi ciently U = ⎜ ⎟ . (4) portional to shear stress (Howard and Kerby, ⎝ (Ce+ )⎠ transported away, so that it is unable to form dw 1983), n = 1. E is proportional to specifi c fl ow an armoring. Elevation changes in an artifi - power (Seidl et al., 1994), the gradient exponent cially generated badland suggested (Howard In equation 4, the entrainment coeffi cient ew 2n/3 = 1. and Kerby, 1983) that erosion rate was propor- has a similar role to the bed friction factor Cd, Some rivers and their associated valleys nar- τ tional to the bed shear stress, b, imposed by the i.e., entrainment stress is equivalent to a fric- row where crossing regions of more rapid tec- streams. Allowing erosion only above a thresh- tion stress. tonic uplift (Duvall et al., 2004; Lavé and Avouac, τ old stress 0, erosion rate, E, can be written (e.g., To allow for changes in C and h from water 2001) or growing anticlines (Harbor, 1998), and Foster and Meyer, 1975): entrainment and changes in speed, a uniform channel narrowing has been observed across sediment fl ux assumption is applied (Komar, knickpoint faces in stream table experiments ∝ τ τ n τ τ E ( b – 0) ; for b > 0, (1) 1977). As sediment fl ux Qs = CRhWU, where W (Gardner, 1983). According to Finnegan et al. is the effective fl ow width (m), substituting CRh (2005), narrowing occurs because fast fl ow on where the exponent n allows for nonlinearity. As in equation 4 and rearranging yields: steep gradients is accompanied by a decreased τ ∝ 2 ∝ b u* and U u* (e.g., Webber, 1971) (u* is fl ow cross-sectional area if is conserved. the near-bed shear velocity [u ≡ √(τ /ρ )], the 13 Their predicted width variation for rivers is: * b w ⎛ gQ S ⎞ erosion rate E ∝ (U2 – U 2)n (where U corre- U = ⎜ s ⎟ . (5) 0 0 ⎝ ( + )⎠ τ WCdw e α α 2/3 3/8 3/8 –3/16 3/8 sponds to 0). W = [ ( + 2) ] Q S nm , (8) The momentum equation for a steady parti- cle-laden current of uniform width (Fukushima Thus, U becomes a function of mainly S and W, where α is the channel width-to-depth ratio and et al., 1985; Parker et al., 1986) is: as g and Qs are constant here, although Cd may nm is Manning’s roughness coeffi cient. Although vary because of varied bed roughness. Water the data presented here have not been analyzed ∂Uh221 ∂Ch =− Rg +−RgChS u 2 , (2) entrainment rates, and hence e , are expected to to work out W(S), some of the submarine chan- ∂ ∂ * w x 2 x increase on steeper slopes and with larger den- nels narrow where crossing active anticlines and where U and C are fl ow depth–averaged speed simetric Froude numbers as the upper interface steep knickpoints. Supposing that the tendency and sediment volumetric concentration, respec- becomes unstable (Middleton, 1966b). Accord- can be represented by a simple correlation (W ∝ –p tively, h is the fl ow thickness (m), g is the accel- ing to Parker et al. (1986), ew can be estimated S , where p is a constant exponent), equation 7 eration due to gravity (m/s2), R is the submerged from the fl ow Richardson number Ri: simplifi es to: ρ ρ ρ particle specifi c gravity [( s – w)/ w or ratio 2n/3(1 + p) of sediment particle buoyant density to water ew = 0.00153/(0.0204 + Ri), E = KaS . (9) ρ 2 density w], and S is bed gradient (positive with where Ri = RgCh/U . (6) declining elevation downstream). The left-hand In rivers, other factors affect erosion rate, term in equation 2 represents the fl uid accel- Above a critical Ri (¼ according to Wright et such as abundance of tools in the fl ow and bed eration, including both acceleration of the fl ow al., 2001), entrainment is small and the quasi- armoring when bedload is excessive (Sklar and and ambient fl uid entrained into the fl ow (i.e., equilibrium formulae apply (Parker et al., Dietrich, 2001). If bedload is removed effi ciently U2∂h/∂x). The three terms on the right represent 1986). Assuming a typical excess density Δρ on steep gradients, the tools effect could vary stresses acting along the direction of fl ow due to = 50 kg/m3, Pirmez and Imran’s (2003) recon- spatially, but, as there are no independent data static pressure gradients caused by variations in structed fl ow velocities and thicknesses in the to constrain bedload cover, this effect can only sediment concentration or fl ow thickness, fl ow upper Amazon fan channel (S = 0.4) all imply Ri be considered qualitatively in the interpretation. weight, and bed friction, respectively, > 1, but Ri < ¼ if Δρ < 2–4 kg/m3. Although Δρ This approach also ignores the possibility that Although progressive fl ow infl ation associ- is poorly known in general, estimates of C = 10−3 channels crossing active anticlines respond to ated with water entrainment means that turbidity to 10−1 and velocities summarized by Normark steepening by changing their plan-view geom- currents never strictly reach equilibrium, a quasi- and Piper (1991) suggest that Ri < ¼ is possible etry, such as sinuosity or braiding (Ouchi, 1985). equilibrium state in which accelerations are for fl ows on steep gradients. Thus, entrain- Further, because of the patchy nature of canyon minor can be envisaged, greatly simplifying the ment can be considered to modify equation 5 fl oor scours, erosion is irregular, and equations analysis. For a steady current on a long, uniform by causing ew(S, W, Cd), i.e., it mostly modifi es such as equation 9 based on reach-scale gradient

Geological Society of America Bulletin, May/June 2006 591 N.C. MITCHELL are simplifi ed, as is also the case for river bed monitored while water fl ow rate was controlled nel (p = 0). Erosion and deposition in Figure 2E erosion models (Hancock et al., 1998). The and longitudinal gradient varied. Bedload fl ux were then calculated by applying the continuity assumption is effectively made that scouring changed by 2–3× when gradient was varied relation (equation 11). As can be seen from the occurs in different places throughout the history from −20° to +20° at a fl ow speed of 0.35 m/s graphs, either a detachment- or a transport-lim- of channel development so that the equations measured at 13 cm above the bed but was invari- ited scheme with a threshold produces a more represent erosion in a long-term average sense. ant with bed gradient at speeds of 0.65 m/s. As angular lip. Considering that the fl ows in reality equation 12 represents only continual bedload impose various stresses relative to the threshold, Transport-Limited Erosion Models transport, it does not account for transforma- the effect will be less defi ned, but the lip should tion of bedload to suspended load by break- still become more angular than in the absence In these models, bed material is effi ciently down of particles or with increasing fl ow stress of a threshold. detached and erosion rate is controlled by the (e.g., Bagnold, 1963; Dade and Friend, 1998). These predictions are clearly idealized, but rate at which bedload transport fl ux is varied This cannot be predicted without more detailed their differences with real turbidity currents can by the fl ow (e.g., Tucker and Whipple, 2002). knowledge of the eroded sediment texture and be anticipated to some extent and allowed for

The diffusive-like evolution of bed topography fl ow stresses. in interpretation. For example, varying Cd or ew predicted by such models has been observed in alters the erosion or transport fl ux responses to experimental and natural alluvial streams (Begin, Morphologic Predictions of the Models gradient (hence differences such as those seen 1988; Begin et al., 1981; Cui et al., 2003; Lisle et in Figs. 2A and 2B probably cannot be dis- al., 1997; Paola, 2000). and ripples com- Many of the following comments repeat those criminated). Sediment is deposited within pig- monly found in submarine channels (Hughes made previously (Howard, 1994; Rosenbloom gyback basins where fl ows have low velocity Clarke et al., 1990; Klaucke et al., 2000; Mal- and Anderson, 1994; Seidl et al., 1994; Stock and over-spill their channels. The upper reaches inverno et al., 1988; Normark and Piper, 1991; and Montgomery, 1999; Tucker and Whipple, in Figure 2 should therefore be aggradational, Piper et al., 1988; Shor et al., 1990) suggest that 2002; Weissel and Seidl, 1998). The simulations whereas seismic refl ection data from knickpoint some transport occurs as bedload, so variations in Figure 2 illustrate the topographic evolution faces studied here show that they are erosional. in bedload fl ux could also signifi cantly affect expected from the models. They were created Depending on the rate of compared submarine channel bed topography. using fi nite difference calculations with an with erosion, these effects could round knick- According to Soulsby (1997), the bedload inverted error function as the initial condition point lips. transport formula originally developed by Bag- representing the outer slope of an anticline or a nold (1963) is still considered reasonably accu- fault (escarpments typically degrade rapidly to Nonequilibrium Flow rate for marine sands: leave a rounded base and lip rather than a sharp profi le; Mitchell et al., 2000). Parameter values For short distances over which stream-wise ∝ τ 1/2 τ τ τ τ Qb (kg/m/s) b ( b – 0); if b > 0. (10) are omitted here for brevity, and the scales are accelerations are important, equations 9 and 12 arbitrary; the intent is merely to show the style no longer represent erosion, because bed shear Simplifying the equation by ignoring the thresh- of morphological change rather than any par- stress is decoupled from local bed gradient. 2 τ old and substituting u* for b, gives transport ticular knickpoint. Equation 9 with the slope Simulations of fi eld turbidity currents (Skene ∝ 3 fl ux Qb (kg/m/s) u* . The continuity relation exponent 2n(1 + p)/3 = 1 has a simple travel- et al., 1997; Pratson et al., 2000) show them (conservation of mass) relates erosion rate to lat- ing wave solution so that knickpoints gener- approaching equilibrium over distances of one eral changes in transport fl ux: ated instantaneously should have the same form or more kilometers, and in experiments (Garcia as their initial topography but are translated and Parker, 1989; Garcia, 1993), equilibrium is ρ ∂ ∂ E = 1/ s Qb/ x, (11) upstream (Fig. 2A). If 2n(1 + p)/3 < 1, propaga- approached over distances that are an order of tion speed is greatest where gradients are small. magnitude larger than fl ow thickness. G. Parker ρ where s is the dry bulk density of bed This rounds off the lip and reduces knickpoint (2005, personal commun.) suggests that the ratio 3 ∝ ∝ 1/3 (kg/m ). Substituting u* U (S/W) , derived relief with time (Fig. 2B). If 2n(1 + p)/3 > 1, the h/S provides a rough estimate of this backwater ∝ 3 ∝ earlier, into Qb U suggests simply Qb S lip becomes sharp, because propagation speed is length scale for streams. For a typical fl ow of h ρ (letting W and s be constant for simplifi cation). greatest where gradients are steep, which under- = 100 m and steep gradient S = 0.1, the back- Since gradient S ≡ –∂z/∂x, differentiating in x mines the lip (Weissel and Seidl, 1998). Dif- water length scale is 1 km. For estimated S and ∂ ∂ and substituting for Qb/ x in equation 11 leads fusion reduces knickpoint relief and gradients, h, fl ow in many of the small knickpoints stud- to a diffusion equation in z (bed elevation): and also broadens the knickpoint’s spatial extent ied here are not in equilibrium, and knickpoint (Fig. 2D), but involves no translation. morphologies should not be compared simply ∂ ∂ ∂2 ∂ 2 E = – z/ t = –Kd z/ x . (12) A threshold of erosion or transport can sig- with those of the simulations in Figure 2. Some nifi cantly affect channel-long profi les (Snyder effects of accelerations are as follows.

Kd incorporates various constants of the above et al., 2003; Tucker, 2004; Tucker and Bras, Equation 2 suggests what happens where a relations (including a constant of proportional- 2000). This is illustrated in Figures 2C and 2E turbidity current crosses to a steeper gradient ity of equation 10) and effects of fl ow frequency by imposing a gradient threshold for erosion (i.e., across a knickpoint lip). The fl ow accel- and duration as before with Ka. rate and transport fl ux, respectively. In deriv- erates because of the increased weight term Additional effects mean that the true bed ing Figure 2C, the simplifi cation has been made RgChS. If entrainment is gradual, the faster fl ow evolution could be more nonlinear than implied that equation 1 can be equally written, given the on a steep reach will be thinner to conserve dis- ∝ τ n by equation 12. For example, recirculating uncertainties in the erosion process, by E b charge, which causes a pressure gradient along τ n ∂ ∂ fl ume experiments on sands have documented – 0 (Tucker, 2004). Similarly, equation 10 can the direction of fl ow ( h/ x negative), reinforc- ∝ τ 3/2 τ 3/2 gravitational effects on bedload (Damgaard et be simplifi ed by writing Qb b – 0 , which ing acceleration in the drawdown (upper) reach. ∝ al., 2003). In those experiments, sand fl ux was implies Qb (S – S0) for a constant-width chan- If water entrainment is considered, infl ation of

592 Geological Society of America Bulletin, May/June 2006 SUBMARINE CANYON KNICKPOINTS the current will tend to oppose acceleration by Barbados channels were taken from published A reducing the pressure term in equation 2, but Figures (Huyghe et al., 2004) derived from Initial E∝S1 otherwise these are comparable effects to those Simrad EM12 multibeam data collected on a that occur across steepening gradients of streams French vessel. Aside from Figure 3 (from the B (Webber, 1971). NGDC Coastal Relief Model, which was pro- In stream table experiments (Gardner, 1983), vided as a grid), the data were binned to reduce E∝S2/3 acceleration in the drawdown reach caused ero- noise and interpolated onto grids using surface C sion above the lip, a feature observed in some fi tting software (Smith and Wessel, 1990) before E∝ S S 2/3 rivers (Bishop and Goldrick, 1992). With ero- being displayed in shaded relief and with depth ( - 0) sion also at the top of the knickpoint face, this contours for interpretation. Because of differing D led to knickpoints progressively losing their noise characteristics, different grid resolutions relief and fl attening (“slope replacement”; Gard- were chosen: (east-west × north-south) 77 × -E∝d2y/dx2 ner, 1983). If the knickpoint face is nearly verti- 111 m (Astoria), 279 × 222 m (San Antonio), E cal (a headcut), the fl ow can separate from the 114 × 111 m (Alaska), and 72 × 92 m (New E∝d S S dx bed, and kinetic energy excavates a , Jersey). Channel paths were manually digitized - ( - 0)/ leading to a more complex evolution (Stein and and sampled by linearly interpolating between Julien, 1993). grid nodes along those paths. Figure 2. Predicted styles of knickpoint Over-spill or fl ow stripping of the current as it Because of diffi culty and cost, very limited evolution if erosion and deposition were to expands with entrainment might be expected to areas of sonar data such as these have corre- follow various simple rules. The one-dimen- be important also. However, in the areas consid- sponding ground-truth data. Interpretation is sional (1-D) simulations were developed ered, the fl ow passes from a shallow piggyback instead guided by knowledge of how artifacts using fi nite difference calculations with an basin channel to a deeper canyon, so it becomes arise, such as from motion-sensor problems, inverted error function as the initial condi- more confi ned. Furthermore, turbidity currents erroneous sound velocity measurements, sound- tion (bold lines). (A) If erosion rate is lin- are expected to be strongly density stratifi ed ing noise, leakage of strong refl ected signals into early proportional to gradient (proportional (Altinakar et al., 1996; Chikita, 1990; Gar- off-specular beams, or delayed response of bot- to fl ow power), the channel topography cia, 1993; Normark, 1989; Stacey and Bowen, tom detection range gates to depth changes (de simply migrates. (B) If erosion rate is pro- 1988). Peakall et al. (2000) used Altinakar et Moustier and Kleinrock, 1986; Hughes Clarke et portional to S2/3 (proportional to bed shear al.’s data to show that removing 50% of the al., 1996). These artifacts are usually not domi- stress), the knickpoint face migrates but top of such a fl ow should reduce its velocity by nant, however; comparisons with higher-reso- with the lip progressively rounding. (C) If only 5% because of its small contribution to the lution bathymetry have shown that multibeam erosion only occurs where the gradient fl ow’s average density and weight. data collected without obvious blunders are exceeds a threshold S , the knickpoint face Below the knickpoint, a hydraulic jump is essentially low-pass versions of the true seabed 0 retreats, but the lip sharpens. (D) If erosion possible if the fl ow slows from supercritical to topography but with a small uncorrelated noise and deposition are governed by the fl ow’s subcritical (Komar, 1971). Laboratory experi- component superimposed (Goff and Kleinrock, ability to transport bedload, the knickpoint ments (Garcia and Parker, 1989) have illustrated 1991). Noise represented by obvious outliers progressively diffuses without retreating. how an abrupt slowing beyond the jump can can easily be interpreted (e.g., Fig. 7). Simi- (E) If bedload transport only occurs above a lead to deposition of bedload, whereas sus- larly, the NGDC Coastal Relief Model (Fig. 3) gradient threshold S , the knickpoint adopts pended loads can be carried farther depending incorporates older soundings that form isolated 0 a sharp lip and a face at close to the thresh- on their settling velocity. Material eroded from anomalies, which can be easily interpreted. old gradient. the knickpoint face could potentially accumulate in the lower reach if not disaggregated and car- OBSERVATIONS OF KNICKPOINTS ried away in suspension. Experiments on even AND CANYON RELIEF subcritical fl ows have shown decreased depo- sition just beyond a break of slope caused by The following fi rst describes the small-scale al.’s observations of hard siliceous porcellanite enhanced turbulence (Gray et al., 2006). Thus, knickpoints (extents are smaller than backwater chalk and more friable chalk outcrops during two the knickpoint lip rather than base is interpreted length scales) and then the larger Barbados chan- submersible dives are reproduced against pro- here from observations. nels, which form the basis for erosion modeling. fi les 1 and 2 in Figure 3. They suggested that the less silica-rich chalk eroded more easily, leaving SONAR DATA SETS New Jersey Continental Slope porcellanite chalk forming knickpoint lips. This is shown imperfectly in the two profi les in Fig- This study draws on multibeam echo-sounder Circular embayments within the middle and ure 3, but dive observations were projected onto data of canyons principally on active margins lower slope of the New Jersey continental slope the profi le assuming a possibly inaccurate nearly (Fig. 1). Most of the data were collected on U.S. resemble landslide headwalls (Farre et al., 1983; horizontal stratigraphy (Robb et al., 1981). The ships and provided by the National Geophysi- McAdoo et al., 2000) that formed abrupt knick- interpretation of the embayments as landslide cal Data Center (NGDC, Boulder, Colorado). points (Fig. 3). Their origin has been controver- headwalls is considered the most convincing Data in Figures 3, 4, 5, and 6 were collected sial. Robb (1984) argued that they resulted from here, based on associations with slide deposits with 1980s-generation SeaBeam systems, sapping and chemical erosion of carbon- (McAdoo et al., 2000) and that their broad lower whereas data in Figure 7 and Figure 6 north ates, whereas McHugh et al. (1993) suggested canyon fl oors lie parallel to strata, as would be of 46°01′N were collected with a more recent that opal-A to opal-CT transformation of silica expected from structurally controlled slope fail- generation of that instrument. The data from the within the chalk caused exfoliation. McHugh et ure (Farre, 1987), although the outcrops have

Geological Society of America Bulletin, May/June 2006 593 N.C. MITCHELL

5 Depth 6 scale (m) 4330 0 P 1 5 km 9 P 7 ? 1 8 500 10

P 11 P 1000 A2176 0 3000 6000 9000 Distance (m) 1 4320 1 6 5 2 3 A2175

9 2

4

2 8 7 UTM distance north (km) 4310 10

Diffusion model Depth kt = 2X105 m2 11 kt = 0 2 scale (m) 0 2 1

Chalk ? 2 3 P P Porcellanite P 500

4 P 4300 1000 700 710 720 730 UTM distance east (km) 0 3000 6000 9000 Distance (m) Figure 3. Bathymetry of the U.S. Atlantic continental slope off New Jersey collected in 1989 with a SeaBeam multibeam sonar on R/V Atlantis II (W.B.F. Ryan, chief scientist) and made available by the National Geophysical Data Center (Coastal Relief Model). The data are plotted in a Universal Transverse Mercator Projection (zone 18). Depth contours are every 50 m, with every 1000 m annotated in kilometers (bold contours with numbers on rectangular white tiles). The two dotted lines marked A2175 and A2176 are submersible dive tracks. Large open white circles mark knickpoints. Also shown by the white lines is a series of channel profi les annotated 1 to 11 (on elliptical white tiles). Their profi les are plotted with a 4:1 vertical exaggeration in the two insets, which also include possible associated knickpoints (arrows) and plunge pools (P). The porcellanite intervals inferred from submersible operations (McHugh et al., 1993) are marked in bold; dashed lines mark the depths of the porcellanite-chalk transitions observed (the upper transition for profi le 1 was projected from A2176, assuming that the stratigraphy was nearly horizontal; Robb et al., 1981). Also shown above the profi les in the lower-right inset is a series of solutions to equation 13, illustrating that knickpoint topography has clearly not evolved according to a simple diffusion equation.

Figure 4. (A) Bathymetry of the lower Gulf of Alaska continental slope collected with a SeaBeam multibeam sonar of National Ocean Ser- vice ship Surveyor and made available by the National Geophysical Data Center. Depth contours are plotted every 50 m. General annota- tions are as in Figure 3. Dotted and medium dashed lines mark the two reference profi les shown with the channel profi les in D. The two bold dashed lines are survey lines of R/V Lee, along which U.S. Geological Survey scientists collected seismic refl ection data in 1981 (lines 13 and 14 of Fruehn et al. [1999], chief scientist R. von Huene). (B–C) Interpretations of seismic refl ectors adapted from Fruehn et al. (1999) for lines Lee-13 and Lee-14, respectively. Locations are shown in A. Only the near-surface refl ectors and interpreted thrust faults are shown to compare with the bathymetry. Nomenclature (A1, etc.) follows the annotation of anticlines by Fruehn et al. The line 14 anticlines are reproduced on A. A, B, and C have equal horizontal (distance) scales. (D) Channel profi les along the continuous white lines marked in A. Although aligned at the frontal thrust, distances are shown along each profi le (not projected along a common line), so individual features do not line up exactly.

594 Geological Society of America Bulletin, May/June 2006 SUBMARINE CANYON KNICKPOINTS

A

7 8 D? 58°50' N 2 2 C2

2

2 6 C1 2 2 9 3 Left 1 B? 58°40' 4 D 4 A1 3

5 3 C2

2 C1 2 R/V 58°30' 3 Lee Right 1 B -13

147°30' 10 km 147°W R/V Lee - 14 146°30'

B Lee-13 NW C2 D C1 SE B A2 2 km A1

10 km

Right D SE 2000 C Lee-14 NW 5 Left 9 6 4 SE 2 Depth (m) NW D C2 C1 3 1f 3000 B (vertically 1e * * 1d 1c 2 km A2 offset) 1b A1 * 1a 4000 Along-profile distance (km) 40 20 0 10 km

Geological Society of America Bulletin, May/June 2006 595 N.C. MITCHELL

probably been modifi ed further by exfoliation and dissolution (McHugh et al., 1993). Figure 3 reveals a number of escarpments separated upstream from the slide headwalls B by narrow slots running upslope for distances of 1–2 km (large open circles). Arrows on the A topographic profi les (insets to Fig. 3 and in sub- 59°0' N sequent fi gures) associate slide headwalls with those escarpments (arrow head). Below the

4 headwalls are depressions (marked “P” on the 3 profi les) interpreted as plunge pools excavated 3 by sedimentary fl ows (Farre and Ryan, 1985; Lee et al., 2002; McHugh et al., 1993). Since typically S ≈ 0.03, these are small-scale knick- points (extents < h/S = 3 km, if h = 100 m). A The fact that the slots are narrower than their 3000 Ab host valleys suggests that, whereas the fl at or U- Aa B shaped fl oors of the host valleys may originate C C 58°50' Bc from slope failure, the slots themselves were Depth (m) 4000 Bb eroded by channelized sedimentary fl ows and Ba that the upslope escarpments are either propa- 010 gated knickpoints or originate from localized Along-profile distance (km) resistance to erosion. Modeling their develop- 146°30' 146°0' W ment would be complicated because of varied Figure 5. Bathymetry of the Alaskan slope; annotations are as in Figure 4. Lower-right inset resistance to erosion of the different shows cross sections along the channels A, B, and C on the map. Knickpoints Aa, Ab, Ba, Bb, (McHugh et al., 1993), but a simple diffusive-like and Bc are discussed in the text. evolution of the long-profi le knickpoint morphol- ogy can at least be ruled out. The model profi les in Figure 3 (lower-right inset) illustrate this for the simplest geometry in which the slope was ini- tially a linear ramp, and the resistant porcellanite 125°30W 125°20W outcrop was maintained as a fi xed boundary con- dition. The appropriate solution to equation 12 is W1 (Hanks et al., 1984; Mitchell, 1996): 5 km

2 z(x,t) = a erf(x/2√(kt)) + bx, (13) 46°0N A where a is the initial erodible layer thickness d W2 and b is its original long-profi le gradient. The c solutions in Figure 3 were calculated using a = 2 B 1000 100 m and b = 0.025 (curves are in intervals of 5 2 2 45˚ 55N kt = 2 × 10 m ).

Alaskan Slope Area A 1500 A Lying within the Gulf of Alaska, the slope is b 2 B a tectonically active accretionary prism formed

a Depth (m) d f 45˚ 50N at the easternmost Aleutian trench by northwest- c e 2000 a b ward subduction of the Pacifi c plate (Bruns, 2 1985; Plafker, 1987; von Huene, 1989). The -20 -10 0 10 20 lower slope is composed of off-scraped trench 125˚ 30W Along-profile 125˚distance 20W (km) turbidites and hemipelagic sediments and slope sediments, bounded by the Aleutian mega thrust. Figure 6. Bathymetry of Astoria Canyon, offshore Oregon. Depth contours are plotted every Four dredges from the lower slope immediately 50 m, and bold contours are annotated in kilometers. Data were collected (south of 46°01′N) northeast of Figures 4 and 5 recovered Paleo- by the National Ocean Service and (north of 46°01′N) on R/V Melville (Chris Goldfi nger, gene sedimentary rock samples containing chief scientist). Inset shows profi les along the two lines A and B, and along the channel reworked material (Plafker, 1987). Glaciation marked on the map (distances are relative to the fi lled circles shown on the map). Open cir- has played an important role in sediment deliv- cles on the profi le and map locate knickpoints a–f. Bars marked W1 and W2 mark the nar- ery to the margin. According to von Huene row width of the channel passing through an anticline compared with a piggyback basin. (1989), sedimentation rates at Deep Sea Drilling

596 Geological Society of America Bulletin, May/June 2006 SUBMARINE CANYON KNICKPOINTS

Project (DSDP) Site 180 (von Huene and Kulm, 3 1973) in the Alaskan Trench west of the area of 72˚ 40W4 72°30W 72°20W Figure 4A have varied by an order of magnitude 1 4 between glacial and interglacial periods, so sed- Depth (km) iment fl ux through the canyons has likely been 3 5 strongly episodic. 2 33°0S Figure 4A shows bathymetry data of part 4 4 Depth (km) of the Alaskan slope collected by the National 3 Ocean Service. Figures 4B and 4C show line 5 drawings of seismic refl ection data collected 01020 Distance east of 72°30’W (km) 4 along tracks R/V Lee-13 and -14 located on

Figure 4A. Near-surface refl ectors and thrust 5 1 faults have been adapted from interpretations of Fruehn et al. (1999), who reprocessed the origi- 3 Noise nal U.S. Geological Survey data with prestack 3 2 depth migration. 2 The bathymetry suggests a complex evolution 4 1 5 33°10S of sedimentary fi ll. Some basins have sharp ridges Depth (km) lying perpendicular to tectonic structure (e.g., at 5 the southern ends of profi les 2 and 5 in Fig. 4A), 4 3 5 km which are possibly a result of sheet-like failure 6 of the sediment (McAdoo et al., 1997). Seismic 0 10 72˚ 40W 72°30W 72°20W data do not provide unequivocal evidence for the Along-profile distance (km) timing of fault movements, because the stratigra- Figure 7. Bathymetry of San Antonio Canyon off Valparaiso, Chile (Hagen et al., 1996). phy depends on the history of sediment supplied Depth contours are shown every 50 m, with every 1000 m in bold (annotated in km). The to the slope and on how much sediment depos- lower-left inset shows along-channel profi les, whereas the upper-left inset shows profi les ited or bypassed to the trench. The presence of projected to compare channel depths with the adjacent topography (dotted and dashed lines dipping stratigraphy generally and some fanning correspond to similar lines on the map). stratigraphy characteristic of growth faults (e.g., between B and D in line 14), however, suggests that uplift along thrust faults has been generally persistent. On the other hand, sediment within with two knickpoints located by the trenchward processed by Fruehn et al. (1999), lie to either the basins on either side of D on line 13 appears circle of profi le 1 (300–350 m and 150–200 m), side of this map. They show multiple uncon- undisturbed, suggesting less activity on this more which lies upstream of the thrust front. Most formities and dipping and fanning refl ectors, landward area. other knickpoints are 50–150 m. Varied and suggesting similar tectonic activity as for Lee- The map and profi les in Figures 4A and 4D small relief is potentially a complicated result 13 and Lee-14 data. Whereas some knickpoints reveal many knickpoints with either sharp (e.g., of episodic tectonic uplift, unsteady erosion occur within anticlines, those marked A and 2) or rounded (e.g., 5) lips. Although the pos- associated with episodic sediment fl ux, or is B are upstream of anticline centers. Knick- sibility that some knickpoints directly overlie simply a fortuitous result of multiple emergent point Ab has 150 m relief, and adjacent Aa has emergent faults cannot be ruled out unequivo- faults. Evidence for unsteady sediment fl ux dur- 50 m relief. Bb has 200 m relief, with knick- cally with these data, much of the topography ing ongoing tectonic movements is provided by points of 50 and 100 m relief lying upstream of anticlinal ridges appears to be generated by closed-contour depressions along channels (* in and downstream of it. Some knickpoint lips thrusts along the trench side of each block and the Fig. 4D). Knickpoints in canyons are markedly angular (e.g., Ab in Fig. 5). The by folding. Some knickpoints lie within anti- eroding piggyback basins (e.g., in channels 2 drawdown reaches above these lips also appear clines (e.g., that beneath the second circle along and 9) are interpreted as having been initiated incised (e.g., A, B, C), as would be expected profi le 1, counting upstream from the trench), so by entrenchment of the main canyon, which led for small-scale knickpoints. they could originate from recent anticlinal uplift to tributary canyons forming hanging valleys. or represent compacted or indurated resistant These knickpoints are also small scale (

Geological Society of America Bulletin, May/June 2006 597 N.C. MITCHELL

Site 174A, or before 1.3–1.4 Ma from the thick- been incised. In the upper-left inset, it could be Orpin, 2004; Soh and Tokuyama, 2002), from ness of trench fi ll (McNeill et al., 2000). interpreted to be associated with the relief on the intraslope basins affected by salt or shale tecton- Figure 6 shows the channel passing through reference profi le south of it (dashed line), with a ics (Adeogba et al., 2005; Pirmez et al., 2000; anticlines and (west of a line through A-B) the rough translation of that profi le landward imply- Prather, 2003), where entrenchment of a main proximal Astoria Fan. East of A-B, the canyon ing slope retreat. However, the profi le below the canyon has left as hanging valleys fl oor narrows where it passes through anticlines lip is not a simple translation of adjacent topog- (Mulder et al., 2004; Popescu et al., 2004) and at W1 compared with piggyback basins (W2), raphy. From channel gradients S = 0.025–0.05, where levees have been breached (O’Connell similar to narrowing of rivers across anticlines. these are also small-scale knickpoints, and inci- et al., 1991; Pirmez et al., 2000). In many of West of A-B, avulsions have created channel- sion or reduced deposition in the drawdown reach these cases, knickpoints lie upstream of a fault like depressions emanating from the main chan- can be interpreted for both channels 1 and 2. or other steep topography (e.g., Tenryu Canyon nel, some of which may be caused by tectonic upstream of Kodai fault; Soh and Tokuyama, blocking (e.g., at knickpoint a), and channel The Southern Barbados Accretionary Prism 2002), which rules out simple diffusion. Ignor- in general refl ects diversion around ing amphitheater-shaped embayments that may growing anticlines as is also seen in rivers (Bur- Multibeam and seismic refl ection data have originated from landsliding (McAdoo bank and Anderson, 2001). (Faugeres et al., 1993; Huyghe et al., 2004) from et al., 2000), knickpoints in uniform turbi- Knickpoints a, c, d, and e can be associated the Barbados accretionary prism show canyons dites have various-shaped lips in profi le, from with faults or anticlines. Knickpoint a lies at the eroded through ridges formed by thrust folds rounded to sharp, and lie upstream of steep north end of an anticline, c crosses the channel (Fig. 8). Turbidity currents that created these topography (Adeogba et al., 2005; Kukowski obliquely but parallel to the anticlines and is canyons originated from Orinoco River sedi- et al., 2001; Pirmez et al., 2000; Prather, 2003). probably an active fault line scarp, d lies ~1 km ments and likely contained sands and gravels Some authors describe rejuvenation (entrench- upstream of a small fault escarpment south of within the channels and overbank fl ows of fi ne ment) upstream of newly formed knickpoints the channel, and e may be associated with the sand and silt (Belderson et al., 1984; Faugeres et (Pirmez et al., 2000; Prather, 2003), suggesting escarpment running north-south immediately al., 1993). The seismic data reveal syntectonic erosion associated with drawdown. north of the canyon. Knickpoint b is less distinct fans in hanging walls of the fi rst 2 to 5 front- and f could have been created by slumping from most thrust faults, which have been interpreted Summary of Observations the north canyon wall. Although the data quality (Huyghe et al., 2004) as evidence that they were does not allow detailed interpretation, the knick- active within the last 500 k.y. Seismic images Figure 9 shows a selection of knickpoint points do not show obvious evidence for simple obtained where the channels traverse thrust folds profi les. The Barbados knickpoints, the larg- diffusion. The best candidate for migration (d) revealed truncated stratigraphy (Faugeres et al., est studied here, are rounded. The other knick- has a rotated face and sharp lip. Because of the 1993; Huyghe et al., 2004). Sediment in two points are generally shorter and have a variety low channel gradient, all knickpoints here are cores taken within the canyons was found to be of lip morphologies, varying from rounded (San small (<100 m relief have been advection and diffusion. For the channel gradi- eroded to the north and south of the small north- ents of 0.01–0.02, h/S = 2.5–10 km, so channel A numerical model is presented here that south topographic ridge lying at the lip of the c is large scale (>h/S) and a and b are marginal. furthers the investigation of the relative impor- large-scale knickpoint. The north channel (1) is The ratio h/S could be smaller, because some tance of advective and diffusive behavior in the presently inactive except for exceptional fl ows, channel depths traversing piggyback basins are based on the relief of the southern channel form- only 50 m deep (Faugeres et al., 1993). ing a barrier to sediment fl ows from up-canyon. 1GSA Data Repository item 2006065, Figures DR1: Its long profi le (insets to Fig. 7) shows a small Other Channel Knickpoints in the Literature graph of knickpoint vertical relief versus distance from the tectonic range front and DR2: misfi t graphs for 50 m knickpoint upstream of the main escarp- models of Barbados prism channels, is available on the ment. The southern channel (2) has a knickpoint Knickpoints are present in data from other Web at http://www.geosociety.org/pubs/ft2006.htm. with a sharp lip where the steep canyon fl oor has convergent margins (Kukowski et al., 2001; Requests may also be sent to [email protected].

598 Geological Society of America Bulletin, May/June 2006 SUBMARINE CANYON KNICKPOINTS

a 2000 A Advection 400 59˚ 0W 58°0W 200 2000 0 b 2500 -200 Diffusion Erosion (m) Topographic K /K = 22248 m Depth (m) 2500 Abandoned 2500 3000 d a Walls channel ridges rms = 18 m 2500 c 3000 (folds) Depth (m) 11˚ 0N Channel 11°0N 3000 -60 -50 -40 -30 -20 -10 0 10

B Advection -60 -50 -40 -30 -20 -10 0 10 400 Trench 200 Distance from deformation front (km) 0 -200 Diffusion Erosion (m) 2500 K /K d a= 19843 m 3000 Channel a rms = 22 m Barbados Depth (m) 3500 -60 -50 -40 -30 -20 -10 0 10

Flow sense C Erosion Advection 400 200 0 0 -200 1 Erosion (m) Core 2000 Deposition Diffusion 2 Channel b scale H t(x) 3 2500 K /K (m) a= 32843 m 4 d 3000 rms = 27 m

Depth (m) Initial channel Model - profile Channel c 3500 progression Frontmost thrusts -60 -50 -40 -30 -20 -10 0 10 10°0N 10°0N Distance from deformation front, x (km) 59°0W 58°0W Figure 10. Relief of the three channels eroded Figure 8. Physiography of the southern Barbados accretionary prism interpreted from a through folds of the southern Barbados bathymetry image in Huyghe et al. (2004). Dashed lines mark the crests of ridges formed accretionary prism (Fig. 8) and best-fi tting by thrust folds, and bold lines with barbs are the frontal thrusts interpreted by Huyghe et results of an erosion model (rms—root- al. The lines of the profi les (inset) are marked with fi ne solid lines (channels) and dotted mean-square). The lines represent the chan- lines (adjacent canyon walls). Circles mark the frontmost thrusts that form the origin of the nel beds (bold continuous lines) and adjacent profi les. Also shown are schematic representations of core logs (Faugeres et al., 1993) (white elevations (dotted lines) of the canyon walls. and gray intervals represent fi nes and sandy sediments, respectively). Inset (top left) shows The distances from the range front shown three channel profi les interpreted by Huyghe et al. from their multibeam data (continuous were measured along each channel. Model lines) and adjacent canyon wall topography (dotted lines). evolution is shown with fi ne lines, progress- ing as indicated by the arrow in C from a linear ramp (initial channel profi le). Graphs Alaska A/5 above each channel show the modeled advec- 1 tive and diffusive components of bed evolu- Barbados a tion, i.e., the evaluated integrals involving, Barbados b respectively, Ka and Kd in equation 14.

Relief (km) 0 Alaska B/A San Antonio 2 Astoria 'd' Barbados c Alaska A/2 0 5 10 Distance (km) over a common period, T, while accepting that Figure 9. Compilation of knickpoint lip morphologies shown with equal 10:1 vertical exag- discrepancies could refl ect irregular tectonic geration. The profi les were derived from lines 2 of Figure 7, d of Figure 6, 2 and 5 of Fig- movements (similar results are recovered for ure 4, A of Figure 5, and a, b, and c of Figure 8. all three canyons, so this effect is probably not signifi cant). The spatial variation in the cumu- lative differential tectonic uplift is represented

by the relief Ht(x) above a trend drawn paral- Barbados channels, chosen for modeling because A number of simplifying assumptions were lel to the channels away from the knickpoint their knickpoints are the largest, so backwater required. Huyghe et al. (2004) argued that the (e.g., “Initial channel profi le” in Fig. 10C). effects are minimized, and the area has already steepest channel topography at −10 km in Fig- It was assumed that turbidity currents passed been well characterized (Faugeres et al., 1993; ure 10C is evidence that thrust movements can through the canyons at a quasi-steady rate over Griboulard et al., 1998; Huyghe et al., 2004). The occur out of sequence. The simplest assump- time, so that a continuous erosion model can channel knickpoints are in a young phase, and tion is adopted, however, in which all excess be applied. Huyghe et al. (2004) interpreted there is less of the ambiguity of multiple knick- topography landward of the frontmost thrust the reverse channel gradient near −40 km in points that has been observed in other data sets. (x < 0 km) was generated linearly with time Figure 10C as implying that, whereas tectonic

Geological Society of America Bulletin, May/June 2006 599 N.C. MITCHELL deformation is ongoing, erosion can be reduced have evolved diffusively as well as advectively. point lips, are unable to reproduce convexity during sea-level highstands, as at present when The origin of diffusion is unclear—the profi les fully. The solutions with primarily advection sediment is mostly stored on the shelf, allow- may have become smooth because coarser mimic the tectonic topography, though with the ing tectonic activity to distort the profi le. sediment load fi lled depressions, temporar- center of the knickpoint face lying upstream The period represented by syntectonic fans ily preventing those areas from eroding, while relative to the center of the tectonic relief, as is around 1 m.y., based on their thicknesses intervening areas with typically negative ∂2z/∂x2 expected (Fig. 2B). However, such solutions and sedimentation time scales (Huyghe et al., were exposed to erosion. Without detailed obser- tend not to represent rounding of the lip par- 2004). Erosion therefore occurred over mul- vations, it is diffi cult to say how both advection ticularly well. The defi ciencies in both methods tiple glacial cycles and can be regarded as epi- and diffusion arise, but equation 14 nevertheless compensate for each other, so that the combined sodic, with a characteristic glacial period that appears to represent the channel topography equation represents the observed channel pro- is still much smaller than the total period over well. The 2/3 power was applied to gradient fi les well. which deformation has built the anticlines; so (erosion rates proportional to bed shear stress; Alternatively, nondeposition or erosion at erosion behavior can be approximated by Howard and Kerby, 1983). Prescribing the expo- the base of the knickpoint slope caused by a steady erosion. A further assumption was that nent reduces the number of free parameters, and hydraulic jump or pore fl uid expulsion could substrate erodibility is uniform laterally and in in practice it would be poorly resolved, because explain the poor fi t of the simple diffusion depth. Various fractures and associated diage- effects of varied n trade off with the diffusive model. In Figure 12, the third set of model netic products observed by Griboulard et al. term. The initial slope H0(x) and tectonic uplift curves for each channel shows the result of

(1998) may have led to some heterogeneity. By Ht(x) were extrapolated at constant gradient imposing a sink in the transport fl ux at the base analogy with Nankai Trough sediments (Bray (H0b) 50 km downstream and 10 km upstream of slope (zero erosion or deposition boundary and Karig, 1986; Screaton et al., 2002), pro- of the domains of the profi les in Figure 10 to condition). Although profi le shapes are not gressively increasing shear strength with depth prevent errors associated with boundaries from reproduced exactly (e.g., in Fig. 11A, a diffu- and a moderate induration is expected at the affecting the domain of interest. sion model cannot reproduce the fl at topogra- maximum 300 m eroded depth of the Barba- The model was repeated and parameters Ka phy in the reach above the lip and the sharp dos channels. Varied bed erodibility was not and Kd were found by grid search, locating solu- curvature of the lip itself), the predicted chan- included, because it would add complexity tions with minimum root-mean-square (rms) nel shapes nevertheless replicate the observed without necessarily making the results more difference between model and observed chan- profi les relatively well (vertical separations can illuminating. Given these assumptions and fur- nel profi les (Figure DR2, see footnote one). be simply ascribed to initial channel relief). ther trade-offs between parameters described As T was unknown, Ka and Kd were scaled to The models were also adapted to investigate in the following, the results are nonunique and T, and their absolute values are not meaningful. effects of a threshold of erosion or bedload trans- should not be read as providing accurate con- Note also that Ka and Kd have different units, so port. Figure 12 reproduces the solutions of Fig- straints on the erosion equation parameters. their magnitudes are not comparable. However, ure 11B for diffusion-only (dashed lines in upper

The evolving channel topography was repre- the ratio Kd/Ka given beside each profi le in Fig- graph) and advection-only (gray lines in lower sented with an array of 100-m-spaced nodes, in ure 10 can be compared between the profi les, to graph) conditions. The transport-limited model which elevations were adjusted iteratively. The indicate variations in the relative importance of with a threshold gradient was represented by: model initial condition was H (x) = H – H x, the diffusive and advective terms in equation 14. 0 0a 0b t ∂ ( ) = ( ) + ( ) t − q where x is the graph ordinate and H and H are Their net (integrated) contributions are also zxt, H0 x Htd x K ∫ dt , (15). 0a 0b T 0 ∂x the offset and gradient of the initial channel pro- shown by the erosion profi les above each graph. Δ ∂ ∂ ∂ ∂ fi le. In each time step t, the channel bed was Considering those profi les and the Kd /Ka ratios, with q = (| z/ x|–S0); – z/ x > S0 (i.e., fl ow Δ Δ 5 elevated by Ht t/T, where t/T = 1/10 iterations the relative importance of advection and diffu- downgradient). The solution is similar to Fig- and Ht(x) is the present thrust-generated topog- sion varies little between the three channels. ure 2E, but the knickpoint face develops a linear raphy defi ned in Figure 10C. The channel bed Despite the smaller rms values, the solutions ramp differently, because initially only a local- ∂ ∂ 2/3 was also eroded by an amount Ka| z/ x| + in Figures 10A and 10B are worse than that in ized channel area is steeper than S0, but it then ∂2 ∂ 2 Kd z/ x (Rosenbloom and Anderson, 1994), Figure 10C at the knickpoint lips and bases. broadens progressively with progressive tec- where the gradient ∂z/∂x and curvature ∂2z/∂x2 The latter error might be explained by hydraulic tonic steepening. Detachment-limited erosion were calculated from fi nite differences of the jumps of currents having led to localized ero- with a threshold was simulated with: profi le topography, and the term in ∂z/∂x applied sion. Alternatively, localized erosion occurred only where ∂z/∂x was negative (downgradient). because of fl uids released along faults or was t Thus, the model channel topography evolved caused by pore water hydraulic gradients modi- zxt( , ) = H( x) + H( x) 0 t T according to: fi ed by the canyon topography (Orange and 23 t ⎛ ∂ ⎞ − z − 23 Breen, 1992). As mentioned earlier, the models Ka ∫ ⎜ S0 ⎟ddt , (16) 0 ⎝ ∂ ⎠ are better compared against the knickpoint lip x t zxt( , ) = H( x) + H( x) − morphology. 0 t T 23 2 To illustrate that neither diffusion nor advec- where the term in brackets was evaluated using t ⎛ ∂ ⎛ ∂ ⎞⎞ − z + z ∂ ∂ ∫ ⎜ KadK ⎜ ⎟⎟dt . (14) tion alone represents the erosion well, Figure 11 – z/ x > S (i.e., fl ow downgradient). 0 ⎝ ∂x ⎝ ∂x 2 ⎠⎠ 0 shows best-fi tting solutions with Ka = 0 for dif- In both cases, the threshold sharpens the

fusion only (dashed lines) and with Kd made knickpoint lip, a tendency not observed in the Equations 7 and 12 were combined to represent small (solid gray lines) for primarily advection actual channel profi le. Unless fortuitously offset erosion, because the profi les are smoother than conditions (retaining some diffusion for numeri- by increasing resistance to erosion with burial the driving tectonic topography Ht in Figure 8 cal stability). The diffusion-only graphs, though depth, the round lips imply that fl ow stress com- (inset), hence, by observation, they appear to partially representing the rounding of knick- monly exceeds thresholds here.

600 Geological Society of America Bulletin, May/June 2006 SUBMARINE CANYON KNICKPOINTS

DISCUSSION A

Although some knickpoints may have arisen during simple entrenchment because of lateral K variations in erosional resistance, those in uni- a = 0 K form turbidites are more diffi cult to explain by d = 400 such mechanisms and are interpreted as having K a = 0 migrated upstream. Migration implies that ero- K d = 185 sion occurs where fl ows become more vigorous on steep gradients. A transport-limited scheme B K a = 0.083 is then less likely than a detachment-limited K d = 5 scheme, although fl ow momentum effects also 1500 need to be considered when interpreting knick- K a = 0 point shapes in detail. G. Parker (2005, personal 1000 K d = 400 commun.) described how eroded steps can migrate upstream associated with cyclic bed 500 K = 0 shear stress focused at the base of each step, a Relief (m) a K migration analogous to that of headcuts (Stein d = 500 and Julien, 1993). 0 The various shapes of knickpoint lips may C K a = 0.025 have arisen for one or more reasons. Rounding K d = 50 could arise from erosion associated with draw- down (Gardner, 1983), because the slope expo- nent in equation 9 is less than unity (Fig. 2B), K a = 0 because increasing induration or shear strength K d = 2000 with burial depth leads to depth-increasing resis- tance (depth-increasing K ), or because erosion a K a = 0 may involve diffusive processes, as suggested K d = 1200 for the Barbados channels. As mentioned, sharp lips are unlikely to have arisen from a resistant K a = 0.0365 cap (Holland and Pickup, 1976), because shear K d = 100 strength typically increases with depth. More likely explanations involve a signifi cant thresh- -60 -50 -40 -30 -20 -10 0 10 Distance from deformation front (km) old of erosion compared with fl ow stresses (Fig. 2C) or fl ow separation over the lip, if it is Figure 11. Erosion model solutions for the Barbados channels with only diffusion (dashed particularly sharp (Stein and Julien, 1993). curves) and with advection and minor diffusion (bold gray curves) and for only diffusion The strong density stratifi cation of turbidity with an imposed nondeposition/erosion boundary condition at the points marked by vertical currents can lead to different behavior com- arrows (thin gray curves). Values for the model parameters are shown on the right (units pared with that expected from layer-averaged of K are m/iteration and of K are m2/iteration). fl ow properties (Kneller and McCaffrey, 1999). a d As the weight and static pressure terms of equa- tion 2 are dominated by the basal dense layer, the base may tend to accelerate faster than the 1500 S = 0.02 broader, less dense upper section across a steep- 0 K a = 0 ening gradient. The extent to which the base K d = 500 approaches equilibrium velocity faster than 1000 the upper fl ow depends on how momentum is transferred vertically, in particular the effi ciency 500 S = 0.02 of eddies, which can reach dimensions of fl ow Relief (m) 0 K thickness (Kneller et al., 1999). Laboratory a= 0.025 K d = 50 experiments are needed to explore how backwa- 0 ter length scales are affected. -60 -50 -40 -30 -20 -10 0 10 Effect of a Threshold of Erosion or Distance from deformation front (km) Transport Figure 12. Effect of a threshold gradient for Barbados channel b. Dashed lines in the top Simulations of river bed erosion illustrate that graph reproduce the diffusion-only solution, and gray lines in the lower graph the advec- it is important to understand both how the shear tion-only solution of Figure 11. Fine solid lines show the result of imposing a threshold gra- stress of a typical fl ood exceeds threshold, and dient of S0 = 0.02 for erosion or bedload transport, in both cases sharpening the knickpoint also the full size distribution of bed shear stress lip more than is observed.

Geological Society of America Bulletin, May/June 2006 601 N.C. MITCHELL resulting from variability of rainfall and catch- et al., 1988), lasting hours to days based on fl ow sediment shear strength typically increases with ment (Snyder et al., 2003; Tucker, reconstructions (Normark and Piper, 1991) and depth of original burial (Skempton, 1970), sub- 2004; Tucker and Bras, 2000). A large fl ood observations (Xu et al., 2004). This is because marine bed erosion by shear failure is limited to may cause long reaches to exceed threshold and experiments have shown that the head’s velocity depths where shear strength is less than stresses erode, whereas a lesser fl ood may erode more varies only weakly with bed gradient (Middle- imposed by the fl ows (Mulder et al., 1998). In localized areas. ton, 1966a). Erosion or transport rate associated other words, unloading of cohesive sediment A rough comparison can be made between with the head should therefore vary indepen- does not obviously reduce its shear strength in river discharge characteristics and turbidite dently of bed gradient and would not obviously an analogous way to joint development in river sequences, which suggests that turbidity cur- affect knickpoint morphology. This is indirect beds. A possible exception to this is biological rents may be comparably varied. The ratio of evidence that the body of the current, which has attack (Dillon and Zimmerman, 1970; Malahoff peak to average discharge (Qfl ood/Qav) of rivers a velocity that responds to gradient, causes most et al., 1982; Paull et al., 2005; Valentine et al., ranges from 100 to 104 (Mulder and Syvitski, of the erosion. 1980; Warme et al., 1978) preparing the bed 1995). Finnegan et al.’s (2005) model for wid- between fl ows, but its effi ciency remains to be ening of a stream with increasing discharge Comparing Submarine with Fluvial Erosion quantifi ed. That canyon fl oors become more suggests (their equations 3 and 4) that the mean resistant to erosion with increasing exhuma- ∝ 1/4 τ ∝ 1/2 fl ow velocity U Q and thus b Q . The The introduction herein outlined evidence tion is implied by U.S. Atlantic slope canyons 0 2 range in Qfl ood/Qav implies a range of 10 –10 in for how erosion by turbidity currents could (Mitchell, 2004, 2005), which have similar gra- τ τ 0 1 fl ood/ av and of 10 –10 in Ufl ood/Uav. involve similar processes to fl uvial erosion. As dients at mid-slope despite a variety of contrib- A strong variability of turbidity current beds incised in submarine settings are often less uting areas, suggesting a buffering of erosion. stresses is suggested by turbidite bed thicknesses indurated than bedrock in the fl uvial examples, Because of its depth limitation, fl ow-induced varying over two or more orders of magnitude in the correspondence of knickpoint morphology shear failure may turn out be less important for a given basin. In one study, thickness distribu- between the two environments is perhaps sur- excavating deep canyons than abrasion. tions for a Nevada fi eld area and a forearc basin prising, but the following suggests that some were almost power law over two orders of mag- differences may yet emerge. The review given CONCLUSIONS nitude (Rothman et al., 1994), with fewer large in the introduction suggests that removal of beds than small beds, i.e., large fl ows were rela- substrate material can occur in an analogous In submarine canyons, sharp changes of chan- tively infrequent, as is the case with river dis- manner to rigid-block quarrying, plucking, and nel gradient are initiated by faults and anticlinal charge. Thicker beds are associated with coarser abrasion in bedrock rivers, leading to a similar folds in convergent margins and in continental basal sediment (Sadler, 1982; Talling, 2001). As dependence of erosion rate on fl ow speed. Scal- slopes affected by shale and salt tectonics, by the mean fl ow speed ≥w/S (Komar, 1977) and ing arguments (Hancock et al., 1998; Whipple et deep entrenchment of main channels leaving unhindered settling velocity w (Gibbs et al., al., 2000) suggest that quarrying should lead to tributaries as hanging valleys, and by breached 1971) implied by Talling’s grain-size data var- E ∝ S2/3, whereas abrasion leads to E ∝ S5/3. The levees in fan channels. The largest knickpoints ies by one order of magnitude, velocities along latter involves a relation for how suspended sed- studied here, from the southern Barbados accre- transport paths can vary signifi cantly between iment concentration rises with river fl ow veloc- tionary prism, are rounded, as though affected fl ows, although full interpretation requires ity. There is a similar expectation that stronger by diffusion, but are also upstream of the trench- knowledge of depositional geography (Bowen turbidity currents carry heavier particles in most faults. A simple model using both advec- et al., 1984). Laboratory experiments have also suspension (Bagnold, 1963), so the abrasion tion and diffusion representing detachment- and revealed large shear stress variations associated dynamics may turn out to be similar. transport-limited erosion represents the chan- with eddies within the current body (Kneller and The arguments for quarrying may trans- nel topography reasonably well, but diffusion Buckee, 2000). late to submarine beds composed of indurated alone can also adequately reproduce the data The net effect of variability within and rock without much diffi culty, but the situation if a boundary condition (nondeposition/erosion between fl ows could thus be as signifi cant as for is complicated if the bed is cohesive sediment. representing sediment mobilized by a hydrau- some rivers of strongly variable discharge, and An analogous argument to quarrying can be lic jump or by pore fl uid expulsion) is applied comparable morphological consequences can envisaged, in which bed shear stress imposed at the base of the slope. A threshold of erosion be expected. As different thickness distributions by the fl ow and uplift resulting from the fl ow’s or transport would sharpen the lip, which is the have been reported for different areas (Talling, velocity cause shear failure. The quarrying argu- opposite tendency to the rounding observed, so 2001), fl ow variability could vary between dif- ment involves fl ow shear stress working against in this setting, threshold effects are minor or for- ferent canyons. The various shapes of knick- frictional shear resistance stress along joints of tuitously compensated (e.g., by increasing sedi- point lips may, therefore, also refl ect differences a rigid block or fl ow-induced pressure reduction ment resistance with burial depth). in fl ow stress variability relative to thresholds. causing uplift opposed by the block’s weight The other knickpoints studied, which are (Hancock et al., 1998). In cohesive sediment, mostly shorter than backwater length scales, Role of the Turbidity Current Head the fl ow stress is opposed by the sediment’s have a variety of forms. Lips vary from sharp to shear strength, or fl ow negative pressure causes rounded. Although an origin by varied resistance Erosion associated with turbulent tunnels and uplift opposed by the sediment’s weight but to erosion is diffi cult to rule out for any individual lobes beneath heads was originally considered also opposed by sediment cohesion. In rivers, knickpoint, several knickpoints lie within uni- to explain spacings of fl ute marks on the lower as deeply buried bedrock is exhumed, joints form turbidites with no obvious sign in the data surfaces of turbidites (Allen, 1971). Knickpoint develop by stress relaxation and bed processes of localized resistant . Their locations migration, however, is more consistent with the so that erosion can continue over the long time upstream of steep topography therefore suggest emerging view that turbidity currents supplying scales associated with mountain uplift and denu- that they have migrated, implying that enhanced deep sedimentary fans are long-lived (Damuth dation (Whipple et al., 2000). However, because fl ow velocity on gradients leads to enhanced ero-

602 Geological Society of America Bulletin, May/June 2006 SUBMARINE CANYON KNICKPOINTS

Bagnold, R.A., 1963, Mechanics of marine sedimentation, can Association of Petroleum Geologists Bulletin, v. 69, sion and topographic advection. Migration is in Hill, M.N., ed., The sea, Volume 3: New York, p. 923–932. more consistent with erosion being carried out by Wiley, p. 507–528. Farre, J.A., McGregor, B.A., Ryan, W.B.F., and Robb, J.M., the body of the current than the head, as the head Begin, Z.B., 1988, Application of a diffusion-erosion model 1983, Breaching the shelfbreak: Passage from youth- to alluvial channels which degrade due to base-level ful to mature phase in submarine canyon evolution, in velocity is unresponsive to bed gradient. lowering: Earth Surface Processes and Landforms, Stanley, D.J., and Moore, G.T., eds., The shelfbreak: The variety of shapes of the lips could origi- v. 13, p. 487–500. Critical interface on continental margins: Society of Begin, Z.B., Meyer, D.F., and Schumm, S.A., 1981, Devel- Economic Paleontologists and Mineralogists Special nate for various reasons. Rounding could arise opment of longitudinal profi les of alluvial channels in Publication 33, p. 25–39. because of erosion associated with drawdown; response to base-level lowering: Earth Surface Pro- Faugeres, J.C., Gonthier, E., Griboulard, R., and Masse, L., erosion rate is related to gradient with a small cesses and Landforms, v. 6, p. 49–68. 1993, Quaternary sandy deposits and canyons on the Belderson, R.H., Kenyon, N.H., Stride, A.H., and Pelton, Venezuelan margin and south Barbados accretion- power-law exponent, because of increasing C.D., 1984, A “braided” system on the Ori- ary prism: Marine Geology, v. 110, p. 115–142, doi: induration or shear strength with depth, because noco deep-sea fan: Marine Geology, v. 56, p. 195–206, 10.1016/0025-3227(93)90109-9. of varied component of bedload transport, or doi: 10.1016/0025-3227(84)90013-6. Finnegan, N.J., Roe, G., Montgomery, D.R., and Hallet, B., Bishop, P., and Goldrick, G., 1992, Morphology, processes 2005, Controls on the channel width of rivers: Implica- because sediment accumulates in depressions, and evolution of two near Cowra, New South tions for modeling fl uvial incision of bedrock: Geol- which protects them while protrusions (areas Wales: The Australian Geographer, v. 23, p. 116–121. ogy, v. 33, p. 229–232, doi: 10.1130/G21171.1. Bowen, A.J., Normark, W.R., and Piper, D.J.W., 1984, Mod- Foster, G.R., and Meyer, L.D., 1975, Mathematical simulation of negative curvature) are eroded. Sharp lips elling of turbidity currents on Navy Submarine Fan, of upland erosion by fundamental erosion mechanics: may arise from a signifi cant threshold of ero- California continental borderland: Sedimentology, v. 31, Present and prospective technology for predicting sedi- sion relative to fl ow-imposed shear stresses. The p. 169–185. ment yields and sources (Proceedings of the 1972 Sedi- Bray, C.J., and Karig, D.E., 1986, Physical properties of ment Yield Workshop USDA-ARS, ARS-S40): Oxford, strong variability of thickness and grain size of sediments from the Nankai Trough, Deep Sea Drilling Mississippi, Agricultural Research Service, U.S. Depart- turbidite sequences suggests that the range of Project Leg 87A, Sites 582 and 583, in Kagami, H., ment of Agriculture Sedimentation Lab, p. 190–207. shear stress imposed by turbidity currents could Karig, D.E., Coulbourn, W.T., et al., Initial Reports of Fruehn, J., von Huene, R., and Fisher, M.A., 1999, Accretion the Deep Sea Drilling Project Volume 87: , in the wake of terrane collision: The Neogene accre- be comparable to those imposed by some rivers D.C., U.S. Government Printing Offi ce, p. 827–842. tionary wedge off Kenai Peninsula, Alaska: Tectonics, of strongly varied discharge. Shear stress vari- Bruns, T.R., 1985, Tectonics of the Yakutat block, an alloch- v. 18, p. 263–277, doi: 10.1029/1998TC900021. thonous terrane in the northern Gulf of Alaska: U.S. Fukushima, Y., Parker, G., and Pantin, H.M., 1985, Predic- ability could vary between different channels, Geological Survey Open-File Report 85-13, 112 p. tion of ignitive turbidity currents in Scripps Subma- providing a further explanation for the variety Burbank, D.W., and Anderson, R.S., 2001, Tectonic geomor- rine Canyon: Marine Geology, v. 67, p. 55–81, doi: of knickpoint forms. phology: Malden, Massachusetts, Blackwell, 288 p. 10.1016/0025-3227(85)90148-3. Carlson, P.R., and Nelson, C.H., 1987, Marine geology and Garcia, M.H., 1993, Hydraulic jumps in sediment-driven bot- The processes of quarrying and abrasion of resource potential of the Cascadia Basin, in Scholl, tom currents: Journal of Hydraulic Engineering, v. 119, bedrock are likely to be similar to those occur- D.W., et al., eds., Geology and resource potential of the p. 1094–1117. ring in rivers. Shear failure of consolidated of western North America and adja- Garcia, M.H., and Parker, G., 1989, Experiments on hydrau- cent ocean basins—Beaufort Sea to Baja California: lic jumps in turbidity currents near a canyon-fan transi- sediment, however, should be limited to the Houston, Texas, Circum-Pacifi c Council for Energy tion: Science, v. 245, p. 393–396. depth at which the fl ow can overcome shear and Mineral Resources, p. 523–535. 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Goff, J.A., and Kleinrock, M.C., 1991, Quantitative com- Center (NGDC, www.ngdc.noaa.gov). Thanks are Damgaard, J., Soulsby, R., Peet, A., and Wright, S., 2003, parison of bathymetric survey systems: Geophysical due to the scientists and crews of the marine surveys Sand transport on steeply sloping plane and ripple beds: Research Letters, v. 18, p. 1253–1256. collecting these data. Gary Parker and Binliang Lin Journal of Hydraulic Engineering, v. 129, p. 706–719, Gray, T.A., Alexander, J., and Leeder, M.R., 2006, Quanti- provided valuable advice on backwater length scales. doi: 10.1061/(ASCE)0733–9429(2003)129.:9(706). fying velocity and turbulence structure in depositing Jim Gardner and two anonymous reviewers helpfully Damuth, J.E., , R.D., Kowsmann, R.O., Belderson, sustained turbidity currents across breaks in slope: commented on an earlier version of this work. Greg R.H., and Gorini, M.A., 1988, Anatomy and growth Sedimentology, v. 52, p. 467–488. 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