Eroding dynamic topography J Braun, X Robert, T Simon-Labric To cite this version: J Braun, X Robert, T Simon-Labric. Eroding dynamic topography. Geophysical Research Letters, American Geophysical Union, 2013, 40 (8), pp.1494 - 1499. 10.1002/grl.50310. hal-03135812 HAL Id: hal-03135812 https://hal.archives-ouvertes.fr/hal-03135812 Submitted on 9 Feb 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. GEOPHYSICAL RESEARCH LETTERS, VOL. 40, 1–6, doi:10.1002/grl.50310, 2013 Eroding dynamic topography J. Braun,1 X. Robert,1 and T. Simon-Labric1 Received 10 January 2013; revised 28 February 2013; accepted 28 February 2013. [1] Geological observations of mantle flow-driven dynamic perturbation to oceanic circulation [Poore and White, 2011], topography are numerous, especially in the stratigraphy large scale continental drainage reorganizations [Shephard of sedimentary basins; on the contrary, when it leads et al., 2010] or the formation of major geomorphic features to subaerial exposure of rocks, dynamic topography must such as the Grand Canyon [Karlstrom et al., 2008]. be substantially eroded to leave a noticeable trace in the [4] Interestingly, quantifying the amplitude and scale geological record. Here, we demonstrate that despite its (extent) of present-day dynamic topography is rather dif- low amplitude and long wavelength and thus very low ficult as it depends on a good knowledge of crustal and slopes, dynamic topography is efficiently eroded by fluvial lithospheric structures, necessary to compute the isostat- erosion, providing that drainage is strongly perturbed by ically compensated contribution to surface topography, the mantle flow driven surface uplift. Using simple scaling as shown in the variability of past and recent estimates arguments, as well as a very efficient surface processes [Bertelloni and Gurnis, 1997; Gurnis et al., 2000; Moucha model, we show that dynamic topography erodes in direct et al., 2007; Steinberger, 2007; Heine et al., 2008; Conrad proportion to its wavelength. We demonstrate that the recent and Husson, 2009]. Consequently, the amplitude and tim- deep erosion experienced in the Colorado Plateau and in ing of dynamic topography might be better constrained by central Patagonia is likely to be related to the passage interrogating the past, whether it is through the sedimentary of a wave of dynamic topography generated by mantle [Mitrovica et al., 1989; Heine et al., 2008], geomorpholog- upwelling. Citation: Braun, J., X. Robert, and T. Simon-Labric ical [Hartley et al., 2011] or thermochronological record (2013), Eroding dynamic topography, Geophys. Res. Lett., [Flowers and Schoene, 2010], as the time-integrated effect 40, doi:10.1002/grl.50310. of mantle flow is less sensitive to our knowledge of crustal thickness. [5] However, in part due to its transient nature, and in part 1. Introduction to its relatively low amplitude (<1000 m), a direct record of dynamic topography is difficult to obtain the resulting [2] Dynamic topography is the surface expression of uplift leads to subaerial exposure of rocks, as our tools mantle convection, resulting from the topographic load for constraining paleo-elevations remain rather imprecise necessary to balance the viscous stresses originating from [Rowley, 2007; Peppe et al., 2010] and our best hope of mantle flow at the base of the lithosphere [Hager et al., documenting past dynamic topography requires that it be 1985]. Revisiting poorly understood aspects of the geologi- eroded to produce a sedimentary or geomorphologic record cal record combined with sophisticated modeling of mantle or reset thermochronological system by exhumation-induced flow has recently led to renewed interest in constraining rock cooling. Interestingly, the very nature of the dynamic and quantifying the dynamic contribution to surface topog- topography (low amplitude, long wavelength and slowly raphy [Mitrovica et al., 1989; Gurnis et al., 2000; Conrad changing) makes it, apparently, unlikely to be affected by and Gurnis, 2003; Forte et al., 2007; Hartley et al., 2011]. erosion [Braun, 2010], which requires large slopes and rapid A summary of recent investigations on the subject can be uplift to be efficient. found in Braun [2010]. [6] In this paper, we will show that, contrary to this view, [3] Understanding and constraining present and past dynamic topography is in many situations a transient fea- dynamic topography is critical to evaluate its contribution ture and, using the most widely accepted parameterization of to global and local sea-level changes [Moucha et al., 2008; fluvial erosion, we will demonstrate that it is likely to be effi- Conrad and Husson, 2009], decipher unexplained parts ciently eroded away by surface processes and, consequently, of the geological record such as the occurrence of broad permanently recorded in a measurable way in the geological continental inundation [Gurnis, 1993] or uplift [Bertelloni record. To achieve this, we will use a recently developed sur- and Gurnis, 1997; Gurnis et al., 2000]. Most interestingly face processes model (FastScape; Braun and Willett [2013]) perhaps, studying dynamic topography has revealed rather that is highly efficient and can thus be used to study the ero- unexpected links between the dynamics of the Earth’s deep sion of very large scale ( 1000 km) surface topography at a interior and its surface components, such as potential resolution (<1000 m) that is sufficient to capture local slopes and drainage evolution. All Supporting Information may be found in the online version of this article. 1ISTerre Université de Grenoble 1, CNRS-IRD, F-38041 Grenoble, France. 2. Fluvial Erosion and Dynamic Topography Corresponding author: J. Braun, ISTerre Université de Grenoble 1, [7] Although mantle flow is relatively steady over tens to CNRS, F-38041 Grenoble, France. ([email protected]) hundreds of millions of years, and the dynamic topography ©2013. American Geophysical Union. All Rights Reserved. that it creates should therefore remain unchanged over the 0094-8276/13/10.1002/grl.50310 same periods of time, the relative motion of tectonic plates 1 BRAUN ET AL.: ERODING DYNAMIC TOPOGRAPHY a Table 1. Numerical Model Parameter Values raphy caused by a mantle plume or upwelling of width 2 Parameter Value beneath a plate that moves at a velocity v in the x-direction –6 –7 0.2 by the following Gaussian function: Kf 4.7 10 to 10 m /yr m 0.4 –(x–vt)2/2 n 1 z(x)=z0e (1) 2 KD 0, 0.01, 0.1, 1 m /yr E 1011 Pa where z0 is the maximum amplitude of the dynamic topog- Te 20 km raphy, and t, is time. The resulting rate of uplift/subsidence 0.25 is given by 3 c 2800 kg/m 3 a 3200 kg/m @z 2vz0(x – vt) –(x–vt)2/2 a zP(x)=v =– e (2) All experiments are 50 Myr in duration, with an initial 10 Myr phase of @x 2 uplift and establishment of the dynamic topography followed by a 40 Myr period of migration of the plate at a rate of 25 km/Myr. which implies that the surface is uplifted in front of the plume and subsides behind it at a rate that is proportional to with respect to the underlying mantle can cause dynamic the plate velocity ( 10 cm/yr) and modulated by the slope topography—as experienced by an observer attached to the of the topography ( 10–3). moving surface plates—to be transient [Gurnis et al., 1998], [8] Because it is driven by mantle flow, dynamic topog- as shown in numerous recent studies of reconstructed past raphy must remain relatively unchanged (to balance the dynamic topography [Moucha et al., 2009]. To illustrate this viscous stress applied at the base of the lithosphere) even point, let us parameterize, to first order, the dynamic topog- if it is eroded away. The characteristic time for adjustment Direction of plate motion Initial position and shape of over fixed source (a) dynamic topography Final position and shape of of dynamic topography dynamic topography 300 km 2 = 1000 km 2 = 500 km 2 = 250 km Erosion 0 2500 m (b) (c) (d) -7 -6 KF = 4.7 x 10 KF = 4.7 x 10 ) ) ) 3 3 3 = 0 K D x m x m x m 13 13 13 = 0.01 KD KD = 0.1 51015 Volume (10 Volume (10 Volume (10 KD = 1 23456789 2.0 2.5 3.0 3.5 4.0 4.5 5.0 200 300 400 500 200 300 400 500 500 1000 1500 2000 (km) (km) z0 (km) Figure 1. (a) Time integrated erosion computed from the landscape evolution model using different dynamic topog- raphy wavelength (2), showing the direct, quasi-linear dependency on wavelength, as suggested by equation 4. Here, –6 Kf =4.7 10 . The two curves on top of Figure 1a show the initial and final position and shape of the imposed vertical stress at the base of the plate for the case ( = 250 km); Total volume eroded over the passage of the “wave” of dynamic topography (b) as a function of imposed wavelength and (c) various values of the diffusion coefficient, KD,and(d)asa function of dynamic topography amplitude (no diffusion). 2 BRAUN ET AL.: ERODING DYNAMIC TOPOGRAPHY (d) (b) (a) (c) Figure 2. Geomorphic evolution of the Colorado Plateau and dynamic topography. (a) Shaded DEM of the Colorado Plateau; white contour curves draw the present-day dynamic topography with 50 m intervals [Moucha et al., 2009]; the red arrow represent the movement of the dynamic topography swell in the last 30 My; diamonds, squares and stars represent minimum apatite (U-Th)/He ages, respectively, from Lee, [2008]; Lee et al., [2011], Flowers et al., [2008] and Hoffman, [2009]; Hoffman et al., [2011]; the red line AA is the transect used to build Figures 2c and 2d; Blue curves represent the drainage network; grey lines mark states boundaries.