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Megathrust shear force controls mountain height at convergent plate margins

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Abstract

The shear force along convergent plate boundary faults (megathrusts) determines the height of mountain ranges that can be mechanically sustained1,2,3,4. However, whether the true height of mountain ranges corresponds to this tectonically supported elevation is debated4,5,6,7. In particular, climate-dependent erosional processes are often assumed to exert a first-order control on mountain height5,6,7,8,9,10,11,12, although this assumption has remained difficult to validate12. Here we constrain the shear force along active megathrusts using their rheological properties and then determine the tectonically supported elevation using a force balance model. We show that the height of mountain ranges around the globe matches this elevation, irrespective of climatic conditions and the rate of erosion. This finding indicates that mountain ranges are close to force equilibrium and that their height is primarily controlled by the megathrust shear force. We conclude that temporal variations in mountain height reflect long-term changes in the force balance but are not indicative of a direct climate control on mountain elevation.

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Fig. 1: Schematic summary of processes and topography at convergent plate margins.
Fig. 2: Megathrust shear strength envelopes derived from the rheological model.
Fig. 3: Maximum mean elevation compared to the tectonically supported elevation.
Fig. 4: Maximum mean elevation compared to the shear-force component supporting mountain height.

Data availability

All data used in this study are from the published literature as referenced14,15,16,17,18,47,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73 in Extended Data Tables 1 and 2. The solutions of the rheological model and the force balance model are available at https://doi.org/10.5880/GFZ.4.1.2020.002.

Code availability

To create the maps in Extended Data Figs. 13, we used the Python package Matplotlib74 and MATLAB75. To create the swath profiles in Extended Data Figs. 6 and 7, we used TopoToolbox76. All force-balance calculations are based on the analytical expressions described in the Methods. The Python scripts used for the calculations of the shear force and the tectonically supported elevation are available from the corresponding author upon reasonable request.

Change history

  • 08 July 2020

    The online publication date in the printed version of this article was listed incorrectly as 10 June 2020; the date was correct online.

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Acknowledgements

We thank S. Brune, A. Hampel and R. Danisi for comments on earlier versions of the manuscript.

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A.D. designed the study, compiled the data and conducted the force analysis. All authors discussed and analysed the results. A.D. and R.H. wrote the manuscript.

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Correspondence to Armin Dielforder.

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Extended data figures and tables

Extended Data Fig. 1 Map with the localities of the convergent margin segments studied.

Red and blue circles indicate margins where the frictional strength of the megathrust has been derived from heat dissipation models and from Coulomb wedge models, respectively. 1, Northern Cascadia; 2, 3 and 4, The Andes at 23° S, 34° S, and 36° S, respectively; 5, Northern Sumatra; 6, Kamchatka; 7, Japan Trench; 8, Nankai Trough; 9, Northern Hikurangi; 10, Himalayas. Maps of the study sites are shown in Extended Data Figs. 2 and 3.

Extended Data Fig. 2 Map view of the convergent margin segments studied.

af, Thick black lines and black rectangles indicate the trace and width (100 km), respectively, of the swath profiles shown in Extended Data Figs. 6 and 7. Small red, yellow, and blue circles are continental earthquakes with normal faulting, strike-slip and thrust faulting focal mechanisms, respectively77. Lines associated with symbols indicate the orientation of the maximum horizontal compressional stress.

Extended Data Fig. 3 Map view of the convergent margin segments studied.

ac, Thick black lines and black rectangles indicate the trace and width (100 km), respectively, of the swath profile shown in Extended Data Fig. 7. Small red, yellow, and blue circles are continental earthquakes with normal faulting, strike-slip, and thrust faulting focal mechanisms, respectively77. Lines associated with symbols indicate the orientation of the maximum horizontal compressional stress.

Extended Data Fig. 4 Coulomb wedge model for the Andean outer wedge at 23° S.

The model is constrained by the wedge geometry (surface slope α and basal dip angle β), the coefficient of friction of the wedge material μw (0.45), and the pore fluid pressure ratio in the wedge λ (see refs. 15,16,50 for details). The open circle indicates the ideal state of basal erosion, which is given by the intersection of the compressively critical strength envelope with the straight line that represents all principal solutions for which the effective strength of the megathrust is equal to the effective strength of the wedge (μ′ = μw(1 − λ)). Basal erosion occurs during coseismic strengthening of the shallow megathrust beneath the outer wedge and constrains the dynamic strength of the fault during great earthquakes16. The average interseismic strength of the megathrust (solid circle) used for the calculation of the megathrust shear force is taken to be lower by 0.01 than the dynamic strength (open circle) of the megathrust during coseismic strengthening of the shallow megathrust.

Extended Data Fig. 5 Analytical force balance model.

a, b, Schematic illustration of the force balance model for subduction and collision zones, respectively. Fs is the shear force along the megathrust and Fg is the gravitational force. \(\bar{\rho }\) is the average density of the triangular wedge above the megathrust. P is the push of the upper plate. L is the downdip extent of the megathrust. dT is the trench depth and γ is the surface slope of the submarine part of the wedge. See Methods and refs. 2,3 for details.

Extended Data Fig. 6 Topographic swath profiles.

ae, Mean elevation (red line) ± 1 standard deviation (grey). Width of the swath profiles is 100 km. The submarine topography and subaerial topography were obtained from the ETOPO1 global relief model78 and the SRTM 90-m digital elevation model21, respectively. To calculate the MME, we first identified the maximum value of the mean elevation along each swath. We then averaged the elevation over the area (black bars) in which the elevation is within 95% of this maximum value. The uncertainty represents one standard deviation of the mean elevation within that area. Dashed horizontal lines indicate sea level. Vertical arrows indicate the position of the trench at subduction zones. Vertical exaggeration is 10.

Extended Data Fig. 7 Topographic swath profiles.

ae, Mean elevation (red line) ± 1 standard deviation (grey). Width of the swath profiles is 100 km. The submarine topography and subaerial topography were obtained from the ETOPO1 global relief model78 and the SRTM 90-m digital elevation model21, respectively. To calculate the MME, we first identified the maximum value of the mean elevation along each swath. We then averaged the elevation over the area (black bars) in which the elevation is within 95% of this maximum value. The uncertainty represents one standard deviation of the mean elevation within that area. Dashed horizontal lines indicate sea level. Vertical arrows indicate the position of the trench at subduction zones and the position of the Main Frontal Thrust for the Himalayas. Vertical exaggeration is 10.

Extended Data Table 1 Parameters of the rheological model
Extended Data Table 2 Parameters of the force balance model
Extended Data Table 3 Components of the megathrust shear force Fs

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Dielforder, A., Hetzel, R. & Oncken, O. Megathrust shear force controls mountain height at convergent plate margins. Nature 582, 225–229 (2020). https://doi.org/10.1038/s41586-020-2340-7

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