1

Supplementary material

Isostatic balance.

Let’s consider two columns of crust (figure A1), one, the reference column, of thickness H and

mean density ρc and the other of arbitrary density ρ(z) and thickness H +∆H.

Fig. 1: Two lithospheric columns of varying crustal thickness used in the isostatic balance.

Note that the mantle part of the lithosphere is common to the two columns and has

therefore been omitted. The principle of isostasy imposes that the vertical position of

the two columns with respect to the compensation depth must always be such that the

weight of the two columns, down to the compensation depth, remains constant.

Assuming that the two columns are in local isostatic balance and that the second one has

been eroded by an amount E, we can estimate the elevation of that column by simply equating

Topographic relief driven by variations in surfacerock densityJean Braun,� Thibaud Simon-Labric,� Kendra Murray,� Peter W. Reiners

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2

the weight of the two columns :

ρcgH + ρag(H + ∆H − E − h−H) =

∫ H+∆H

E

ρ(z)g dz (1)

where ρa is the density of the underlying asthenosphere. Note that we have neglected the

weight of the lithospheric mantle as it is common to the two columns and therefore does not

contribute to their weight difference.

Rearranging, we find:

h =ρcH + ρa(∆H − E) −

∫ H+∆H

Eρ(z) dz

ρa(2)

Following Leibniz’s rule for differentiation under an integral sign, the rate of change of

topographic height, h, with erosion, E, is given thus by:

∂h

∂E= −1 +

1

ρa

∂

∂E

∫ E

H+∆H

ρ(z) dz = −1 +ρ(E)

ρa= −1 +

ρSρa

(3)

where ρS = ρ(E) is surface density. This means that the rate of change of elevation with

erosion only depends on surface density (i.e., the density of the material being eroded) and how

different it is from basal (asthenospheric) density. This makes sense as erosion only affects the

weight of the lithospheric column at the surface.

The same result can be expressed in terms of the (temporal) instantaneous rate of surface

uplift, h, and the erosion rate, E:

h = (−1 +ρSρA

)E (4)

This results implies that, for a given erosion rate, E, the rate of surface lowering, h decreases

as the density of the material being eroded away increases. If the material being eroded has a

nil density, the rate of surface lowering is equal to (minus) the rate of erosion; if the material

being eroded has a density equal to that of the asthenosphere, the rate of surface lowering is nil

(the surface remains at a constant elevation, despite being actively eroded away). Interestingly,

if the surface rock density is larger than the asthenospheric density, a situation that is likely

to be rare but may be encountered when eroding exposed mantle rocks, erosion causes “true”

uplift of the surface.

3

The landscape evolution model.

To illustrate our basic hypothesis that granitic intrusions form topographic highs in landscapes

where they are exhumed, we have used a Surface Processes Model (SPM), FastScape, that one

of the authors recently developed[1]. It solves the basic stream power equation:

E = KfAmSn (5)

where m, n and Kf are poorly constrained parameters that depend on lithology, climate, and

local hydrology (balance between precipitation and runoff) in a very efficient and stable manner.

We have recently modified the model to include the effect of sediment on erosion, allowing also

for deposition. This has been done by incorporating the theory recently developed by Davy et

al[2] where topographic height change is equal to tectonic or rock uplift rate, U , minus erosion

rate (given by the stream power law) plus deposition rate which is taken to be proportional to

sediment discharge Qs, but inversely to water discharge, Qw:

h = U −KfAmSn +

Qs

αQw

(6)

α is a dimensionless parameter that can be adjusted to represent systems that are in a detachment-

limited (α >> 1) or transport-limited (α << 1) state.

The SPM FastScape has also been modified to link it to a flexural isostatic model by

assuming that any change in surface topography from a reference configuration (here the initial

topography, h0, which we imposed to be nil) acts as a load proportional to surface density,

on a thin elastic plate of uniform properties (effective elastic thickness (EET), Te, and elastic

properties, Ym, young modulus and ν, Poisson’s ratio). The resulting surface deflection, w,

obtained by solving the following bi-harmonic equation[3]:

D(wxxxx + 2wxxyy + wyyyy) = (ρa − ρS)w + ρSg(h− h0) (7)

where

D =YmT

3e

12(1 − ν2)(8)

is added to the surface topography.

4

Isostatic balance including the flexural response of the lithosphere.

The flexural resistance of the lithosphere depends on the wavelength of the forcing (or load).

Loads that are much smaller than the flexural wavelength, wD defined by:

wD =4

√4D

g(ρa − ρS)(9)

are not isostatically compensated because the lithosphere strength is sufficient to support the

differential stress they generate, whereas loads that are much larger than the flexural wavelength

are locally compensated.

The isostatic response of a thin elastic plate to a sinusoidal surface load representing topo-

graphic variations at a wavelength λ and amplitude h0 can be obtained by solving Eq. 7 [3],

which gives:

w = w0 sin(2πx/λ) (10)

where:

w0 =h0

ρa/ρS − 1 + κ(11)

and:

κ =D

gρS(2π

λ)4 (12)

To cause a change in surface elevation δh by erosion (figure A2), one needs to erode δh + δw

where δw is the isostatic adjustment corresponding to the change in surface elevation δh:

δw =δh

ρa/ρS − 1 + κ(13)

This leads to:∂h

∂E=

δh

δh+ δw=

δh

δh+ δhρa/ρS−1+κ

(14)

which, after some simple algebra, leads to:

∂h

∂E= −1 +

ρS

ρa + Dg

( πW

)4(15)

where W = λ/2.

5

Fig. 2: Flexure and erosion of periodic topography. Changing surface topography by

erosion by an amount δh (light grey area) requires to erode the sum of δh and the

associated isostatic rebound δw (darker grey area). Note that the isostatic rebound

associated to a periodic, sinusoidal change in topography is also a sinusoidal function,

of same period/wavelength.

6

Flexural strength of the continental lithosphere.

Estimates of the EET, Te, for the continental lithosphere vary greatly in part due to the complex

rheological layering of the continental crust and lithosphere[4, 5]. Unlike the oceanic lithosphere

which, apart from a relatively thin crust, is characterized by a homogeneous composition and

thus mechanical behavior that is a relatively well known function of its thermal age, the con-

tinental lithosphere is made up of a series of chemically distinct layers: a granitic crust where

composition varies with depth from a quartz-rich upper crust to a more feldspathic lower crust,

all overlying an olivine-rich mantle. This chemical heterogeneity is compounded by a complex

thermal structure that depends strongly on the concentration of radiogenic elements in the

upper crust and the thickness of the mantle part of the lithosphere[4, 5]. The end result is

a strongly layered rheological behavior with zones of relatively high strength alternating with

regions of reduced strength. As demonstrated by several authors, the flexural behaviour of

such a complex lamina is difficult to assess as it depends ont only on the relative strength of

each of the layers but also on the degree of linkage between them[4, 5, 6]. Furthermore, it is

expected that the EET will depend on the nature of the load. Surface load will preferentially

be supported by the uppermost crust, with a low viscosity middle or lower crustal layer being

the effective isostatic compensation depth, resulting in a very small apparent EET [4, 5, 7].

This explains, for example, the rapid jump from large to small apparent EETs between the

Indian craton and the Tibetan Plateau, across the Himalayan range[7].

For these reasons, estimates of EET values vary greatly between a few kilometers to over one

hundred kilometers[?, 8, 9]. See also the recent worldwide compilation in Moutherau et al[10].

It is worth noting, however, that the commonly used joint analysis of Bouguer gravity anomaly

and topography tends to yield overestimates of the EET[11] due to the effect of erosion, which

preferentially removes the short wavelength components of topography. In recent years, more

sophisticated methods have been developed, such as the multitaper and wavelet methods[12],

which tend to yield lower EET estimates, especially in regions where high resolution gravity

data exists[13, 14, 15].

7

Method to compute the synthetic cooling ages.

The synthetic cooling ages are computed using Pecube [16, 17] which solves the three-dimensional

heat transfert equation including the effects of conduction, advection and production as well as

the effect of a finite amplitude, time-varying surface topography. In Pecube, rock particles that

end up at the surface of the model (or at prescribed points in the subsurface, for example in a

hypothetical well) at the end of the model run are tracked through space and time. This allows

one to compute a time-temperature time for each of these particles from which a cooling history

and a set of cooling ages, corresponding to a variety of low-temperature thermochronological

methods, are derived. For this Pecube uses complex diffusion or annealing models [18, 19]. In

the present study, we performed three landscape evolution experiments using the same setup,

except for the assumed EET. A 100 km wide cylindrical intrusion of infinite vertical extent was

placed half way between the centre of the model and one of its boundaries (figure A3). The

cylinder is 400 kg/m3 heavier than its surroundings and 1.25 times harder. The resulting syn-

thetic landscapes as well as the horizontal sections along which the ages have been calculated

are shown in figure A3. After bringing the system to steady-state at an imposed uplift rate

of 30 m/Myr, we extracted the surface topography as well as the total uplift rate distribution

which we imposed as surface boundary condition and uplift function in the Pecube software

to compute the resulting steady-state thermal field. We then tracked the path of a series of

particles along the transects as well as down a hypothetical well located at the center of the

transect to compute their time-temperature history and their age.

Correction to the low-temperature age datasets shown in Figure 5.

The age of a rock collected at the Earth’s surface is a direct measure of the time since the rock

cooled through the closure temperature characterizing the corresponding thermochronological

system. The age is thus directly proportional to the distance between the surface and the

depth to the closure temperature isotherm and inversely proportional to the exhumation rate.

For systems that have a low closure temperature, the corresponding isotherm may be deflected

by the surface topography[20]. For very long wavelength topography (the Shakhdara gneiss

domes), the isotherm follows perfectly the shape of the topography, and the distance between

8

a) Te = 1 km b) Te = 10 km

c) Te = 20 km

Fig. 3: Three synthetic landscapes corresponding to the erosion of a cylindrical body that

is both denser and harder than its surrounding (dashed circle) and from which the age

profiles (dashed line) and age-elevation profiles (black square) of figure 4 have been

computed.

9

the surface and isotherm is the same for all samples collected at the surface. In this case, no

correction needs to be made to relate the ages to the inverse of the local exhumation rate.

In cases where the surface topography is of short wavelength compared to the depth to the

closure temperature isotherm (Mount Kinabalu), the isotherm is unaffected by the topography

and the distance between the surface and the isotherm varies linearly with the topography.

The ages need to be corrected for this topographic effect before being directly related to local

exhumation rate. Due to its relatively small size and the low closure temperature of the apatite

(U-Th)/He isotopic system (35-90◦C), the data from Mount Kinabalu has been corrected for

this effect using the age marked with an asterisc in figure 5 as a reference. The data from the

Shakhdara gneiss domes have not been corrected.

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