Article
λP
P
melt=1−.melt
solidAccording to this rheological model, the pore fluid pressure Pfluid and
melt pressure Pmelt reduces the yield strength σyield of fluid/melt-bearing
rocks^70. In the numerical experiments we used fixed values of λfluid = 0.1
and λmelt = 0.01 to characterize weakening of rocks due to the fluid and
melt propagation, respectively^51. Fluid weakening was applied only to
cells in which free fluid markers were present. Thus weakening mainly
affects the forearc region above the dehydrating subducting slab (see
refs.^51 ,^70 ). By contrast, melt weakening was applied to a vertical column
of cells above any melt extraction volume found in the mantle (see dis-
cussion in Gerya et al.^38 ). Thus, weakening affects mainly the intra-arc
and back-arc regions of the modelled subduction zone (see refs.^51 ,^70 ).
As established in our previous study^22 , these values of λfluid and λmelt
provide realistic volumes and compositions of arc-volcanic rocks for
contemporary intraplate subduction.
To account for strength reduction of active faults we also applied
strain weakening of plastically deforming rocks so that both com-
pressive strength c and internal friction coefficient γdry decrease with
increasing plastic strain, εplastic:
ccεεcε εcc
εεεε εcεε=≤+( −)−
−≤≤>,0plastic 00plastic 010
100plastic 11plastic 1γγεεγε εγγ
εεεε ε
γεε=≤+( −)−
− ≤≤
>dry ,0 plastic00 plastic010
10 0plastic^1
1 plastic1
where c 0 and c 1 are the initial and final compressive strength, respec-
tively, γ 0 and γ 1 are the initial and final friction coefficient, respectively,
and ε 0 = 0 and ε 1 = 1 are the lower and upper limits for the strain weaken-
ing interval, respectively.
Deciphering chemical tomography sections
Chemical tomography sections^28 , derived using garnet and chromite
xenocrysts from kimberlites and related rocks worldwide, integrated
where possible with data from mantle-derived xenoliths and Re-Os
dating of sulfides^71 –^85. These sections are constructed using garnet and
chromite concentrates from kimberlites and other mantle-derived
magmatic rocks. Temperatures are derived using Ni-in-garnet ther-
mometry^86 , Zn-in-chromite thermometry^87 and garnets are classified,
on the basis of trace elements, into types that reflect degrees of deple-
tion and styles of metasomatism^14 ,^74. Temperatures are converted to
depth by reference to empirical geotherms derived either from xeno-
lith thermobarometry or garnet-based techniques^88. For a garnet of
known composition and temperature, it is also possible to estimate
the Mg# of coexisting olivine, and the Al 2 O 3 content of the whole-rock
sample^28 ,^89. Similarly, the depth distribution of eclogite xenoliths can
be estimated by projection of garnet–clinopyroxene equilibration
temperatures to the local geotherm, and chromite TZn (temperature
based on Zn-in-chromite thermometry) can be similarly projected to
derive a depth of derivation^78 ,^79 ,^81 ,^82.
Although these chemical tomography sections have proved to be
very useful in understanding lithospheric evolution, they have several
limitations. (i) They can only illustrate the parts of the sub-cratonic
lithospheric mantle that contain garnet (supplemented by information
from chromites), and garnet may be a secondary metasomatic phase,
heterogeneously introduced after initial depletion. (ii) They do not
sample depths shallower than the spinel/garnet transition, typically
around 90 km deep. (iii) The kimberlite sample is now recognized to
be strongly biased, as it is confined to metasomatized zones where
kimberlites can gain access to the surface^13 ,^29 ,^90.Computing the characteristic thickness of oceanic
sublithospheric depleted mantle layer
The characteristic thickness of oceanic sublithospheric depleted
mantle layer (Fig. 4b) computed using (i) oceanic geotherm defined
by oceanic plate cooling model^48 and (ii) vertical profile for adiabatic
(T = Tp at the surface, vertical temperature gradient 0.5 K km−1) mantle
decompression melting degree based on the melting model of Katz
et al.^47. The thickness has been computed as the (non-negative) vertical
distance between the depth of the 1,300 °C isotherm found along the
oceanic geotherm of a given age (40 Myr) and the depth of 20% melting
degree found along the mantle decompression melting degree profile.
Mantle potential temperature values (Tp) and respective absolute ages
for the calculation taken from Herzberg et al.^8 as estimated for non-arc
basalts (Fig. 4a).Data availability
All input and output files used in the petrologic thermal-mechanical
modelling are available on request.Code availability
The numerical code I2VIS and MatLab code used for the calculations
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