HEAT FLUX BY CRUSTAL UNDERPLATING IN THE CALABRIAN-SICILIAN CONTINENTAL MARGIN
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GNGTS – Atti del 18° Convegno Nazionale / 08.02
P. Chiozzi, V. Pasquale and M. Verdoya
Dipartimento per lo Studio del Territorio e delle Sue Risorse, Università di Genova Viale Benedetto XV
5, I-16132 Genova
HEAT FLUX BY CRUSTAL UNDERPLATING IN THE CALABRIAN-
SICILIAN CONTINENTAL MARGIN
Abstract. We propose a physical model of continental lithosphere stretching above a moderately
heated asthenophere. Adiabatic upwelling generates partial melt by decompression. Consequently a
magma layer, some kilometres thick, underplates the crust. The magma composition depends on the
melt fraction and, as for magmas originated by subduction, from the crustal contamination degree. By
incorporating the heat produced by the emplaced magma and a crustal growth correction on
lithosphere extension, the thermal budget fits the observed heat flux.
FLUSSO TERMICO DA UNO STRATO CROSTALE DI MAGMA NEL MARGINE
CONTINENTALE CALABRO-SICULO
Riassunto. Viene proposto un modello di stiramento di litosfera continentale sopra un'astenosfera
moderatamente più calda. Il sollevamento adiabatico che ne deriva dà origine, per decompressione, a
fusione parziale del mantello e, quindi, ad un accumulo sotto la crosta di uno strato di magma spesso
alcuni chilometri. La composizione dei magmi è controllata dalla frazione di fuso e, come avviene per i
magmi che si generano lungo il piano di subduzione, dal grado di contaminazione crostale. Se si tiene
conto del raffreddamento dei corpi intrusivi, e s'introduce una correzione sullo stiramento per il
conseguente aumento di spessore crostale, il bilancio termico è in accordo con il flusso di calore
osservato.
INTRODUCTION
Physical models of mantle melting processes, producing the lavas erupted by
volcanoes and the igneous rocks of the geological record, have reached new levels
of sophistication. They are largely used by petrologists, who previously considered
chemical information as a major constraint to elucidate magmatic processes.
However, some intriguing questions are still open. One particular puzzle is the
potential volume of mafic crustal materials which can be derived from an upwelling
asthenospheric mantle, producing pressure relief melting, melt segregation, and
accumulation.
In order to unravel the problem of the regional thermal state and the deep
earthquakes in the Southern Tyrrhenian basin, Pasquale et al. (1999) assumed, in a
first approximation, that the crustal volume is conserved during extension and,
consequently, the stretching factor equals the ratio of the pre-rift to post-rift crustal
thickness. In this paper we examine emplacement of mafic magma at the base of the
continental crust in the Calabrian-Sicilian margin (Southern Tyrrhenian) as a function
of both initial and equilibrium pressure and temperature conditions. Therefore, we
calculate the heat-flux budget by incorporating a correction for crustal growth as well
as the heat from the emplaced magma.GNGTS – Atti del 18° Convegno Nazionale / 08.02
BASIC ASSUMPTIONS
In presence of a thermally anomalous asthenosphere, pressure release of
mantle, upwelling adiabatically due to rifting processes, can generate basaltic melts.
Magmas ascend to the Moho, where they cool, release heat and solidify forming new
crust, and they may create intrusion and volcanism. Therefore, one can define a true
stretching factor β that is given by
β a hc
β= , (1)
hc − β a hb
where βa is the apparent stretching factor determined from the change in crustal
thickness resulting from stretching when all the melt of thickness hb is assumed to be
added to the crust of initial thickness hc.
The volume of melt generated and the potential crustal addition will depend on
the amount by which the mantle temperature exceeds its solidus and the melting
behaviour of the material involved. The mantle material can be assumed to be
emplaced with negligible heat loss so that an adiabatic rise is reasonable. This is
verifiable if one considers the upwelling volume of an infinite cylinder of radius r0
embedded in an infinite medium in which the initial temperature is ϑ0 for 0 r ≤ r0 and
zero in the region r > r0. The temperature as a function of the radius r and time t is
ϑ r2 r0 2 r r'
ϑ (r,t) = 0 exp − ∫ exp − r' Io r' dr' , (2)
2 χt 4χ t 0 4 χ t 2 χ t
where χ is the thermal diffusivity and Ιo the modified Bessel function (Carslaw and
Jaeger, 1959). This equation can be evaluated analytically only at r = 0, where it
becomes
r02
ϑ (0,t) = ϑ 0 1 − exp − . (3)
4 χ t
Fig. 1 illustrates the minimum radius of the cylinder, calculated from Eq. 3, for
which the material along the axis will cool by less than a specified fraction in a
specified time. By considering that a 1% cooling satisfies assumption of adiabatic rise
and do not cause observable deviation in the results reported further on, a minimum
radius of about 40 km is sufficient if the mantle material is emplaced at 3 cm yr–1, that
is a typical rate of plate motion.GNGTS – Atti del 18° Convegno Nazionale / 08.02
Fig. 1 - Cylinder radius vs. the rate of emplacement for different fractional cooling (1-ϑ/ϑ0). The
emplacement velocity is given for an upwelling of 100 km.
MELT GENERATION
In our extensional model we adopted a solidus with temperature of 1100 °C at
normal pressure with a gradient of 3 mK m–1 and the function M[ϑ(z),z] proposed by
Ahern and Turcotte (1979) for describing the melting behaviour of the material as a
function of temperature ϑ and depth z. The temperature and the melt fraction function
for a set of assumed initial conditions is given by the following equation on the energy
content of the material undergoing partial melting:
ρ c θ (z ) = ρ c ϑ(z ) + L M [ϑ(z ), z] . (4)
The function θ(z) describes the potential temperature, ϑ(z) is the actual temperature
and ρ c and L are the density, the specific heat and enthalpy of melting, respectively.
Equation 4 is nonlinear in the temperature, and it requires numerical calculations to
its evaluation.
The partial melting generated by extension depends strongly on the potential
temperature. Equation 4 was solved for a potential temperature of 1230°C at the
base of a 114 thick lithosphere, corresponding to 0.9 of the mantle melting
temperature. The assumed initial geotherm is typical of a Variscan crust with surface
heat flux of 60 mW m–2. Other two models with moderately increased basal
temperature (by 50 and 100°C, respectively) were made. By using a value of βa = 2
for the Calabrian-Sicilian margin, as suggested by the present-day crustal thickness,
in the first case (lowest temperature) no melting occurs. For 1280 and 1330 °C
instead, underplating of about 1 km and 5 km thick melt can occur, respectively, andGNGTS – Atti del 18° Convegno Nazionale / 08.02
true stretching factors (Eq. 1) should be 2.2 and 3.0. Fig. 2 shows the process of
pressure relief melting for initial potential temperature of 1330°C.
Fig. 2 - Adiabatic upwelling due to stretching of an initially 114 km thick lithosphere with basal
potential temperature of 1330°C. Stretched geotherms are labelled with values of β. The dashed
lines are the solidus and the melt fractions forming new crust.
THERMAL BUDGET
The study margin presents a heat-flux value of 122 ± 36 mW m–2, that is
decidedly higher than those of the older margins of the Western Mediterranean (80-
98 mW m–2). This is partly a consequence of the age of the tectono-thermal events
which, initially located west of the Corsica-Sardinian block, progressively migrated
eastward in time and space together with the front of the Apennines (Pasquale et al.,
1996). In the absence of a melt layer, the heat flux q0 of the margin is envisaged as a
sum of a component qr due to the heat generation A of radiogenic elements and a
contribution qt controlled by the rift time t and extension amount ###, plus the heat flux
qa from the asthenosphere:
q0 = qr (A,β) + q t (t,β) + qa . (5)
The heat flux qr reduces with the increase of the crustal thinning amount. It can
be estimated by means of available data of radioactive heat-production rate in the
crystalline basement of the northwestern Mediterranean margins, integrated with
information on the seismic structure (Pasquale et al., 1995). Its exponential
dependence on the thinning factor isGNGTS – Atti del 18° Convegno Nazionale / 08.02
qr(###) = 43.2 exp(-0.39 ###). (6)
This equation gives values of radiogenic heat production of the lithosphere in
agreement with those observed for the Variscan Europe. On average, the
contribution is almost equally shared out between the uppermost 10 km of the crust
(15 mW m–2) and the lithosphere levels below it (about 14 mW m–2).
The transient component qt can be estimated by modelling lithosphere
stretching according to McKenzie (1978). In the Calabrian-Sicilian margin, for β
from 2.2 to 3.0 and t = 5 Ma the sum of the two contributions corresponds to
65-88 mW m-2. The third contribution, i.e. the constant background heat flux from the
asthenosphere, can be fixed to 30 mW m–2, a representative value for the heat flux
from below the crust of the Variscan areas (29-32 mW m–2; Verdoya et al., 1998a). In
summary, the heat flux as a result of different components (Eq. 5) is 95-118 mW m–2.
This range is lower by 4-27 mW m–2 than that observed in the margin.
A further component produced by the radiogenic heat of the Aeolian volcanic
arc rocks should be take into account in the heat-flux budget. In order to estimate this
contribution we can use available heat-production data of several volcanic rocks
cropping out on the island of Lipari and Vulcano (Chiozzi et al., 1998 and 1999;
Verdoya et al., 1998b). These data allow us to model the heat flux vs. depth in the
volcanic cover, which can be schematised with a simple structural model consisting
of 0.5 km of pyroclastics with essentially felsic composition overlying 1.5 km of
andesite lava flows. On the basis of the thickness of the volcanic products and by
assuming a uniform distribution vs. depth, the heat flux produced is estimated to be
about 5 mW m-2.
HEAT BY MELT COOLING
A possible explanation to the foregoing heat flux deficit could lie in the heat
supplied by magma. By assuming that at distances greater than 1/4 of hb the
temperature may be modelled as a conductive cooling of the melt, the heat flux qb
released by cooling is given by
ϑ b + ∆ϑ 2 2 2 2
qb = k −2exp − c2 + 2exp − c3 + exp − c 4 − exp − c5 , (7)
2 πtχ c1 c1 c1 c1
with c1 = 4χt, c2 = h1+hb, c3 = h1, c4 = 2h2+2hb and c5 = 2h2+h1+hb, where t is time, k
is the thermal conductivity, χ is the thermal diffusivity, and h1 and h2 are the thickness
of the crust and the lithospheric mantle above and below the underplated magmatic
layer, respectively (Jaeger, 1964). ϑb is the temperature of the magma corrected by 1
mK m-1 for the liquid adiabatic upwelling in excess of what the temperature would
have been in the region occupied by the magma layer if there was no melt, but
accounting for the rise of the lithospheric isotherms caused by rifting. The
temperature ∆ϑ = L / c ≈ 500°C is added to account for the latent heat of magma as it
solidifies.
We applied Eq. 7 to two layers of thickness equal to 1 and 5 km and potential
temperature of 1280 and 1330°C, respectively, with k = 3.2 W m–1K–1 and χ = 1 mm2
s–1. The results are shown in Fig. 3. By considering a mean formation age of 5 Ma for
the Southern Tyrrhenian, the heat flux produced by crustal melt is 7 mW m–2 for hb =GNGTS – Atti del 18° Convegno Nazionale / 08.02
1 km and 32 mW m–2 for hb = 5 km. Thus it is necessary to invoke a layer of melt with
thickness ranging from 1 to 5 km to balance the heat-flux budget.
Fig. 3 - Heat flux generated by cooling of two melt layers underplating the crust. Melt thickness are 5
(curve I) and 1 km (curve II), and the mantle potential temperatures are 1330 and 1280°C,
respectively.
The heat flux contribution from cooling melt lasts for some years after the rift
episode and for time periods longer than the thermal time constant or the
solidification time of the melt layers. The explanation is that heat in the magma is
stored in the surrounding medium and it is available also after the magma has
solidified.
CONCLUSIONS
Our results demonstrate that new crust can have been generated in the
Southern Tyrrhenian back-arc basin by continental extension above a moderately
heated (50-100°C) asthenosphere. In the process of pressure relief melting, the
mantle materials initially at or near its solidus moved by upwelling into the
supersolidus field. Then, melting begins, and the temperature path of the rising
materials deviates from the adiabat. This could have originated melts with
composition depending on the asthenosphere temperature. Such magmas
underplated the continental crust and have probably controlled the transition from
continental lithosphere stretching to ocean accretion in the abyssal part of the basin.
Their interaction with magmas originated by the subduction process renders the
interpretation of the surface magmatic history complex.
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