Heat flow and geodynamics in the Tyrrhenian Sea

Heat flow and geodynamics in the Tyrrhenian Sea

G. Zito,1 F. Mongelli,1 S. de Lorenzo1 and C. Doglioni21Dipartimento di Geologia e Geofisica, Universita di Bari, Italy; 2Dipartimento di Scienze della Terra, Universita La Sapienza, Roma, Italy

Introduction

The Tyrrhenian Sea is the Neogene-to-Present backarc basin developed inthe hangingwall of the west-directedApennines subduction in Italy (e.g.Scandone, 1980; Malinverno andRyan, 1986). The basin is asymmetricin various respects: extension is gre-ater in the south; and extension andrelated magmatism have migrated intime from west to east (e.g. Kastenset al., 1988; Bigi et al., 1989; Sartori,1989; Savelli, 2001). Extensionevolved to ocean formation in twomain areas, i.e. the Vavilov (7–3.5 Ma) and the Marsili (1.7–1.2 Ma)subbasins (Bigi et al., 1989). Subduc-tion-related magmatism also occurs inthe Tyrrhenian basin to form theEolian islands (e.g. Savelli, 2001).The basin has high heat flow values

(Fig. 1), which are probably relatedto the stretching of the lithosphere inthe backarc area. Subduction-relatedmagmatism does not seem to be sig-nificant for the regional heat flow ofthe entire backarc basin, being locali-zed in the narrow belt of the Eolianvolcanic arc, whereas the high heatflow is distributed over the entirebasin. The asymmetric pattern persistsin the heat flow values, which arehigher on the eastern side (Mongelli,1991). Erickson (1970) carried out thefirst measurements of heat flow inthe Tyrrhenian basin for 12 stations;the average value of the best ten siteswas 147.5 mW m)2.Sclater (1972) identified a relation-

ship between heat flow and elevationof the marginal basins of the western

Pacific. However, when applying thesetypes of models, Loddo and Mongelli(1975) pointed out that Erickson’svalue was too high with respect tothe elevation, denoting an anomalousstate of the basin. Malinverno (1981)and Malinverno et al. (1981) inter-preted the existing data by consideringthat the Tyrrhenian basin was createdbehind an eastward-migrating trenchsystem, with associated stretching ofthe hangingwall lithosphere. Hutchin-son et al. (1985) produced new heatflow data and applied the simplestretching model of McKenzie (1978)to the western Tyrrhenian (heatflow ¼ 134 ± 8 mW m)2) and ob-tained a very high stretching factor(b ¼ 6). They maintained that, whenstretching is long and continuous,oceanic crust is created in the centralrift. They modelled this phase in theSouthern Tyrrhenian where the heatflow was 151 ± 10 mW m)2 with theoceanic plate model of Parsons andSclater (1977), and obtained a value ofb¼ 8.Mongelli and Zito (1994) compiled a

heat flow map of the Tyrrhenian Seaand surrounding areas based both onpre-existing data and on new measure-ments. This map (Fig. 1) shows a veryhigh regional value of 120 mW m)2

and two strong local maxima of143 mW m)2 and 245 mW m)2 inareas of recent tectonic and volcanicactivity, and also probably convectivewater movements.There is general agreement that

extensional thinning of the lithospherehas resulted from stresses generated byboundary forces related to slab pull(e.g. Forsyth and Uyeda, 1975; Angel-ier and Le Pichon, 1979) or to differ-ential drag exerted by an eastward-migrating mantle (Doglioni et al.,1998). Evidence indicates that exten-

sion rates in backarc basins, such as theTyrrhenian or Pannonian basins, arerelated to the rates of subduction.Episodic backarc extension in the Tyr-rhenian basin would suggest either thatthe subduction rate is not continuousor, alternatively, that stretching in thebackarc is not continuous during asteady-state subduction process. Theaverage rate of the subduction, in-ferred by comparing the subductedslab length (500–700 km) with its ini-tiation age (about 30–20 Ma), is of theorder of about 2.5 cm yr)1. The totalamount of subduction developed withcontemporaneous retreat of the slab.The amount of retreat almost equalsthe backarc extension, particularlywhen subduction occurs in the absenceof E–W convergence.With new geological and geophysi-

cal data for the basin, we propose anupdated geodynamic interpretation ofthe heat flow data, suggesting a sim-plified physical model to explain thethermal asymmetry.

Geological and geophysical setting

Understanding of the geological his-tory of the Tyrrhenian Sea has greatlyimproved owing to several DSDP andODP wells, seismic reflection profiles,dragging and volcanological studies(e.g. Zitellini et al., 1986; Ellam et al.,1988; Kastens et al., 1988; Franca-lanci et al., 1993; Pascucci et al.,1999). Several papers have proposedgeophysical and geodynamic modelsfor the opening of the basin (e.g.Scandone, 1980; Malinverno et al.,1981; Mantovani, 1982; Finetti andDel Ben, 1986; Malinverno and Ryan,1986; Moussat et al., 1986; Pataccaand Scandone, 1989; Mongelli andZito, 1994; Gueguen et al., 1997; Cellaet al., 1998). Here we summarize some

ABSTRACT

The present heat flow in the southern Tyrrhenian Sea appears asa transient thermal wave that has migrated eastward in time.The higher heat flow in the south-eastern side of the basinconfirms the suggestion of an eastward-migrating rift. Punctu-ation of the Tyrrhenian backarc extension in lithosphericboudins is accompanied by a concentrated increase in heat

flow generated by asthenospheric intrusions and relatedmagmatism progressively moving eastward. The migration ofthe asthenosphere in the same direction could explain thesephenomena.

Terra Nova, 15, 425–432, 2003

Correspondence: F. Mongelli, Diparti-

mento di Geologia e Geofisica, Universita

di Bari, Campus Universita, 70100 Bari,

Italy. E-mail: [email protected]

� 2003 Blackwell Publishing Ltd 425

doi: 10.1046/j.1365-3121.2003.00507.x

important results that are useful forour study.Subduction of the Adriatic micro-

plate began in the Late Oligocene –Early Miocene and developed to theeast of the former Alpine chain. TheApenninic accretionary prism formedin sequence at the front of thepre-existing Alpine back-thrust belt.Apenninic backarc extension migrated

eastward and resulted in boudinage ofthe former Alpine nappe stack(Doglioni et al., 1998). Kinematicsand geophysical data support thepresence of an eastward-migratingasthenospheric wedge at the subduc-tion hinge of the retreating Adriaticplate (Gueguen et al., 1997).Rifting initiated in the Oligocene in

the Liguro-Provencal basin to the west

of Corsica–Sardinia, floored by ocea-nic crust 19–15 Ma ago. This riftingmoved east of Corsica and Sardiniaproceeding in steps and in thesouthern Tyrrhenian generated severalmajor subbasins, marked by homon-ymous volcanoes, i.e. Magnaghi,Vavilov and Marsili (Fig. 2).Basalts at the Mt Vavilov volcano

are OIB-MORB type with an age of4.1 Ma (Sartori, 1989), whereas thebasalts of Mt Marsili are also calc-alkaline (Beccaluva et al., 1990) withoverlying sediments that have an ageof 1.8 Ma (Kastens et al., 1988), indi-cating very young basaltic crust.Subduction of the Southern Adri-

atic and Ionian lithosphere beneaththe Apennines and the Tyrrhenian Seais demonstrated by seismicity, mantletomography, calc-alkaline magma-tism, a well-developed accretionaryprism, etc. Many authors (Gaspariniet al., 1982; Anderson and Jackson,1987; Amato et al., 1991, 1993; Giard-ini and Velona, 1991; Selvaggi andChiarabba, 1995; Cimini, 1999; Sel-vaggi, 2001) have tried to define thegeometry of the subducted slab bydifferent seismological methods. Sel-vaggi and Chiarabba (1995) have des-cribed a continuous slab having agentle slope down to 50 km depth,with a rapid increase at the hinge,where the slope reaches 70�, therafterremaining constant down to 500 km.

Fig. 1 Contour plot of the heat flow density (mW m)2) of the Tyrrhenian Sea andsurrounding areas. Contour lines are at 10 mW m)2, UTM kilometric coordinates(modified after Mongelli and Zito, 1994).

Fig. 2 The western Mediterranean consists of subbasins progressively opening toward the east, in the hangingwall of the Apenninesubduction zone. The backarc extension in the Tyrrhenian sea stretched the pre-existing Alpine double-verging orogen (dark grey).Oceanic crust is shown in black (slightly modified after Gueguen et al., 1997).

Heat flow and geodynamics in the Tyrrhenian Sea • G. Zito et al. Terra Nova, Vol 15, No. 6, 425–432

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426 � 2003 Blackwell Publishing Ltd

Calcagnile and Panza (1981) inter-preted the lithosphere thickness of theTyrrhenian area based on dispersionof surface waves; they found that thelithosphere is thinned up to 30 kmin the central sector of the area.Recently, Pontevivo and Panza(2002) found that the thickness isabout 20 km in the southernmostsector of the basin (Fig. 3).The structure of the Tyrrhenian

crust has been studied extensively bygravimetric methods (Morelli, 1970,1981; Morelli et al., 1975) and seismicexploration (Finetti and Del Ben,1986; Pascucci et al., 1999).The Tyrrhenian Sea is the site of

an intense Bouguer anomaly (> 250mgal); its interpretation (Cella et al.,1998), by assuming density valuesconstrained by the results of the seis-mic exploration, confirms the exist-ence of very thin crust (Fig. 4).A map of the depth to the Moho

(Nicolich, 1989; Nicolich and DalPiaz, 1991) shows values lower than15–20 km in the bathyal plain, withtwo minima of 10 km centred on theVavilov and Marsili basins. Note thatthese minima coincide with the highestheat flow values. The lithosphericboudinage proposed by Gueguenet al. (1997) and shown in Fig. 2 issuggested to be slightly asymmetricby the gravimetric reconstruction ofCella et al. (1998), with the continen-tal roots of Corsica–Sardinia shiftedto east with respect to areas of highertopography. This would confirm thepresence of an underlying eastward-migrating asthenosphere.

The Tyrrhenian Sea can be dividedinto three parts, i.e. northern, centraland southern areas. The southern area(Fig. 1) is the widest and moststretched; it is also the deepest partof the Tyrrhenian Sea (> 3500 m)and it corresponds to the main areaof the present study, being subdividedinto the above-mentioned subbasins.The south-eastern part is also the areaof highest heat flow values(> 200 mW m)2). The central partof the Tyrrhenian Sea is characterizedby the lowest heat flow values of thebasin (�100 mW m)2). In the nor-thern Tyrrhenian Sea, close to Tus-cany, heat flow values are again high(> 160 mW m)2). Stretching in theTyrrhenian Sea decreases from southto north, and therefore there does notappear to be a linear relation betweentotal extension and heat flow. How-

ever, there does appear to be a corre-lation between active magmatismand heat flow, with the magmatismdirectly correlated to the rate of sub-duction and composition of the slab inthe Apennines. In fact, the most activesubducting part of the Apennines is inthe Southern Tyrrhenian–Calabria,where the foreland is the oceanicIonian basin. To the north, the fore-land of the southern Apennines isalmost locked by the thick lithosphereof the Puglia area, which is barelysubducting and buckled (Doglioniet al., 1994). This area of slow, ifany, subduction is recorded in thebackarc basin where extension is min-imal, there is low or absent magmaticactivity, and low heat flow. The cen-tral northern part of the Apenninessubduction is more rapid, generatingseismicity and latent magmatism in

Fig. 3 Lithospheric thickness (km) inItaly and surrounding areas (after Cal-cagnile and Panza, 1981).

Fig. 4 Moho isobaths (km) in Italy and surrounding areas. Adriatic plate, thick lines;European plate, fine lines; stretched continental crust, dashed lines (modified afterLocardi and Nicolich, 1988).

Terra Nova, Vol 15, No. 6, 425–432 G. Zito et al. • Heat flow and geodynamics in the Tyrrhenian Sea

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Latium and Tuscany, and relativelyhigh heat flow (see Mongelli and Zito,2000, and references therein). Theshallower seismicity in the northernApennines can be related to the con-tinental nature of the downgoinglithosphere, which behaves in a moreductile manner at shallower depthwith respect to the oceanic lithosphereof the Ionian basin, subductingbeneath the southern Tyrrhenian Sea(Carminati et al., 2002).

Geodynamic model of the SouthernTyrrhenian basin opening

Let us suppose that during Oligocenetime, the European and Adriaticplates were sutured by the Alpineorogen giving a thickened lithospherehL, ideally comprising two sectors BCand CD, to the east of sector AB ofthe Alpine foreland where the thick-ness of the plate is L (Fig. 5). In theEarly Miocene, between 19 and15 Ma ago, sector AB first stretchedby a factor b so that it thinned to

L ⁄b. Further stretching caused thelaceration of the thinned lithosphere,favouring the passive rising at thesurface of an asthenospheric body(a). As a consequence, blocksBC + CD rifted and drifted byAB Æ (b ) 1) + a.During Late Miocene – Early Plio-

cene times (7 and 3.5 Ma ago), sectorBC stretched by the factor b1, andthinned to hL ⁄b1. At 3.5 Ma ago,further stretching caused laceration ofthe thinned lithosphere, favouring thepassive rising of an asthenosphericbody of width b. As a consequence,block CD further drifted and rifted byBC Æ (b1 ) 1) + b (Vavilov basin).During Pleistocene times (1.7 and

1.2 Ma ago), block CD stretched by afactor b2 and thinned to hL ⁄b2. At1.2 Ma ago further stretching causedthe laceration and the rising of an-other asthenospheric body (c). PointD further drifted and rifted byCD Æ (b2 ) 1) + c (Marsili basin).These latter two extensions formedthe southern Tyrrhenian Sea basins.

At present, the distance BD is about550 km, that is the distance betweenSardinia and Calabria.

Thermal model

Figure 6 shows the heat flow map ofthe Tyrrhenian Sea, which has beensmoothed to eliminate small localanomalies. This map is the result ofthe superimposition of the effects oflithospheric extension and of localasthenospheric intrusions in two dif-ferent areas: the Vavilov basin, whichis older, where the heat flow reaches avalue of 143 mW m)2, and the Marsilibasin, where the heat flow reaches avalue of 245 mW m)2.From a thermal point of view, we

need to consider the mantle and theradioactive components of the heatflow, together with intrusion effects.

Mantle component

McKenzie (1978) showed that themantle component of the temperatureand heat flow in a basin after a suddenpassive pure shear extension, assumingthe surface temperature to be zero, is:

qm ¼ kT1hL

�1þ 2

X1n¼1

�bnp

sin

�npb

��

� exp

�� n2t

s

��ð1Þ

where k is the thermal conductivity ofthe lithosphere,T1 the temperature at thebase of the lithosphere, hL the thicknessof the lithosphere before thinning, b thethinning factor of the lithosphere,

s ¼ h2Lp2j

j the thermal diffusivity of the litho-sphere, t the time after thinning andkT1 ⁄hL is the mantle heat flow beforethinning.We assume that before the exten-

sion phase the lithosphere had thesame structure as the present Alpinechain (because it was part of thischain), i.e. comprising lithosphere130 km thick (Calcagnile and Panza,1980) and crust 45–50 km thick(Locardi and Nicolich, 1988).To calculate b values in both basins

we use the numerical relation (Mong-elli, 1991) that expresses the re-thick-ening of the lithosphere afterstretching:

Fig. 5 Sketch of the evolution of the lithospheric extension and thinning, from theOligocene to present. See text for further explanation.


.............................................................................................................................................................


hL � hhL

¼ 0:0109þ 1� 1

b

� �0:99

� exp�10tbs

� �

where hL is the original thickness ofthe lithosphere, h is the lithosphericthickness at time t after extension.We obtain b1 ¼ 6.3 for the older

period of extension and b2 ¼ 7.0 forthe younger extension. We assumeTa ¼ 1330 �C, j ¼ 24.3 km2 Ma)1

and k ¼ 2.5 W m)1 K)1 for involvedrocks at high temperature (Zito et al.,1993; Zoth and Haenel, 1988). Themantle component of the heat flowbefore thinning is 25.6 mW m)2.Figure 7 shows the evolution of the

heat flow; it is possible to see that, atpresent, the value relative to the firstextension is 112.5 mW m)2, whereasthat relative to the second extension is170.8 mW m)2.

Radioactive component

The radioactive component of the heatflow in the Tyrrhenian basin can bededuced from the crust structure of theAlps. As a result of the collision, thecontinental crust beneath the Alps isalmost doubled (Pfiffner, 1990; Ye &Ansorge, 1990).Cermak and Bodri (1991, 1996)

modelled the thermal evolution ofthe Alps by assuming an exponentialdistribution of heat production ineach crustal component. As the totalcrust is 50 km thick, we assume eachcrust component to be 25 km thick.

This crustal thickness beneath theSouthern Tyrrhenian sea is reduced,by extension, to 15 km by a factorbc ¼ 3.3, and each crustal componentto Hr ¼ 7.5 km.In the southernmost sector the crust

is reduced to 10 km by a factor ofbc ¼ 5 and each crustal component to

Hr ¼ 5 km.As a consequence, the con-tribution of radioactivity to the surfaceheat flow is strongly reduced. We sug-gest that, the contribution is nearequilibrium in a relatively short periodof time. For simplicity, we calculate thethermal contribution of the radioactiv-ity of this thinned crust at steady state.We solve the equation:

d2Trdz2

¼ �AðzÞk

ð3Þ

where:

AðzÞ ¼ A0

bc

exp�zD

� �0 < z < Hr

AðzÞ ¼ A0

bc

exp � z�Hr

D

� �Hr < z<

hLb

that is we assume that the pre-exten-sion radioactive heat productionA0 ¼ 3 lW m)3 is depleted by thefactor bc (Waples, 2002). Moreover,D ¼ 8 km, hL ⁄b ¼ 30 km, Hr ¼ 7.5km for the older basin, and hL ⁄b ¼20 km andHr ¼ 5 km for the youngerbasin.With the following boundary con-

ditions:

Fig. 6 Smoothed heat flow density map (in mW m)2) of the Southern TyrrhenianSea. UTM kilometric coordinates.

Fig. 7 Time variation of the surface heat flow (mW m)2) for different stretchingfactors b according to Eq. (1).


.............................................................................................................................................................


Trðz ¼ 0Þ ¼ Trðz ¼ hL=bÞ ¼ 0 C

Trðz ¼ H�r Þ ¼ Trðz ¼ Hþ

r Þ

dTrdz z ¼ H�

r¼ dTr

dz

��z¼Hþ

r

we have the solution given in Eq. (A1).By taking k¼ 3 W m)1 K)1 for

granitic rocks, the surface contribu-tion to heat flow is 7.95 mW m)2, forthe older and 6.2 mW m)2 for theyounger basin.As a consequence, the calculated

surface heat flow of the first extensionis about 120 mW m)2, and that ofthe second extension is about177 mW m)2. The present heat flowvalue in the area of the first extension ismore than 140 mWm)2, whereas it ismore than 240 mWm)2 in the eastwardyounger Marsili basin (Fig. 6). Thesevalues can be related to asthenosphericintrusions, and confirm that when b >6 laceration of the lithosphere occurs.

Thermal effect of asthenosphericintrusion

We suppose that the asthenosphericintrusion reaches the surface andcools. The magma has a melt tem-perature Tm at which the phasechange from liquid to solid occurs.The position of the phase changeboundary zm moves downward assolidification proceeds and, addition-ally, at this interface latent heat offusion L is liberated. This is the Stefanproblem. The solution, in one dimen-sion, is (Turcotte and Schubert, 1982):

Tiðz; tÞ � ToTm � To

¼erf z

2ffiffiffikt

p� �

erfk1ð4Þ

where T0 is the surface temperature,

k1 ¼Zm2

ffiffiffiffikt

p ð5Þ

and k1 is determined by the transcen-dental equation:

exp �k21

�k1erfk1

¼ Lffiffiffip

p

cðTm � T0Þð6Þ

where c is the specific heat.The surface heat flow is:

kdTidz

��z¼0

¼ kffiffiffip

pkt

Tmerfk1

ð7Þ

Along the first western intrusion themodelled heat flow is 120 mW m)2,little less than the measured surround-ing value of 140 mW m)2 derivingfrom the first extension.In the second intrusion to the

east, the modelled heat flow is177 mW m)2, whereas the measuredsurrounding value is 240 mW m)2

deriving from the second extension.We suggest that the second exten-

sion is so recent (1.2 Ma) that thelateral effects may be neglected andtherefore the one-dimensional Stefanmodel may be applied to the centralpart of the basin.We assume T0 ¼ 0 �C, Tm ¼

1330 �C, c ¼ 1 kJ kg)1 K)1, L ¼400 kJ kg)1 and for ultrabasic rocks at1300 �C thermal conductivity k ¼1.45 W m)1 K)1 (Zoth & Haenel,1988).

From Eq. (5) we obtain k1 ¼0.932 W m)1 K)1 and erf(k1) ¼ 0.812.Figure 8 shows: A) the geotherm inthe second intrusion and B) the vari-ation of the surface heat flow withtime, on which the value relative to thesecond intrusion is well fitted.From Eq. (4), and taking k ¼

21.8 km2 Ma)1 we obtain zm ¼ 7.0km. This is the thickness of the newlycreated lithosphere. Moreover, thecontour 10 km below the Marsilibasin in Fig. 4 indicates the thicknessof the lithosphere.The intrusion below the Vavilov

basin is older, and the new lithosphereis thicker. By assuming approximatelythe one-dimension solution, we obtainzm ¼ 11.2 km. However, because ofthe lateral loss of heat, zm should bemore than 11.2 km. We expect thatwithin the new lithosphere, new thinoceanic crust is differentiated. In thiscase we suggest that the 10-km contourin Fig. 4 below the Vavilov basin indi-cates effectively the depth to theMoho.

Conclusions

According to our results, a few inter-pretations can be drawn for theSouthern Tyrrhenian basin:1 The opening of the SouthernTyrrhenian basin occurred by tworapid and separate episodes, whichmoved from west to east andstretched the lithosphere by a factorb >6.

2 Stretching of the lithosphere al-lowed the contemporaneous passiverise of the asthenosphere, whichcooled, liberating the latent heat offusion, and solidified.

3 New lithosphere was formed withinthe intrusion, whose thickness isdefined by the depth of the solidifi-cation boundary.

4 The Moho depth in the Tyrrhenianbasin has a different origin: in thecontinental areas it is dependent onstretching of the primitive crust–lithosphere, whereas within theintrusion it is a new oceanic discon-tinuity, formed by differentiation ofasthenospheric material.

Acknowledgement

We would like to thank B. Gelabert forcritical reading of this article.

0

–2

–4

–6

–8

–10

–12

–14

–16

–18

–20

0 250 500 750 1000 1250 1500

°C0 1 2 3 4 5 6 7 8 9 10

Ma

500

400

300

200

100

0

mW

/m2

km

0 Ma

1.2 Ma

A B

Fig. 8 A) the present geothermat the center of the asthenospheric body c (Marsili basin)according to equation (4); B) Time variations of the surface heat flow (mW ⁄m2) of anasthenospheric body according to the Stefan problem. The theoretical cuve well fits theexperimental data, represented by the bar, relative to the Marsili basin intrusion.


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Received 16 December 2002; revised versionaccepted 25 August 2003

Appendix

The steady-state heat conductionequation to be solved is:

d2Tdz2

¼ �AðzÞk

where:

AðzÞ ¼ A0

bcexp � z

D

� �0 < Z < Hr

AðzÞ ¼ A0

bcexp � z� Hr

D

� �

Hr < Z < hL=b

with the following boundary condi-tions:

Trðz ¼ 0Þ ¼ Trðz ¼ hL=bÞ ¼ 0 C

Trðz ¼ H�r Þ ¼ Trðz ¼ Hþ

r Þ

dTrdz

��z ¼ H�

r

¼ dTrdz

��z¼Hþ

r

in which b and bc are the lithosphericand crustal stretching factors, respect-ively.The solution in the layer 0 < z< Hr, is

given by:

T ðzÞ¼ A0D2

bck1� exp � z

D

� �h i

þ bA0DHr

bckhLz exp �Hr

D

� �� 1

� �

þ bA0D2

bckhL

� z�exp

��ðhL � bHrÞ

bD

�

þ exp

��Hr

D

�� 2

�

þA0Dbck

z�1� exp

��Hr

D

��

and in layer Hr < z < hL ⁄b:

T ðzÞ ¼ � A0D2

bckexp

��ðz� HrÞ

D

�

þ bA0DHr

bckhLz�exp

��Hr

D

�� 1

�

þ bA0D2

bckhLz�exp


bD

�

þ exp

��Hr

D

�� 2

�

þ 2A0D2

bck

�2� exp

��Hr

D

��

þ A0DHr

bck

�1� exp

��Hr

D

��

The respective gradients are:

dTdz

¼A0Dbck

�exp

�� zD

��

þ bA0DHr

bckhL

�exp

��Hr

D

�� 1

�

þ bA0D2

bckhL

�exp


bD

�

þ exp

��Hr

D

�� 2

�

þ A0Dbck

�1� exp

�Hr

D

��

dTdz

¼A0Dbck

exp

��ðz� HrÞ

D

�

þ bA0DHr

bckhL

�exp

��Hr

D

�� 1

�

þ bA0D2

bckhL

�exp


bD

�

þ exp

��Hr

D

�� 2

�

The gradient at the surface is:

dTdz

��z¼0

¼ bA0DHr

bckhL

�exp

��Hr

D

�� 1

�

þ bA0D2

bckhLz�exp

��ðhL � bHr

bD

�

þ exp

��Hr

D

�� 2

�

þ A0Dbck

�2� exp

��Hr

D

��


.............................................................................................................................................................


Heat flow and geodynamics in the Tyrrhenian Sea

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