Thermo-mechanical model of the mantle wedge in Central ...usuarios.geofisica.unam.mx/vladimir/papers_pdf/Manea PEPI 2005.pdf · give us advance insights on the geodynamic processes

Physics of the Earth and Planetary Interiors 149 (2005) 165–186

Thermo-mechanical model of the mantle wedge in CentralMexican subduction zone and a blob tracing approach for the

magma transport

Vlad Constantin Maneaa,∗, Marina Maneaa,Vladimir Kostoglodova, Granville Sewellb,1

a Instituto de Geof´ısica UNAM, Circuito de la Inv. Cient´ıfica s/n, Ciudad Universitaria, 04510 M´exico D.F., Mexicob University of Texas, UTEP, Mathematical Department, El Paso, TX 79968, USA

Accepted 26 August 2004

Abstract

The origin of the Central Mexican Volcanic Belt (CMVB) and the influence of the subducting Cocos plate on the CMVBvolcanism are still controversial. In this study, the temperature and mantle wedge flow models for the Mexican subduction zoneare developed using the finite element method to investigate the thermal structure below CMVB. The numerical scheme solvesa system of 2D Stokes equations and 2D steady-state heat transfer equation.

Two models are considered for the mantle wedge: the first one with an isoviscous mantle wedge and the second one with◦ h

rsect the

ng of thisperidotite

volcanic–10.0 km

he arrivalage. The rise

4 0715.

strong temperature-dependent viscosity. The first model reveals a maximum temperature of∼830 C in the mantle wedge, whicis not sufficient for melting of wet peridotite. Also, the geotherm of the subducting plate upper surface does not intedehydration-melting solidus for mafic minerals. The second model predicts temperatures of more than 1200◦C beneath theCMVB for a wide range of rheological parameters (reference viscosity and activation energy). Up to 0.6 wt.% H2O can bereleased down to 60 km depth through metamorphic changes in the oceanic crust of the subducting slab. The meltioceanic crust apparently occurs in a narrow depth range of 50–60 km and also melting of the mantle wedge hydratedis now expected to take place beneath CMVB.

Considering that the melting processes on and in the vicinity of the subducting plate surface generate the most of thematerial, a dynamic model for the blob tracers is developed using Stokes flow at infinite Prandtl number. The blobs of 0.2in diameter migrate along very different trajectories only at low wrapping viscosities (ηw = 1014–5× 1017 Pa s). The modelingresults show that the “fast” trajectories terminate at the same focus location at the base of the continental crust, while tpoints of “slow” trajectories, which are common for the blobs of smaller size (∼0.4–0.5 km), are scattered away from the averfocus location. This observation may give us a hint on a possible mechanism of strato and mono volcanoes genesis

∗ Corresponding author. Present address: Seismological Laboratory, CalTech, Pasadena. Tel.: +52 626 395 6984; fax: +52 626 56E-mail addresses:[email protected] (V.C. Manea), [email protected] (M. Manea),

[email protected] (G. Sewell).1 Fax: +1 915 747 6502.

0031-9201/$ – see front matter © 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.pepi.2004.08.024

166 V.C. Manea et al. / Physics of the Earth and Planetary Interiors 149 (2005) 165–186

time, which the blob detached from the subducted plate, needs to reach the bottom of the continental crust, is from 0.001 up to14 million years depending on the blob diameter and surrounding viscosity.© 2004 Elsevier B.V. All rights reserved.

Keywords:Mexican subduction zone; Thermal models; Mantle wedge flow; Blobs

1. Introduction

Thermal and flow models in the mantle wedge cangive us advance insights on the geodynamic processesin the forearcs as well as beneath the volcanic arcs.There are only a few thermal models of the subduc-tion zone in Mexico (Currie et al., 2002; Manea et al.,2004), but none of them presents a reliable and de-tailed thermal structure beneath the volcanic arc con-sidering the rheology of the asthenosphere. The presentmodels are further development of the previous studyof the Mexican subduction zone in Guerrero (Maneaet al., 2004), which plausibly constrained the ther-mal structure for the forearc area only. The thermo-mechanical modeling of the mantle wedge with tem-perature and/or stress-dependent rheology is proposed(Furukawa, 1993; Conder et al., 2002; Van Keken etal., 2002; Kelemen et al., 2003). Mantle wedge dy-namics and thermal structure of shallow flat subduc-tion zones in general have been investigated recentlybyvan Hunen et al. (2002). In this study, we explore thethermal structure of the mantle wedge in a specific sub-duction zone of the Central Mexico (Guerrero), whichhas an anomalously wide, subhorizontal plate inter-face and a distant volcanic arc. The models describea stationary slab-induced convection, in the cases ofthe constant viscosity (isoviscous mantle) and strongtemperature-dependent viscosity of the asthenosphere.

The previous thermal model for the Guerrero sub-duction zone with a shallow plate interface (Currie eta fort of∼ anicf eb doesn

ta ntleb IB-l as-t cos

plate was proposed as a possible source of the OIB-like magmas (Luhr, 1997; Wallace and Carmichael,1999). There are several mineralogical and geochem-ical studies of the CMVB (e.g.Marquez and DeIgnatio, 2002) suggesting the existence of two differentprimitive mafic magmas, one with an “asthenospheric”OIB-like component and another with a “lithospheric”component. Although the relationship between thevolcanism and the subduction of the Cocos plate iscommonly recognized (e.g.Pardo and Suarez, 1995;Wallace and Carmichael, 1999), there are different hy-pothesis regarding the source of the volcanism in thisarea: the extension of the Gulf of California trans-form fault system (Ferrari et al., 1994), an old weak-ened cortical zone (Cebull and Schubert, 1987), corticaltranspression mechanisms (Shubert and Cebull, 1984;Ferrari et al., 1990) and rifting (Luhr, 1997; Marquezet al., 1999a,b).

The source of fluids that metasomatize the mantleis also unclear. There are three possibilities proposedto explain the metasomatized mantle (Marquez et al.,1999c; Wallace and Carmichael, 1999; Verma, 1999,2000): (a) the mantle wedge affected by the fluids orig-inated from dehydration of the subducted Cocos plate;(b) old enriched lithospheric mantle; (c) mantle meta-somatized by volatiles from a mantle plume. Direct evi-dences that the mantle wedge metasomatized by fluidsreleased from the down-going oceanic slab is essen-tially difficult, because the mantle xenolites are rarelydiscovered in arc lavas. In the CMVB, quaternary horn-b eF esex andt rysts( ss labi

ardt truc-t scat-t stra-

l., 2002) with predefined analytical expressionhe mantle corner flow predicts the temperature900◦C in the asthenosphere beneath the volc

ront (Popocatepetl volcano). In Currie’s model, thasaltic component of the subducting plate crustot reach the melting temperature.

Recent geological studies (Luhr, 1997; Marquez el., 1999a) suggest the existence of a complex maeneath the CMVB. However, the origin of the O

ike basalts is still unclear there. Advection of thehenospheric mantle caused by sinking of the Co

lende andesites erupted near the El Penon area (seig. 1) contain xenolites of 1–2 cm in diameter. Thenolites are rich in phenocrysts of hornblendehe host andesite is depleted in plagioclase phenocBlatter and Carmichael, 1998). All these observationuggest an influx of volatiles from the subducting snto the mantle wedge.

Underneath the CMVB, the magma ascents towhe earth surface producing large strato-volcanic sures and smaller-sized monogenetic volcanoesered in large areas. The CMVB includes several

V.C. Manea et al. / Physics of the Earth and Planetary Interiors 149 (2005) 165–186 167

Fig. 1. Tectonic setting and position of the modeled cross-section(straight line), in Guerrero. Triangles show the location of activevolcanoes in Mexico. Dashed ellipse is the CMVB – Central MexicanVolcanic Belt. Light blue rectangle represents the El Penon area,where mantle xenolites have been found. Arrows show convergencevelocities between the Cocos and North American plates (DeMets etal., 1994).

tovolcanoes like Popocatepetl, Iztaccıhuatl and Nevadode Toluca (Fig. 1). The monogenetic volcanoes are ba-sically cinder cones, lava cones, domes and lava flows.While the stratovolcanoes are characterized by a pe-riodicity of magma eruptions, the monogenetic vol-canoes present a single one eruptive event, and as aresult have a smaller size compared with stratovolca-noes.Fedotov (1981)suggested that the occurrence ofone or another type of volcanoes might be related withthe magma supply. Other scientists (e.g.Takada, 1989,1994) propose a dual-mechanism related with both themagma supply and regional stress. While the align-ment of the monogenetic volcanoes can be parallel to amain normal fault system, the arrangement of the largestratovolcanoes seems to be rather orthogonal to thevolcanic belt (Alaniz-Alvarez et al., 1998).

Using the phase diagrams for mafics (e.g.Hackeret al., 2003), it is possible to investigate whether themantle wedge is subjected to the hydration by flu-ids released from the subducting slab. A very thinsedimentary fill at the Mexican trench suggests thatabout of 95% of these sediments (∼200 m) are sub-ducted (Manea et al., 2003). An influx of volatiles fromthe metamorphosed oceanic crust and sediments mighttrigger partial melting of the peridotite just above thesubducted slab (Tatsumi, 1986; Davies and Steven-son, 1992). Gerya and Yuen (2003)showed that aRayleigh–Taylor instability developed above the sub-

ducting slab generates positively buoyant plumes upto 10 km in diameter that can penetrate the overlyingmantle wedge.

Albeit various mechanisms of magma genera-tion have been proposed (e.g. anhydrous decom-pression melting of peridotite (Klein and Lang-muir, 1987; Langmuir et al., 1992); porous flow of hy-drated partial melt (Davies and Stevenson, 1992)), inthe present study, the magma generation and migra-tion is assumed in a form of partially melted positivelybuoyant blobs. Regardless of the oversimplification ofthe blob properties, this model can help to understandthe existence of different sources of the volcanism in thearea. The buoyant blobs of different size and compo-sition may be generated by melting of the Cocos plateand overlying mantle peridotite, when the pressure andtemperature reach the solidus conditions (e.g.,Geryaand Yuen, 2003).

It is important to estimate the viscosity range forthe reasonable trajectories and average rise times forthe blobs reaching the bottom of the continental crust.A recent study byGerya and Yuen (2003)revealedthat these plume-like blobs may be lubricated by thepartially melted material of the subducted crust andhydrated mantle, thus producing a very low viscositywraps around the blob structures.Burov et al. (2000)apply a similar extremely low viscosity in order tomodel the exhumation in the continental lithosphere.

2

ady-s rreroc erP nsi

C

. Modeling procedure

A system of 2D Stokes equations and 2D stetate heat transfer equation is solved for the Gueross-section (Fig. 1) using the finite element solvDE2D (http://pde2d.com/). The system of equatio

n an explicit form is

∂(−P + 2η∂u

∂x

)∂x

+∂(η

(∂u∂y

+ ∂v∂x

))∂y

= 0,

∂(η

(∂u∂y

+ ∂v∂x

))∂x

+∂(−P + 2η∂v

∂y

)∂y

= −ρg − Ra · T,

p

(u

∂T

∂x+ v

∂T

∂y

)

= ∂

∂x

(k

∂T

∂x

)+ ∂

∂y

(k

∂T

∂y

)+ Q + Qsh (1)

http://pde2d.com/


whereP is pressure (Pa), and

η = η0 e[(Ea/RT0)(T0/T−1)]

is the mantle wedge viscosity (Pa s).Other parameters are as follows:η0 is the mantle

wedge viscosity at the potential temperatureT0 (refer-ence viscosity) (1017–1021 Pa s),T0 the mantle wedgepotential temperature (1450◦C), Ea the activation en-ergy for olivine (kJ/mol),R the universal gas constant(8.31451 J/mol K),T the temperature (◦C), u the hor-izontal component of the velocity (m/s),v the ver-tical component of the velocity (m/s),ρ the density(kg/m3),Cp the thermal capacity (MJ/m3 K), k the ther-mal conductivity (MJ/m3 K), Q the radiogenic heat-ing (W/m3), Qsh the volumetric shear heating (W/m3),

Ra = ραg�TL3

η0kthe thermal Rayleigh number,α the

thermal expansion (3.5× 10−5 ◦C−1), L the lengthscale (330 km),�T the temperature difference betweenthe bottom and top model temperatures (1450◦C),k thethermal diffusivity (10−6 m/s2) andg the gravitationalacceleration (9.81 m/s2).

The Stokes equations are solved only for the man-tle wedge, while the heat transfer equation is solvedfor the entire model. The linear system solver used bythe present numerical scheme is the frontal method,which represents an out-of-core version of the bandsolver (uses a reverse Cuthill–McKee ordering). Forthe model with strong temperature-dependent viscos-i nlin-e rdert y of1 .F ed ao es ndf cest eartwn ands ignif-i rated

altym

− f

η√ε

(ε is the machine-relative precision). In other words,

the material is taken to be “almost” incompressible, sothat a large pressure results in a small decrease in vol-

ume, and the continuity equation[(

∂u∂x

) +(

∂v∂y

)= 0

]is almost satisfied.

The finite elements grid extends from 25 km sea-ward of the trench up to 600 km landward of it, andconsists of 12,000 triangular elements with the higherresolution in the tip of the wedge (Fig. 2). The trian-gles have the height to width ratio equal to 1. A se-ries of benchmark tests with different grid resolutionshave been done to verify the accuracy of numericalscheme realized in the present study. The slab–mantlewedge interface is the area where the isotherms have avery small incidence angle with this interface, thus sig-nificant errors might appear along this boundary. Thebenchmark tests on this boundary quantify the numer-ical errors as a function of mesh resolution. Grids witha systematic increase in element number from 4000 to12,000 elements in steps of 2000 elements are used forthis benchmark.

The benchmark results are presented inFig. 3. Largetemperature fluctuations (up to 22◦C) close to the tip ofthe wedge occur for grids with 4000 and 6000 elements.Increasing the mesh resolution (8000 and 10,000 trian-gles), this fluctuation is diminished and the maximumtemperature fluctuation along the slab-wedge interfaceis of∼7◦C. Increasing the grid resolution to 12,000 tri-angles, the numerical error is less then 5◦C. We stop theb e isi omh r am m 4P fi-n s ourtl b-da as afi ot-t em

nedm them omt ling( -

ty, the system of equations becomes strongly noar, therefore Picard iterations are applied, and in o

o achieve a convergent solution a cut-off viscosit024 Pa s for the temperature less than 1100◦C is usedor such highly nonlinear problems, we constructne-parameter family of problems using a variablV,uch that forV= 1 the problems is easy (e.g. linear) aorV>N (N is less NSTEPS = 20), the problem reduo the original highly nonlinear problem. The nonlinerms are multiplied by MIN(1.0,(V− 1.0)/N). With aide viscosity range from 1017 to 1024 Pa s, the fullyonlinear viscosity formulation (e.g., temperaturetress dependence of the viscosity) presented scant numerical instabilities; therefore the strain-ependence is neglected in the present study.

In the present numerical scheme, the penethod formulation is used,P being replaced byP =α′

[(∂u∂x

) +(

∂v∂y

)], whereα′ is large, on the order o

enchmark at this point because the computing timncreasing exponentially with the grid resolution (fralf of hour for 4000 triangles to more than 10 h foodel with 12,000 elements, running on a PentiuC at 3 GHz and 2 GB RAM memory). To obtainal results we used the 12,000 elements grid, thu

hermal models have the numerical error <5◦C. Theower limit of the grid follows the shape of the suucting plate upper surface (Kostoglodov et al., 1996)t 100 km depth distance. The top of the model hxed temperature of 0◦C. The temperature at the bom of the model is of 1450◦C which represents thantle temperature at∼100 km depth (Fig. 4).The continental lithosphere in Guerrero is defi

ostly by the crust, which thickness is 40 km inodel. This is consistent with the values inferred fr

he seismic refraction surveys and gravity modee.g.,Valdes et al., 1986; Arzate et al., 1993). The bend


Fig. 2. The grid with 12,000 elements used to solve the numerical models. This particular shape of the grid is designed to better resolve thevelocity field nearby the tip of the mantle wedge.

ing geometry of the subducting slab (up to the hingepoint: 270 km) is well constrained by gravity model-ing (Kostoglodov et al., 1996), seismicity data and re-cently estimated extension of the coupled plate inter-face inferred from GPS measurements during the lastslow slip event in Guerrero (2001–2002) (Kostoglodovet al., 2003).

A dip of the subducting plate beneath the volcanicarc is poorly constrained because of a very limitednumber of intraslab earthquakes. The dip of 20◦ and ahinge point at 270 km from the trench match better thehypocenter locations of the intraslab events (Fig. 5) andas a result, these are enveloped by the modeled “seis-micity cut-off” temperature ofT≈ 800◦C (Gorbatovand Kostoglodov, 1997). The continental crust consistsof two layers: the upper crust of 15 km and the lowercrust of 25 km. A summary of the thermal parametersused in the models is presented inTable 1(compila-

tion from:Peacock and Wang, 1999; Smith et al., 1979;Ziagos et al., 1985; Vacquier et al., 1967; Prol-Ledesmaet al., 1989).

The radiogenic heat generation in the continentalcrust decreases exponentially from 1.3�W/m3 in theuppermost crust down to 0.2�W/m3 in its lowermostpart (Ziagos et al., 1985). The radiogenic heat produc-tion in the models is taken as 50% from the above val-ues to fit the surface heat flow with the observed heatflow data (Fig. 6). This reduction has a minor effect onthe thermal structure of the subduction interface andmantle wedge.

A long-term sliding between the subducting and thecontinental plates along the thrust fault should pro-duce frictional heating. We introduced in the modelsa small degree of volumetric frictional heating usingthe Byerlee’s friction law (Byerlee, 1978). Frictionalheating is ceased at a maximum depth of 40 km, which

170V.C

.Maneaeta

l./Physics

ofth

eEarth

andPlanetary

Interio

rs149(2005)165–186

Fig. 3. Boundary conditions and parameters used in the modeling. The upper and lower boundaries have constant temperatures of 0 and 1450◦C, accordingly. The continentalplate is fixed. The right (landward) vertical boundary: 20◦C/km thermal gradient in the continental crust (down to 40 km); between 40 and 100 km depth the thermal gradient is of10◦C/km; no horizontal conductive heat flow is specified beneath 100 km depth. Zero traction is considered beneath Moho (40 km), at the boundary, which belongs to the mantlewedge. The convergence velocity is specified for the intersection between the right boundary and the subducting slab. The left (seaward) boundary condition is a one-dimensionalgeotherm for the oceanic plate. The Cocos plate motion is referred to the North American plate with the convergence velocity of 5.5 cm/year. Volumetric shear heating is imposedalong the plate interface up to a maximum depth of 40 km, using the Byerlee’s friction law (Byerlee, 1978).


Fig. 4. Calculated steady-state thermal field for the isoviscous mantle wedge. Horizontal black dashed line shows the Moho (40 km depth). Thehinge point is at 270 km from the trench. Thick violet solid line denotes the top of the subducting slab. Orange triangles are the two principalstratovolcanoes in CMVB: Nevado de Toluca and Popocatepetl. The maximum temperature beneath Popocatepetl volcano is about of 830◦C.The lower left inset is the magnified thermal structure close to the tip of the mantle wedge. Thin dark blue arrows in the mantle wedge representthe velocity field. The intraslab earthquakes with magnitudes, Mw≥ 5.5, are represented by the focal mechanisms. The two brown clouds ofhypocenters beneath the coast denote the smaller magnitude seismicity associated probably with the bending of the subducted plate.

corresponds to the contact between the oceanic plateand the mantle wedge (Fig. 4). The volumetric shearheating is calculated as follows:

Qsh = τv

w(2)

where Qsh is the volumetric shear heating(mW/m3), τ the shear stress (τ = 0.85σn(1− λ)for σn(1− λ) ≤ 200 MPa and τ = 50 + 0.6σn(1− λ)for σn(1− λ) > 200 MPa),σn the lithostatic pressure(MPa), λ the pore pressure ratio (the ratio betweenthe hydrostatic and lithostatic pressures;λ = 0.98 inthe present study; the maximum value,λ = 1, means

Table 1Summary of the thermal parameters used in the models

Geological unit Density (kg/m3) Thermal conductivity(W/m K)

Radiogenic heatproduction (�W/m3)

Thermal capacity(MJ/m3 K)

Oceanic sediments 2200 1.00–2.00a 1.00 2.50Upper continental crust (0–15 km) 2700 2.00 0.65 2.50Lower continental crust (15–40 km) 2700 2.00 0.15 2.50Mantle wedge 3100 3.10 0.01 3.30Oceanic lithosphere 3000 2.90 0.02 3.30

Compilation fromPeacock and Wang (1999), Smith et al. (1979), Ziagos et al. (1985), Vacquier et al. (1967)andProl-Ledesma et al. (1989).a Increase linearly with distance from the deformation front up to a depth of 10 km.

no frictional heating),v the convergence velocity(5.5 cm/year) andw the thickness of the oceanic crustinvolved in friction (200 m).

The right landward vertical boundary condition isdefined by 20◦C/km thermal gradient in the continen-tal crust. This value is in agreement with the back-arc thermal gradient of 17.8–20.2◦C/km reported byZiagos et al. (1985). Underneath Moho (40 km), theright boundary condition is represented by 10◦C/kmthermal gradient down to the depth of 100 km. Below100 km, no horizontal conductive heat flow is specified.Beneath Moho (40 km depth), for the right boundarycorresponding to the mantle wedge, the boundary con-


Fig. 5. Variation of the surface heat flow along the Guerrero profile. The dots with vertical error bars are heat flow data reported byZiagoset al. (1985). (A) Surface heat flow for steady-state thermal models reference viscositiesη0 = 1017–1021 Pa s andEa = 300 kJ/mol. (B) Surfaceheat flow for steady-state thermal models activation energiesEa = 150–350 kJ/mol andη0 = 1020 Pa s.

ditions are:(−P + 2η

∂u

∂x

)�nx + η

(∂u

∂y+ ∂v

∂x

)�ny = GB1,

η

(∂u

∂y+ ∂v

∂x

)�nx +

(−P + 2η

∂v

∂y

)�ny = GB2 (3)

which are obtained by balancing the internal (stress-induced) forces against the external boundary forces,called tractions (GB1 and GB2). Therefore, beneathMoho, where there is no “external” force applied,GB1 = GB2 = 0.

At the intersection between the subducted slab andthe right boundary, the velocity of the subducting slabis used.

The left seaward boundary condition is a one-dimensional geotherm calculated for the oceanic plateby allowing a half-space to cool from zero age tothe oceanic plate age at the trench. This geotherm isobtained using a time-dependent sedimentation his-

tory (Wang and Davis, 1992) and assuming a constantporosity–depth profile of the sediment column with auniform sediment thickness of 200 m (Moore et al.,1982) at the trench (Fig. 4). The sedimentation historyand the porosity–depth profile are used only to calcu-late the oceanic geotherm and are not included in themodeling procedure.

In terms of displacements, the velocity of theoceanic plate is considered with reference to the conti-nental plate. Thus the convergence rate of 5.5 cm/yearbetween the Cocos and North American plates is usedfor the Guerrero subduction zone (DeMets et al., 1994).The velocities in the subducting Cocos slab are setof 5.5 cm/year; therefore the interface with the mantlewedge is predefined. The boundary between the mantlewedge and overlying lithosphere is considered fixed.

The Cocos plate age at the trench is 13.7 Ma ac-cording to the interpretation of Pacific-Cocos seafloorspreading magnetic anomaly lineations (Klitgord andMammerickx, 1982; Kostoglodov and Bandy, 1995).


Fig. 6. Steady-state thermal models with strong temperature-dependent viscosity in the mantle wedge. The reference viscosity,η0, varies from1017 Pa s (A) up to 1021 Pa s (E). The activation energy for olivine of 300 kJ/mol is used. Note an important increase of the temperature closeto the tip of the wedge (A–D). NP and P represent the Nevado de Toluca and Popocatepetl volcanoes. The maximum temperature beneath thePopocatepetl volcano is about of 1230◦C. Other notations are the same as inFig. 5.

The forearc thermal model constraints are describedin detail by Manea et al. (2004). The present studyis focusing mostly on the mantle wedge thermal andvelocity structure.

Based on the velocity field obtained in the case oftemperature-dependent viscosity, a dynamic model forthe blob tracers is developed using Stokes flow at in-finite Prandtl number (Turcotte and Schubert, 1982).The blob moves under the action of drag, mass andbuoyancy forces in the mantle wedge stationary ve-locity field generated in the previous model(1). Toinvestigate the mere dynamic effect of the mantlewedge convection on the hypothetical blobs rising fromthe subducted plate up to the base of the continen-

tal lithosphere, the following main assumptions aredone:

1. The motion of the asthenosphere is described by theabove 2D Stokes equations(1);

2. The blobs are spherical and the drag force isassumed to be similar to that of non-deformingspheres;

3. The velocity field is steady state and the liquid ac-celeration is negligible because the related forceshave small magnitude compared to the steady dragforce;

4. The influence of the blob motion on themantle wedge circulation is irrelevant and


there is not interaction between individualblobs.

According to these assumptions the total force act-ing on the blob is

�F = �Fg + �FA + �FD (4)

where

�F = 4πr3

3ρb · d�vb

dt(resultant force)

�Fg = 4

3πr3ρb�g (gravitational force)

�FA = −4

3πr3ρa�g (buoyancy force)

�FD = 1

2πr2ρaCD(Re)(�va − �vb)|�va − �vb|

(steady drag force)

CD(Re) = 24

Re

Re = 2r|�va − �vb|ηw/ρa

(Reynolds number)

Here �vb is the blob velocity,�va the mantle wedgevelocity, r the blob radius (0.1–5.0 km),ρb the blobdensity (3000 kg/m3), ρa the mantle wedge den-sity (3200 kg/m3), �g the gravitational acceleration( y(

f theb

T asa woe city.T

be-t nda tst TFr theb tepso red

with the result when one step of size DT is taken. Ifthe maximum difference between the two answers isless than the relative tolerance (0.001), the time stepDT is accepted. Then, the next step DT is doubled, ifthe agreement is “too” good; otherwise DT is halvedand the process is repeated. As the tolerance is de-creased, the global error decreases correspondingly.The Crank–Nicolson scheme is used to discretize thetime. The steady mantle wedge velocity (�va) field isobtained previously, for the model with temperature-dependent viscosity(1).

The trajectories of blobs with the diameters varyingbetween 0.2 and 10.0 km are calculated for differentvalues ofηw. The total rise times that the blobs requireto reach the base of the continental crust are also esti-mated.

3. Modeling results

The thermal models, which correspond to the isovis-cous mantle wedge and to the temperature-dependentviscosity, are presented inFigs. 5, 7 and 8. The iso-viscous mantle wedge model predicts temperatures of∼830◦C in the asthenosphere (Fig. 5), beneath thePopocatepetl volcano, indicating that melting shouldnot occur at least for dry olivine. The geotherm ofthe oceanic plate surface does not intersect the solidusfor basalt (Fig. 9A), suggesting that the oceanic platedoes not suffer melting as well. The temperature att hingv em n-t rel-a lem cre-a theC

beeni log-i )s atedf turesa her elf rep -s

9.81 m/s2) and ηw the blob’s wrapping viscositPa s).

Using the expressions for forces, the equation olob motion has the following form:

d�vb

dt= �g − ρa

ρb�g + 3ρaCD(Re)

8rρb(�va − �vb)|�va − �vb| (5)

he equations of the blob motion can be writtensystem of four ordinary differential equations: t

quations for the coordinates and two for the velohen the system is solved using PDE2D.

The time step size will be chosen adaptively,ween an upper limit of DTMAX = TF/NSTEPS a

lower limit of 0.0001DTMAX. NSTEPS represenhe minimum number of steps (NSTEPS = 5) andepresents the time necessary for a blob to touchase of the continental crust. Each time step, two sf size DT/2 are taken, and that solution is compa

he base of the continental crust is also low, reacalues of∼800◦C, which is not sufficient to producelting. The backflow velocity field from the ma

le wedge (the inflow into the mantle wedge) istively small,∼1.5 cm/year. It is evident that simpodel with the isoviscous mantle wedge cannotte any source of the volcanic material beneathMVB.The temperature-dependent viscosity case has

nvestigated for a systematic variation of the rheocal parametersη0 andEa. Hirth and Kohlstedt (2003howed that the viscosities experimentally estimor olivine at upper mantle pressures and temperare in the range of 1017–1021 Pa s. Consequently, teference viscosity,η0, has been varied in our modrom 1017 up to 1021 Pa s. The modeling results aresented inFig. 7. The activation energy for diffuion creep in olivine is fixed at 300 kJ/mol (Karato


Fig. 7. Steady-state thermal models with strong temperature-dependent viscosity in the mantle wedge for activation energies,Ea, from 150 kJ/mol(A) to 350 kJ/mol (E). The reference viscosity of 1020 Pa s is used. The maximum temperature beneath the Popocatepetl volcano is about of∼1250◦C (A–D) and more than 1300◦C (E). Other notations are the same as inFig. 5.

and Wu, 1993). For the viscosity,η0, in the rangefrom 1017 to 1020 Pa s, only a small increase of tem-perature (<15◦C) is observed beneath Popocatepetl(Fig. 10). The maximum temperature underneath thePopocatepetl is around 1260◦C. On the other hand,for the reference viscosity ofη0 = 1021 Pa s, a signif-icant decrease of temperature (∼200◦C) occurs. Forthis case a maximum temperature below Popocatepetlis ∼1170◦C. The viscosity distributions in the man-tle wedge forη0 = (1017–1021 Pa s) are presented inFig. 11.

Experimentally obtained values of the activation en-ergy for diffusion creep in olivine are of 300 kJ/mol

(Karato and Wu, 1993) and of 315 kJ/mol (Hirth andKohlstedt, 1995). The thermal models with variableactivation energy from 150 up to 350 kJ/mol are pre-sented inFig. 8. Since the variation of the referenceviscosity has a little effect on the overall thermal dis-tribution (except forη0 =1021 Pa s), the modeling isdone for constantη0 = 1020 Pa s. Increase of the acti-vation energy from 150 up to 300 kJ/mol results in arelatively small increase of temperature (<25◦C). Forhigher activation energies (∼350 kJ/mol) an importantincrease in temperature (up to 70◦C) is observed, andthe maximum temperature below the Popocatepetl vol-cano reaches∼1330◦C (Fig. 12). The mantle wedge


Fig. 8. (A) Phase diagrams for the MORB (Hacker et al., 2003). 1 – zeolite (4.6 wt.% H2O), 2 – prehnite–pumpellyite (4.5 wt.% H2O), 3– pumpellyite–actinolite (4.4 wt.%H2O), 4 – greenschist (3.3 wt.% H2O), 5 – lawsonite–blueschist (5.4 wt.% H2O), 6 – epidote–blueschist(3.1 wt.% H2O), 7 – epidote–amphibolite (2.1 wt.% H2O), 8 – jadeite–epidote–blueschist (3.1 wt.% H2O), 9 – eclogite–amphibole(2.4 wt.% H2O), 10 – amphibolite (1.3 wt.% H2O), 11 – garnet–amphibolite (1.2 wt.% H2O), 12 – granulite (0.5 wt.% H2O), 13 –garnet–granulite (0.0 wt.% H2O), 14 – jadeite–lawsonite–blueschist (5.4 wt.% H2O), 15 – lawsonite–amphibole–eclogite (3.0 wt.% H2O), 16 –jadeite–lawsonite–talc–schist, 17 – zoisite–amphibole–eclogite (0.7 wt.% H2O), 18 – amphibole–eclogite (0.6 wt.% H2O), 19 – zoisite–eclogite(0.3 wt.% H2O), 20 – eclogite (0.1 wt.% H2O), 21 – coesite–eclogite (0.1 wt.% H2O), 22 – diamond–eclogite (0.1 wt.% H2O). Slab surfacegeotherms are calculated for the reference viscosity range: 1017–1021 Pa s (see inset). (B) Phase diagram for harzburgite (Hacker et al., 2003).A – serpentine–chlorite–brucite (14.6 wt.% H2O), B – serpentine–chlorite–phase A (12 wt.% H2O), C – serpentine–chlorite–dunite (6.2 wt.%H2O), D – chlorite–harzburgite (1.4 wt.% H2O), E – talc–chlorite–dunite (1.7 wt.% H2O), F – anthigorite–chlorite–dunite (1.7 wt.% H2O), G –spinel–harzburgite (0.0 wt.% H2O), H – garnet–harzburgite (0.0 wt.% H2O). Calculated geotherms for the slab surface are the same as in (A).The vertical temperature profile beneath the Popocatepetl volcano are the same as inFig. 10. The amount of serpentine (greenish-yellow hatchedinsets) in the tip of the mantle wedge is noticeably smaller for the model with temperature-dependent viscosity (upper left inset) than for themodel with the isoviscous mantle wedge (upper right inset).

viscosity distributions forEa = 150–350 kJ/mol are pre-sented inFig. 13.

The geotherms along the slab surface are pre-sented in the phase diagram for mafics and harzburgite(Hacker et al., 2003) for a variable reference viscosity,η0, in Fig. 9, and for variable activation energy,Ea, inFig. 14. The slab geotherm intersects the dehydrationmelting solidus for basalt at 50–60 km for the refer-ence viscositiesη0 = 1017–1020 Pa s and the activationenergyEa = 150–300 kJ/mol (Figs. 9A and 14A).

The effect of the mantle wedge flow on the blob’strajectory is an interesting aspect of the volcanicmagma source problem. We selected an initial pointfor the blob trajectories at the depth of 70 km on thesurface of the subducted slab. This initial point cor-

responds to the geometric vertical projection of thePopocatepetl volcano on the subducting Cocos plate.Estimated blob trajectories are presented inFig. 15fordifferent wrapping viscosities (1014–5× 1017 Pa s) andblob diameters (0.2–10.0 km).

For a wide range of activation energies(150–350 kJ/mol) and reference viscosities(1017–1020 Pa s), the blob trajectories and risingtimes are practically indistinguishable (Fig. 16). Onlyfor the reference viscosity of 1021 Pa s, an∼1 Maincrease in rising time is obtained due to lowervelocities in the mantle wedge. A very low wrappingviscosity is essential to let the blob to rise up to thecontinental crust. Such low viscosity could resultfrom the lubricating wrap around the blob. The source


Fig. 9. The results of benchmark test with different grid resolutions: 4000, 6000, 8000, 10,000 and 12,000 triangles. The temperature differencesbetween two subsequent models are calculated along the slab–wedge interface. Note the temperature fluctuation up to 22◦C for low gridresolution (blue curve). Less than 5◦C numerical error results when the grid with 12,000 triangles is used (red curve).

of the wrapping is apparently the melted materialcoming from the subducting slab, including the meltedsubducted sediments. Indeed, the water-saturatedsediments are likely to melt at a depths of 50–58 kmfor η0 = 1017–1021 Pa s (Fig. 17A), and of 45–50 kmfor Ea = 150–350 kJ/mol (Fig. 17B).

For the blobs of 2 km size (Fig. 15C) and the wrap-ping viscosity,ηw > 2× 1016 Pa s, the drag force is pre-dominant and the blob cannot rise. Decreasing the vis-cosity the drag force is less significant and at the depthof ∼110 km the blob intercepts the mantle wedge back

flow, which returns it toward the tip of the wedge. Fi-nally the blob rises up and touches the continental crustafter ∼8 Ma. For the lower viscosity (<9× 1015 Pa s)the blobs are rising faster (Fig. 16) and pop up at ap-proximately the same point below the Popocatepetlvolcano (∼350 km from the trench). The larger theblob’s size, the less time is necessary to reach thecontinental crust. Any blob of the size >0.6 km willtouch the bottom of the continental crust in less then4 Ma when the wrapping viscosity is of 1× 1015 Pa s(Fig. 15A). For the blob with the diameter of∼2 km,

Fig. 10. Vertical temperature profile (A–A′) for the mantle wedge thermal models with the reference viscosities of 1017–1021 Pa s. The activationenergy is fixed at 300 kJ/mol. The temperature profile for the model with the isoviscous mantle is also shown as a dashed line.


Fig. 11. Distribution of the mantle wedge viscosity for steady-state thermal (Fig. 5) models with strong temperature-dependent viscosity. Thereference viscosity,η0, is from 1017 Pa s (A) up to 1021 Pa s (E).

Fig. 12. Vertical temperature profile (A–A′) through the mantle wedge. The thermal modeling is done for activation energies of 150–350 kJ/mol.The reference viscosity is fixed at 1020 Pa s. Dashed line shows, for a comparison, the temperature profile for the model with the isoviscousmantle wedge.


Fig. 13. Distribution of mantle wedge viscosity with strong temperature dependence for steady-state thermal models (Fig. 12). Activationenergies,Ea, are from 150 up to 350 kJ/mol.

∼1 Ma is necessary to pop up if theηw < 3× 1015 Pa s.The buoyancy force of large size blobs becomes moredominant than the drag force and this yields a sub-stantially upright trajectory. A 10 km blob touches theMoho in almost the same location forηw < 1017 Pa s(Fig. 15B). On the other hand, 10 km blobs with theηw >5× 1017 Pa s would never rise up to the continen-tal crust (Fig. 15D). For aηw fixed at 1017 Pa s, blobswith diameters grater than 4 km will be able to tra-verse the mantle wedge flow and to go up toward thesurface.

4. Discussion and conclusions

Numerical models of temperature and velocity fieldsin the mantle wedge can contribute to our understand-ing of the magma generation, dynamics and volcanicsources in very atypical subduction zone of CentralMexico. In particular, the models, allowing for the as-cending of buoyant material melted from the subductedslab and mantle in the form of plumes or blobs, can re-veal the mechanisms of magma transport to the bottomof the continental plate.


Fig. 14. (A) Phase diagrams for the MORB and maximum H2O contents (Hacker et al., 2003). Modeled slab surface geotherms are plotted forthe activation energy range: 150–350 kJ/mol (see inset). The other notations are the same as inFig. 9. (B) Phase diagram for harzburgite, andmaximum H2O contents (Hacker et al., 2003). The calculated geotherms are the same as in (A), as well as those from the vertical profile beneathPopocatepetl (seeFig. 13). The amount of serpentine (greenish-yellow hatch upper insets) in the tip of the wedge decreases as the activationenergy increases.

Two basic thermo-mechanical models for the man-tle wedge in the Central Mexico are considered inthis study. The first model is restricted with the iso-viscous mantle wedge whereas the second one is ad-vanced with the temperature-dependent mantle viscos-ity. The first model (Fig. 5) does not predict any meltingconditions in the asthenosphere, beneath the CMVB,at the base of the continental crust and on the sur-face of the subducting slab. The slab surface geothermintersect neither the dehydration melting solidus forbasalt (Fig. 9A) nor the solidus for H2O-saturated sed-iments (Fig. 17A). The vertical temperature profile justbeneath the Popocatepetl volcano through the mantlewedge does not encounter the wet peridotite solidus(Fig. 9B), thus the melting of the hydrated peridotiteshould not occur.

The temperature and velocity fields in the secondmodel depend on the rheological parameters, the refer-ence viscosity,η0, and the activation energy,Ea. Varia-tion of the reference viscosity,η0, from 1017to 1020 Pa scauses a slight temperature increase (<15◦C) close tothe tip of the wedge (Fig. 10). Increasing the refer-ence viscosity up toη0 = 1021 Pa s provokes a signifi-

cant drop of the tip temperature of about 200◦C. Thephase diagram for mafic minerals shows (Fig. 9A) thatthe melting of basaltic oceanic crust might take placeat the depths of∼58 km forη0 = 1017–1020 Pa s), andat∼80 km forη0 = 1021 Pa s. The water-saturated sed-iments start to melt at shallower depths, between 50and 55 km (Fig. 17A). The vertical temperature profilebeneath the Popocatepetl volcano achieves the temper-ature which is high enough to melt the wet peridotite(Fig. 9B).

The thermal models show that basalt meltinginitiates at ∼60 km depth for the activation en-ergy,Ea = 150–300 kJ/mol, and at∼50 km depth forEa = 350 kJ/mol (Fig. 14A). In the range of referenceviscosity values (1017–1021 Pa s), the saturated sedi-ments may melt at the depth between 45 and 50 km(Fig. 14B). The temperature below the Popocatepetlvolcano is well beyond the wet peridotite solidus forthe whole range of activation energies applied in thisstudy (150–350 kJ/mol).

The modeling results ascertain that the melting ofthe oceanic crust is likely to occur in a narrow depthrange of 50–60 km (except for a reference viscosity of


Fig. 15. Blob trajectories in the steady mantle wedge flow. Initial points for all trajectories are selected on the surface of the slab, right belowthe Popocatepetl volcano at 70 km depth. (A) The wrapping viscosity is fixed at 1015 Pa s. The blobs with the diameter less than 0.4 wouldnever rise up to the continental crust. (B) The blob diameter is fixed at 10 km. The trajectories corresponding to different wrapping viscosities ofless than 1017 Pa s have the same final point below the Popocatepetl volcano. The blobs would never rise up to the continental crust if with thewrapping viscosities is >5× 1017 Pa s. (C) The blob’s diameter is fixed at 2 km. The trajectories corresponding to different wrapping viscositiesof less than 9× 1015 Pa s, have the same final point below the Popocatepetl volcano. The blobs with the wrapping viscosities >2× 1016 Pa swould never rise up to the continental crust. (D) The wrapping viscosity is fixed at 1017 Pa s. The trajectories correspond to different blob size(4–10 km). The blobs with the diameter less than 4 km would never rise up to the continental crust.


Fig. 16. Blob rising time as a function of the wrapping viscosity. For a wide range of rheological parameters (η0 = 1017–1020 Pa s andEa = 150–350 kJ/mol) the blob trajectories and rising times are nearly identical (blue curves). For the reference viscosity of 1021 Pa s, therising time becomes longer after∼1 My, for a given wrapping viscosity (dashed green curves). The curves annotated with the blob’s diametershow that the rising time is decreasing for the bigger blobs and the lower viscosity. The blobs with the size of∼2 km can reach the continentalcrust in less than 1 Ma (black dashed line) at a wide range of low wrapping viscosities.

1021 Pa s which predicts the melting at∼80 km depth).The subducted sediments begin to melt at shallowerdepths of 45–55 km for the entire range ofη0 andEa.

As the oceanic crust melting starts, at first, thedacitic–rhyolitic magma is formed; afterward as it as-

cends and interacts with the mantle wedge, the adakiticmagma might be formed. The oceanic slab contributionto the volcanism in Eastern Mexican Volcanic Belt hasbeen reported byGomez-Tuena et al. (2003). Magmaticrocks with the adakitical signature have been found

Fig. 17. (A) Calculated slab surface geotherms for models with reference viscosities in the range of 1017–1021 Pa s (see inset), and fluid-saturatedsediment solidus from (Nichols et al., 1994). The horizontal dashed arrows mark the depths where the sediment meting might occur. Dashed linerepresents the geotherm for the isoviscous mantle. (B) Calculated slab surface geotherms for models with activation energy range: 150–350 kJ/mol(see inset) and fluid-saturated sediment solidus fromNichols et al. (1994). The horizontal dashed arrows mark the depths where sediment metingmight occur.


recently in the quaternary series in CMVB. The stra-tovolcano Nevado de Toluca shows evidences of thesame adakitic mark as well (Gomez-Tuena, personalcommunication).

The temperature of the hydrated peridotite belowthe CMVB is beyond wet peridotite solidus, but it isstill lower the dry solidus. This suggests that the hy-dration of the mantle wedge by fluids released fromthe subducted Cocos plate is a necessary condition forthe partial melting of the mantle. Indeed, the meta-morphic dehydration predicted by our thermal mod-els might occur down to 80 km depth. The estimatedvariation of wt.% H2O content with the depth alongthe subducting plate is presented inFig. 9A (inset). Bythe transformation of zoisite and amphibole into eclog-ite, ∼0.6 wt.% H2O may be released into the mantlewedge from the hydrous phases in the subducting slabthrough a dehydration at the depths between 40 and60 km.

Mantle xenolites (oxidized peridotite) have beenfound in Mexico near El Penon (Fig. 1), suggestingan important flux of volatiles from the subducting Co-cos slab (Blatter and Carmichael, 1998). This dehydra-tion would drop down the mantle viscosity in the tipof the wedge. This effect is not included in the presentthermal models. The amount of serpentine in the tipof the wedge is much smaller for the model with tem-perature dependent viscosity (Fig. 9B, upper left inset)than for the model with the isoviscous mantle wedge(Fig. 9B, upper right inset). Furthermore, the amount ofs ease( them imito ex-te

se-r ousr ter-i oc-c tion,w offl hem gersp slab( -j tedb

originally might represent low degrees of partial melt-ing in the mantle wedge. In fact, the wet solidus condi-tions for peridotite (Wyllie, 1979) are developed closeto the slab surface (seeFig. 8A).

Felsic magma formations were found in the mono-genetic volcanic field of Chichinautzin (Marquez andDe Ignatio, 2002). The models with the temperature-dependent viscosity show that at the base of thecontinental crust, the temperature exceeds 1100◦C(Figs. 7 and 8). That may create felsic magma sources inSierra Chichinautzin by partial melting of the basalticlower crust under low water fugacity conditions.

Recent paper ofGerya and Yuen (2003)demon-strates that Rayleigh–Taylor instabilities can developand rise up from the surface of the cold subductingslab. They also suggest that the plumes detached fromthe slab might be lubricated by partially melted, lowviscosity material of the subducted crust and hydratedmantle.

The modeling of the blob motion in the mantlewedge viscous flow induced by the subducting slabshows that this simple approach may help to under-stand the origin of the volcanism in the CMVB. Theplume-like blobs might origin at the slab–mantle wedgeinterface as a consequence of the thermal instability. Itappears that the detachment area along the subductedslab from which the blobs might emerge is not verylarge. Within the wide range of values of the rheologi-cal parameters, the sediment and oceanic crust melting,and metamorphic dehydration is expected to occur int

nec-e d tof mentp cteds ure,P pa-t them latei foret ati-b po-s Thep om-p e,m

lobs blob

erpentine decreases as the activation energy incrFig. 14B, upper insets). The serpentinized tip ofantle wedge may have bearing on the down dip lf the forarc coupled plate interface that controls an

ension of aseismic slow slip transients (Kostoglodovt al., 2003; Manea et al., 2004).

The calcalkaline rocks are the most commonies in the CMVB. This series includes the igneocks from basalts up to rhyolites, and is characzed by depletion of Fe. The depletion probablyurs because of the Fe and Ti oxides crystallizahich initially might be facilitated by the presenceuids in the magma. The influx of volatiles from tetamorphosed oceanic crust and sediments trigartial melting of peridotite above the subductedTatsumi, 1986; Davies and Stevenson, 1992). The maority of the calcalkalines in the CMVB is represeny the rocks with high content of K2O and Na2O, which

she present models at depths of 45–60 km.A certain distance along the slab surface is

ssary for the melted material to accumulate anorm the blob. Nevertheless, the same blob detachoint in the present model is selected on the subdulab surface, just below the main volcanic structopocatepetl volcano (70 km depth). In reality, the s

ial (and temporal) variation of the composition ofaterial transferred from the subducted Cocos p

nto the overlying mantle wedge is expected. Therehe volcanic arc lavas may be enriched with incomple elements and volatiles, and highly variable comition of the subducted-related lavas is probable.roposed positively buoyant blobs might have a clex composition of melted H2O-saturated peridotitelted sediments and oceanic crust.Two parameters control the trajectories of the b

tructures rising from the slab: the diameter of the


and the wrapping viscosity. Very low values of thewrapping viscosity (1014–5× 1017 Pa s) are necessaryto reduce the drag force, which is critical for the blob topop up. The lowest dynamic viscosity reported for drymantle is∼1017 Pa s (Moore et al., 1998). On the otherhand, the viscosity of hydrated, partially molten blobsmight be as low as 1014 Pa s (Gerya and Yuen, 2003).Since the viscosity of the surrounding dry mantle con-trols the propagation of the blob, a certain mechanismis responsible for the occurrence of the low wrappingviscosity.

As the blob ascents through the mantle wedge,porous flow (Davies and Stevenson, 1992) of the meltand fluid might penetrate the mantle around the blob,dropping there the viscosity down to 1014 Pa s. The rateof this penetration by porous flow has to be at least thesame as the ascending rate of the blob. Recent labo-ratory experiments byHall and Kincaid (2001)showthat the positively buoyant blobs might pass throughthe low-viscosity, low-density paths created by pre-vious blobs. The mechanism that produces the lowwrapping viscosities may be a combination of theporous flow and a low viscosity conduit left by previousblobs.

Since the rigid sphere approximation is used to es-timate the drag force applied to weak partially moltenblobs, the estimates of wrapping viscosity in the presentstudy should be considered as rather approximate. Theblobs of 10 km diameter reach the base of the con-tinental crust in∼6 Ma when the wrapping viscosityi int ,1 d int allyt vis-cf cos-i int

e-t en-t vis-c y.I arlya cos-i s-i lee no-

ticed for the higher values of the reference viscosity(1021 Pa s) when the raising time is more than∼2 Ma(Fig. 16).

The blob tracing dynamic model in the mantlewedge velocity field shows that the “fast” trajectoriesend at the same focus location (below the Popocatepetlvolcano,∼350 km from trench) on the base of thecontinental crust (Fig. 15). This result may be inter-preted as a possible condition for the development ofthe stratovolcanoes. The ending points of “slow” tra-jectories, which are common for the blobs of smallersize (∼0.4–0.6 km), are scattered from the focus loca-tion (Fig. 15A). This observation may give us a hint ona possible mechanism of monovogenic volcanism.

Recent studies (Lucia Capra, personal communi-cation) revealed at least two magmatic pulses with atime span of∼1 Ma on the stratovolcano Nevado deToluca. The maximum volume of each of these mag-matic events is of 3.5 km3 (equivalent blob diameteris of ∼2 km). It is interesting that both pulses startedwith a magmatic signature of melted sediments (Csanomaly). These new studies will provide importantconstrains on the blob size, rising time and the blobcomposition. From our model (Fig. 15), a blob of 2 kmin diameter reaches the base of the continental crust in1 Ma, if the wrapping viscosity is of∼2× 1015 Pa s.The low viscosity is essential for the smaller size blobsto rise to the base of the continental crust.

The average volume of a monogenic cinder conein the CMVB is less than 1 km3 (Hasenaka, 1994),wo blobt beo s.W re-l theo theC

A

ives andP ovet NA-C antI

s of ∼3× 1017 Pa s. Since this viscosity value ishe lower range reported for dry mantle (Moore et al.998), no wrapping viscosity mechanism is neede

his case. The blobs of such big size can affect loche mantle wedge flow pattern and the effectiveosity distribution (Gerya and Yuen, 2003), especiallyor the temperature- and strain-rate-dependent visty (Ranalli, 1995). These effects are not includedhe present models.

The time required for the blob of 1 km diamer to rise from the slab surface up to the continal crust varies between 0.001 and 14 Ma for theosity between 1014 and 5× 1017 Pa s, respectiveln general, the blob rising time decreases nonlines its diameter increases and the wrapping vis

ty is diminishing (Fig. 16). The reference viscoty, η0, in the range up to 1020 Pa s, has a negligibffect on the blob trajectory. The effect can be

hich corresponds to blob diameters of∼1.3 km. If therigin of monogenic cones are described by the

racing model, then the wrapping viscosity shouldf η > 5× 1015 Pa s to produce the “slow” trajectoriee need further model enhancement to verify the

ation between the blob (or plume) hypothesis andrigin of the strato and monogenic volcanism inMVB.

cknowledgments

Very helpful critical comments and constructuggestions by Jeroen van Hunen, Taras Geryaeter van Keken were very important to impr

he manuscript. This study was supported by COYT grants G25842-T, 37293-T, and PAPIIT gr

N104801.


References

Alaniz-Alvarez, S.A., Nieto-Santiago, A.F., Tolson, G., 1998. Agraphical technique to predict slip along a preexisting plane ofweakness. Eng. Geol. 49, 53–60.

Arzate, J.A., Mareschal, M., Urrutia-Fucugauchi, J., 1993. A prelim-inary crustal model of the Oaxaca continental margin and sub-duction zone from magnetotelluric and gravity measurements.Geofis. Int. 32, 441–445.

Blatter, D.L., Carmichael, I.S.E., 1998. Hornblende peridotite xeno-liths from central Mexico reveal the highly oxidized nature ofsubarc upper mantle. Geology 26 (11), 1035–1038.

Burov, E., Jolivet, E., Le Pourhiet, L., Poliakov, A., 2000. A ther-momechanical model of exhumation of high pressure (HP) andultra-high pressure (UHP) metamorphic rocks in Alpine-type col-lision belts. Tectonophysics 342, 113–136.

Byerlee, J.D., 1978. Friction of rocks. Pure Appl. Geophys. 116,615–626.

Cebull, S.E., Schubert, D.H., 1987. Mexican Volcanic Belt—an in-traplate transform. Geofis. Int. 26, 1–13.

Conder, J.A., Weins, D.A., Morris, J., 2002. On the decompressionmelting structure at volcanic arcs and back-arc spreading centers.Geophys. Res. Lett. 29, 17.1–17.4.

Currie, C.A., Hyndman, R.D., Wang, K., Kostoglodov, V., 2002.Thermal models of the Mexico subduction zone: implications forthe megathrust seismogenic zone. J. Geophys. Res. 107 (B12),2370, doi: 10.1029/2001JB000886.

Davies, J.H., Stevenson, D.J., 1992. Physical model of source regionof subduction zone volcanism. J. Geophys. Res. 97, 2037–2070.

DeMets, C., Gordon, R., Argus, D., Stein, S., 1994. Effect of recentrevisions to the geomagnetic reversal time scale on estimates ofcurrent plate motions. Geophys. Res. Lett. 21, 2191–2194.

Fedotov, S.A., 1981. Magma rates in feeding conduits of differentvolcanic centers. J. Volcan. Geotherm. Res. 9, 379–394.

Ferrari, L., Garduno, V., Innocenti, F., Manetti, P., Pasquere,co:

F onicsn its

F for-09–

G omnes.

G .O.,mag-ntleubed

G citypir-

87.H ctory

, and27.

Hall, P., Kincaid, C., 2001. Diapiric flow at subduction zones: a recipefor rapid transport. Science 292, 2472–2475.

Hasenaka, B.R., 1994. Size, distribution, and magma output rate forshield volcanoes of the Michoacan-Guanajuato volcanic field,central Mexico. J. Volcan. Geotherm. Res. 63, 13–31.

Hirth, G., Kohlstedt, D.L., 1995. Experimental constraints on thedynamics of the partially molten upper mantle: deformationin the diffusion creep regime. J. Geophys. Res. 100, 1981–2001.

Hirth, G., Kohlstedt, D.L., 2003. Rheology of the mantle wedge.In: Eiler, J. (Ed.), Inside the Subduction Factory, GeophysicalMonograph 138. AGU, Washington DC, pp. 83–105.

Karato, S., Wu, P., 1993. Rheology of the upper mantle: a synthesis.Science 260, 771–778.

Kelemen, P.B., Rilling, J.L., Parmentier, E.M., Mehl, L., Hacker,B.R., 2003. Thermal structure due to solid-state flow in the man-tle wedge beneath arcs. In: Eiler, J. (Ed.), Inside the Subduc-tion Factory. Geophysical Monograph 138. Am. Geophys. Union,Washington, DC, pp. 293–311.

Klein, E.M., Langmuir, C.H., 1987. Global correlations of oceanridge basalt chemistry with axial depth and crustal thickness. J.Geophys. Res. 92, 8089–8115.

Klitgord, K., Mammerickx, J., 1982. Northern East Pacific Rise:magnetic anomaly and bathymetric framework. J. Geophys. Res.87, 6725–6750.

Kostoglodov, V., Bandy, W., 1995. Seismotectonic constraints on theconvergence rate between the Rivera and North American plates.J. Geophys. Res. 100, 17977–17989.

Kostoglodov, V., Bandy, W., Domınguez, J., Mena, M., 1996. Gravityand seismicity over the Guerrero seismic gap, Mexico. Geophys.Res. Lett. 23, 3385–3388.

Kostoglodov, V., Singh, S.K., Santiago, J.A., Franco, S.I., Larson,K.M., Lowry, A.R., Bilham, R., 2003. A large silent earthquakein the Guerrero seismic gap, Mexico. Geophys. Res. Lett. 30 (15),1807.

L em-nera-man,n atsical

L vol-eral

M ll oflies.

M G.,the

t. 58,

M kalicelt:rifting

M playin

G., Vaggeli, G., 1994. Volcanic evolution of central MexiOligocene to present. Geofis. Int. 33, 91–105.

errari, L., Pasquare, G., Tybaldi, A., 1990. Plio-quaternary tecton the central Mexican Volcanic Belt and some constraints orifting mode. Geofis. Int. 29, 5–18.

urukawa, F., 1993. Magmatic processes under arcs andmation of the volcanic front. J. Geophys. Res. 98, 838319.

erya, T.V., Yuen, D.A., 2003. Rayleigh–Taylor instabilities frhydration and melting propel ‘cold plumes’ at subduction zoEarth Planet. Sci. Lett. 212, 47–62.

omez-Tuena, A., LaGatta, A.B., Langmuir, C.H., Gutierrez, FCarrasco-Nunez, G., 2003. Temporal control of subductionmatism in the eastern Trans-Mexican Volcanic Belt: masources, slab contributions, and crustal contamination. G-c4 (8).

orbatov, A., Kostoglodov, V., 1997. Maximum depth of seismiand thermal parameter of the subducting slab: worldwide emical relation and its application. Tectonophysics 227, 165–1

acker, B.R., Abers, G.A., Peacock, S.M., 2003. Subduction fa1. Theoretical mineralogy, densities, seismic wave speedsH2O contents. J. Geophys. Res. 108. 10.1029/2001JB0011

angmuir, C.L., Klein, E.M., Plank, T., 1992. Petrological systatics of mid-ocean ridge basalts: constraints on melt getion beneath ocean ridges. In: Phipps Morgan, J., BlackD.K., Sinton, J.M. (Eds.), Mantle Flow and Melt GeneratioMid-Ocean Ridges. AGU Monograph 71. American GeophyUnion, Washington, DC, pp. 183–280.

uhr, J.F., 1997. Extensional tectonics and the diverse primitivecanic rocks in the western Mexican Volcanic Belt. Can. Min35, 473–500.

anea, M., Manea, V.C., Kostoglodov, V., 2003. Sediment fithe Middle America trench inferred from the gravity anomaGeofis. Int. 42 (4), 603–612.

anea, V.C., Manea, M., Kostoglodov, V., Currie, C., Sewell,2004. Thermal structure, coupling and metamorphism inMexican subduction zone beneath Guerrero. Geophys. J. In775–784.

arquez, A., Oyarzun, R., Doblas, M., Verma, S.P., 1999a. Al(OIB-type) and calc-alkalic volcanism in Mexican volcanic ba case study of plume-related magmatism and propagatingat an active margine? Geology 27, 51–54.

arquez, A., Oyarzun, R., Doblas, M., Verma, S.P., 1999b. Reto comment to: alkalic (OIB-type) and calc-alkalic volcanism


Mexican volcanic belt: a case study of plume-related magma-tism and propagating rifting at an active margine? Geology 27,1055–1056.

Marquez, A., Verma, S.P., Anguita, F., Oyarzun, R., Brandle,J.L., 1999c. Tectonics and volcanism of Sierra Chichinautzin:extension at the front of the central Trans-Mexican Volcanic Belt.J. Volcan. Geotherm. Res. 93, 125–150.

Marquez, A., De Ignatio, C., 2002. Mineralogical and geochemi-cal constrains for the origin and evolution of magmas in SierraChichinautzin, Central Mexican Volcanic Belt. Lithosphere 62,35–62.

Moore, J.C., Watkins, J.S., Shipley, T.H., McMillen, K.J., Bachman,S.B., Lundberg, N., 1982. Geology and tectonic evolution of ajuvenile accretionary terrane along a truncated convergent mar-gin: synthesis of results from Leg 66 of the Deep Sea DrillingProject, Southern Mexico. Geol. Soc. Am. Bull. 93, 847–861.

Moore, W.B., Schubert, G., Tackley, P.J., 1998. Three-dimensionalsimulations of plume-lithosphere interaction at the Hawaiianswell. Science 279, 1008–1011.

Nichols, G.T., Wyllie, P.J., Stern, C.R., 1994. Subduction zone melt-ing of pelagic sediments constrained by melting experiments.Nature 371, 785–788.

Pardo, M., Suarez, G., 1995. Shape of the subducted Rivera and Co-cos plates in southern Mexico: seismic and tectonic implications.J. Geophys. Res. 100, 12357–12373.

Peacock, S.M., Wang, K., 1999. Seismic consequences of warm ver-sus cool subduction metamorphism: Examples from southwestand northeast Japan. Science 286, 937–939.

Prol-Ledesma, R.M., Sugrobov, V.M., Flores, E.L., Juarez, G.,Smirnov, Y.B., Gorshkov, A.P., Bondarenko, V.G., Rashidov,V.A., Nedopekin, L.N., Gavrilov, V.A., 1989. Heat flow varia-tions along the Middle America Trench. Mar. Geophys. Res. 11,69–76.

Ranalli, G., 1995. Rheology of the Earth, 2nd ed. Chapman & Hall,London, p. 413.

S the.

S stri-hern

T by a

Takada, A., 1994. The influence of regional stress and magmaticinput on styles of monogenetic and polygenetic volcanism. J.Geophys. Res. 99, 13563–13573.

Tatsumi, Y., 1986. Formation of the volcanic front in subductionzones. Geophys. Res. Lett. 13, 717–720.

Turcotte, D.L., Schubert, G., 1982. Geodynamics, Applications ofContinuum Physics to Geological Problems. Wiley, New York.

Vacquier, V., Sclater, J.G., Corry, C.E., 1967. Studies of the thermalstate of Earth. The 21st paper: Heat-flow, eastern Pacific. Bull.Earthquake Res. Institute 45, 375–393.

Valdes, C.M., Mooney, W.D., Singh, S.K., Meyer, R.P., Lomnitz, C.,Luetgert, J.H., Helsley, C.E., Lewis, B.T.R., Mena, M., 1986.Crustal structure of Oaxaca, Mexico, form seismic refractionmeasurements. Bull. Seis. Soc. Am. 76, 547–563.

van Hunen, J., van den Berg, A., Vlaar, N., 2002. On the role ofsubducting oceanic plateaus in the development of shallow flatsubduction. Tectonophysics 352, 317–333.

van Keken, P.E., Kiefer, B., Peacock, S.M., 2002. High-resolutionmodels of subduction zones: implications for mineral dehydra-tion reactions and the transport of water into deep mantle. G-cubed 3, 10, 20.

Verma, S.P., 1999. Geochemistry of evolved magmas and their rela-tionship to subduction un-related mafic volcanism at the volcanicfront of the central Mexican Volcanic Belt. J. Volcan. Geotherm.Res. 93, 151–171.

Verma, S.P., 2000. Geochemistry of subducting Cocos plate andthe origin of subduction-unrelated mafic volcanism at volcanicfront of central Mexican Volcanic Belt. In: Delgado-Granados,H., Aquirre-Diaz, G.J., Stock, J. (Eds.), Cenozoictectonics andVolcanism of Mexico Special Paper, vol. 334, pp. 195–222.

Wallace, P., Carmichael, I.S.E., 1999. Quaternary volcanism near theValley of Mexico: implications for subduction zone magmatismand the effects of crustal thickness variations on primitive magmacompositions. Contrib. Mineral Petrol. 135, 291–314.

Wang, K., Davis, E.E., 1992. Thermal effect of marine sedimenta-70–

W eral

Z hernRes.

hubert, D.H., Cebull, S.E., 1984. Tectonic interpretation ofTrans-Mexican volcanic belt. Tectonophysics 101, 159–165

mith, D.L., Nuckels, C.E., Jones, R.L., Cook, G.A., 1979. Dibution of heat flow and radioactive heat generation in nortMexico. J. Geophys. Res. 84, 2371–2379.

akada, A., 1989. Magma transport and reservoir formationsystem of propagating cracks. Bull. Volcan. 52, 118–126.

tion in hydrothermally active areas. Geophys. J. Int. 110,78.

yllie, P.J., 1979. Magmas and volatile components. Am. Min654, 469–500.

iagos, J.P., Blackwell, D.D., Mooser, F., 1985. Heat flow in soutMexico and the thermal effects of subduction. J. Geophys.90, 5410–5420.

Documents

Thermo-mechanical model of the mantle wedge in Central ...usuarios.geofisica.unam.mx/vladimir/papers_pdf/Manea PEPI 2005.pdf · give us advance insights on the geodynamic processes