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Driving Forces: Slab Subduction and Mantle Convection

B. H. Hager

Seismological Laboratory, 252-21

Division of Geological and Planetary Sciences

California Institute of Technology

Pasadena, CA 91125

Introduction

Mantle convection is the mechanism ultimately responsible for most geological activity at

Earth's surface. To zeroth order, the lithosphere is the cold outer thermal boundary layer

of the convecting mantle. Subduction of cold dense, lithosphere provides the major source

of negative buoyancy driving mantle convection and, hence, surface tectonics (e.g.,

Forsyth and Uyeda, 1975; Richter and McKenzie, 1978; Hager and O'ConneU, 1986).

There are, however, important differences between plate tectonics and the more familiar

convecting systems observed in the laboratory. Most important, the temperature

dependence of the effective viscosity of mantle rocks makes the thermaJ boundary layer

mechanically strong, leading to nearly rigid plates. This strength stabilizes the cold

boundary layer against small amplitude perturbations and allows it to store substantial

gravitational potential energy. Paradoxically, through going faults at subduction zones

make the lithosphere there locally weak, allowing rapid convergence, unlike what is

observed in laboratory experiments using fluids with temperature dependent viscosities.

This bimodal strength distribution of the lithosphere distinguishes plate tectonics from

simple convection experiments. In addition, Earth has a buoyant, relatively weak layer (the

crust) occupying the upper part of the thermal boundary layer. Phase changes lead to extra

sources of heat and buoyancy (e.g., Schubert et al, 1975; Anderson, 1987). These

phenomena lead to the observed richness of behavior of the plate tectonic style of mantle

convection.

In this note, I summarize the current paradigms, then state my view of the key questions

that need to be addressed, as well as techniques for addressing them. This review is

inevitably biased towards the research in which I have been most heavily involved.

Empirical

State of Current Knowledge

Much of the current state of understanding of the subcluction process is based on empirical

associations. For example, plates with subducting slabs attached move faster than plates

without subducting slabs, consistent with the negative buoyancy associated with slabs

being a dominant driving force (Forsyth and Uyeda, 1975). The maximum size of

earthquakes at subduction zones is directly proportional to convergence velocity and

inversely proportional to the age, and hence negative buoyancy, of the subducting plate

(Ruff and Kanamori, 1980). The presence of back-are spreading is associated with steep

subduction of old lithosphere, while back-arc spreading is absent where the dip of the

subducting slab is shallow and where rapid convergence is occurring (e.g., Uyeda and

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Kanamori,1979).While at short wavelengths, deep sea trenches have gcoid lows over

them, at wavelengths of 4,000-10,000 kin, there is a spectacular association of geoid highs

with subduction zones (Chase, 1979; Hagen', 1984) as can be seen in Figure 1.

Long-wavelength geoid highs are also associated with hotspot provinces (e.g., Africa and

the central Pacific; Crough and Jurdy, 1980; Richards and Hager, 1988). Inversions of

lower mantle smacture using seismic tomography have revealed that these hotspot

provinces at the surface are associated with anomalously slow, presumably hot, regions in

the lower mantle, suggesting a thermal link between the surface and the deepest mantle

(Hager et al, 1985; Hager and Clayton, 1988).

Seismicity traces the location of and state of stress within subducted slabs down to the base

of the upper mantle at the 670 km discontinuity. Slabs are generally in extension above

300 km depth (e.g., Isacks and Molnar, 1971) and in down-dip compression below 300

km depth. Seismic activity is high at the surface, decreases exponentially with depth to

about 350 km depth, then increases exponentially with depth to 670 kin, where is abruptly

ceases (e.g., Vassiliou et al, 1984).

Observations

Several more specific observations seem important in understanding the dynamics of

mantle convection and subduction. The fate of subducted slabs when they reach the 670

km discontinuity is a first order question, related to the geochemical evolution of Earth.

Important observations relevant to this question include the topography and sharpness of

this discontinuity (Hager and Clayton, 1988; Hager and Richards, 1988). At present, there

is no observational evidence for any substantial topography (i.e., greater than 20 kin) on

this discontinuity. Reflection and conversion of seismic phases suggests that this boundary

is, at least locally, very sharp (e.g., Bock and Ha, 1984).

Analysis of navel time residuals from deep seismic events indicates that subducted material

extends over significantly greater volumes than have seismic activity. Long-wavelength

variations of travel time anomalies projected onto the focal spheres of deep earthquakes

have been interpreted as showing slabs extending deep into the lower mantle, often with a

kink at the 670 km discontinuity (e.g., Creager and Jordan, 1984, 1986). Local

tomographic analyses of these navel time anomalies reveal significant thickening of

subducted slabs in the transition zone, consistent with the state of stress inferred from focal

mechanisms (Zhou et al, 1987). Regional tomographie studies of the lower mantle beneath

North America reveal high velocity anomalies that have been interpreted as the fossil

remains of the Farallon Plate (Grand, 1987).

While subducted slabs are thought to have high density and provide a major source of the

body forces driving global plate motions, in two locations in South America, the subducted

slab seems to be moving subhorizontally, rather than sinking into the mantle (e.g., Isacks

and Barazangi, 1977). This subhorizontal subduetion has been proposed for North

America during the Laramide orogeny (e.g., Bird, 1988)

The state of stress in subduction zones is intimately related to the dynamic processes

occurring. Recent observations of changes in stress state associated with major

earthquakes at converging plate boundaries seem potentially important in illuminating the

absolute level of stress in these regions. Before these major events focal mechanisms show

compression updip of the events and tension downdip, while this situation seems to be

reversed afterward (Astiz and Kanamori, 1983; Dmowska and Rice, 1988; Christensen and

Ruff, 1983). Since stress drops associated with these events are 100 bars or less, this

change in sign of the apparent stress state is suggestive of a low overall stress level.

2
Local tomographic studiesof theupper mantle beneath southernCaliforniahave revealeda

curtainof high velocitymaterialextendingtoa depthof 250 km beneath theTransverse

Ranges inthe Big Bend regionof theSan Andreas fault(Figure2,afterHumphreys etal,

1984). While thereareno dccp earthquakesassociatedwith thisfeature,and hence itisnot

typicalsubduction,ithas bccn interpretedastheconvectivedownwelling of thecold,dense

base of thethermallithosphere.The basaltractionsfrom thisconvectioncellhave been

proposed as thedynamic explanationforthe maintenance of theBig Bend ffIumphreys,

1985),although kinematicmodels have alsobccn proposed toexplaintheBig Bend asthe

resultof theeffectsofrelativemotion between plates(Birdand Rosenstock, 1984).

Models

Many of theseobservationshave been interpretedquantitativelyinterms ofnumerical

models. The gcoid observations have been interpreted in terms of fluid mechanical models

that include the effects on the geoid of the mass anomalies introduced by dynamically

maintained topography (Richards and I-lager, 1984). The geoid can be explained by two

families of models (Hager and Clayton, 1988; Hager and Richards, 1988). The first

allows mantle-wide flow and requires a substantial increase in viscosity across the 670 km

discontinuity. The second class of models has a mantle which is chemically stratified; it

requires that subducted slabs have very high density and predicts many hundreds of km of

dynamically maintained topography on the 670 km discontinuity.

Fluid mechanical models of subduction zones based on the first model of mantle structm_

show a variety of features, including kinking at the 670 km discontinuity (Gumis and

Hager, 1988). Such a model is also consistent with the state of stress in subducted slabs

and the inferred advective thickening of slabs at the base of the upper mantle.

Simple viscoelastic models of subduction zones have been proposed to address the

observed change in stress state associated with great subduction zone earthquakes

(Dmowska and Rice, 1988).

Key Questions

There area number of importantquestionssuggested by theseand otherobservations.One

of themost generalistherelationshipbetween theobserved kinematicsof subductionand

the dynamics of the process. What driving forces arc transmitted over great distances

through the strong plates and what are generated by local sources of buoyancy? Related

issues are the stress level and amount of dissipation occurring locally in subduction zones -

- since the driving forces from density contrasts arc eventually balanced by dissipative

resisting forces, the distribution of this dissipation is a crucial question (e.g. Christcnsen,

1985).

A related question is the amount of negative buoyancy associated with subducting slabs. Is

this mainly the result of simple thermal expansion, or are the effects of phase changes

dominant (Anderson, 1987)? Knowing the phase diagram of subducting slabs is im_t

for understanding the driving forces, as well as determining whether the slab penetrates the

670 km discontinuity.

Determining the fate of subducting material at 670 km is an important issue for much of

Earth Science. What happens to the crust? Is it stirred back into the depleted lithosphere or

does it separate? Does subducted material mix into the lower mantle? Does it penetrate

3
briefly only to be regurgitated when reheated? Is it stopped at 670 km depth? How are

subducted slabs distorted in this region (see, e.g., Silver et al, 1988)?

On a more regional scale, important questions include the mechanics of fiat subduction and

the dynamics of back arc basins. What forces are responsible for sliding a subducting plate

for ~I,000 km beneath an overriding plate? Once back arc spreading is initiated, how is the

back arc spreading center shut off?.

The variation of the dip of subducted flabs from place to place has not yet been explained in

a comprehensive model. What are the competing effects of slab buoyanc.y, mantle

viscosity, and global flow (e.g., I-Iager et al, 1983)? How are the dynamics of slab dip and

back arc spreading related?

While the empirical association of maximum earthquake size with convergence velocity and

plate age has intuitive appeal, it is generally recognized that earthquake size is controlled by

the distribution of asperities on the fault plane (e.g., Kanamori, 1986). How do the

empirical variables relate to the physical state of the fault plane?

On a local scale, the process of small scale convection such as is seen tomographicaUy

beneath southern California raises a number of questions. How arc these mantle motions

linked to deformation in the upper crust? How is the convective timcscale linked to the

timescale associated with earthquakes? What is the distribution of crustal rhcologies? Why

does the lithosphere go unstable in some places, but not elsewhere? The latter question is

closely related to the process of creating stable cratonic nuclei.

The premier questionassociatedwith subductionzones iswhat causes the initiationof a

new subduction zone? How isthestrong,cold lithosphereinitiallyfracturedtoform a

weak plate boundary? The subduction process is extremely important in regulating the

thermalbalanceof Earth; understandingtheinitiationof subductioniscrucialin

understandingthedynamic evolutionofour planet.

New Observations, Experiments, and Models

Understanding theprocessof subducfionwillrequireactivitiesin a number of areas

spanning a range of gcosciences.Given the limitedresolutionofmost techniques,these

activities will be most Productive if they are carried out in such a way as to answer specific

questions and test specific, relevant hypotheses. Suggested activities arc grouped by

discipline, roughly in order of priority within each group.

Seismology

The fate of subducted slabs when they reach the 670 km discontinuity is a first order

question that can be addressed by seismologists. The topography and sharpness of the 670

km discontinuity are two features that can discriminate between mantle-wide and chemically

stratified convection scenarios. Imaging of the 670 km discontinuity in the vicinity of

subducted flabs is of highest priority.

Determinationof theseismicvelocitystructureinthevicinityof flabs by tomographic

means is also a high priority. Determining the shape of subducting slabs places strong

constraints on dynamic models. Investigation of locations in the deep mantle beneath fossil

subduction zones are important to increase the temporal coverage of the subduction

process.

4
Regional tomographic studies of the upper mantle in both tectonically active areas and

cratons would help to understand the distribution of "lithospheric drips" such as have been

observed beneath southern California, as well as the processes of eratonization.

Further investigation of temporal and spatial variations in focal mechanisms associated with

large earthquakes will help to constrain the absolute level of stress in subduction zones, as

well as the mechanical properties of the lithosphere-asthenosphere system.

Given the importance of the concept of asperities, direct imaging of fault asperities by

reflection seismology would be an important accomplishment.

Reflection seismology and other seismological techniques should also be used to image the

deep crust to constrain the structures and material properties involved in the coupling

between mantle convection and crustal deformation.

Determination of whether other phase boundaries within the slabs are elevated or depressed

is of high importance, bearing on questions of the mineralogy of the mantle, the thermal

state of the slab, and the magnitude of body force driving subduetion.

A regional tomographic study of the upper mantle in the vicinity of the flat lying subducted

slabs beneath South America would place important constraints on the dynamics of flat

subduction. Such a study would address whether mantle heterogeneity outside the slab is

important in driving the system.

Geodesy

The newly developed, highly accurate space based geodetic techniques (e.g., GPS) make it

possible to obtain crucial observations at relatively little cost. Surveys should be carried

out in regions such as southern California where good tomographic images of mantle

structure exist in order to better constrain the coupling of mantle convection to surface

tectonics. These measurements should be made frequently enough that the coupling of

forces from convective timescales to the timescales of the seismic cycle can be addressed.

Since the basic temporal specaaam of regional crustal deformation is as yet unconstrained

by observations, permanent, continuously monitored regional strain networks should be

installed in a few active regions.

Transfer of stress and strain after large subduetion zone events should be monitored to

address the questions of stress level and coupling of subduetion zones. This requires initial

epoch surveys. Development of high precision underwater geodetic controls is also very

important.

Observations of spatial variations in gravity have proven useful in discriminating among

geodynamic models. Gathering of data sets spanning the continent-ocean transitions in

active margin areas would be very valuable to increasing our understanding of dynamic

processes associated with subduction.

Mineral physics

Determination of the state and physical properties of materials under ambient conditions is

crucial for making further progress in understanding Earth dynamics. Determining phase

diagrams for subducted slabs is important for constraining the body forces associated with

subducted slabs. The predictions of these phase diagrams must be tested using

seismological observations to discriminate among different models of mantle structure,

temperature, and composition.

5
Better constraints on crustal and mantle rheology are also important. Rheological

descriptions are needed on all timescaies, fi'om brittle failure to viscoelastic deformation to

slow, creeping convection.

Numerical Modeling

Progress in geodynamics requires quantitative testing of hypotheses against observations.

Numerical modeling helps to provide the intuition needed to formulate hypotheses to be

tested, as well as providing quantitative predictions to be tested. With increasing

computationai power available, numerical models will continue to become more realistic.

An important improvement will be the ability to address the effects of three dimensions and

time dependence. Advances in computational geophysics will be most rapid ff trained

numerical analysts work closely with geophysicists.

For convection modeling, important problems to address include the effects of phase

changes and variations in composition and theology on flow. Specifically, the interaction

of subducted slabs with the 670 km discontinuity must be addressed for a wide range of

models of upper and lower mantle composition. In these models, it will be important to

consider realistic geometries for subduction (i.e., asymmetrical convergence and three

dimensions), as well as the effects of global flow. The models must be sufficiently well

resolved to address the amount of entrainment of layers with differing compositions. The

process of stabilization of subcratonic lithosphere is another problem involving variations

in composition and phase.

The problem of the mechanics of subhorizontal subduetion is another important problem

that requires a fully dynamic treatment. It is important that these models be guided by

observations of mantle structure and rheology discussed above.

Transmission of stress and strain through viscoelastic effects should be addressed. These

models should include three dimensional effects, as well as realistic parameterizations of

the rheological variations within the crust and mantle.

Dynamical models of flow in the back arc region, including dynamically determined slab

dips, should be posed to address the questions of initiation and cessation of back arc

spreading.

6
BIBLIOGRAPHY

Anderson, D.L., 1987. Thermally induced phase changes, lateral heterogeneity of the mantle,

continental roots and deep slab anomalies, J. Geophvs. Res., 9P., 10341-10349.

Astiz, L. and Kanamori, H., 1986. Interplate coupling and temporal variation of mechanisms of

intermediate-depth earthquakes in Chile, BSSA, 76, 1614-1622.

Bird, P., 1988, Formation of the Rocky Mountains, Western United States: A continuum computer model, Science, e89, 1501-1507.

Bird, P. and Rosenstock, R.W., 1984. Kinematics of present crust and mantle flow in Southern

California, Geol. Soc. Amer. Bull., 95, 946-957.

Bock, G. and Ha, J., 1984. Short period S-P conversion at a depth near 700 krn, Geophl/s. J.R.

astr. Sot., 77, 593-614.

Christensen, U.R., 1985. Thermal evolution models for the Earth, J. Geophys. Res., 90,

2995-3007.

Christensen, C. and Ruff, L., 1983. Outer-rise earthquakes and seismic coupling, Geophsls. Res.

Lctt., I0, 697-700.

Creager, K.C. and Jordan, T.H., 1984. Slab penetration into the lower mantle, d. Geophys.

Res., 89, 3031-3049.

Creager, K.C. and Jordan, T.H., 1986. Slab penetration into the lower mantle beneath the Marina

and other island arcs in the Northwest Pacific, d. Gcoph_ls. Re6., 91, 3573-3589.

Crough, S.T. and Jurdy, D.M., 1980. Subducted lithosphere, hotspots and the geoid, Earth

Planet. Sci. Lctt., 48, 15-22.

Dmowska, R., Rice, J._ Lovison, L., and Josell, D., 1988. Stress transfer and seismic phenomena

in coupled subduction zones during the earthquake cycle, J. Geophvs. Rcs., 98, 7869-7884.

Forsyth,D.W. and Uyeda, S., 1975. On the relativeimportance of the drivingforces of plate

motions, Geophl/8. J. R. astr. Soc., 48, 163-200.
Grand, S. P., 1987, Tomographic inversion for shear velocity beneath the North American plate,

d. Geophlls. Rcs., 9_ 14065-14090.

Hager, B.H., 1984. Subducted slabs and the geoid: Constraints on mantle rheology and flow,

d. Geophys. Res., 89, 6003-6015.

Hager, B.H. and Clayton, R.W., 1988. Constraints on the structure of mantle convection using

seismic observations, flow models, and the geoid, in W.R. Peltier, exl. Mantle Convection,

Gordon and Breach, New York, in press.

Hager, B.H., Clayton, W.R., Richards, M.A., Comer, R.P., and Dziewonski, M., 1985. Lower

mantle heterogeneity, dynamic topography and the geoid, Nature, 818, 541-545.

Hager, B.H. and O'Connell, R.J., 1981. A simple global model of plate dynamics and mantle

convection, ,7. Geophlls. Rcs., 86, 4843-4867.

Hager, B.H., O'Connell, R.J., and Raefsky, A., 1983. Subduction, back-arc spreading and global

mantle flow, Tcetonophvsics, 99, 165-189.

Hager, B.H. and Richards, M.A., 1988. Long-wavelength variations in Earth's geoid: Physical

models and dynamical implications, submitted to Phil. Trans. ROll. $oc. Lond. A.

Humphreys, Eugene D., 1985. Studies of the crust-mantle system beneath Southern California,

Ph.D. Thesis, California Institute of Technology, 189 pp.

Humphreys, E., Clayton, R.W., and Hager, B.H., 1984. A tomographic image of mantle structure

beneath southern California, Geophlls. Res. Left., 11, 625-627.

Isacks, B.L. and Barazangi, M., 1977. Geometry of Benioff zones: Lateral segmentation and

downwards bending of the subducted lithosphere, in Island Arcs, Deep Sea Trenches, and

Back-Are Basins, ed by M. Talwani and W.C. Pitman, I/1, American Geophllsieal Union,

Washington, D.C., 480 pp.

Isacks, B. and Molnar, P., 1971. Distribution of stresses in the descending lithosphere from a

global survey of focal mechanisms solutions of mantle earthquakes, Roy. Gcophlls. Sp.

Phlls., 9, 103-174.

Kanamori, H., 1986. Rupture process of subduction-zone earthquakes, Ann. Rev. Earth

Planet. Sci., I4, 293-322.

Lerch, F.J., Klosko, S.M., and Patch, G.B., 1983. A refined gravity model from LAGEOS

(GEM-L2), NASA Tcch. Memo., 84086.

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Richards,M.A. andHager,B.H., 1984.Geoidanomalies in a dynamic Earth, J. Geophys. Res.,

89, 5987-6002.

Richards,M.A. and Hager, B.H., 1988. The Earth'sgcoid and thelarge-scalestructureof mantle

convection, The Physics of the Planets,exl.by S. K. Runcorn, John Wiley & Sons Ltd.,

247-272.

Richter, F.M. and McKcnzie, D.P., 1978. Simple plate models of mantle convection, J. Geophvs., 44, 441-471,

Ruff, L. and Kanamori, H., 1980. Seismicity and the subduction process, Phys. Earth Planet.

Inter., P.3, 240-252.

Schubert, G., Yuen, D.A., and Turcotte, D.L., 1975. Role of phase transitions in a dynamic

mantle, Geophys. J. R. astr. $oe., 41_, 705-735.

Silver, P. G., Carlson, R. W., and Olson, P., 1988, Deep slabs, geochemical heterogeneity,

and the large-scale structure of mantle convection, Ann. Rev. Earth Planet. Sei., 16,

477-541.

Uyeda, S. and Kanamori, H., 1979. Back-arc opening and the mode of subduction, J. Geophys.

Res., 84, 1049-1061.

Vassiliou, M.S., Hager, B.H., and Raefsky, A., 1984. The distribution of earthquakes with depth

and stress in subducting slabs, J. Geodvn., 1, 11-28.

Zhou, H.-W. and Clayton, R.W., 1987. Abstract, EOS, Trans. Am. Geophlls. U., 68, 1379.

9
Figure Captions

Figure la) The observed long-wavelength geoid (Lerch et al, 1983) referred to the

hydrostatic figure of the earth ( f = 1/299.63), with plate boundaries and hotspots

indicated. The contour interval is 20m and geoid lows are shaded. Cylindrical

equidistant projection.

Figure lb) The observed geoid, filtered to include spherical harmonic degrees 4-9 to

emphasize the association with subduction zones.

Figure lc) A model geoid calculated from a fluid dynamical model of mande flow driven

by density contrasts inferred for subducted slabs (I-lager, 1984).

Figure 2) Tomographic reconsn'uction of the mantle structure beneath southern California.

In the upper-left panel a map view of the velocity structure at a depth of 100 km is

superimposed on a location map. Also shown are the locations of the cross sections

shown in the other three panels. These sections extend from the surface to 500 km

depth, with no vertical exaggeration. The contour interval is 1.5% relative velocity

variations, with regions faster than 1.5% dotted and regions slower than -1.5%

hatched. The major feature is a slab-like high velocity anomaly penetrating the

uppermost mantle beneath the Transverse Ranges (After Humphreys et al.).
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