Sea-level fluctuations due to subduction: The role of mantle rheology

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Sea-level fluctuations due to subduction: The role of

mantle rheology

C. Piromallo, G. Spada, R. Sabadini, Y. Ricard

To cite this version:

C. Piromallo, G. Spada, R. Sabadini, Y. Ricard. Sea-level fluctuations due to subduction: The role of

mantle rheology. Geophysical Research Letters, American Geophysical Union, 1997, 24 (13),

pp.1587-1590. �10.1029/97GL01561�. �hal-02046755�

GEOPHYSICAL RESEARCH LETTERS, VOL. 24, NO.13, PAGES 1587-1590, JULY 1, 1997

Sea-level fluctuations

due to subduction:

The role of

mantle rheology

C. Piromallo G. Spada

2, R. Sabadini

a, Y. Ricard

4

Abstract. By means of a stratified viscoelastic Earth

model we study the effect of sinking slabs on the dynamic topography, the non-hydrostatic geoid and the long-term sea

level variations. Sea level fluctuations due to subduction are found to be sensitive to the nature of the 670 km seismic

discontinuity and to the theological layering of the mantle.

The response of our model to both a single subduction and a realistic distribution of slabs is studied by a numerical simulation based on a simplified approach. Consistent with previous results, we find that an upper bound to relative sea

level time variations associated with the initiation of a new subduction in the upper mantle is •0 0.1 mm/yr. Relative

sea level changes driven by the dynamic readjustment of internal mass heterogeneities may thus be comparable with those attributed to other changes in the tectonic regime on a large scale. This confirms the relevance of subduction as an important contributor to long-term sea level fluctuations.

Introduction

In the past, relative sea-level (hereafter RSL) fluctuations occurring on geological time-scales have been attributed to changes in the oceanic spreading rates with associated

modifications in the volume of the oceanic basins [Hays •4 Pitman, 1973; Turcotte • Schubert, 1982]. However, in the

last decade it has been recognized that mass redistribu- tion due to internal convection may contribute significantly to surface topography and hence to RSL variations. As

pointed by Gurnis [1990a], this mechanism accounts for

mass conservation of the mantle-lithosphere system, which

was previously neglected. According to Gurnis [1990a] the

study of subduction-induced sea level changes may place

constraints on the internal viscosity structure of the Earth and on the style of convection.

The potential role of subduction on RSL variations has

been first addressed by Mitrovica • Jarvis [1985] by means

of a 2-D model of time-dependent convection. This approach

has been later refined to describe the Late Cretaceous to

Tertiary tilting of North America due to the Farallon sub- duction and the Devonian-Permian tilting of the Russian

Platform [Mitrovica et al., 1989, 1996]. The competing role

of dynamic topography and non-hydrostatic geoid caused

by internal loading on RSL has been deeply investigated

by Gurnis [1990-bc] by means of a 2-D convection model.

Xlstituto Nazionale di Geofisica, Roma

2Dipartimento di Fisica, Universirk di Bologna

aDipartimento di Scienze della Terra, Universirk di Milano 4Laboratoire de Sciences de la Terre, ENS-Lyon

Copyright 1997 by the American Geophysical Union. Paper number 97GL01561.

0094-8534/97/97GL-01561 $05.00

Gurnis [1993] has employed a spherical Earth model to

compute the RSL variations above subducting slabs, which have been found to be well correlated with the geological

records.

In this paper, we use a spherical self-gravitating model to

analyse the sensitivity of RSL variations to the nature of the mantle discontinuities and to viscosity profile. To describe

in a realistic way the build up of the dynamic topography and to account for time-dependent effects, we employ a model with Maxwell viscoelastic properties, first proposed

by Ricard et al. [1992] to study the role of deep-seated mass

heterogeneities on time-dependent geoid anomalies.

In the following, the effects of mantle heterogeneities on

the geoid and on dynamic topography are studied separately

to appreciate the relative contributions of these two observ-

ables to RSL variations. We confirm that RSL variations

are basically determined by surface topography, because of

the low admittance (geoid to topography ratio) predicted by our models [see also Gurnis, 1990a].

We have also analysed the effects of simplified subduction

models in which a point mass mimics a slab vertically sinking

within the mantle. The purpose of these simulations is to

enlighten the role of mantle theology and of the nature of the transition zone on long-term sea-level variations. In this respect our work constitutes a significant advance over

Ricard et al. [1992, 1993]. Our predicted RSL variations are comparable with those obtained by Gurnis [1993]. The

RSL variations forced by subduction in a viscoelastic Earth

are found to be regional in character and localized along subduction areas.

Loading Love Numbers for Internal Sources

We perform a direct modelling of the time-dependent geoid and dynamic topography induced by mass anoma- lies embedded at different depths. Through the use of

the correspondence principle, viscoelastic problems can be

solved by dealing with the equivalent elastic problems in

the Laplace domain [e.g. Peltier, 1974]. The offset between

the equipotential surface of the non-hydrostatic geoid and

the surface of the dynamic topography provides RSL [e.g. Lainbeck, 1988]. The harmonic component of degree /• of

RSL is expressed by

Q(a,d,s) = [1 + kt(a,d,s)- ht(a, d, s)]SVtø

(a, d, s) (1)

where kt, hi are the loading Love numbers for internal sources for geoid and topography, respectively [Farrell •

Clark, 1976; Hinderer et al., 1991], a is the Earth's radius, s the Laplace variable and d the load depth. Eq. (1)

represents, for example, the sea-level variation measured by a tide-gauge along a continental margin. In a rigid Earth,

kt = hi = 0, and the RSL is only determined by the

direct effect of the mass heterogeneities on the geopotential,

expressed

by (•Vt

ø.

In a dynamic Earth, internal mass heterogeneities pro-

duce both a topographic effect, described by hi, and geoid undulations, described by kt. The RSL in (1) is therefore the 1587

1588 PIROMALLO ET AL.: SEA LEVEL FLUCTUATIONS

result of dynamic compensation of internal anomalies and its

amplitude depends, through ht and kt, on the theological stratification of the mantle and on the source depth [Ricard et al., 1992]. In (1) we have neglected the hydro-isostatic term and the effects due to modifications of the ocean-

continents distribution, which could only be predicted by

an iterative procedure [e.g. Farrell •4 Clark, 1976]. From post-glacial rebound studies [e.g. Peltier, 1974] it

is well known that ht and kt for impulsive loading can be

written as the sum of an elastic contribution and of a delayed

effect associated with mantle relaxation. Spada [1992] have

shown that this also holds for deep-seated density anoma-

lies.

Dynamic Topography, Geoid and RSL due to sub-

duction

We employ a self-gravitating, incompressible Earth model,

including an elastic lithosphere, a layered mantle with linear

Maxwell rheology, and an inviscid core. Some of the models

discussed in this paper are characterized by an isoviscous

mantle (r] -- 1, where r] is the ratio between lower and upper mantle viscosity), others by a stiff lower mantle (r] ---- 30).

In Fig. I we study the degree 2 signatures associated

with internal mass heterogeneities for various viscosity and density profiles. For a point mass anomaly characterized

by a Heaviside time-history and located at a normalized

depth d/a (a is the Earth's radius),

we examine

both the

the forcing mass anomaly [Piromallo, 1993].

The four top panels show the results for a fully adiabatic

phase-change

transition

with Ap/p=0% across

the 670 km

the four bottom models this boundary is assumed to behave

as a non adiabatic chemical transition [Yuen et al., 1986]

with Ap/p=9% (chemical

models).

Models

a,b,e,f

are iso-

For the whole set of models of Fig. I and for most of the

source depths the fluid RSL response is strongly dominated

by the topographic signal, as it can be noticed by the

approximate anti-symmetry of the thick and dashed lines. In

these situations there is a relatively small contribution from the non-hydrostatic geoid (thin lines). The vanishing geoid

associated with surface mass anomalies for L-0 km denotes

a perfect compensation on long time-scales; for L - 100

L--O kin, q =1 L=100 kin, q =1 L--O kin, q =30 L=100 km, q =30

0.6 • 0.3 ..9. ø • o.o m -0.3 -0.6 0.6 • 0.3 ._o E• 0.0 0 -0.3 -0.6 0.0 0.2 0.4 0.0 0.2 0.4 0.0 0.2 0.4 0.0 0.2 0.4

Normalized source depth, d/a

Figure 1. Long-term dynamic topography (dashed), non-

hydrostatic geoid (thin), and RSL (thick) for œ = 2, as a

function of the normalised source depth. Each panel refers to one of the eight models considered (see text for details).

km surface heterogeneities are partially supported by elastic lithospheric stress, giving rise to a small, positive geoid even on long time-scales. Masses located in the vicinity of the CMB (d/a -• 0.45) or close to an internal compositional boundary (the 670 km depth discontinuity for chemical

mbdels) are, on the contrary, always fully compensated in the fluid limit [Ricard et al., 1992].

An increase in lower mantle viscosity has the tendency to reduce the amplitude of the surface observables. In the case

of the chemical models with r/ = 30 these signatures are

very close to zero, except for upper mantle mass anomalies.

Notice how the presence of an elastic lithosphere produces an overall amplification of the topographic and geoid signals. This is due to the stress concentration above the anomaly,

which induces larger deflections of the external surface. For a physical interface, a positive mass anomaly placed in the mantle systematically induces a positive RSL, i.e. a possible

transgression of an overlying continental platform. Lower

mantle anomalies are associated with negative variations of sea-level (i.e., oceanic regression) when the chemical models

are considered. This is rather intuitive: by viscous coupling a two-layered convection system is excited with counter-

rotative cells, so that a downwelling in the lower mantle

gives rise to an upwelling in the upper mantle [e.g. Hager, 1984].

The sensitivity of long-wavelength sea-level variations to mantle theological layering is analysed in deeper detail in Fig. 2, where the long-term RSL is plotted as a function of r/. As in Fig. (1), the load is represented by a degree 2 mass anomaly located at various depths d within the mantle. The

mass

of this load is comparable

to that of a slab

of 2 x 10 •u

kg, which

corresponds

to a slab pull of 5.10

• N/m along

a 4000 km trench [e.g., Turcotte • Schubert, 1982; Spada,

1992].

The reference

upper

mantle

viscosity

is 10

• Pa.s

in

for both a physical (left) and a chemical (right) upper-lower

mantle interface, in models without lithosphere.

An increase of r/ is associated with a rapid reduction of RSL, especially for lower mantle heterogeneities. How-

ever, when a chemical interface is considered, the RSL

fluctuations are basically unaffected by an increase in lower mantle viscosity for r/ _• 50. This is not found in the case of a physical interface, which exhibits an overall larger sensitivity to changes of r/. This different behaviour may be

attributed to the larger shielding effects of the compositional discontinuity, which exhibits a strong tendency to decouple upper and lower mantle flows.

Physical, L=O km Chemical, L=O km

10

•._•

] 10

[L

•

o=okrn

8

6

•

•oo

'•' 6

2•__ 4o

ø

2

ar

V1800

Figure 2. Degree 2 RSL induced by a point density

anomaly located at various depths, as a function of the viscosity jump between lower and upper mantle. Physical

and chemical models are depicted in the left and right panel,

PIROMALLO ET AL.' SEA LEVEL FLUCTUATIONS 1589

Subducted Slabs and Relative Sea Level

Up to now, we have only examined the response of our

model to oversimplified loads in the fluid limit. We now

simulate the time-dependent effects of a realistic subduc-

tion process, using the method described by Ricard et al.

[1993]. To this purpose, we investigate in Fig. (3) the

RSL variations associated with a slab sinking vertically in a

visCoelastic mantle. The effects of changing the subduction angle have been discussed by Mitrovica et al. [1989]. To

increase the spatial resolution of our model, we expand the

anomalous mass of the slab up to harmonic degree œ -- 36.

In contrast to Fig. (2), the rate of RSL has been computed taking into account the contributions of the whole spectrum

of viscoelastic relaxation modes. The subduction process

is simulated by the linear superposition of the effects due to several 'slablets' acting successively down to the 670

km depth boundary, where subduction comes to rest. No

density heterogeneity sinks beyond this depth.

The rate of RSL shown in Fig. (3) is computed on top of a slab sinking at a constant velocity of 5 cm/yr, confining the analysis to the lapse of time during which subduction is active. A 100-km thick elastic lithosphere is included in the

right panel, whereas the left one presents the results for L

= 0 km. The rate of RSL attains its larger amplitude

I mm/yr) at the very beginning of the subduction process,

and then decreases with increasing time. During the early

stages of subduction, the chemical models (e, f, g, h) display

slightly larger rates than the physical ones with the same

r/ ratio (a, b, c, d). However, as subduction evolves, the

rates of RSL for chemical models progressively decrease to zero, while physical models exhibit an appreciable non- vanishing rate of sea level even on long time-scales. This

rate is very large in the case of a uniform mantle (-• .3 mm/yr after 12 Myr) and drops to • .02 mm/yr for •/=30.

The slowing down of the RSL is due to the decrease in amplitude with depth peculiar to the Green's functions for the dynamic topography, which mostly contributes to RSL (see Fig. 1). Due to the presence of an elastic lithosphere (right), we observe that the rate of RSL is not sensitive to the viscosity increase at 670 km depth during the early stages of subduction (t<_3 Myr). For longer time-scales, models with different r/ predict significantly different RSL rates, especially in the case of a physical transition.

In Fig. 4 we study the geophysical signatures associated with a more realistic subduction, including all of the slabs along the currently active trenches. The slabs are supposed

to penetrate within the mantle at time t-0 and to deepen

•-0.9 •o.8

0.4

Figure 3. Time-derivative of RSL (in mm/yr) driven by a slab sinking at a velocity of 5 cm/yr, as a function of time, ranging from the beginning to the end of subduction. The left panel shows models without lithosphere (a, c, e, g) and the right one those with lithosphere (b, d, f, h).

TOPOGRAPHY, L=100 km, model b (a)

ß

-:-.- . , O 0

i q"') o

RSL, L=100 kin, mod,I b (e)

.... :.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:. ============================= i• ... i'•i::i:?:•i•ii?:?:ii:•::!i!::i:.-i?:: , .... •:::? ... .. I[ es • • :':':"":'"•'"':••:'--- I -•-• RS.._L, L__--0 kin, mode_, a :::::::::::::::::::::::::::::::::::: vl=l

TOPOGRAPHY, L=100 kin, model d

-::

'"'

GEOID, L=100 kin, model d (d

- ...:ii: ....

1[ 17 8] m ::::•:'-• RSL, L=100 kin, model d

RSL, L=0 kin, model c (h)

yl=30

Figure 4. Dynamic topography (a,b: contour interval is

400 m), geoid (c,d: contour interval is 10 and 5 m, respec-

tively) and RSL (e,f: contour interval is 400 m) induced by

a realistic distribution of slabs. We consider physical models

with elastic lithosphere and r/-- I (left) or r/-- 30 (right). Negative and positive values are displayed by light and dark

shades of gray, respectively. The insets show the range of

variation. RSL for models without lithosphere is shown in

g and h (contour interval is 400 m).

vertically with constant velocity v=5 cm/yr. The results shown in this figure refer to time t-15 Myr, when all of

the slabs have reached the upper-lower mantle interface. The spherical harmonic expansion is truncated at degree

20 and a phase change is assumed at 670 km depth. Mass conservation is enforced by subtracting from a thin shell an

amount of mass equal to that injected into the mantle at a given depth.

The left and right columns display the results for r/-- 1 and r/ -- 30, respectively. The RSL shown in (e) and (f), is computed by using the dynamic topography shown in (a) and (b) and the geoid anomalies in (c) and (d). An elastic

lithosphere is always included in these computations, except

in (g) and (h). The model considered in (h) is therefore very similar to the one preferred by Ricard et al. [1993] on

the basis of its large degree of correlation with the observed

geoid at long-intermediate wavelengths. This model predicts a positive geoid anomaly on top of a subducting slab, in agreement with Fig. lc, and contrarily from what obtained

with models including a lithosphere.

Peak-to-peak variations for the geoid (-• 80 m) are more

than one order of magnitude smaller than those for the

dynamic topography (-• 2 kin). The amplitude of the

dynamic topography shown in Fig. (4) is in full agreement

with previous estimates based on a similar model [Ricard et al., 1993]. The RSL variations are therefore basically governed by this signature, whose minima are essentially

confined along active margins. It is well known that this dynamically supported topography is not easily observable, due to the shielding effect of crustal and lithospheric density

1590 PIROMALLO ET AL.' SEA LEVEL FLUCTUATIONS

data have suggested the existence of a dynamic topography

which exhibits a good correlation with the geoid although

with an amplitude smaller than predicted [Gazenave et al., 1989; Gazenave • Lago, 1991; Thoraval et al., 1995].

Comparing the values obtained for different viscosity pro- files, it is evident that geoid is much more affected by vis-

cosity changes than topography. For the models considered

in this study, the patterns of non-hydrostatic geoid and dy-

namic topography show depressions along the trenches, and

bulges away from subduction zones. The same peripheral

bulges were found by Mitrovica et al. [1989] and Gumis [1992]. However, as seen in the previous sections, the sign

and the amplitude are strongly influenced by the combi- nation of the different factors marking the various models: the nature of the 670 km depth discontinuity, the viscosity profile, and the presence of an elastic lithosphere. The topography depression associated with slabs partly includes the well known subduction trench but is obviously of much larger extent, as a consequence of the global dynamics of the

mantle.

Conclusions

By means of a spherically symmetric Earth model with

viscoelastic theology we have examined the effects induced

on long time-scale relative sea level fluctuations by subduct- ing slabs. In spite of its simple structure, our model permits to evaluate the sensitivity of RSL to the theological profile of the Earth and provides new insights to the interpretation

of the RSL fluctuations on geological time-scales. According

to our results, the dynamic topography plays a crucial role upon the determination of these fluctuations, the contribu- tion of the geoid being basically negligible for the whole

set of models considered here. An upper bound for global

RSL variations along the continental margins located in the

proximity of subduction zones may amount -• 0.1 mm/yr,

in agreement with the 2-D computations by Mitrovica •4

Jarvis [1985] and Gumis [1992].

On the strength of this result we confirm the important role of subduction in driving long-term RSL variations, together with glacial instabilities, polar wander, thermal and compaction-induced subsidence. These different processes have different geographical signature. Glacial instabilities and oceanic thermal subsidence induce, at first order, a global sea level modification (eustatic). True polar wander should induce RSL with a C21-S21 symmetry which means that two antipodal locations experience the same RSL, but two locations symmetric with respect to the equator expe-

rience opposite RSL [Ricard et al. 1992]. The RSL due to

subduction changes corresponds to a regional inundation of the convergent margins.

A further development of this investigation will focus on

the spatial and temporal aspects of the subduction process,

that has been oversimplified in this study. The knowledge

of the evolution of mantle heterogeneity since the Mesozoic

[Ricard et al., 1993] should allow for a reconstruction of the

history of long-term sea-level changes due to subduction, as

done by Gumis [1993].

Acknowledgments. We are indebted to J. Mitrovica,

M. Gurnis, an anonymous reviewer for their helpful sugges-

tions and to Enzo Boschi for stimulating conversations.

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