Lecture 1 Historical Background

Lecture 1

Historical Background 1.1 Introduction 3

“The fundamental physical process behind all major geological events is heat transfer from the deep interior

Figure 1.2. James Hutton (1726–1797), the to the surface.” father of Geology and proponent of internal heat as the driving force for Earth’s evolution. - James Hutton

The idea that flow in the Earth’s interior is a form of thermal convection developed slowly. Recognition of the significance of thermal convection as a primary fluid mechanical phenomenon in nature came from physicists.Theory Count Rumford of isostacy is usually given creditthat for allowed recognizing the phenomenon around 1797 (Brown, 1957), although the term convection (derived from convectio, to carry) was firstfor used vertical by Prout (1834) adjustment to distinguish it from the other known heat transfer mechanisms, conduction and radiation. Subcrustal convection in the Earth was first suggested by W. Hopkins in 1839 and the first interpretations of geological observations using convection were made by Osmond Fisher (1881). Both of these presumed a fluid interior, so when the solidity of the mantle was established, these ideas fell out of favor. The earliest experiments on convection in a layer of fluid heated from below and cooled from above were reported by J. Thompson (1882), who observed a “tesselated structure” in the liquid when its excess temperature, compared to that of the overlying air, was sufficiently large. But the name most closely associated with convection is Henri Bénard (Figure 1.3). Bénard (1900, 1901) reported the first quantitative experiments on the onset of convection, including the role of viscosity, the cellular planform, and the relationship between cell size and fluid layer depth. Bénard produced striking photographs of the convective planform in thin layers of viscous fluids heated from below (Figure 1.4). The regular, periodic, hexagonal cells in his photographs are still referred to as Bénard cells. Since Bénard used fluid layers in contact with air, surface tension effects were surely present in his experiments, as he himself recognized. It has since been shown that Bénard’s cells were driven as much by surface tension gradients as by gradients in buoyancy. Still, he correctly identified the essentials of thermal convection, and in doing so, opened a whole new field of fluid mechanics. Motivated by the “interesting results obtained by Bénard’s careful and skillful experiments,” Lord Rayleigh (1916; Figure 1.5) developed the linear stability theory for the onset of convection 4 Historical Background

Figure 1.3. Henri Bénard (1880–1939) (on the left) made the ﬁrst quantitative experiments on cellular convection in viscous liquids. The picture was taken in Paris about 1920 • Earliest experiment:with Reabouchansky Benjamin on the right. Thomson

• Also developed the science of thermodynamics

1.2 Continental Drift 5

Figure 1.4. Photograph of hexagonal convection• cellsLord in a viscous Rayleigh: ﬂuid layer heated from below, taken by Bénard (1901). Linear stability theory

Figure 1.5. Lord Rayleigh (1842–1919) developed the theory of convective instability in fluids heated from • Rayleigh-Bbelow. énard Bénard cells (1901) in a horizontally infinite fluid layer between parallel surfaces heated uniformly convection from below and cooled uniformly from above, and isolated the governing dimensionless parameter that now bears his name. It was unfortunate that these developments in fluid mechanics were not followed more widely in Earth Science, for they might have removed a stumbling block to acceptance of the milestone concept of continental drift.

1.2 Continental Drift The earliest arguments for continental drift were largely based on the fit of the continents. Ever since the first reliable maps were available, the remarkable fit between the east coast of South America and the west coast of Africa has been noted (e.g., Carey, 1955). Indeed, the fit was pointed out as early as 1620 by Francis Bacon (Bacon, 1620). North America, Greenland, and Europe also fit as illustrated in Figure 1.6 (Bullard et al., 1965). Geological mapping in the southern hemisphere during the nineteenth century revealed that the fit between these continents extends beyond coastline geometry. Mountain belts in South America match mountain belts in Africa; similar rock types, rock ages, and fossil species are found on the two sides of the Atlantic Ocean. Thus the southern hemisphere geologists were generally more receptive to the idea of continental drift than their northern hemisphere colleagues, where the geologic evidence was far less conclusive. Further evidence for continental drift came from studies of ancient climates. Geologists recognized that tropical climates had existed in polar regions at the same times that arc- tic climates had existed in equatorial regions. Also, the evolution and dispersion of plant and animal species was best explained in terms of ancient land bridges, suggesting direct connections between now widely separated continents. As previously indicated, most geologists and geophysicists in the early twentieth century assumed that relative motions on the Earth’s surface, including motions of the continents relative to the oceans, were mainly vertical and generally quite small – a few kilometers in extreme cases. The first serious advocates for large horizontal displacements were two visionaries, F. B. Taylor and Alfred Wegener (Figure 1.7). Continental drift was not widely discussed until the publication of Wegener’s famous book (Wegener, 1915; see also Wegener, 1924), but Taylor deserves to share the credit for his independent and somewhat earlier account (Taylor, 1910). Wegener’s book includes his highly original picture of the breakup 1.2 Continental Drift 7

Figure 1.7. Alfred Wegener (1880–1930), the father of continental drift.

1.3 The Concept of Subsolidus Mantle Convection 9

“Thermal convection in the highly rigid mantle not possible on mechanical grounds” Figure 1.8. Harold Jeffreys (1891–1989), theFigure 1.9. Arthur Holmes (1890–1965), the ﬁrst most inﬂuential theorist in the early debate overprominent advocate for subsolidus mantle convection. continental drift and mantle convection. - Harold Jeffreys

How can mantle be both elastic and viscous? rotational forces were also responsible for driving the mantle ﬂows resulting in continental drift.) At the same time, seismologists were exploring the Earth’s deep interior, and were impressed by the high elastic rigidity of the mantle. In his inﬂuential book, The Earth (Jeffreys, 1929), Sir Harold Jeffreys (Figure 1.8) referred to the mantle as the “shell,” arguing that this term better characterized its elastic strength. Paradoxically, Jeffreys was at the same

Arthur Holmes’ (1931)

Figure 1.10. Arthur Holmes’ (1931) depiction of mantle convection as the cause of continental drift, thirty years prior to the discovery of seaﬂoor spreading.

than that required for the onset of convection. He also outlined a general relation between the ascending and descending limbs of mantle convection cells and geological processes, illustrated in Figure 1.10. Holmes argued that radioactive heat generation in the continents acted as a thermal blanket inducing ascending thermal convection beneath the continents. Holmes was one of the most prominent geologists of the time, and in his prestigious textbook Principles of Physical Geology (Holmes, 1945), he articulated the major problems of mantle convection much as we view them today. The creep viscosity of the solid mantle was ﬁrst determined quantitatively by Haskell (1937). Recognition of elevated beach terraces in Scandinavia showed that the Earth’s surface • Viscosity of mantle first determined quantitatively by Haskell

• Explained the uplift of Fennoscandia

• GIA

(Credit: Finnish Geospatial Research Institute) How to reconcile both solid and fluid behavior of mantle?

• Slow creep of crystalline materials At temperatures less than melt temperatures rocks can flow at low stress levels on timescales greater than 10,000 years 14 Historical Background

(a) Observed Profile

500 γ W

Reversed Profile

150 0 150 km

(b)

Gilbert Gauss MatuyamaBrunhesBrunhesMatuyamaGauss Gilbert

3.3 3.3 Million Years

Mid-Ocean Ridge

Zone of Cooling and Magnetization

Figure 1.13. (a) Magnetic profile across the East Pacific Rise at 51◦S; the lower profile shows the observed profile reversedMagnetic for comparison. (b)profile The spreading across ocean floor. the Hot East material Pacific wells up along Rise the oceanic ridge. It acquires a remanent magnetism as it cools and travels horizontally away from the ridge. At the top of the diagram are shown the known intervals of normal (gray) and reversed (white) polarity of the Earth’s magnetic field, with their names. The width of the ocean-floor stripes is proportional to the duration of the normal and reversed time intervals.

Carey (1958, 1976) had been concerned about the geometrical reconstruction of former continental masses. These studies led him to view the Earth as undergoing rapid expansion. This view did not receive wide support and it will not be considered further. There is no satisfactory physical explanation of how such a large volume expansion might have occurred and it is inconsistent both with estimates of the change in the Earth’s rate of rotation and with paleomagnetic constraints on changes in the Earth’s radius. Rayleigh number:

• Measures the vigor of convection

• Measure of the competition between gravitational thermal buoyance forces that acts to drive convective flow and the resistive effects of fluid viscosity that retards convective motion and thermal diffusion which acts to diminish thermal anomalies

• Very high viscosity of mantle

• Various complex rheologies and deformation mechanisms BERCOVICI ET AL.: MANTLE DYNAMICS AND PLATE TECTONICS 19

1 they become more readily deformed, causing further strain 1 to concentrate there, thereby inducing further softening, etc. 0.8 2 (Comparable effects can be caused with other rheologies such as Bingham plastics and bi-viscous laws; however, 0.6 these are just further mathematical models for essentially the same strain-softening effect represented by a power-law rhe- 0.4 3 ology.) Such non-Newtonian rheologies have been incorpo-

0.2 rated into numerous 2-D convection models for and have found little plate like behavior [e.g., Parmentier et al.,

0 1976; Christensen, 1984c]. Other models, concentrating on 0 0.1 0.2 0.3 0.4 0.5 plate formation, placed a thin non-Newtonian “lithospheric” 1

stress ﬂuid layer atop a thicker convecting layer, or mathemati- cally conﬁned the non-Newtonian behavior to a near-surface 0.8 layer [Weinstein and Olson, 1992; Weinstein, 1996; Moresi 5 4 and Solomatov, 1998; see also Schmeling and Jacoby, 1981] 0.6 (Fig. 11). In these latter models, the non-Newtonian ef-

0.4 fect does indeed yield an upper layer with reasonably high plateness for basally heated convection: the layer becomes

0.2 weaker over both divergent zones (i.e. over upwellings) and convergent zones (downwellings), and is relatively immo- 0 0 0.1 0.2 0.3 0.4 0.5 bile and strong in between the these two zones. Moreover, as strain rate noted by King et al. [1992], 2D models with non-Newtonian rheology are often indistinguishable in some respects from Figure 10. Constitutive (stress versus strain-rate) laws for (1) plastic, (2) non-Newtonian power law, (3) Newtonian, (4) brittle stick-slip and (5) those with imposed plate geometries [e.g., Olson and Cor- self-lubricating (also called continuous stick-slip) rheologies. cos,Bercovici1980; Da etvies, al., 20001988a] and lithospheric weak zones [e.g., King and Hager, 1990; Zhong and Gurnis, 1995a]. How- ever, to obtain sufficient plateness with the non-Newtonian layer will tend to be weakest at the divergent zone (where models, it is necessary to use a power-law index con- the boundary layer is thinnest) which approaches plate-like siderably higher than inferred from rheological experiments behavior. However, the viscosity will be highest over the (typically is needed). Thus, it seems that a general cold convergent zone, tending to immobilize it and eventu- strain-weakening type rheology is a plausible and simple so- ally the entire boundary layer, which is of course one of the lution to generating high plateness, i.e. weak boundaries root causes for the subduction initiation problem (see 4.6); and strong plate interiors, in a convection model. However, in the end, this also leads to a thermal boundary layer with when the convective flow is driven by internally heated con- little plateness. Therefore, it is a reasonable assumption that vection, which has little or no concentrated upwellings, then plate-like strength distributions – or high plateness – require the divergent zones in the lithospheric layer tend to be broad a lithospheric rheology that permits boundaries to be weak, and diffuse, i.e., not at all like narrow, passively spreading regardless of temperature. ridges [Weinstein and Olson, 1992] (Fig. 11). At high stresses mantle rocks undergo non-Newtonian It is undoubtedly naive to assert that plate-like behavior creep wherin deformation responds nonlinearly to the ap- simply requires the generation of weak boundaries; in fact plied stress; i.e., the stress–strain-rate constitutive law is each type of boundary, i.e., convergent, divergent and strike- nonlinear through a power-law relation such that slip, develops under very different deformational and thermal environments. Obtaining sufficient plateness is invari- (10) ably related to the the nature of how the different boundaries where is strain-rate, is stress, and is the power-law in- form. As each type of boundary is uniquely enigmatic, they dex (see Fig. 10); for mantle rocks, , typically [Weert- warrant individual discussion. These will be the focus of the man and Weertman, 1975; Evans and Kohlstedt, 1995]. The following sections. effective viscosity is 4.6. Convergent margins: initiation and asymmetry of (11) subduction The downwelling currents in simple convection are for which means that for viscosity decreases with in- the most part very symmetric; i.e., one downwelling is com- creasing strain-rate. The power-law rheology causes regions posed of two cold thermal boundary layers converging on of the material that are rapidly deformed to become softer, each other (Plate 1). In the Earth, the downwellings associ- while slowly-deforming regions become relatively stiff. This ated with plate motions – i.e., subducting slabs – are highly rheology not only yields reasonable plateness, but also leads asymmetric, i.e., only one side of the convergent zone – only to a feedback effect: as the deformed parts of the fluid soften • Is mantle layered at 660 km?

• Is mantle layered at 660 km?

http://instruct.uwo.ca/earth-sci/240a/Part_D.htm Vo l . 7 , N o . 4 April 1997 1997 Annual GSA TODAY Meeting Call for Papers A Publication of the Geological Society of America page 13 Electronic Abstracts Submission Global Seismic Tomography: A page 14 Snapshot of Convection in the Earth Registration Issue June GSA Today Stephen P. Grand, Department of Geological Sciences, University of Texas, Austin, TX 78712 Rob D. van der Hilst, Department of Earth and Planetary Sciences, Massachussetts Institute of Technology, Cambridge, MA 02139 Sri Widiyantoro, Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia

ABSTRACT Two new global high-resolution models of the P-wave and S-wave seismic structure of the mantle were derived independently using different inversion techniques and different data sets, but they show excellent correlation for many large-scale as well as smaller Vo l . 7 , N o . 4 April 1997 1997 scale structures throughout the lower Annual mantle. The two models show that Meeting high-velocity anomalies in the lower GSA TODAY mantle are dominated by long linear Call for Papers A Publication of the Geological Society of America page 13 features that can be associated with the Electronic sites of ancient subduction. The images Abstracts suggest that most subduction-related Submission mantle flow continues well into the Global Seismic Tomography: A page 14 lower mantle and that slabs may ulti- Snapshot of Convection in the Earth Registration Issue June GSA Today mately reach the core-mantle boundary. Stephen P. Grand, Department of Geological Sciences, University of Texas, The models are available from anony- Austin, TX 78712 mous ftp at maestro.geo.utexas.edu in A 2770 km depth Rob D. van der Hilst, Department of Earth and Planetary Sciences, Massachussetts Institute of Technology, Cambridge, MA 02139 directory pub/grand and at brolga.mit. Sri Widiyantoro, Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia edu in directory pub/GSAtoday. ABSTRACT Two new global high-resolution INTRODUCTION models of the P-wave and S-wave seismic structure of the mantle were Since forming about 4.5 Ga, planet derived independently using different EarthP-wave has been cooling by means of rela- inversion techniques and different data sets, but they show excellent correlation tively vigorous convection in its interior for many large-scale as well as smaller and by conductive heat loss across the scale structures throughout the lower cold thermal boundary layer at the top mantle. The two models show that high-velocity anomalies in the lower of the mantle (mainly the oceanic litho- mantle are dominated by long linear sphere). The primary force driving convec- features that can be associated with the tion is the downward pull of gravity on sites of ancient subduction. The images suggest that most subduction-related the cold, dense lithosphere resulting in mantle flow continues well into the downwellings of slabs of subducted litho- lower mantle and that slabs may ulti- mately reach the core-mantle boundary. sphere. Understanding the nature of the The models are available from anony- 2770 km depth mous ftp at maestro.geo.utexas.edu in A Tomography continued on p. 2 directory pub/grand and at brolga.mit. S-wave edu in directory pub/GSAtoday. 2700 km depth INTRODUCTION B Since forming about 4.5 Ga, planet FARALLON SLAB Earth has been cooling by means of rela- 40°N tively vigorous convection in its interior and by conductive heat loss across the Figure 1. Cross sections of mantle P-wave (A) and S-wave (B) velocity variations along a section cold thermal boundary layer at the top through the southern United States. The endpoints of the section are 30.1°N, 117.1°W and 30.2°N, of the mantle (mainly the oceanic litho- 56.4°W. The images show variations in seismic velocity relative to the global mean at depths from the sphere). The primary force driving convec- surface to the core-mantle boundary. Blues indicate faster than average and reds slower than average tion is the downward pull of gravity on 20°N the cold, dense lithosphere resulting in seismic velocity. The large tabular blue anomaly that crosses the entire lower mantle is probably the downwellings of slabs of subducted litho- descending Farallon plate that subducted over the past ~100 m.y. Differences in structure between the sphere. Understanding the nature of the two models in the transition zone (400 to 660 km depth) and at the base of the mantle are probably 120°W 100°W 80°W 60°W 40°W due to different data sampling in the two studies. Tomography continued on p. 2 2700 km depth B FARALLON SLAB 40°N Grand et al., GSA, 1997 Figure 1. Cross sections of mantle P-wave (A) and S-wave (B) velocity variations along a section through the southern United States. The endpoints of the section are 30.1°N, 117.1°W and 30.2°N, 56.4°W. The images show variations in seismic velocity relative to the global mean at depths from the surface to the core-mantle boundary. Blues indicate faster than average and reds slower than average 20°N seismic velocity. The large tabular blue anomaly that crosses the entire lower mantle is probably the descending Farallon plate that subducted over the past ~100 m.y. Differences in structure between the two models in the transition zone (400 to 660 km depth) and at the base of the mantle are probably 120°W 100°W 80°W 60°W 40°W due to different data sampling in the two studies. 40, 4 / REVIEWS OF GEOPHYSICS STERN: SUBDUCTION ZONES

Figure 2. Structure of subducted slabs as inferred from mantle tomography (from Ka´rason and van der Hilst Karason & Van der Hilst, Geophys. Monograph, 2000 [2000]). Red lines show the surface projection of each section. The base of each section is the core-mantle boundary (CMB); dashed lines show the location of mantle discontinuities at 410, 660, and 1700 km. Red and blue colors in each section denote regions where the P wave velocities are relatively slow and fast, respectively, compared to average mantle at the same depth. Fast regions are most easily interpreted as relatively cool areas corresponding to the subducted slab and its viscous mantle blanket. This allows the cool, subducted slab to be traced well below the deepest earthquake. Note that some slabs penetrate the 660 km discontinuity and descend into the lower mantle (e.g., Central America, central Japan, and Indonesia), while other slabs seem to stagnate in the upper mantle (such as Izu-Bonin). The subducted slab beneath Tonga seems to stagnate at the 660 km discontinuity for a while, then cascade into the lower mantle.

Figure 6. (opposite) Geophysical images of subduction zones. (a) P wave tomographic image of NE Japan (modified after Zhao et al. [1994]). There is no vertical exaggeration. (b) P wave tomographic image of Tonga subduction zone (modified after Zhao et al. [1997]). There is no vertical exaggeration. For both Figures 6a and 6b, red and blue colors denote regions where the P wave velocities are relatively slow and fast, respectively, compared to average mantle at the same depth. (c) P wave velocity structure across the Cascadia Subduction Zone (modified after Parsons et al. [1998]). Yellow dots show earthquakes during 1970–1996 between 45Њ and 47Њ latitude, Ͼ M1 at depths Ͼ 25 km and Ͼ M4 at shallower depths. Note vertical exaggeration is 2x. Note that the subduction zones in Figure 6a and 6b subduct old, cold lithosphere, which is relatively easy to identify tomographically, whereas the subduction zone in Figure 6c subducts young lithosphere, which differs less in velocity relative to the surrounding mantle and is more difficult to image tomographically. ● 3-5 and 3-11 ● • Is mantle layered at 660 km?

• Do plumes exist?

Montelli et al., G3, 2006