Wolfgang R. Jacoby

Paraffin model experiment of plate tectonics

Qualitatively or semi-quantitatively, model experiments can teach us problems of plate tectonics, although they are difficult to scale mechanically and thermally at the same time. Our model consists of molten paraffin with a frozen skin on top (+0.05 g/cm3). Surface tension, cohesion effects, and fast thin skin freezing prevent even thick skins from sinking by themselves. If sinking is initiated forcefully, it occurs very similarly to that of the lithosphere. However, we cannot yet generate or melt the skin with the same rate as that of sinking. Convection cells caused by localized heating at the bottom of the tank interact with sinking plates in a way suggesting that deep-mantle convection rising below oceans, particularly the Pacific, is not important for plate dynamics.

On the effects of the lithosphere on mantle convection and evolution

Abstract An idealized model is discussed for plate motion and mantle convection. It consists of a “numerical” square box filled with a Newtonian-Boussinesq fluid heated from below. At the surface, the fluid has a high viscosity, i.e. it contains a stiff lid which may or may not be laterally decoupled by weakness zones. Lid stiffness and coupling were varied systematically. Only if the lid is effectively decoupled laterally, does it move as a quasi-rigid plate. It is then driven by the lateral pressure differential from the rising and descending plumes in the fluid and it moves against viscous shear at its bottom. Gravitational sliding and sinking may also drive the plate if allowed for in the model. A decoupled freely-moving stiff plate effectively removes heat from the interior. A strongly-coupled stiff lid, on the other hand, or one with a very large aspect ratio inhibits heat transfer through the convecting layer. If heating occurs by a given flux through the bottom or internal heat generation the internal cell temperatures become very high, because the “stagnant” surface lid can only conduct the heat by assuming the required temperature gradient throughout its thickness. Since the Earth is partly covered by conducting continental lids which in addition contain much of the heat sources, the thermal history may be affected; caution must be exercised in parameterized convection modelling in this respect. The overall effect cannot easily be predicted because mantle flow and continental plates will interact. The importance of mechanical decoupling for plate motion strongly calls for thorough studies of the decoupling mechanisms, particularly at convergent plate boundaries, bending, stick-slip processes, and the role of volatiles.

Teleseismic p-wave traveltime residuals and deep structure of the Aegean region

Abstract Teleseismic P-wave traveltime residuals have been measured at the Greek seismic stations with respect to the Herrin 68 tables. In spite of the large scatter, some insight into crustal and upper-mantle structure of the Aegean region can be gained. The average absolute residuals (observed minus Herrin traveltimes) are of the order of + 2 s. The most plausible interpretation is an efficient low-velocity zone in the upper mantle. Simple estimates of densities and subsequently gravity with the aid of Birchs law suggest that the Aegean region is underlain by hot expanded upper mantle, perhaps involving partial melting. The relative P residuals (observed minus Herrin traveltime differences between a station and Athens) are generally positive and can be interpreted with lateral variations of the LVZ or of the crust. The latter interpretation is supported in some cases by seismic refraction data. The azimuthal variation of the relative residuals at stations on the non-volcanic arc bears a distinct relation with the arc orientation. At Archangelos (Rhodes) where we “see” through the Benioff zone, the residuals from N to W are between -1 and -2 s and indicate a high-velocity slab sinking below the Aegean sea. At Vamos (Crete), Valsamata (Kephallenia), and Joanina (Pindus Range) the largest (smallest) residuals are along directions parallel (perpendicular) to the arc. This can be interpreted by crustal thickening under the sedimentary arc and/or by velocity anisotropy with the maximum perpendicular to the arc. On the whole, our study supports the hypothesis that the Aegean region is a trench—island-arc—marginal-sea system.

Rayleigh wave dispersion along Reykjanes Ridge

Abstract Group velocities of Rayleigh waves in the period range of 15–40 s have been measured at Akureyri, northern Iceland, for events on southern Reykjanes Ridge and Charlie-Gibbs fracture zone. Phase velocities have not been measured because the source mechanisms are unknown. At all periods the group velocities increase significantly with the age of the lithosphere from 0 to 20 or 30 Ma. However, a slight intervening group velocity decrease from the axial zone (0–3 Ma) to the flank (6–8 Ma) is suggested for periods from 20 s up. To obtain “pure” oceanic velocities, an “Iceland correction” has been attempted; although it is uncertain, it doubtlessly accentuates the group velocity variations with period and with age of the lithosphere traversed. Inversion to S-velocity structure of the developing lithosphere is difficult because of insufficient data precision. It has been attempted by a systematic search method. In a model with a lithospheric lid and an asthenospheric channel, we may determine the S velocity of the lid, perhaps its thickness but hardly the S velocity of the channel. Very low S velocities in the uppermost mantle near the ridge axis are clearly indicated and suggest partial melting. The average S velocity in the upper 60–80 km increases from 0.3 to 0.4 km/s during the first 20 Ma of age. The group velocity decrease from the axis to the flank (at 6–8 Ma) suggests that the development of the lithosphere is more complex than simple thickening.

Modern concepts of Earth dynamics anticipated by Alfred Wegener in 1912

In his first publication on continental drift, Alfred Wegener anticipated sea-floor spreading, the functional relationship between bathymetry and age or temperature below the sea floor, perhaps mantle convection, and some aspects of plate tectonics. Some of these insights, such as sea-floor spreading and bathymetry with age, did not appear in his later work; others, such as convection and plate tectonics, were taken up when new evidence became available. His intuition led him to these insights, and he had a very clear perception of the distinction between facts and speculation.

Convection experiments and the driving mechanism

ZusammenfassungDas Problem der Mantelkonvektion wird im Lichte neuer Laboratoriums- und Computerexperimente diskutiert. Seit Wegener haben wir über das Verhalten des Erdkörpers manches hinzugelernt, so daß wir bessere Aussichten haben, die Kontinentalverschiebung zu erklären. Die Erklärung muß den Aspekt der Konvektion einschließen, ihre Form ist jedoch noch offen. Das Problem ist ein dreifaches: es umfaßt die Lösung physikalischer Gleichungen, es beinhaltet unzureichend bekannte Randbedingungen, und es schließt die von der Lösung beeinflußten — nicht a priori vorhersagbaren — Materialeigenschaften mit ein. Ein heute wahrscheinliches Modell ist Konvektion bei hoher Rayleigh-Zahl in einem Medium mit temperatur-, druck- und spannungsabhängiger Rheologie. Es sind thermische Grenzschichten zu erwarten, deren obere durch die kalten hochviskosen bzw. „festen“ und schweren Lithosphärenplatten gebildet wird, während die untere an der Kern-Mantel-Grenze heiß, flüssig und leicht ist. Die Platten sind gravitativ instabil und üben einen stark ordnenden Einfluß auf die großräumige Mantelströmung aus. Die untere Grenzschicht ist ebenfalls instabil und hat die Tendenz, die großräumige Zirkulation diapirartig zu durchbrechen. Durch dieses Modell kann der Konflikt zwischen Horizontal- und Vertikaltektonik gelöst werden.AbstractThe problem of mantle convection is discussed in light of laboratory and numerical experiments. Since Wegeners time our knowledge of earth behaviour has increased, so that we are in a better position to explain continental drift. The explanation of this phenomenon must inevitably include mantle convection. The problem has three aspects: the physical laws, the boundary conditions, and the material. We find that a likely model is high-Rayleigh number convection in a medium of temperature, pressure, and stress-dependent rheology; in this model we expect a strong and heavy upper thermal boundary layer and a fluid and light lower boundary layer. The upper one consists of the lithospheric plates which highly organize the large-scale circulation, while the lower one at the core-mantle boundary becomes unstable in the form of diapirs, plumes, or blobs in a fashion rather independent of the large-scale circulation. This model has the potential of reconciling the conflicting views of horizontal and vertical tectonics.RésuméLe probléme de la convection du manteau est discuté à la lumière de nouvelles expériences de laboratoire et à lordinateur. Depuis Wegener nous avons appris bien des choses sur le comportement du corps terrestre ce qui nous donne de meilleurs vues pour expliquer le déplacement des continents. Lexplication doit comporter laspect de la convection, dont la forme reste encore ouverte. Le problème est triple: il comporte la solution déquations physiques, il implique les conditions à la limite qui ne sont pas assez connues, ainsi que les proprietés des matériaux, qui, non prévisibles a priori, sont influencées par les solutions. Un modèle probable est la convection, dans le cas dun nombre de Rayleigh élevé, dans un milieu à rhéologie dépendant de la température, de la pression et de la tension. Il faut s áttendre à lexistence de couches-limites thermiques, dont la supérieure consiste dans les plaques lithosphériques froides et denses, visqueuses, voire «consolidées», tandis que linférieure, située à la limite du manteau et du noyau, est chaude, liquide et légère. Les plaques sont instables et exercent une forte influence dans lordonnance à grande échelle des courants du manteau. La couche limite inférieure est également instable et possède la tendance de pénétrer diapiriquement dans cette grande circulation. Ce modèle donne la possiblité de régler le conflit entre la tectonique horizontale et verticale.Краткое содержаниеС помощью электронно-счетной машины произ вели рассчет конвекционн ых потоков мантии. Со вре мен Вегенера накопил ось так много материала, что имеется возможность разумно объяснить ра схождение материков. Это объясн ение должно включать и вли яние конвекционных п отоков, хотя форма этих последних остае тся ещё нерешенной. Зд есь сталкивается с трояк ой проблемой: необходим остью решить уравнен ие, причем условия на краях щитов известны недос таточно, и определить свойства материала, влияющего на решение задачи, пре дсказать которые а пр иорно невозможно. Наиболее реальная модель пред ставляется, как конве нция при воздействии высоког о значения числа Рейли в среде с зависимой от температуры, давлени я и напряжения реологией. Можно ожид ать присутствие погр аничных слоев, из которых верхние обра зованы холодными, оче нь вязкими, или даже „твердыми“ и тяжелыми плитами ли тосферы, в то время, как нижние, находящиеся на границе ядро/манти я, являются горячими, ж идкими и легкими. Плиты оказываются в гравит ационном смысле нест абильными и оказывают влияние на большие потоки в ма нтии. Нижний погранич ный слой оказывается также нестабильным и проявляет тенденцию, прорвать обширную циркуляцию на подобие диапирам. Э та модель разрешает у странить противоречия между горизонтально й и вертикальной тект оникой.

One-dimensional modelling of mantle flow

A one-dimensional model of flow between a fixed boundary at the bottom and a moving one on top with no net flow through vertical sections is tested for geophysically interesting mantle viscosity-depth functions. Such a model, although simplistic, may help in answering the question to what depth the return flow extends, at least in the case of moving plates measuring many thousand kilometers across, such as the Pacific plate.It the viscosity in the asthenosphere is less than three orders of magnitude smaller than that of the mantle below, the return flow extends to great depth and the asthenosphere is a zone of concentrated shear. If the viscosity contrast is greater, the return flow is concentrated in the asthenosphere. For a wide range of model parameters typical flow velocities below the asthenosphere are about one-tenth of the plate velocity. The pressure gradient required by the mantle flow may be manifest in gravity trends across moving plates, but no excessive gravity anomalies are required by the model if the absolute viscosity values conform to those inferred from post-glacial rebound data. A thinner and lower-viscosity layer is favored over a thicker and more viscous layer if both fit glacial rebound evidence. The present model may not be applicable if down to the core the viscosity is as low as about 1021 N s m−2 with a free-slip bottom boundary.

Plate kinematics and the gravity field

Abstract Both the system of plate motions and the global gravity field or the geoid are now so precisely known that it seems worthwhile to look for quantitative relationships. Some aspects, such as the general occurrence of positive gravity and geoid anomalies in regions of plate convergence, have long been known. Our aim is to describe the gravitational field in terms of plate-kinematic parameters and we present a preliminary step in this direction: for four plates (Pacific, Nazca, Indian, American) we have computed the correlation of the Gem 8 geoid heights (with reference to an ellipsoid of 1/298.255 ellipticity) with distance from the poles of motion and distance from the axes in an “absolute” frame. The geoid tends first to drop from the ridge axes to at least 10° distance and then to rise toward the convergence zones. This trend is strongest for the Indian plate in collision with Eurasia, is smaller, but very clear for the oceanic Pacific and Nazca plates, and is not developed for the American plate which does not subduct. We did not find a consistent relationship for the geoid with distance from the pivots. A possible interpretation of the results is the return flow of the large-scale mantle circulation.

Plate theory, epeirogenesis and eustatic sea-level changes

Abstract The consistent rise of the cratons with respect to sea level and the arching-up of the Precambrian shields through time may be due at least in part to the old continental lithosphere floating upwards in an environment of increasing density. A densification of the asthenosphere and oceanic lithosphere will arise from fractionation inherent in the process of plate generation and destruction and the building of new island arcs, if the system in exchange of matter is closed. Temperature variations in the mantle with time are likely to superimpose density variations with time on the general trend of densification. Other important influences on sea level are a change in total volume of free water, the area of the oceans and erosion or sedimentation on land. It is not possible to separate the above effects. The assumption of isostasy, however, permits the different effects to be interrelated and places limits on the individual effects.

On the global gravity field and plate kinematics

Abstract In this paper we investigate the relation between the geopotential as represented by low-order harmonics and present plate kinematics. Using coordinates connected to the poles of absolute plate motion we demonstrate certain systematics of the geoid along and across the trajectories of the eight major plates PAC, AFR, IND, EUR, NAM, SAM, ANT and NAZ. Although the systematics varies from plate to plate this variation is not arbitrary but is related to additional parameters, such as the magnitude of “absolute” velocity, the occurrence of subduction and the existence of continents on the plates. Our main conclusion is that the low-order geoid is related dominantly to two phenomena: to current subduction and to the past Pangea, or in other words, to a flow field that has accompanied, or has caused, the break-up of Pangea. Such a conclusion is, of course, speculative and requires much further investigation.