A.P. van den Berg

The effective viscosity of rocksalt: implementation of steady-state creep laws in numerical models of salt diapirism

A steady-state creep law for rocksalt, describing the two parallel mechanisms of dislocation creep and fluid-enhanced grain-boundary diffusion creep, has been used in numerical models of salt diapirism, to study the effective viscosity of rocksalt. Typical models included a 3-km-thick sedimentary layer on top of 1 km of rocksalt. The grain size of the salt has been varied between 0.5 and 3 cm and the geothermal gradient between 25 and 35 K/km. For strain rates of 10−12−10−15 s−1, typical of salt diapirism driven by buoyancy alone, the diffusion creep mechanism dominates at the fine grain sizes, with dislocation creep becoming important in coarsely grained salt. The effective viscosity ranges from 1017 Pa s for small grain size and high-temperature salt to 1020 Pa s for large grain size and low-temperature salt. The viscosity is strongly dependent on grain size and moderately dependent on temperature. For the larger grain sizes, the dislocation creep mechanism is most effective during the diapiric stage, but the non-Newtonian effects in the salt are not important in determining the growth rate and geometry of the diapirs. The estimates for the Newtonian viscosity of salt that have traditionally been used in modelling of salt dynamics are at the lower end of the range that we find from these numerical experiments.

Underpinning tectonic reconstructions of the western Mediterranean region with dynamic slab evolution from 3-D numerical modeling

No consensus exists on the tectonic evolution of the western Mediterranean since ~35 Ma. Three disparate tectonic evolution scenarios are identified, each portraying slab rollback as the driving mechanism but with rollback starting from strongly different subduction geometries. As a critical test for the validity of each tectonic scenario we employ thermomechanical modeling of the 3-D subduction evolution. From each tectonic scenario we configure an initial condition for numerical modeling that mimics the perceived subduction geometry at ~35 Ma. We seek to optimize the fit between observed and predicted slab morphology by varying the nonlinear viscoplastic rheology for mantle, slab, and continental margins. From a wide range of experiments we conclude that a tectonic scenario that starts from NW dipping subduction confined to the Balearic margin at ~35 Ma is successful in predicting present-day slab morphology. The other two scenarios (initial subduction from Gibraltar to the Baleares and initial subduction under the African margin) lead to mantle structure much different from what is tomographically imaged. The preferred model predicts slab rotation by more than 180°, east-west lithosphere tearing along the north African margin and a resulting steep east dipping slab under the Gibraltar Strait. The preferred subduction model also meets the first-order temporal constraints corresponding to Mid-Miocene (~16 Ma) thrusting of the Kabylides onto the African margin and nearly stalled subduction under the Rif-Gibraltar-Betic arc since the Tortonian (~8 Ma). Our modeling also provides constraints on the rheological properties of the mantle and slab, and of continental margins in the region.

The evolution of continental roots in numerical thermo-chemical mantle convection models including differentiation by partial melting

Abstract Incorporating upper mantle differentiation through decompression melting in a numerical mantle convection model, we demonstrate that a compositionally distinct root consisting of depleted peridotite can grow and remain stable during a long period of secular cooling. Our modeling results show that in a hot convecting mantle partial melting will produce a compositional layering in a relatively short time of about 50 Ma. Due to secular cooling mantle differentiation finally stops before 1 Ga. The resulting continental root remains stable on a billion year time scale due to the combined effects of its intrinsically lower density and temperature-dependent rheology. Two different parameterizations of the melting phase-diagram are used in the models. The results indicate that during the Archaean melting occurred on a significant scale in the deep regions of the upper mantle, at pressures in excess of 15 GPa. The compositional depths of continental roots extend to 400 km depending on the potential temperature and the type of phase-diagram parameterization used in the model. The results reveal a strong correlation between lateral variations of temperature and the thickness of the continental root. This shows that cold regions in cratons are stabilized by a thick depleted root.

Stability and growth of continental shields in mantle convection models including recurrent melt production

The long-term growth and stability of compositionally layered continental upper mantle has been investigated by numerical modelling. We present the first numerical model of a convecting mantle including differentiation through partial melting resulting in a stable compositionally layered continental upper mantle structure. This structure includes a continental root extending to a depth of about 200 km. The model covers the upper mantle including the crust and incorporates physical features important for the study of the continental upper mantle during secular cooling of the Earth since the Archaean. Among these features are: a partial melt generation mechanism allowing consistent recurrent melting, time-dependent non-uniform radiogenic heat production, and a temperature- and pressure-dependent rheology. The numerical results reveal a long-term growth mechanism of the continental compositional root. This mechanism operates through episodical injection of small diapiric upwellings from the deep layer of undepleted mantle into the continental root which consists of compositionally distinct depleted mantle material. Our modelling results show the layered continental structure to remain stable during at least 1.5 Ga. After this period mantle differentiation through partial melting ceases due to the prolonged secular cooling and small-scale instabilities set in through continental delamination. This stable period of 1.5 Ga is related to a number of limitations in our model. By improving on these limitations in the future this stable period will be extended to more realistic values.

Early formation and long-term stability of continents resulting from decompression melting in a convecting mantle

The origin of stable old continental cratonic roots is still debated. We present numerical modelling results which show rapid initial formation during the Archaean of continental roots of ca. 200 km thick. These results have been obtained from an upper mantle thermal convection model including diVerentiation by pressure release partial melting of mantle peridotite. The upper mantle model includes time-dependent radiogenic heat production and thermal coupling with a heat reservoir representing the Earth’s lower mantle and core. This allows for model experiments including secular cooling on a time-scale comparable to the age of the Earth. The model results show an initial phase of rapid continental root growth of ca. 0.1 billion year, followed by a more gradual increase of continental volume by addition of depleted material produced through hot diapiric, convective upwellings which penetrate the continental root from below. Within ca. 0.6 Ga after the start of the experiment, secular cooling of the mantle brings the average geotherm below the peridotite solidus thereby switching oV further continental growth. At this time the thickness of the continental root has grown to ca. 200 km. After 1 Ga of secular cooling small scale thermal instabilities develop at the bottom of the continental root causing continental delamination without breaking up the large scale layering. This delaminated material remixes with the deeper layers. Two more periods, each with a duration of ca. 0.5 Ga and separated by quiescent periods were observed when melting and continental growth was reactivated. Melting ends at 3 Ga. Thereafter secular cooling proceeds and the compositionally buoyant continental root is stabilized further through the increase in mechanical strength induced by the increase of the temperature dependent mantle viscosity. Fluctuating convective velocity amplitudes decrease to below 10 mma’1 and the volume average temperature of the sub-continental convecting mantle has decreased ca. 340 K after 4 Ga. Surface heatflow values decrease from 120 to 40 mW m’2 during the 4 Ga model evolution. The surface heatflow contribution from an almost constant secular cooling rate was estimated to be 6 mW m’2, in line with recent observational evidence. The modelling results show that the combined eVects of compositional buoyancy and strong temperature dependent rheology result in continents which overall remain stable for a duration longer than the age of the Earth. Tracer particles have been used for studying the patterns of mantle diVerentiation in greater detail. The observed ( p, T, F, t)-paths are consistent with proposed stratification and thermo-mechanical history of the depleted continental root, which have been inferred from mantle xenoliths and other upper mantle samples. In addition, the particle tracers have been used to derive the thermal age of the modelled continental root, defined by a hypothetical closing temperature.

Radial profiles of temperature and viscosity in the Earth's mantle inferred from the geoid and lateral seismic structure

Abstract In the framework of dynamical modelling of the geoid, we have estimated basic features of the radial profile of temperature in the mantle. The applied parameterization of the geotherm directly characterizes thermal boundary layers and values of the thermal gradient in the upper and lower mantle. In the inverse modelling scheme these parameters are related to the observables (geoid and seismic structure of the mantle) through the viscosity profile which is parameterized as an exponential function of pressure and temperature. We have tested ∼104 model geotherms. For each of them we have found proper rheological parameters by fitting the geoid with the aid of a genetic algorithm. The geotherms which best fit the geoid show a significant increase of temperature (∼600–800°C) close to the 660-km discontinuity. The value of the thermal gradient in the mid-mantle is found to be sub-adiabatic. Both a narrow thermal core–mantle boundary layer and a broad region with a superadiabatic regime can produce a satisfactory fit of the geoid. The corresponding viscosity profiles show similarities to previously presented models, in particular in the viscosity maximum occurring in the deep lower mantle. The best-fitting model predicts the values of activation volume V ∗ and energy E ∗ which are in a good agreement with the data from mineral physics, except for V ∗ in the lower mantle which is found somewhat lower than the estimate based on melting temperature analysis. An interesting feature of the viscosity profiles is a local decrease of viscosity somewhere between 500 and 1000 km depth which results from the steep increase of temperature in the vicinity of the 660-km discontinuity.

Numerical study of the origin and stability of chemically distinct reservoirs deep in earth’s mantle

Seismic tomography is providing mounting evidence for large scale compositional heterogeneity deep in Earths mantle; also, the diverse geochemical and isotopic signatures observed in oceanic basalts suggest that the mantle is not chemically homogeneous. Isotopic studies on Archean rocks indicate that mantle inhomogeneity may have existed for most of the Earths history. One important component may be recycled oceanic crust, residing at the base of the mantle. We investigate, by numerical modeling, if such reservoirs may have been formed in the early Earth, before plate tectonics (and subduction) were possible, and how they have survived-and evolved-since then. During Earths early evolution, thick basaltic crust may have sunk episodically into the mantle in short but vigorous diapiric resurfacing events. These sections of crust may have resided at the base of the mantle for very long times. Entrainment of material from the enriched reservoirs thus produced may account for enriched mantle and high-μ signatures in oceanic basalts, whereas deep subduction events may have shaped and replenished deep mantle reservoirs. Our modeling shows that (1) convective instabilities and resurfacing may have produced deep enriched mantle reservoirs before the era of plate tectonics; (2) such formation is qualitatively consistent with the geochemical record, which shows multiple distinct ocean island basalt sources; and (3) reservoirs thus produced may be stable for billions of years.

Absolute plate motions and regional subduction evolution

We investigate the influence of absolute plate motion on regional 3-D evolution of subduction using numerical thermomechanical modeling. Building on our previous work, we explore the potential impact of four different absolute plate motion frames on subduction evolution in the western Mediterranean region during the last 35 My. One frame is data-based and derived from the global moving hotspot reference frame (GMHRF) of Doubrovine et al. (2012) and three are invented frames: a motion frame in which the African plate motion is twice that in the GMHRF, and two frames in which either the African plate or the Iberian continent is assumed fixed to the mantle. The relative Africa-Iberia convergence is the same in all frames. All motion frames result in distinctly different 3-D subduction evolution showing a critical dependence of slab morphology evolution on absolute plate motion. We attribute this to slab dragging through the mantle forced by the absolute motion of the subducting plate, which causes additional viscous resistance affecting subduction evolution. We observed a strong correlation between increase in northward Africa motion and decrease in the speed of westward slab rollback along the African margin. We relate this to increased mantle resistance against slab dragging providing new insight into propagation and dynamics of subduction transform edge propagator (STEP) faults. Our results demonstrate a large sensitivity of 3-D slab evolution to the absolute motion of the subducting plate, which inversely suggests that detailed modeling of natural subduction may provide novel constraints on absolute plate motions.

Seismic waves and sources Ari Ben-Menahem and Sarva Jit Singh (Book review)

In recent years several excellent books on the subject of theoretical seismology have appeared on the market. This might be seen as an indication that seismology has finally become a full grown branch of physics since its foundations were laid, theoretically and empirically, in the 19th century. One of these recent books, “Quantitative seismology” by Aki and Richards, appeared in 1980 and has become a standard reference already. The present book “Seismic waves and sources” by Ben-Menahem and Singh appeared in 1981, and it has a somewhat different and more limited scope than that by Aki and Richards. The book contains some 100 pages of appendices on various mathematical techniques applied in the main text, which makes the book rather self contained. The book is clearly written, and contains many references to the literature in the bibliographies at the end of each chapter. Unfortunately there are no references within the text to these bibliographies. The choice of subjects in the book is somewhat subjective and the emphasis is fully on the analytical treatment of the material; methods of a more numeric nature, like the reflectivity method, for the calculation of synthetic seismograms are not treated. This book will certainly become a classic and it should be recommended to anyone involved in seismological research.