Mantle Creep Research Articles

Identifying Geographical Patterns of Transient Deformation in the Geological Sea Level Record

AbstractIn this study, we examine the effect of transient mantle creep on the prediction of glacial isostatic adjustment (GIA) signals. Specifically, we compare predictions of relative sea level (RSL) change from GIA from a set of Earth models in which transient creep parameters are varied in a simple Burgers model to a reference case with a Maxwell viscoelastic rheology. The model predictions are evaluated in two ways: first, relative to each other to quantify the effect of parameter variation, and second, for their ability to reproduce well‐constrained sea level records from selected locations. Both the resolution and geographic location of the RSL observations determine whether the data can distinguish between model cases. Model predictions are most sensitive to the inclusion of transient mantle deformation in regions that are near‐field and peripheral relative to former ice sheets. This sensitivity appears particularly true along the North American west coast in the region of the former Cordilleran Ice Sheet, which experienced rapid sea‐level fall following deglaciation between 14 and 12 kyr BP. Relative to the Maxwell case, Burgers models better reproduce this rapid phase of regional postglacial sea‐level fall. As well, computed goodness‐of‐fit values in this region show a clear preference for models where transient deformation is present in the whole or lower mantle, and for models where the rigidity of the Kelvin element is weakened relative to the rigidity of the Maxwell element. In contrast, model predictions of relative sea‐level change in the far‐field show weak sensitivity to the inclusion of transient deformation.

Mode of slip and crust–mantle interaction at oceanic transform faults

Oceanic transform faults, connecting offset mid-ocean spreading centres, rupture quasi-periodically in earthquakes up to about magnitude M 7.0 that are often preceded by foreshocks. In addition to seismic slip, a large portion of slip takes place as aseismic creep, which likely influences initiation of large earthquakes. Although oceanic transform faults are one of the major types of plate boundaries, the exact mode of slip and interaction between the seismic and aseismic motion remains unclear. Here we present a detailed model of the mode of slip at oceanic transform faults based on data acquired from a recent temporary deployment of ocean-bottom seismometers at the Blanco Transform Fault and existing regional and teleseismic observations. In the model, the crustal part of the fault is brittle and fully seismically coupled, while the fault in the mantle, shallower than the depth of the 600 °C isotherm, creeps partially and episodically. The creep activates small asperities in the mantle that produce seismic swarms. Both mantle and the crustal zones release most of the plate-motion strain during large-magnitude earthquakes. Large earthquakes appear to be preceded by a brief episode of shallow mantle creep, accompanied by seismic swarms, which explains the observation of foreshocks and shows that mantle creep likely influences initiation of large seismic events. Earthquakes in the crust and mantle at transform faults are distinct yet coupled, with seismic swarms in the mantle apparently preceding large earthquakes, according to ocean-bottom seismic monitoring of the Blanco Transform Fault.

Continental crust formation: Numerical modelling of chemical evolution and geological implications

Oceanic plateaus develop by decompression melting of mantle plumes and have contributed to the growth of the continental crust throughout Earth's evolution. Occasional large-scale partial melting events of parts of the asthenosphere during the Archean produced large domains of precursor crustal material. The fractionation of arc-related crust during the Proterozoic and Phanerozoic contributed to the growth of continental crust. However, it remains unclear whether the continents or their precursors formed during episodic events or whether the gaps in zircon age records are a function of varying preservation potential. This study demonstrates that the formation of the continental crust was intrinsically tied to the thermoconvective evolution of the Earth's mantle. Our numerical solutions for the full set of physical balance equations of convection in a spherical shell mantle, combined with simplified equations of chemical continent–mantle differentiation, demonstrate that the actual rate of continental growth is not uniform through time. The kinetic energy of solid-state mantle creep (Ekin) slowly decreases with superposed episodic but not periodic maxima. In addition, laterally averaged surface heat flow (qob) behaves similarly but shows peaks that lag by 15–30Ma compared with the Ekin peaks. Peak values of continental growth are delayed by 75–100Ma relative to the qob maxima. The calculated present-day qob and total continental mass values agree well with observed values. Each episode of continental growth is separated from the next by an interval of quiescence that is not the result of variations in mantle creep velocity but instead reflects the fact that the peridotite solidus is not only a function of pressure but also of local water abundance. A period of differentiation results in a reduction in regional water concentrations, thereby increasing the temperature of the peridotite solidus and the regional viscosity of the mantle. By plausibly varying the parameters in our model, we were able to reproduce the intervals of the observed frequency peaks of zircon age determinations without essentially changing any of the other results. The results yield a calculated integrated continental growth curve that resembles the curves of GLAM, Begg et al. (2009), Belousova et al. (2010), and Dhuime et al. (2012), although our curve is less smooth and contains distinct variations that are not evident in these other curves.

New constraints on upper mantle creep mechanism inferred from silicon grain-boundary diffusion rates

The creep in the Earth's interior is dominated either by diffusion creep which causes Newtonian mantle flow, or by dislocation creep which results in non-Newtonian mantle flow. Although previous deformation studies on olivine claimed a transition from dislocation creep to diffusion creep with depth in the upper mantle, they might misunderstand the creep rates due to experimental difficulties. Since creep in olivine is controlled by silicon diffusion, we measured the silicon grain-boundary diffusion coefficient in well-sintered iron-free olivine aggregates as a function of temperature, pressure, and water content, showing activation energy, activation volume, and water content exponent of 220±30 kJ/mol, 4.0±0.7 cm3/mol, and 0.26±0.07, respectively. Our results based on Si diffusion in forsterite predict that diffusion creep dominates at low pressures and low temperatures, whereas dislocation creep dominates under high pressure and high temperature conditions. Water has negligible effects on both diffusion and dislocation creep. There is a transition from diffusion creep in the shallow upper mantle to dislocation creep in deeper regions. This explains the seismic anisotropy increases at the Gutenberg discontinuity beneath oceans and at the mid-lithosphere discontinuity beneath continents.

Postseismic GRACE and GPS observations indicate a rheology contrast above and below the Sumatra slab

AbstractMore than 7 years of observations of postseismic relaxation after the 2004 Sumatra‐Andaman earthquake provide an improving view on the deformation in the wide vicinity of the 2004 rupture. We include both Gravity Recovery and Climate Experiment (GRACE) gravity field data that show a large postseismic signal over the rupture area and GPS observations in the back arc region. With increasing time GPS and GRACE show contrasting relaxation styles that were not easily discernible on shorter time series. We investigate whether mantle creep can simultaneously explain the far‐field surface displacements and the long‐wavelength gravity changes. We interpret contrasts in the temporal behavior of the GPS‐GRACE observations in terms of lateral variations in rheological properties of the asthenosphere below and above the slab. Based on 1‐D viscoelastic models, our results support an (almost) order of magnitude contrast between oceanic lithosphere viscosity and continental viscosity, which likely means that the low viscosities frequently found from postseismic deformation after subduction earthquakes are valid only for the mantle wedge. Next to mantle creep, we also consider afterslip as an alternative mechanism for postseismic deformation. We investigate how the combination of GRACE and GPS data can better discriminate between different mechanisms of postseismic relaxation: distributed deformation (mantle creep) versus localized deformation (afterslip). We conclude that the GRACE‐observed gravity changes rule out afterslip as the dominant mechanism explaining long‐wavelength deformation even over the first year after the event.

Coupling the atmosphere with interior dynamics: Implications for the resurfacing of Venus

We calculated 2D and 3D mantle convection models for Venus using digitized atmosphere temperatures from the model of Bullock and Grinspoon (Bullock, M.A., Grinspoon, D.H. [2001]. Icarus 150, 19–37) to study the interaction between interior dynamics and atmosphere thermal evolution. The coupling between atmosphere and interior occurs through mantle degassing and the effect of varying concentrations of the greenhouse gas H 2O on the surface temperature. Exospheric loss of hydrogen to space is accounted for as a H 2O sink. The surface temperature enters the mantle convection model as a boundary condition. Our results suggest a self-consistent feedback mechanism between the interior and the atmosphere resulting in spatial–temporal surface renewal. Greenhouse warming of the atmosphere results in an increase in the surface temperature. Whenever the surface temperature reaches a critical value, the viscosity difference across the lithosphere becomes smaller than about 10 5 and the surface becomes locally mobile. The critical surface temperature depends on the activation energy for mantle creep, the stress exponent in the non-Newtonian mantle rheology law, and the mantle temperature. Surface renewal together with surface lava flow may explain why the surface of Venus is young on average, i.e. not older than a few hundred million years. The mobilization of the near-surface lithosphere increases the rate of heat removal from the mantle and thereby the interior cooling rate. The enhanced cooling results in a reduction of the water outgassing rates. As a consequence of decreasing water concentrations in the atmosphere, the surface temperature decreases. Our model calculations suggest that Venus should have been geologically active until recently. This is in agreement with several lines of observational evidence from thermal emissivity measurements and crater distribution analyses.

Three-dimensional lithospheric deformation and gravity anomalies associated with oblique continental collision in South Island, New Zealand

SUMMARY Isostatic considerations exhibit differences between the northern, central and southern parts of the Pacific‐Australian plate collision in South Island, New Zealand. In the northern part mean elevations are moderate and the gravity low is small; the central part contains the highest elevations, and gravity and elevations correspond to each other relatively well; and in the southern part the gravity low is strongest whereas the mean elevations are moderate again. These differences indicate changes in the character of the isostatic compensation and are explained by increased thickening and widening of the crustal root from north to south, and also by the long wavelength gravity response to a mantle density anomaly that increases towards the south. A simple 3-D gravity model is derived that includes the detailed crustal structures from the South Island GeopHysical Transect (SIGHT) experiment as well as a high-density anomaly in the mantle inferred from teleseismic data. The model indicates that cold and, therefore, dense upper mantle material penetrates the asthenosphere to a greater extent in the south, similar to the behaviour of an apparently highly ductile lower crust. As plate reconstruction suggests more lithospheric shortening in the north, our model corresponds to lithospheric material escaping laterally to the south, almost perpendicular to the compression caused by lithospheric shortening of the mantle. Therefore, in addition to the prevailing mantle shear in New Zealand, there may also be a component of extrusional mantle creep beneath the Southern Alps orogen, which could have caused some of the observed large seismic anisotropy in this region. We may have also found evidence for submerged Eocene‐Miocene oceanic lithosphere beneath the southeastern part of South Island that has been unaccounted for after plate reconstruction.

Seismic anisotropy and mantle creep in young orogens

��������� � �� ���������� SUMMARY Seismic anisotropy provides evidence for the physical state and tectonic evolution of the lithosphere. We discuss the origin of anisotropy at various depths, and relate it to tectonic stress, geotherms and rheology. The anisotropy of the uppermost mantle is controlled by the orthorhombic mineral olivine, and may result from ductile deformation, dynamic recrystallization or annealing. Anisotropy beneath young orogens has been measured for the seismic phase Pn that propagates in the uppermost mantle. This anisotropy is interpreted as being caused by deformation during the most recent thermotectonic event, and thus provides information on the process of mountain building. Whereas tectonic stress and many structural features in the upper crust are usually orientated perpendicular to the structural axis of mountain belts, Pn anisotropy is aligned parallel to the structural axis. We interpret this to indicate mountainparallel ductile (i.e. creeping) deformation in the uppermost mantle that is a consequence of mountain-perpendicular compressive stresses. The preferred orientation of the fast axes of some anisotropic minerals, such as olivine, is known to be in the creep direction, a consequence of the anisotropy of strength and viscosity of orientated minerals. In order to explain the anisotropy of the mantle beneath young orogens we extend the concept of crustal ‘escape’ (or ‘extrusion’) tectonics to the uppermost mantle. We present rheological model calculations to support this hypothesis. Mountain-perpendicular horizontal stress (determined in the upper crust) and mountain-parallel seismic anisotropy (in the uppermost mantle) require a zone of ductile decoupling in the middle or lower crust of young mountain belts. Examples for stress and mountain-parallel Pn anisotropy are given for Tibet, the Alpine chains, and young mountain ranges in the Americas. Finally, we suggest a simple model for initiating mountain parallel creep.

Glide-Climb Based GBS Model Applied to Submicrocrystalline Superplasticity

Research on superplasticity in metals have clearly established the importance of microstructural evolution combined with several phenomena: (i) dislocation emission and absorption at and near grain boundaries (ii) concurrent grain growth and (iii) grain boundary sliding (GBS) during deformation [1] . The combined evolutionary aspects of these processes is essential to superplasticity mechanism. With current interest in submicrocrystalline metallic alloys produced by severe deformation processes, and their reported large degree of strain hardening under the condition of low temperature superplasticity, it is necessary to critically examine the understanding and modeling of their response in these materials containing subgrains and ultrafine grains. After examining several steady state and evolutionary hardening-recovery models, it has become clear that an existing superplasticity model involving a mix of two mechanisms: glide-climb based deformation in the grain mantle and general dislocation creep within the grain corc (proposed in 1994) appear to capture all essential features of the experimental behavior. Data for both microcrystalline and submicrocrystalline materials have been reviewed relative to our model and presented here.

Evolution‐Motion of Crustobodies and Geotectonic Metallogeny

Abstract Following the paper entitled A Preliminary Proposal on Crustobody Geotectonics presented by the first author to the 30th IGC in 1996, this paper further extends and elucidates the concept of crustobody in order to make a unifying study of the evolution and motion of crustal structures and to understand the law governing the formation and development of the earth' crust. In this paper the characteristics of crustobody evolution‐motion are given. The authors lay emphasis on the relationship between crustobody evolution‐motion and tectonic metallogeny. In the end, a multiple dynamic system of the crustobody evolution‐motion is discussed from internal and external dynamic forces, and the mantle creep in internal dynamic factors is paid special attention to.

Grain size and temperature dependence of superplastic deformation in an Al–Mg alloy under isostructural condition

The mechanical behavior of a superplastic Al–4.7% Mg–0.8% Mn–0.4% Cu alloy has been characterized by a new type of step strain-rate test which preserves the initial microstructure of the alloy (i.e. an isostructural test). Four different grain sizes of the alloy (8–30 μm), prepared by variations in thermomechanical processing practice, were examined. A sigmoidal relationship between log σ and log ε ̇ is observed for each isostructural condition. The value of maximum m ( = dlog σ/ dlog ε ̇ ) increased with increasing temperature and with decreasing grain size. The isostructural log σ vs log ε ̇ data are evaluated using the grain mantle based quantitative model proposed by Ghosh. In the dislocation creep region ( ε ̇ >10 −1/ s ), the stress exponent is 4.55 and activation energy is close to that for lattice self-diffusion, but the grain size exponent is non-zero (∼0.37). In the grain mantle deformation region ( ε ̇ <10 −3/ s ), the value of the stress exponent based on effective stress ( σ− σ 0, where σ 0 is threshold stress) is ∼1.7, and the grain size exponent is 2.3; but interestingly activation energy is the same as that for dislocation creep. Grain mantle creep is now also believed to be controlled by dislocation glide and climb processes, but its rate is enhanced many times due to a high concentration of vacancies near grain boundaries. σ 0 computed based on the model shows that it increases with increasing grain size and with decreasing temperature.

Engineering geology of the Agaba-Ras El Naqab highway re-alignment, Jordan

A detailed geological investigation was conducted along the section of highway between Station 00 and Station 88 km of the proposed Aqaba to Ras El Naqab highway in Jordan including the Ras El Naqab Escarpment (Station 75–80 km). The Escarpment area is characterized by soil-rock slope failures, and a complex geological pattern of rock units and faults in a rugged terrain. The geological sequence along the highway alignment consists initially of the Kurnub Sandstones Group and mainly within the Upper and Lower Ajlun Formations. The mechanics of movements associated with the Kurnub Sandstone Group include erosion and toppling of sandstone blocks where undercut. Movements manifested within the Upper Ajlun Formation are due to the opening of joints, formation of gulls, cambering, toppling, sliding, rockfalls and the dislocation of limestone blocks. These slope failures associated with the Lower Ajlun Formation are relatively small while large-scale movements and slips occur within the marl and clay. After extensive slope stability analyses were performed an alignment for the proposed road, including the Escarpment stretch was selected, that also included any special construction considerations. Three locations were selected for the detailed slope stability analyses; initially the critical soil parameters were determined assuming that the slopes are marginally stable. Alternate measures for the stability were then considered and the relative effects on the safety factor were analyzed to determine optimum solutions for locating the proposed road. The recommended alignment is situated adjacent to the existing road and located on the west up to Station 75 + 000 km and from Station 76 + 000 km to Station 79 + 700 km. Between Station 75 + 000 km and Station 79 + 700 km to the crest of the Escarpment the new alignment is located east of the existing road. Design criteria adopted for slopes constructed within the Upper Ajlun Formation include protection of exposed marl and clay slopes, sealing of open joints and fractures within the limestone and minimizing the surface areas of marls and clays in slope faces. Criteria for design of slopes within the Lower Ajlun include those presented for the Upper Ajlun as well as proper design of slope angles, placement of interceptor drains, and specific construction techniques to be adopted where mantle creep is anticipated. Features associated with the Kurnub Sandstones require the installation of surface drainage measures as well as revetment techniques to prevent encroachment of rock-block falls onto the highway or into drainage channels.

Axisymmetric finite element analysis of a debonded total hip stem with an unsupported distal tip.

A tapered femoral total hip stem with a debonded stem-cement interface and an unsupported distal tip subjected to constant axial load was evaluated using two-dimensional (2D) axisymmetric finite element analysis. The analysis was performed to test if the mechanical condition suggest that a "taper-lock" with a debonded viscoelastic bone cement might be an alternative approach to cement fixation of stem type cemented hip prosthesis. Effect of stem-cement interface conditions (bonded, debonded with and without friction) and viscoelastic response (creep and relaxation) of acrylic bone cement on cement mantle stresses and axial displacement of the stem was also investigated. Stem debonding with friction increased maximum cement von Mises stress by approximately 50 percent when compared to the bonded stem. Of the stress components in the cement mantle, radial stresses were compressive and hoop stresses were tensile and were indicative of mechanical taper-lock. Cement mantle stress, creep and stress relaxation and stem displacement increased with increasing load level and with decreasing stem-cement interface friction. Stress relaxation occur predominately in tensile hoop stress and decreased from 1 to 46 percent over the conditions considered. Stem displacement due to cement mantle creep ranged from 614 microns to 1.3 microns in 24 hours depending upon interface conditions and load level.

A new understanding of the uplift of the Qinghai-Xizang (TIBET) plateau

The uplift of the Qinghai-Xizang (Tibet) Plateau happened in different crustal movements and different time from those of the collision of Asia continent with the allochthonous India crustobody, and the uplift occurred very long after the finish of the collision. According to its temporal evolution, the uplift happened in another active stage of the mantle creep flow after the active stage resulting in the collision and the interruption of the 140Ma’s quiet stage. On the basis of the dynamic analysis, the uplift resulted from the multiple compressing stresses in the reactivation stage after weakening of the colliding stress and the following compressing stress, and after the interruption of the stable stage dominating the vertical movements and represented by formation of the universal Qinghai-Xizang (Tibet) ancient platform. It was the production of another stress field existing in another crustobody evolution stage and growth age. In the light of the nature of the orogeny, the uplift was caused by the intracontinental Diwa (geodepression)-type orogeny after converging connection of the Central Asia Crustobody and the India crustbody which immediately became a part of the Asia continent, and hence after the substitution for the colliding stress and the following compressing stress by the platform-type crustal movements.

Computer simulations of Alaskan neotectonics

Ongoing deformation and fault slip (neotectonics) in the Alaskan/Bering Sea region were modeled with thin‐plate finite‐element methods by computing anelastic strain rate, stress, and velocity fields which represent time averages over several seismic cycles. Models included variable crust and lithosphere thickness, heat flow, and elevation and incorporated all faults known or thought to be active. Three sets of experiments, totaling 46 models, were computed with systematic variations of shear traction on the megathrust, fault friction within North America, internal friction of lithospheric blocks, and mantle creep strength. Model quality was scored by comparing predictions to geologic data on fault slip rates, the most compressive horizontal principal stress direction , and geodimeter and very long baseline interferometry (VLBI) baseline rates. Best results were obtained with a driving traction of only 10∼15 MPa on the Aleutian megathrust and fault friction of only 0.17 within North America; this is clearly a “low‐stress” model. The fanning of away from the syntaxis was reproduced but does not imply high deviatoric stress magnitudes within the North American plate. The Aleutian forearc west of Kodiak Island moves westward along strike at rates which increase to 65 mm yr−1 in the Komandorsky region. However, no crust is presently escaping westward from the Alaskan syntaxis. Instead, it is shortened and stacked by thrusting, principally in the vicinity of the Chugach and Wrangell Mountains. Because stresses in this model are low and are delicately balanced against topography, it is likely that the present regime represents a transient response to Plio‐Pleistocene glacial mass redistribution and differs from typical tectonic flow in the Tertiary.

Pulsating diapiric flows: Consequences of vertical variations in mantle creep laws

Recent laboratory work has suggested that the rheology of the lower mantle may be Newtonian. We have studied the time-dependent dynamics of plumes interacting with a rheological interface separating an upper non-Newtonian mantle and a Newtonian lower mantle. Pulsating diapiric structures with fast time scales are promoted by the interaction of the rising plumes with this rheological boundary. Surface heat flow signals are discernible as pulses, which remain relatively stationary. They correlate well with the localized upwellings just below the surface. The presence of a mobile lithosphere from increasing the non-Newtonian power-law index helps to produce a large-scale circulation in the upper mantle which draws large hot patches away from nearby upwellings. In our calculations the resultant averaged effective viscosity of the non-Newtonian upper mantle is about two orders of magnitude lower than that of the Newtonian lower mantle. A viscously stratified Newtonian model produces more incoherent and broad-scale diapiric structures and is less efficient for generating sharply varying time-dependent thermal signatures.

Viscosity structure implied by mantle convection

The total mechanical dissipation by convective motion in the mantle is well constrained by thermodynamic arguments to ∼ 5.6 × 10 12 W. By adopting a simple convection model we can use the observed mean plate speed υ = 3.25 cm y −1 to estimate the mean mantle creep rate, ϵ ̇ ≈ 7.2 × 10 −16 s −1 , which implies a mean effective stress σ ≈ 8.5 × 10 6 Pa and a corresponding viscosity υ ⋍ 1.2 × 10 22 Pa s. This viscosity estimate is biased low by the nature of the implied averaging, but for better estimates we must make assumptions about the internal convective pattern. If we assume that the convection is self-sustaining at all depths, and therefore that the depth distribution of dissipation is the same as the depth distribution of generated power, and that the convective pattern is self-adjusted to make stress independent of depth, then we can specify the mantle viscosity profile. These assumptions imply quasi-steady convection. The fact that viscosities inferred from convection are higher than values from isostatic rebound most plausibly arises as a difference between steady state and transient creep.

Influence of modal composition on deformation in garnet Iherzolite nodules

A textural distinction has been drawn, in peridotites derived from kimberlite pipes, between relatively undeformed granular types and strongly deformed sheared types1, that corresponds roughly with the absence and presence of large strained olivine grains (porphyroclasts) surrounded by smaller, recrystallized grains (neoblasts). More detailed classifications have also been proposed2–6. The textural variety is probably caused by both widespread mantle creep and more localized phenomena connected with kimberlite eruption7–12. From consideration of dynamically recrystallized grain size11 and dislocation densities12, it seems that nodules that contain neoblasts have been deformed in high stress and strain rate conditions, over short periods of time, before eruption. The formation of the sheared textures and the eruption of the kimberlite are approximately simultaneous. I report here detailed textural observations on 10 garnet Iherzolite nodules collected from kimberlite pipes in South Africa and Lesotho. They all have sheared textures, as defined above, showing a range from small amounts of grain boundary recrystallization to almost complete consumption of olivine porphyroclasts. Sections were cut parallel to the foliation and modal analyses were accurately determined by point counting one slide from each sample. The number of olivine porphyroclasts on each slide was then independently counted. The fewer the grains, the greater is the accuracy of estimating their number. Average porphyroclast areas were then calculated (Table 1). The data suggest that modal composition controls the extent of shearing.

The cooling Earth: A reappraisal

By treating the lithosphere as a diffusive boundary layer to mantle convection, the convective speed or mantle creep rate, ϵ ̇ , can be related to the mantle-derived heat flux, Q ̇ . If cell size is independent of Q ̇ 2 then ϵ ̇ ∝ Q ̇ . (If cell size varies with Q ̇ , then a different power law prevails, but the essential conclusions are unaffected.) Then the factthat for constant thermodynamic efficiency of mantle convection, the mechanical power dissipation is proportionalto Q ̇ , gives convective stress σ ∝ Q ̇ −1 , i.e. the stress increases as the convection slows. This means an increasing viscosityor stiffness of the mantle which can be identified with a cooling rate in terms of a temperature-dependent creep law. If we suppose that the mantle was at or close to its melting point within 1 or 2 × 10 8 years of accretionof the Earth, the whole scale of cooling is fixed. The present rate of cooling is estimated to be about 4.6 × 10 −8 deg y −1 for the average mantle temperature, assumed to be 2500 K, but this very slow cooling rate represents a loss ofresidual mantle heat of 7 × 10 12 W, about 30% of the total mantle-derived heat flux. This conclusion requires theEarth to be deficient in radioactive heat, relative to carbonaceous chondrites. A consideration of mantle outgassing and atmospheric argon leads to the conclusion that the deficiency is due to depletion of potassium, and that the K/U ratio of the mantle is only about 2500, much less than either the crustal or carbonaceous chondritic values. Thetotal terrestrial potassium is estimated to be about 6 × 10 20 kg. Acceptance of the cooling of the Earth removes the necessity for potassium in the core.

Petrography and geological history of upper mantle xenoliths from the matsoku kimberlite pipe

Upper mantle (garnet-peridotite facies) xenoliths from the Matsoku kimberlite pipe consist predominantly of olivine, orthopyroxene, clinopyroxene and garnet, with a wide range of modal values. In some xenoliths metasomatism, under the ambient mantle P.T. conditions indicated by all xenoliths, has added the primary-metasomatic minerals: phlogopite, ilmenite, rutile, pyrrhotite, pentlandite and chalcopyrite. This metasomatism has probably occurred within the kimberlite magma envelope at depth, and been caused by fluid derived from the kimberlite magma. Omitting metasomatic aspects, the xenoliths show a wide and broadly continuous range of textural varieties, which may be referred to three major groups: coarse-grained (showing restricted deformation and recrystallization), flaser (relatively strongly deformed and showing extensive recrystallization) and even-textured (extensively annealed following deformation). These form a progressive sequence of deformation and annealing, the latter involving recovery, recrystallization and grain growth. It is evident from the textural features, in conjunction with aspects of mineral chemistry, that the xenoliths cannot be in any simple sense cognate with the kimberlite magma, and that a wide variety of textural types occurs within a restricted location in the upper mantle. The deformation and annealing responsible for the textural variety are probably caused both by widespread mantle creep and more localized phenomena occurring within the kimberlite magma envelope at depth. Petrographic and chemical characteristics suggest that the banding seen in some xenoliths is dominantly of cumulate igneous origin.