Three-dimensional strain analysis in physical models of geological structures

A method is outlined for calculating three-dimensional finite strain in physical models of geological structures containing passive strain markers. This method makes it possible to determine the three-dimensional strain pattern in models of structures that lack any of the types of symmetry (such as that imparted by cylindrical folding) that simplified calculations in previous work. The strain markers in the new method are in the shape of stubby rectangular prisms or cubes. These form a three-dimensional grid or array occupying each of the active layers in a model (e.g., for a simple two-layer gravitationally unstable system, one grid for the overburden layer and one for the buoyant layer). Each of the grids can be described by positions of three families of “strain marker surfaces”, which are contacts between layers of strain markers.

After deformation, the model is serial-sectioned horizontally and the traces of the strain marker surfaces on the sections are digitized. The strain state is calculated at each of several hundred points arranged in a three-dimensional “output grid” extending throughout the mechanically active part of the model. An interpolation procedure is used to estimate the spacing and orientation of the strain marker surfaces in the vicinity of each of the output grid points. The following quantities are determined for each of the three families of strain marker surfaces:

1. (1) the local horizontal orientation of the strain marker surfaces;

2. (2) the local spacing of the surfaces; and

3. (3) the local inclination of the surfaces, calculated from their change in position from the serial section above, to the serial section below, the output grid point.

This information is used to generate a parallelepiped representing the strain marker geometry in the neighbourhood of the output grid point. The edges of the parallelepiped are equivalent to the coefficients of the strain matrix, from which the three principal strain magnitudes and orientations are readily derived.     

The duisburg method of metro-construction, a successful application of the gap freezing method

Between March 1977 and August 1979 contract No.4 of the Stadtbahnbau (Metro-construction) in Duisburg was executed, making successful use of gap freezing.

The gap freezing was necessary because the Metro-tunnel is crossed by a groundwater stream (flow velocity up to 15 m/d) and it had to be assured that open cut construction of the tunnel was possible and that the original situation could be reinstated as far as possible after completion.

The Duisburg building ground also made a special construction method necessary. Ground strata: from surface to 2–4 m, civilisation deposits; from ˜ 4 m to ≈ 25–28 m below surface, glacial sand and gravel deposits, containing stones with a diameter > 20 cm and even boulders of 1 m³ and more; from approximately 28 m below surface, layers of Tertiary clay and silt; the groundwater table is ˜ 8 m below the surface, the stream flowing within the sand and gravel deposits from SE to NW (towards the Rhine).

Installing a groundwater barrier, for instance by erecting a continuous diaphragm wall enclosure, was already ruled out in early design stages as was the use of driven steelpiles.

At the inception of the design in 1974, it was decided first to carry out a measuring scheme to establish the groundwater flow velocity. This was followed by a large scale (1:1) trial freezing to ascertain the feasibility of the gap-freezing method.

When these experiments were scientifically valued it was established, that the risk involved was acceptable. The contract documents were prepared prescribing a combination of “cover and cut” with gap-freezing, which is tentatively called the “Duisburg method of Metro-construction”.

During the construction a large scale measuring and scientific research programme was carried out.     

Decelerating precursory seismicity in Vrancea

Preshock seismic excitation followed by seismic quiescence has been observed in the seismogenic region of strong shallow mainshocks. The strain released by such preshocks is decelerating with the time to the mainshock and is fitted by a power-law with a power value larger than unit. This model is tested in the present work for the intermediate-depth earthquakes of the Vrancea region, generated in an isolated seismogenic zone proper for such testing. A backward application of this “decelerating preshock strain” model for the case of 4.3.1977 (M = 7.5) earthquake, for which reliable data are available, shows a good fit of the power-law pattern to the seismic activity preceding the main shock. The occurrence rate of recent intermediate-depth shocks in Vrancea indicates that this region is currently in a state of decelerating seismic deformation, which may lead to the generation of a strong intermediate-depth mainshock there at about the beginning of the third decade of the present century. The respective uncertainties are unknown due to lack of previous relative studies.     

Space–time distribution of interplate moment release including slow earthquakes and the seismo-geodetic coupling in the Sanriku-oki region along the Japan trench

Along the Japan trench where some Mw8 class interplate earthquakes occurred in the past century such as the 1896 Sanriku tsunami earthquake (M6.8, Mt8.6, 12×10²⁰ N m) and the 1968 Tokachi-oki earthquake (Mw8.2, 28×10²⁰ N m), the Pacific plate is subducting under northeast Japan at a rate of around 8 cm/year. The seismic coupling coefficient in this region has been estimated to be 20–40%. In the past decade, three ultra-slow earthquakes have occurred in the Sanriku-oki region (39°N–42°N): the 1989 Sanriku-oki (Mw7.4), the 1992 Sanriku-oki (Mw6.9), and the 1994 Sanriku-oki (Mw7.7) earthquakes. Integrating their interplate moments released both seismically and aseismically, we have the following conclusions. (1) The sum of the seismic moments of the three ultra-slow earthquakes was (4.8–6.6)×10²⁰ N m, which was 20–35% of the accumulated moment (18.6–23.0)×10²⁰ N m, in the region (39°N–40.6°N, 142°E–144°E) for the 21–26 years since the 1968 Mw8.2 Tokachi-oki earthquake. This is consistent with the previous estimates of the seismic coupling coefficient of 20–40%. On the other hand, the sum of the interplate moments including aseismic faulting is (11–16)×10²⁰ N m, leading to a “seismo-geodetic coupling coefficient” of 50–85%, which is an extension of the seismic coupling coefficient to include slow events. (2) The time constants showed a large range from 1 min (10² s) for the 1968 Tokachi-oki earthquake to 10–20 min (10³ s) for the 1896 Sanriku tsunami earthquake, to one day (10⁵ s) for the 1992 Sanriku-oki ultra-slow earthquake, to on the order of one year (10⁷ s) for the 1994 Sanriku-oki ultra-slow earthquakes. (3) Based on the space–time distribution, three “gaps of moment release,” (40.6°N–42°N, 142°E–144°E) 39°N–40°N, 142°E–143°E) and (39°N–40°N, 142°E–144°E), are identified, instead of the gaps of seismicity.     

Main features of crustal structure in western and southern Europe based on data of explosion seismology

During the past two decades deep seismic sounding measurements have been carried out in western and southern Europe, mainly using the refraction method. These investigations were performed partly on a national basis but as well within international cooperative programs under the sponsorship of the European Seismological Commission.

In France, a systematic study has been executed to determine the main feature of deep structures under the Central Massif and the Paris Basin. In the Forez and Margeride regions, the sub-crustal velocity is lower (7.2 km/sec) than the normal value (8.0 km/sec) observed in the adjacent areas.

The central and southern part of Western Germany is covered by an extensive network of refraction profiles. The crustal thickness varies, similarly to France, from 25 to 35 km. A great amount of deep reflection data was obtained by commercial and special reflection work. The crust beneath the Rhinegraben area shows the typical “rift system” structure with a low subcrustal velocity (7.4–7.7 km/sec).

Very intensive refraction work has been carried out in the Alpine area. The maximum crustal thickness found near the axis of the negative gravity anomaly is about 55–60 km. Furthermore, a clear lowvelocity layer at a depth between 10 and 30 km has been detected. A key position with regard to the geotectonic structure of the Alps is held by the zone of Ivrea characterized by a pronounced gravity high. From the refraction work it may be concluded that there material of the lower crust and the upper mantle (7.2–7.5 km/sec) is overlying a layer of extremely low velocity (5.0 km/sec) which is interpreted as sialic crust.

Three years ago, a systematic study of crustal structure of the Italian peninsula has been started. Reversed profiles were observed on Sicily, in Calabria, and in Puglia. On Sicily, the structure is very complicated; the crust of the western part looks like a transition between a continental and oceanic structure whereas the eastern side shows a continental-type crust. In Calabria and Puglia, the crustal thickness has been determined to be about 25–35 km.     

Structure of the earth''s crust on the territory of the U.S.S.R.

The compilation of statistical data for 269 seismic crustal sections (total length: 81,000 km) which are available in the U.S.S.R. has shown that the preliminary conclusions drawn on relations between the elevation of the surface relief and Bouguer anomalies on one hand and crustal thickness (depth to the M-discontinuity) on the other hand are not fulfilled for the continental part of the U.S.S.R. The level of isostatic compensation has been found to be much deeper than the base of the earth's crust due to density inhomogeneities of the crust and upper mantle down to a depth of 150 km.

The results of seismic investigations have revealed a great diversity of relations between shallow geological and deep crustal structures:

Changes in the relief of the M-discontinuity have been found within the ancient platforms which are conformable with the Precambrian structures and which can exceed 20 km. In the North Caspian syneclise, extended areas devoid of the “granitic” layer have been discovered for the first time in continents. The crust was found to be thicker in the syneclises and anteclises of the Turanian EpiHercynian plate. In the West Siberian platforms these relations are reversed to a great extent.

Substantial differences in crustal structure and thickness were found in the crust of the Palaeo zoides and Mesozoides. Regions of substantial neotectonic activity in the Tien-Shan Palaeozoides do not greatly differ in crustal thickness if compared to the Kazakhstan Palaeozoides which were little active in Cenozoic time. The same is true for the South Siberian Palaeozoides.

The Alpides of the southern areas in the U.S.S.R. display a sharply differing surface relief and a strongly varying crustal structure. Mountains with roots (Greater Caucasus, Crimea) and without roots (Kopet-Dagh, Lesser Caucasus) were found there.

The Cenozoides of the Far East are characterized by a rugged topography of the M-discontinuity, a thinner crust and a less-pronounced “granitic” layer. A relatively small thickness of the crust was discovered in the Baikal rift zone.

The effective thickness of the magnetized domains of the crust as well as other calculations show that the temperature at the depth of the M-discontinuity (i.e., at depths of 40–50 km) is not higher than 300–400° C for most parts of the U.S.S.R.     

Twenty years of paleoseismology in Italy

Italy has one of the most complete and historically extensive seismic catalogues in the World due to a unique and uninterrupted flow of written sources that have narrated its seismic history since about the end of the Iron Age. Seismic hazard studies have therefore always been mainly based upon this huge mass of data. Nevertheless, the Italian catalogue probably “lacks” many M ≥ 6.5 events, the seismogenetic structures responsible for which are characterized by recurrence times that are longer than the time span covered by our historical sources. For these reasons, and as in other countries, earthquake data that in Italy have been derived from paleoseismological studies should finally become a necessary ingredient in seismic risk assessment. Indeed, over the past 20 years, some hundred trenches have been excavated, supplying reliable and conclusive data on the recent activities of many faults. Through to many robust datings of surface fault events, these studies have provided the ages of several unknown or poorly known M ≥ 6.5 earthquakes. Here, we summarize the state of the art of paleoseismology in Italy, and present a first catalogue of 56 paleoearthquakes (PCI) that occurred mainly in the past 6 kyr. The PCI integrates the historical/instrumental seismic catalogue, and extends it beyond the recurrence time of the seismogenetic faults (2000 ± 1000 yr). We feel confident that the use of the PCI will enhance future probabilistic seismic hazard assessment, and thus contribute to more reliable seismic risk mitigation programs.     

Constraining diamond metasomatic growth using C- and N-stable isotopes: examples from Namibia

The present paper provides C- and N-stable isotope characteristics, N-contents and N-aggregation states for alluvial diamonds of known paragenesis from placers along the Namibian coast. The sample set includes diamonds with typical peridotitic and eclogitic inclusions and the recently reported “undetermined” suite of Leost et al. [Contrib. Mineral. Petrol. 145 (2003) 15] which resulted from infiltration of high temperature, carbonate-rich melts. δ¹³C-values range from −20.3‰ to −0.5‰ (n=48) for peridotitic diamonds and from −38.5‰ to −1.6‰ (n=45) for eclogitic diamonds. Diamonds belonging to the “undetermined” suite span a narrower range in δ¹³C from −8.5‰ to −2.7‰ (n=13). When compared with previous studies, diamonds from Namibia are characterised by unusually low proportions of N-free (i.e. Type II) peridotitic and eclogitic diamonds (3% and 2%, respectively) and an unprecedented high proportion of N-rich diamonds (15% and 73%, respectively, have N-contents >600 ppm). δ¹⁵N-values for diamonds of the peridotitic, eclogitic and “undetermined” suites range from −10‰ to +13‰ without correlations with either N-content or δ¹³C. The similarity in N-isotopic composition and the N-rich character of diamonds belonging to the eclogitic, peridotitic and “undetermined” suites is striking and suggests a close genetic relationship. We propose that a large part of the diamonds mined in Namibia formed during metasomatic events of similar style that introduced carbon and nitrogen into a range of different host lithologies.     

Features of coated diamonds from the Snap Lake/King Lake kimberlite dyke, Slave craton, Canada, as revealed by optical topography

Confocal photoluminescence (PL) and local absorption spectroscopy were used to study the types and spatial distribution of point defects in coated diamonds, the input of which is about 30% in the Snap Lake deposit, Canada. Nitrogen concentration is on the level of several hundreds of ppm in the core, with a nitrogen-poor layer in its outer part, whereas in the coat it is usually several times higher as a result of fast growth. Nitrogen defects in the core are strongly aggregated with N3, B and B′-forms dominating, whereas A-defects are typical of the coat. The rounded shape of the coated diamonds is a result of the combined effect of partial dissolution of the octahedral core and the “abnormal” growth of the coat, which produces a fibrous structure. Analysis of PL and PL excitation spectra showed that structureless yellow-green PL of the coat is likely to be due to nickel-nitrogen complexes with their fine structure broadened in the strain fields. The presence of irradiation/annealing products such as vacancies V⁰ and nitrogen-vacancy complexes NV⁻, N₂V₂ shows that the diamonds studied have undergone post-growth ionizing irradiation with further low-temperature annealing in natural conditions.     

Strength of frozen silt as a function of ice content and dry unit weight

A total of 45 unconfined compression tests were conducted on frozen specimens of remolded, saturated Fairbanks silt at dry unit weights ranging from 993 to 1490 kg/m³ with total water contents ranging from 0.28 to 0.58. The rate of strain was 0.005 s⁻¹ . Using the criterion that the ice matrix in the soil fractures at the first point of significant yield shown in the stress-strain curve, which occurs at less than 0.01 strain in this study, the “ice matrix strength” is shown to be nearly proportional to the volumetric ice content of the soil for these tests. The strength at 0.2 strain appears to be nearly independent of the dry unit weight and water content of the soil.     

The deep-seated crustal structure in the western part of the Black Sea and adjacent areas: Seismic reflection measurement

In recent years the northwestern Black Sea has been investigated by a great number of geophysical methods. Charts of the M discontinuity and (isopachous) charts of the “granitic”, the “basaltic”, the Paleozoic, the Jurassic-Triassic, the Upper and Lower Cretaceous and the Eocene layers were plotted based on the results of the combined data of these investigations together with associated drilling data. The data for different velocity levels confirms the concept of layered-block structure of the crust, where large blocks are divided by deep faults penetrating to the upper mantle. Sedimentation within each block is continuous while reverse fault zones, dividing the East European Platform with a crustal thickness of more than 40 km and the Scythian Platform with a crust of about 30 km thick, and the latter from the Black Sea depression with crust of about 20 km, are discontinuous. Therefore, one can speak of a continuous-discontinuous nature of the sedimentation.

An inverse relationship in thicknesses of the “granitic” and sedimentary layers has been established. In places of intensive sedimentation the thickness of the “granitic” layer is less than that within the stable unsagging blocks. On the whole the greater the thickness of “basaltic” layer, the greater is the crustal thickness.

The relationship between the main geological structures of the area should be sought in the nature of structure of these “granitic” and “basaltic” layers.     

The Oslo Rift: P-T relations and lithospheric structure

Extrusion temperatures for basaltic lavas in the Permo-Carboniferous Oslo Rift, estimated from whole rock major element compositions, are estimated to be 1270 to 1340°C. This means that magmatism during the Oslo rifting event was not associated with a large temperature anomaly in the underlying upper mantle. Partial melting is believed to be caused by a combination of crustal extension, a weak temperature anomaly in the underlying asthenosphere, and/or high fluid-contents in the mantle source region (“wet-spot”). Petrological and gcochemical data imply that large masses of cumulate rocks were deposited in the deep crust during the Oslo rifting event. The densities and seismic velocities (V_p) of these cumulate rocks are estimated to be 2.8–3.5 g/cm³ and 7.5–8.0 km/s. A rough estimate suggests that cumulus minerals alone account for a net transfer of at least 2 × 10¹⁷ kg of magmatic material from the mantle into the deep crust. In addition comes material representing

1. (a) cumulate minerals corresponding to eroded magmatic surface and subsurface rocks

2. (b) intercumulus material, and

3. (c) magmas crystallized to completion in the deep crust.

Estimates based exclusively on geophysical data tend to underestimate the true transfer of mass into the lower crust as gabbroic cumulate rocks, and melts crystallizing to completion in the lower crust have densities and seismic velocities similar to those of lower crustal wallrocks.     

Crustal structure of the Rhinegraben area

Numerous ge ological and geophysical investigations within the past decades have shown that the Rhinegraben is the most pronounced segment of an extended continental rift system in Europe. The structure of the upper and lower crust is significantly different from the structure of the adjacent “normal” continental crust.

Two crustal cross-sections across the central and southern part of the Rhinegraben have been constructed based on a new evaluation of seismic refraction and reflection measurements. The most striking features of the structure derived are the existence of a well-developed velocity reversal in the upper crust and of a characteristic cushion-like layer with a compressional velocity of 7.6–7.7 km/sec in the lower crust above a normal mantle with 8.2 km/sec. Immediately below the sialic low-velocity zone in the middle part of the crust, an intermediate layer with lamellar structure and of presumably basic composition could be mapped.

It is interesting to note that the asymmetry of the sedimentary fill in the central Rhinegraben seems to extend down deeper into the upper crust as indicated by the focal depths of earthquakes. The top of the rift “cushion” shows a marked relief which has no obvious relation to the crustal structure above it or the visible rift at the surface.     

Einübertragungsnetz zur kluftstatistik

This paper describes the application and characteristics of a new net for crack statistics. The net, here called transmission net or “u-net” (“Übertragungsnetz”, “Ü-Netz”) is used in combination with a transmission table or “u-table” (“Übertragungstabelle”, “Ü-Tabelle”). Its purpose is to obtain a sphere of crack locations from a series of cracks, having been measured according to strike and inclination.

The “u-net” is composed of a grid subdivided into degrees or degree-grid (“Gradnetz”) and an equal-area-grid (“flächengleiches Netz”). Having replaced the direction σ of strike by its normal δ, the cracks are registered into the meshes of the degree-grid and are there counted. Then they are transmitted into the equal-area-grid according to the percent values of the u-table. From the pattern of frequency numbers (“Häufigkeitszahlen”) in the equal-area-grid the sphere of crack locations is obtained.

Particular specifications regulate the procedure for special measure values, i.e., those of the integral multiples of 5°, especially the angles of inclination τ = 0° and τ = 90° (see 1.4). With greater inaccuracies in measurements, one changes, by means of a given table (see Table V), to a degree-grid of 10°. With very small inaccuracies, on the other hand, the procedure may be simplified, the degree-grid becoming unnecessary (see 1.5). The meshes near the centre, being too long, may be avoided by an additional circle (“Zusatzkreis”—see 1.3).

The “u-net” was constructed in such a way that the spheres of crack locations report the real frequency distribution at all times, free from systematic errors. This is achieved by the method that all calculations follow the principle of area equality or area proportionality on the hemisphere (see 2.1). The procedure using the “u-net” can be adapted to differential accuracies of measuring. It is especially suitable for large numbers of cracks; it is simple in calculation and may easily be programmed for digital computers. Thus the “u-net” is advantageous for all applications in which a large number of cracks has to be dealt with. Such applications are very frequent in rock mechanics, in engineering geology for the purpose of foundation of large hydraulic buildings (dams, caverns), in petrography, tectonics and in geophysical investigations such as the determination of crack structures with a view to explaining micromagnetic occurrences, for instance. Furthermore, the “u-net” is applicable not only to crack statistics but also to other similar statistical methods, e.g., to the statistics of cristal axes or to geographic frequency analyses.     

Lower lithospheric structure beneath the Trans-European Suture Zone from POLONAISE''97 seismic profiles

The large-scale POLONAISE'97 seismic experiment investigated the velocity structure of the lithosphere in the Trans-European Suture Zone (TESZ) region between the Precambrian East European Craton (EEC) and Palaeozoic Platform (PP). In the area of the Polish Basin, the P-wave velocity is very low (Vp <6.1 km/s) down to depths of 15–20 km, and the consolidated basement (Vp5.7–5.8 km/s) is 5–12 km deep. The thickness of the crust is 30 km beneath the Palaeozoic Platform, 40–45 km beneath the TESZ, and 40–50 km beneath the EEC. The compressional wave velocity of the sub-Moho mantle is >8.25 km/s in the Palaeozoic Platform and 8.1 km/s in the Precambrian Platform. Good quality record sections were obtained to the longest offsets of about 600 km from the shot points, with clear first arrivals and later phases of waves reflected/refracted in the lower lithosphere. Two-dimensional interpretation of the reversed system of travel times constrains a series of reflectors in the depth range of 50–90 km. A seismic reflector appears as a general feature at around 10 km depth below Moho in the area, independent of the actual depth to the Moho and sub-Moho seismic velocity. “Ringing reflections” are explained by relatively small-scale heterogeneities beneath the depth interval from 90 to 110 km. Qualitative interpretation of the observed wave field shows a differentiation of the reflectivity in the lower lithosphere. The seismic reflectivity of the uppermost mantle is stronger beneath the Palaeozoic Platform and TESZ than the East European Platform. The deepest interpreted seismic reflector with zone of high reflectivity may mark a change in upper mantle structure from an upper zone characterised by seismic scatterers of small vertical dimension to a lower zone with vertically larger seismic scatterers, possible caused by inclusions of partial melt.     

Experimental studies on the effects of fracture on the P and S wave velocity propagation in sedimentary rock (“Calcarenite del Salento”)

Experimental studies were carried out in laboratory in order to investigate the effects of fracture on compressional (P) wave and shear (S) wave velocity propagation and therefore the relations between seismic properties and rock mass parameters. The discontinuity index, I_d, fracture density parameter C, linear fracture parameter Γ and the rock quality designation (RQD) were used to describe the rock mass parameters. These parameters are analyzed and then related to the seismic properties. Four vertical aligned fractures were created on an intact calcarenite block, 0.6 m long, 0.4 m thick and 0.4 m width, by sawing. The measures were carried out in four different blocks of cacarenite, having the same physical properties, and in four different phases: in first block the fractures were filled with air; in the second block the fractures were filled with “terra rossa”; in third block the fractures were filled with wet “terra rossa” and in the fourth block the fractures were filled with clay. The test results were statistically analysed using the method of least squares regression and polynomial relationships with high correlation coefficient were found between the fractured rock parameters and P-wave, S-wave velocities and V_p/V_s ratio. The investigations suggest that the P-wave and S-wave velocities decrease with increasing the fracture parameters, while the V_p/V_s ratio increases with decreasing the fracture parameters.

Furthermore the results of the experimental studies were applied on the seismic refraction tomography data acquired in a great measurements campaign undertaken in the Adriatic salentina coast (south Italy) in order to monitor the coastal erosion.

The geophysical results, using the polynomial relationships between the fractured rock parameters and P-wave velocity, are in good agreement with the geomorphological and geological results.     

Determination of strain from stretched belemnites

Belemnites are valuable strain markers and can be used to determine the elongation that has been suffered by the matrix in which they are situated. Experiments simulating the development of stretched belemnites have been performed to verify their deformation history. The analysis of the experimental results is used in the interpretation of field examples collected from Leytron, Valais, Switzerland. The amount of strain suffered by Leytron belemnites has been evaluated using the “least square” method and the result has been compared with that obtained by the “average elongation” method. The relationship between the final orientation of the whole specimen (θ′_b) and that of the fragments (θ′_f) demonstrates that the Leytron belemnites have suffered an irrotational type of deformation.     

The crust-mantle boundary beneath cratons and craton margins: a transect across the south-west margin of the Kaapvaal craton

“Lower-crustal suite” xenoliths occur in “on-craton” and “off-craton” kimberlites located across the south-western margin of the Kaapvaal craton, southern Africa.

Rock types include mafic granulite (plagioclase-bearing assemblages), eclogite (plagioclase-absent assemblages with omphacitic clinopyroxene) and garnet pyroxenite (“orthopyroxene-bearing eclogite”). The mafic granulites are subdivided into three groups: garnet granulites (cpx + grt + plag + qtz); two pyroxene garnet granulites (cpx + opx + grt + plag); kyanite granulites (cpx + grt + ky + plag + qtz). Reaction microstructures preserved in many of the granulite xenoliths involve the breakdown of plagioclase by a combination of reactions: (1) cpx + plag → grt + qtz; (2) plag → grt + ky + qtz; (3) plag → cpx (jd-rich) + qtz. Compositional zoning in minerals associated with these reactions records the continuous transition from granulite facies mineral assemblages and pressure (P) — temperature (T) conditions to those of eclogite facies.

Two distinct P-T arrays are produced: (1) “off-craton” granulites away from the craton margin define a trend from 680 °C, 7.5 kbar to 850 °C, 12 kbar; (2) granulite xenoliths from kimberlites near the craton margin and “on-craton” granulites produce a trend with similar geothermal gradient but displaced to lower T by ˜ 100 °C. Both P-T fields define higher geothermal gradients than the model steady state conductive continental geotherm (40 mWm²) and are not consistent with the paleogeotherm constructed from mantle-derived garnet peridotite xenoliths.

A model involving intrusion of basic magmas around the crust/mantle boundary followed by isobaric cooling is proposed to explain the thermal history of the lower crust beneath the craton margin. The model is consistent with the thermal evolution of the exposed Namaqua-Natal mobile belt low-pressure granulites and the addition of material from the mantle during the Namaqua thermal event (c. 1150 Ma). The xenolith P-T arrays are not interpreted as representing paleogeotherms at the time of entrainment in the host kimberlite. They most likely record P-T conditions “frozen-in” during various stages of the tectonic juxtaposition of the Namaqua Mobile Belt with the Kaapvaal craton.     

Recent discussion about the North-South bias of the major rift-valleys

The formation of the major rift-valleys is proposed to have been triggered off by the E—W oriented tensional “wave” caused by the slow rotation of the equatorial bulge passing as a stretching hoop through the Earth (Paleozoic—Mesozoic). This ‘wave’ follows the wandering of the polar axis through a great circle (e.g. Creer et al., 1969). The polar wandering is regarded as the readjustment of the Earth's rotational instability caused by the growth of a “weight” fixed on the surface of the Earth and endeavouring to increase its moment of inertia until the weight rotates on the new equator (Gold, 1950). This weight, which must topple the Earth through its fixed spacial axis of rotation, may be slowly developing Pangea. The “wave” of E—W tension is imposed on zones already under E—W tension, e.g., crests of N—S running welts, alias “craton ridges”. The intruding asthenosphere expands the crests and fractures them along tensional rift-valleys. These rifts may develop as spreading centers by gliding of the plates over a lubricating basalt magma.

The idea proposed by R. Schweickert (pers. commun., 1979) that the lithosphere is decoupled from the asthenosphere to an extent that the shell may rotate as a separate unit (as a means to explain how fixed plumes move in unison under the “roll” of the lithosphere) is dismissed. The subducted slabs act as braking flaps and cannot overcome the friction against the asthenosphere. The “roll” would be too young (50 m.y.), because the polar wandering according to Creer is much older.     

Carbonatite melt–CO2 fluid inclusions in mantle xenoliths from Tenerife, Canary Islands: a story of trapping, immiscibility and fluid–rock interaction in the upper mantle

Three types of fluid inclusions have been identified in olivine porphyroclasts in the spinel harzburgite and lherzolite xenoliths from Tenerife: pure CO₂ (Type A); carbonate-rich CO₂–SO₂ mixtures (Type B); and polyphase inclusions dominated by silicate glass±fluid±sp±silicate±sulfide±carbonate (Type C). Type A inclusions commonly exhibit a “coating” (a few microns thick) consisting of an aggregate of a platy, hydrous Mg–Fe–Si phase, most likely talc, together with very small amounts of halite, dolomite and other phases. Larger crystals (e.g. (Na,K)Cl, dolomite, spinel, sulfide and phlogopite) may be found on either side of the “coating”, towards the wall of the host mineral or towards the inclusion center. These different fluids were formed through the immiscible separations and fluid–wall-rock reactions from a common, volatile-rich, siliceous, alkaline carbonatite melt infiltrating the upper mantle beneath the Tenerife. First, the original siliceous carbonatite melt is separated from a mixed CO₂–H₂O–NaCl fluid and a silicate/silicocarbonatite melt (preserved in Type A inclusions). The reaction of the carbonaceous silicate melt with the wall-rock minerals gave rise to large poikilitic orthopyroxene and clinopyroxene grains, and smaller neoblasts. During the metasomatic processes, the consumption of the silicate part of the melt produced carbonate-enriched Type B CO₂–SO₂ fluids which were trapped in exsolved orthopyroxene porphyroclasts. At the later stages, the interstitial silicate/silicocarbonatite fluids were trapped as Type C inclusions. At a temperature above 650 °C, the mixed CO₂–H₂O–NaCl fluid inside the Type A inclusions were separated into CO₂-rich fluid and H₂O–NaCl brine. At T<650 °C, the residual silicate melt reacted with the host olivine, forming a reaction rim or “coating” along the inclusion walls consisting of talc (or possibly serpentine) together with minute crystals of NaCl, KCl, carbonates and sulfides, leaving a residual CO₂ fluid. The homogenization temperatures of +2 to +25 °C obtained from the Type A CO₂ inclusions reflect the densities of the residual CO₂ after its reactions with the olivine host, and are unrelated to the initial fluid density or the external pressure at the time of trapping. The latter are restricted by the estimated crystallization temperatures of 1000–1200 °C, and the spinel lherzolite phase assemblage of the xenolith, which is 0.7–1.7 GPa.