Probabilistic analysis of peak response of MDOF systems with uncertain PSD function

The use of uniform hazard spectra which have the same probability of exceedance at different frequencies has been proposed for the future version of the National Building Code of Canada. Commonly used combination rules to estimate the peak responses of multi‐degree‐of‐freedom (MDOF) systems are the square root of sum of squares rule and the complete quadratic combination rule. However, the probability that the peak response of a MDOF system exceeds the one estimated by using these rules with the peak modal responses from the uniform hazard spectra cannot be inferred directly. The assessment of the probability of exceedance of the peak response of MDOF systems is presented by considering that the uncertainty in seismic excitation due to all potential earthquakes can be lumped in the power spectral density function of the ground acceleration with uncertain model parameters. This probability is evaluated based on the random vibration of linear systems and the first‐order reliability method. It is found that the under‐ or over‐estimations are less than about 5 or 10% if the modal contributions are not within 10–90% of, or not within 20–80% of, the absolute sum of the effective modal peak responses, respectively. Otherwise, severe under‐ or over‐estimation could result. Copyright © 2002 John Wiley & Sons, Ltd.     

Geomorphological, geochemical and geo-environmental aspects of karstification in the urban areas of Kerman city, southeastern, Iran

Kerman city has a semiarid-arid climate with an average annual precipitation of about 158 mm. The area is underlain by soluble subsoil and alluvial deposits, overlying highly fractured Cretaceous limestones. Geo-environmental studies indicate that both paleokarst and active karst features are developed in the area. The paleokarsts were developed in the Upper Cretaceous limestone during the cold, humid periods of Post Cretaceous and probably Early Quaternary time and include honeycombs, solution flutes, rillenkarren, caverns, and solution collapse dolines. Active karst landforms occur by combined piping-induced and limestone solution at depth in subsoils, and alluvial deposits and bajada that overly potent karstic limestones and cover subsidence sinkholes and subjacent alluvial karst collapse dolines. Many factors, such as soluble compounds (salt and gypsum), desiccation cracks, and Qanat (dug water wells), could contribute to the development of karstic landforms. The most immediate cause for active karst landforms is considered to be the drawdown of the water table in the area. There is an increasing demand for groundwater consumption to irrigate pistachio fields. Excessive pumping of the groundwater lowers the water table about 80 cm per year. This rate of drawdown accelerates land subsidence (about 6 cm per year), creates circular patterns of fractures in the ground and in buildings, disrupts agricultural work and urbanization projects, and tilts foundations. These geohazards indicate that ground sinking and karstification are in progress in the alluvial deposits and underlying limestones. The disturbance and expense caused by the geohazards could be mitigated by the application of overhead sprinkler irrigation for pistachio fields or by planting less thirsty plants.     

Chlorophyll modulation of mixed layer thermodynamics in a mixed-layer isopycnal General Circulation Model — An example from Arabian Sea and equatorial Pacific

Western tropical Indian Ocean, Arabian Sea, and the equatorial Pacific are known as regions of intense bio-chemical-physical interactions: the Arabian Sea has the largest phytoplankton bloom with seasonal signal, while the equatorial Pacific bloom is perennial with quasi-permanent upwelling. Here, we studied three dimensional ocean thermodynamics comparing recent ocean observation with ocean general circulation model (OPYC) experiment combined with remotely sensed chlorophyll pigment concentrations from the Coastal Zone Color Scanner (CZCS). Using solar radiation parameterization representing observations that a higher abundance of chlorophyll increases absorption of solar irradiance and heating rate in the upper ocean, we showed that the mixed layer thickness decreases more than they would be under clear water conditions. These changes in the model mixed layer were consistent with Joint Global Ocean Flux Study (JGOFS) observations during the 1994-1995 Arabian Sea experiment and epi-fluorescence microscopy (EFM) on samples collected during Equatorial Pacific Ocean Climate Study (EPOCS) in November, 1988. In the Arabian Sea, as the chlorophyll concentrations peak in October (3 mg/m³) after the summer plankton bloom induced by coastal upwelling, the chlorophyll induced biological heating enhanced the sea surface temperature (SST) by as much as 0.6‡C and sub-layer temperature decreases and sub-layer thickness increases. In the equatorial Pacific, modest concentrations of chlorophyll less than 0.3 mg/m³ is enough to introduce a meridional differential heating, which results in reducing the equatorial mixed layer thickness to more than 20 m. The anomalous meridional tilting of the mixed layer bottom enhances off equatorial westward geostrophic currents. Consequently, the equatorial undercurrent transports more water from west to east. We proposed that these numerical model experiments with use of satellite andin situ ocean observations are consistent under three dimensional ocean circulation theory combined with solar radiation transfer process.     

Isotopic constraints on growth conditions of multiphase calcite–pyrite–barite concretions in Carboniferous mudstones

Carbonate concretions in the Lower Carboniferous Caton Shale Formation contain diagenetic pyrite, calcite and barite in the concretion matrix or in different generations of septarian fissures. Pyrite was formed by sulphate reduction throughout the sediment before concretionary growth, then continued to form mainly in the concretion centres. The septarian calcites show a continuous isotopic trend from δ¹³C=?28·7‰ PDB and δ¹⁸O=?1·6‰ PDB through to δ¹³C=?6·9‰ PDB and δ¹⁸O=?14·6‰ PDB. This trend arises from (1) a carbonate source initially from sulphate reduction, to which was added increasing contributions of methanogenic carbonate; and (2) burial/temperature effects or the addition of isotopically light oxygen from meteoric water. The concretionary matrix carbonates must have at least partially predated the earliest septarian cements, and thus used the same carbonate sources. Consequently, their isotopic composition (δ¹³C=?12·0 to ?10·1‰ PDB and δ¹⁸O=?5·7 to ?5·6‰ PDB) can only result from mixing a carbonate cement derived from sulphate reduction with cements containing increasing proportions of carbonate from methanogenesis and, directly or indirectly, also from skeletal carbonate. Concretionary growth was therefore pervasive, with cements being added progressively throughout the concretion body during growth. The concretions contain barite in the concretion matrix and in septarian fissures. Barite in the earlier matrix phase has an isotopic composition (δ³⁴S=+24·8‰ CDT and δ¹⁸O=+16·4‰ SMOW), indicating formation from near‐surface, sulphate‐depleted porewaters. Barites in the later septarian phase have unusual isotopic compositions (δ³⁴S=+6 to +11‰ CDT and δ¹⁸O=+8 to +11‰ SMOW), which require the late addition of isotopically light sulphate to the porewaters, either from anoxic sulphide oxidation (using ferric iron) or from sulphate dissolved in meteoric water. Carbon isotope and biomarker data indicate that oil trapped within septarian fissures was derived from the maturation of kerogen in the enclosing sediments.     

Analogue study of particle segregation in pyroclastic density currents, with implications for the emplacement mechanisms of large ignimbrites

Abstract Analogue flume experiments were conducted to investigate the transport and sedimentation behaviour of turbulent pyroclastic density currents. The experimental currents were scaled approximately to the natural environment in three ways: (1) they were fully turbulent; (2) they had a very wide range of particle sizes and associated Rouse numbers (the ratio of particle settling velocity to effective turbulent eddy velocity in the current); and (3) they contained particles of two different densities. Two sets of surge‐type experiments were conducted in a 5 m long, water‐filled lock‐exchange flume at five different volumetric particle concentrations from 0·6% to 23%. In one set (one‐component experiments), the currents contained just dense particles; in the other set (two‐component experiments), they contained both light and dense particles in equal volume proportions. In both sets of experiments, the population of each component had a log‐normal size distribution. In the two‐component experiments, the size range of the light particle population was selected in order to be in hydrodynamic equivalence with that of the dense particles. Dense particles were normally graded, both vertically and downstream, in the deposits from both sets of experiments. The mass loading (normalized to the initial mass of the suspension) and grain size of the dense component in the deposits decreased with distance from the reservoir and were insensitive to initial total particle concentration in the currents. On the other hand, in the two‐component experiments, the light particles were extremely sensitive to concentration. They were deposited in hydrodynamic equivalence with the dense particles from dilute currents, but were segregated efficiently at concentrations higher than a few per cent. With increasing particle concentration, the large, light particles were carried progressively further down the flume because of buoyancy effects. Deposits from the high‐concentration currents exhibited reverse vertical grading of the large, light particles. Efficient segregation of the light component was observed even if the bulk density of the current was less than that of the light particles. In both sets of experiments, marked inflexions in the rate of downstream decline in mass loading and maximum grain size of the dense component can be attributed to the presence of two different particle settling regimes in the flow: (1) particles with Rouse numbers >2·5, which did not respond to the turbulence and settled rapidly; and (2) particles with Rouse numbers <2·5, which followed the turbulent eddies and settled slowly. The results are applied to the transport and sedimentation dynamics of pyroclastic density currents that generate large, widespread ignimbrites. Field data fail to reveal significant departures from aerodynamic equivalence between pumice and lithic clasts in three such ignimbrites: the particulate loads of some large ignimbrites are transported principally in turbulent suspensions of low concentration. In some ignimbrites, the well‐developed inflexions in curves of maximum lithic (ML) size vs. distance can be attributed to the existence of distinct high and low Rouse number particle settling regimes that mark the transition from an overcharged state to one in which the residual particulate load is transported more effectively by turbulence.     

High-T, low-P metamorphism in the Palaeoproterozoic Halls Creek Orogen, northern Australia: the middle crustal response to a mantle-related transient thermal pulse

High‐T, low‐P metamorphic rocks of the Palaeoproterozoic central Halls Creek Orogen in northern Australia are characterised by low radiogenic heat production, high upper crustal thermal gradients (locally exceeding 40 °C km^?1) sustained for over 30 Myr, and a large number of layered mafic‐ultramafic intrusions with mantle‐related geochemical signatures. In order to account for this combination of geological and thermal characteristics, we model the middle crustal response to a transient mantle‐related heat pulse resulting from a temporary reduction in the thickness of the mantle lithosphere. This mechanism has the potential to raise mid‐crustal temperatures by 150–400 °C within 10–20 Myr following initiation of the mantle temperature anomaly, via conductive dissipation through the crust. The magnitude and timing of maximum temperatures attained depend strongly on the proximity, duration and lateral extent of the thermal anomaly in the mantle lithosphere, and decrease sharply in response to anomalies that are seated deeper than 50–60 km, maintained for <5 Myr in duration and/or have half‐widths <100 km. Maximum temperatures are also intimately linked to the thermal properties of the model crust, primarily due to their influence on the steady‐state (background) thermal gradient. The amplitudes of temperature increases in the crust are principally a function of depth, and are broadly independent of crustal thermal parameters. Mid‐crustal felsic and mafic plutonism is a predictable consequence of perturbed thermal regimes in the mantle and the lowermost crust, and the advection of voluminous magmas has the potential to raise temperatures in the middle crust very quickly. Although pluton‐related thermal signatures significantly dissipate within <10 Myr (even for very large, high‐temperature intrusive bodies), the interaction of pluton‐ and mantle‐related thermal effects has the potential to maintain host rock temperatures in excess of 400–450 °C for up to 30 Myr in some parts of the mid‐crust. The numerical models presented here support the notion that transient mantle‐related heat sources have the capacity to contribute significantly to the thermal budget of metamorphism in high‐T, low‐P metamorphic belts, especially in those characterised by low surface heat flow, very high peak metamorphic geothermal gradients and abundant mafic intrusions.     

Constraints on the application of carbon isotope thermometry in high- to ultrahigh-temperature metamorphic terranes

Nine marble horizons from the granulite facies terrane of southern India were examined in detail for stable carbon and oxygen isotopes in calcite and carbon isotopes in graphite. The marbles in Trivandrum Block show coupled lowering of δ¹³C and δ¹⁸O values in calcite and heterogeneous single crystal δ¹³C values (? 1 to ? 10‰) for graphite indicating varying carbon isotope fractionation between calcite and graphite, despite the granulite facies regional metamorphic conditions. The stable isotope patterns suggest alteration of δ¹³C and δ¹⁸O values in marbles by infiltration of low δ¹³C–δ¹⁸O‐bearing fluids, the extent of alteration being a direct function of the fluid‐rock ratio. The carbon isotope zonation preserved in graphite suggests that the graphite crystals precipitated/recrystallized in the presence of an externally derived CO₂‐rich fluid, and that the infiltration had occurred under high temperature and low f_O2 conditions during metamorphism. The onset of graphite precipitation resulted in a depletion of the carbon isotope values of the remaining fluid+calcite carbon reservoir, following a Rayleigh‐type distillation process within fluid‐rich pockets/pathways in marbles resulting in the observed zonation. The results suggest that calcite–graphite thermometry cannot be applied in marbles that are affected by external carbonic fluid infiltration. However, marble horizons in the Madurai Block, where the effect of fluid infiltration is not detected, record clear imprints of ultrahigh temperature metamorphism (800–1000 °C), with fractionations reaching <2‰. Zonation studies on graphite show a nominal rimward lowering δ¹³C on the order of 1 to 2‰. The zonation carries the imprint of fluid deficient/absent UHT metamorphism. Commonly, calculated core temperatures are > 1000 °C and would be consistent with UHT metamorphism.     

Far field effects of Alpine plate tectonism in the Iberian microplate recorded by fault-related denudation in the Spanish Central System

Apatite fission track analysis was performed on 56 samples from central Spain to unravel the far field effects of the Alpine plate tectonic history of Iberia. The modelled thermal histories reveal complex cooling in the Cenozoic, indicative of intermittent denudation. Accelerated cooling events occurred across the Spanish Central System (SCS) from the Middle Eocene to Recent. These accelerated cooling events resulted in up to 2.8±0.9 km of denudation in the western Sierra de Gredos and 3.6±1.0 km in the central and eastern Gredos (assuming a paleogeothermal gradient of 28±5 °C and a surface temperature of 10 °C). The greatest amount of denudation (5.0±1.6 km) occurred in the Sierra de Guadarrama. Accompanying rock uplift was 4.7±1.0 and 5.9±1.6 km in the eastern Gredos and Guadarrama, respectively. Most denudation in the Gredos occurred from the Middle Eocene to the Early Miocene and can be related to the N–S stress field, induced by the Pyrenean compression. In the Guadarrama, the greatest denudation was Pliocene to Recent of age and seems related to the ongoing NW–SE Betic compression. The fact that the formation of the E–W trending Gredos coincides with the N–S Pyrenean compression and the creation of the present day morphology of the NE–SW trending Guadarrama with the younger NW–SE Betic compression, indicates that they record the far field effects of Alpine plate tectonics on Iberia. The trend of pre-existing lineaments was of major importance in influencing the style and magnitude of these of far field effects.     

Stability of earthquake moment tensor inversions: effect of the double-couple constraint

We show that spurious large non-double-couple components can be obtained in inversions for the full deviatoric moment tensor for shallow crustal earthquakes due to inaccurate Earth models. The traditional “best double-couple” solution does not in general provide an optimal estimate of a double-couple mechanism, and is only reliable when the non-double-couple component of the full deviatoric solution is small. The inverse problem for the moment tensors of the 1998 Antarctic Plate and 2000 Wharton Basin strike-slip earthquakes is shown in each case to have two well-fitting minima in the misfit function of pure double-couple solutions. Such pairs of solutions are most likely to exist for earthquakes which are close either to vertical strike-slip or to dip-slip on a fault plane dipping at 45°. It is shown theoretically that these pairs of solutions arise from the combination of the pure double-couple constraint and the instability of two elements of the moment tensor. No significant non-double-couple component is found for the shallow thrusting 1996 Biak, Indonesia earthquake.