Numerical viscoelastic modelling by the spectral Laguerre method

Seismic wave propagation in a viscoelastic media can be described by a system of integro-differential equations. The solution of such equations requires special methods when using finite-difference techniques in the time domain. In the frequency domain, the integral terms are represented by complex elastic parameters. This paper presents an efficient algorithm for viscoelastic modelling based on the integral Laguerre transform for the approximation of temporal derivatives and for the calculation of convolution integrals. For the calculation of spatial derivatives, it is possible to use various methods: finite-difference and finite-element techniques, spectral and pseudo-spectral methods. We then obtain a system of algebraic equations with a matrix independent of the parameter m , i.e. the degree of the Laguerre polynomials. In this case, only the right-hand side of the system has recurrent dependence on the parameter m , which is an analogue of the temporal frequency in the frequency domain. The obtained system with a large number of right-hand sides can be solved using fast methods, where the matrix is transformed only once, as opposed to the frequency-domain approach, when the matrix is transformed for each temporal frequency.     

Frequency-dependent anisotropy due to meso-scale fractures in the presence of equant porosity

Fractured rock is often modelled under the assumption of perfect fluid pressure equalization between the fractures and equant porosity. This is consistent with laboratory estimates of the characteristic squirt-flow frequency. However, these laboratory measurements are carried out on rock samples which do not contain large fractures. We consider coupled fluid motion on two scales: the grain scale which controls behaviour in laboratory experiments and the fracture scale. Our approach reproduces generally accepted results in the low- and high-frequency limits. Even under the assumption of a high squirt-flow frequency, we find that frequency-dependent anisotropy can occur in the seismic frequency band when larger fractures are present. Shear-wave splitting becomes dependent on frequency, with the size of the fractures playing a controlling role in the relationship. Strong anisotropic attenuation can occur in the seismic frequency band. The magnitude of the frequency dependence is influenced strongly by the extent of equant porosity. With these results, it becomes possible in principle to distinguish between fracture- and microcrack-induced anisotropy, or more ambitiously to measure a characteristic fracture length from seismic data.     

Dublin days: the 2003 NAM

Mark E Bailey and Tom Ray give an overview of the National Astronomy Meeting in Dublin, where record numbers of astronomers went to talk, listen and network.     

He and Ne isotopes in oceanic crust: implications for noble gas recycling in the mantle

In an attempt to determine the helium and neon isotopic composition of the lower oceanic crust, we report new noble gas measurements on 11 million year old gabbros from Ocean Drilling Program site 735B in the Indian Ocean. The nine whole rock samples analyzed came from 20 to 500 m depth below the seafloor. Helium contents vary from 3.3×10⁻¹⁰ to 2.5×10⁻⁷ ccSTP/g by crushing and from 5.4×10⁻⁸ to 2.4×10⁻⁷ ccSTP/g by melting. ³He/⁴He ratios vary between 2.2 and 8.6 Ra by crushing and between 2.9 and 8.2 by melting. The highest R/Ra ratios are similar to the mean mid-ocean ridge basalt (MORB) ratio of 8±1. The lower values are attributed to radiogenic helium from in situ α-particle production during uranium and thorium decay. Neon isotopic ratios are similar to atmospheric ratios, reflecting a significant seawater circulation in the upper 500 m of exposed crust at this site. MORB-like neon, with elevated ²⁰Ne/²²Ne and ²¹Ne/²²Ne ratios, was found in some high temperature steps of heating experiments, but with very small anomalies compared to air. These first results from the lower oceanic crust indicate that subducted lower oceanic crust has an atmospheric ²⁰Ne/²²Ne ratio. Most of this neon must be removed during the subduction process, if the ocean crust is to be recirculated in the upper mantle, otherwise this atmospheric neon will overwhelm the upper mantle neon budget. Similarly, the high (U+Th)/³He ratio of these crustal gabbros will generate very radiogenic ⁴He/³He ratios on a 100 Ma time scale, so lower oceanic crust cannot be recycled into either MORB or oceanic island basalt without some form of processing.     

Computer Simulation of Shaped Charge Detonation Using Meshless Particle Method

Shaped charges are widely applied in the defense industry and civil engineering for penetrating hardened targets. Simulations of shaped charges are generally based on traditional grid-based numerical methods. Different from the existing literature, the SPH method is applied in this paper to simulate the detonation process of shaped charge explosive. The combination of the meshless, Lagrangian and particle nature inherent in the SPH method is very attractive in dealing with large deformations and large inhomogeneities in extremely transient situations such as detonation process. The SPH method and some related numerical aspects are briefly discussed first, followed by applications in simulating shaped charge detonations. The effects of different detonation cavity angles and different charge head lengths are investigated. The results demonstrate that major shaped charge detonation phenomena are captured with revealing observations.     

Mesozoic thermal evolution of the southern African mantle lithosphere

The thermal structure of Archean and Proterozoic lithospheric terranes in southern Africa during the Mesozoic was evaluated by thermobarometry of mantle peridotite xenoliths erupted in alkaline magmas between 180 and 60 Ma. For cratonic xenoliths, the presence of a 150–200 °C isobaric temperature range at 5–6 GPa confirms original interpretations of a conductive geotherm, which is perturbed at depth, and therefore does not record steady state lithospheric mantle structure.

Xenoliths from both Archean and Proterozoic terranes record conductive limb temperatures characteristic of a “cratonic” geotherm (40 mW m⁻²), indicating cooling of Proterozoic mantle following the last major tectonothermal event in the region at 1 Ga and the probability of thick off-craton lithosphere capable of hosting diamond. This inference is supported by U–Pb thermochronology of lower crustal xenoliths [Schmitz and Bowring, 2003. Contrib. Mineral. Petrol. 144, 592–618].

The entire region then suffered a protracted regional heating event in the Mesozoic, affecting both mantle and lower crust. In the mantle, the event is recorded at 150 Ma to the southeast of the craton, propagating to the west by 108–74 Ma, the craton interior by 85–90 Ma and the far southwest and northwest by 65–70 Ma. The heating penetrated to shallower levels in the off-craton areas than on the craton, and is more apparent on the southern margin of the craton than in its western interior. The focus and spatial progression mimic inferred patterns of plume activity and supercontinent breakup 30–100 Ma earlier and are probably connected.

Contrasting thermal profiles from Archean and Proterozoic mantle result from penetration to shallower levels of the Proterozoic lithosphere by heat transporting magmas. Extent of penetration is related not to original lithospheric thickness, but to its more fertile character and the presence of structurally weak zones of old tectonism. The present day distribution of surface heat flow in southern Africa is related to this dynamic event and is not a direct reflection of the pre-existing lithospheric architecture.     

A coupled,dynamical and chemical model for the prestellar core L1544: Comparison of modeled and observed C<Superscript>18</Superscript>O,HCO<Superscript>+</Superscript>, and CS emission spectra

We consider radiative transfer in C¹⁸O, HCO⁺, and CS molecular lines in a spherically symmetrical, coupled, dynamical and chemical model of a prestellar core whose evolution is determined by ambipolar diffusion. Theoretical and observed line profiles are compared for the well-studied core L1544, which may be a collapsing protostellar cloud. We study the relationship between the line shapes and model parameters. The structure of the envelope and kinematic parameters of the cloud are the most important factors determining the shape of the lines. Varying the input model parameters for the radiative transfer—the kinetic temperature and microturbulent velocity—within the limits imposed by observations does not result in any substantial variations of the line profiles. The comparison between the model and observed spectra indicates that L1544 displays a flattened structure, and is viewed at an oblique angle. A two-dimensional model is needed to reproduce this structure.     

Possible refugia for reefs in times of environmental stress

This paper investigates the refuge potential of (1) upwelling areas, (2) coral areas at medium depth, and (3) offshore bank and island reefs in a scenario of increased global warming, and thus increased sea surface temperature (SST) and increased solar UV radiation. (1) Observations on coral health and water temperature in the subtropical Atlantic (Eleuthera and Cat Island, Bahamas) and Indian Ocean (Sodwana Bay, South Africa) suggest a link between cool water delivered by upwelling and coral health. After the 1998 bleaching event, caused by strong SST anomalies, coral health and recovery from the previous year's bleaching was significantly better on the narrow southern Cat Island shelf (70% of corals healthy) where the presence of cold water was observed, which was attributed to small-scale upwelling, than on the wide northern Eleuthera shelf (44% of corals healthy), where downwelling of hot bank waters was believed to have damaged corals. In South Africa, regular, short-term upwelling events in five summers reduced SST to well below bleaching level. (2) In the northern Red Sea (Safaga Bay) and in South Africa (Sodwana Bay), wide areas with either coral frameworks or non-framework communities exist. Calculations show that if the top 10 m (20 m) of the ocean became inhospitable to corals, still 50.4% (17.5%) of the coral area would remain intact in the Red Sea and 99% (40%) in South Africa. (3) Offshore bank and island reefs investigated in the Turks, Caicos, and Mouchoir Banks and Grand and Little Cayman showed high rates of mortality and coral diseases. The most remote sites (Mouchoir Bank) were not the healthiest. Refuge areas appear to exist in (1) and (2), but in (3) only if vigorous water-circulation is encountered.