Development and sensitivity analysis of a model for assessing stratification and safety of Lake Nyos during artificial degassing

To prevent the recurrence of a disastrous eruption of carbon dioxide (CO₂) from Lake Nyos, a degassing plan has been set up for the lake. Since there are concerns that the degassing of the lake may reduce the stability of the density stratification, there is an urgent need for a simulation tool to predict the evolution of the lake stratification in different scenarios. This paper describes the development of a numerical model to predict the CO₂ and dissolved solids concentrations, and the temperature structure as well as the stability of the water column of Lake Nyos. The model is tested with profiles of CO₂ concentrations and temperature taken in the years 1986 to 1996. It reproduces well the general mixing patterns observed in the lake. However, the intensity of the mixing tends to be overestimated in the epilimnion and underestimated in the monimolimnion. The overestimation of the mixing depth in the epilimnion is caused either by the parameterization of the k-epsilon model, or by the uncertainty in the calculation of the surface heat fluxes. The simulated mixing depth is highly sensitive to the surface heat fluxes, and errors in the mixing depth propagate from one year to the following. A precise simulation of the mixolimnion deepening therefore requires high accuracy in the meteorological forcing and the parameterization of the heat fluxes. Neither the meteorological data nor the formulae for the calculation of the heat fluxes are available with the necessary precision. Consequently, it will be indispensable to consider different forcing scenarios in the safety analysis in order to obtain robust boundary conditions for safe degassing. The input of temperature and CO₂ to the lake bottom can be adequately simulated for the years 1986 to 1996 with a constant sublacustrine source of 18 l s^–1 with a CO₂ concentration of 0.395 mol l^–1 and a temperature of 26 °C. The results of this study indicate that the model needs to be calibrated with more detailed field data before using it for its final purpose: the prediction of the stability and the safety of Lake Nyos during the degassing process.Responsible Editor: Hans Burchard     

Mineral-scale Sr-isotope constraints on magma evolution and chamber dynamics in the Rum layered intrusion,Scotland

Sr isotopic zoning within single plagioclase crystals from rocks from Unit 9 of the Rum layered intrusion is used to infer events during crystal growth in a magma undergoing contamination. The ⁸⁷Sr/⁸⁶Sr diversity among minerals and between cores and rims of plagioclase crystals increases as the boundary between unit 9 and the overlying Unit 10 peridotite is approached. Models of near-solidus interaction of the cumulate with a fluid or melt, or large scale textural re-equilibration, cannot easily account for the systematic differences in ⁸⁷Sr/⁸⁶Sr between small crystals and the rims of larger crystals.We propose a simple interpretation in which crystal growth is concentrated along the cool margins of the reservoir. Crystals are subsequently advected to a site of accumulation at the base of the reservoir, probably by episodic plume-like dense downwellings allowing mixing of isotopically zoned and unzoned crystals.If the core-rim isotope variations are inherited from primary magmatic growth, then the small distances over which they are now preserved (1–2 mm) place constraints on the minimum cooling rate of the intrusion. Although the length scale of diffusive equilibration is influenced by a number of poorly-constrained variables (starting temperature, feldspar composition, temperature-time path) cooling was clearly very rapid with cooling to effective closure (~1,000 °C) within a few thousand years.Editorial responsibility: I. Parsons     

Activity–composition relations for phases in petrological calculations: an asymmetric multicomponent formulation

For petrological calculations, including geothermobarometry and the calculation of phase diagrams (for example, P–T petrogenetic grids and pseudosections), it is necessary to be able to express the activity–composition (a–x) relations of minerals, melt and fluid in multicomponent systems. Although the symmetric formalism—a macroscopic regular model approach to a–x relations—is an easy-to-formulate, general way of doing this, the energetic relationships are a symmetric function of composition. We allow asymmetric energetics to be accommodated via a simple extension to the symmetric formalism which turns it into a macroscopic van Laar formulation. We term this the asymmetric formalism (ASF). In the symmetric formalism, the a–x relations are specified by an interaction energy for each of the constituent binaries amongst the independent set of end members used to represent the phase. In the asymmetric formalism, there is additionally a "size parameter" for each of the end members in the independent set, with size parameter differences between end members accounting for asymmetry. In the case of fluid mixtures, for example, H₂O–CO₂, the volumes of the end members as a function of pressure and temperature serve as the size parameters, providing an excellent fit to the a–x relations. In the case of minerals and silicate liquid, the size parameters are empirical parameters to be determined along with the interaction energies as part of the calibration of the a–x relations. In this way, we determine the a–x relations for feldspars in the systems KAlSi₃O₈–NaAlSi₃O₈ and KAlSi₃O₈–NaAlSi₃O₈–CaAl₂Si₂O₈, for carbonates in the system CaCO₃–MgCO₃, for melt in the melting relationships involving forsterite, protoenstatite and cristobalite in the system Mg₂SiO₄–SiO₂, as well as for fluids in the system H₂O–CO₂. In each case the a–x relations allow the corresponding, experimentally determined phase diagrams to be reproduced faithfully. The asymmetric formalism provides a powerful and flexible way of handling a–x relations of complex phases in multicomponent systems for petrological calculations.     

New density measurements on carbonate liquids and the partial molar volume of the CaCO<Subscript>3</Subscript> component

Density measurements on nine liquids in the CaCO₃–Li₂CO₃–Na₂CO₃–K₂CO₃ quaternary system were performed at 1 bar between 555 and 969 °C using the double-bob Archimedean method. Our density data on the end-member alkali carbonate liquids are in excellent agreement with the NIST standards compiled by Janz (1992). The results were fitted to a volume equation that is linear in composition and temperature; this model recovers the measured volumes within experimental error (±0.18% on average, with a maximum residual of ±0.50%). Our results indicate that the density of the CaCO₃ component in natrocarbonate liquids is 2.502 (±0.014) g/cm³ at 800 °C and 1 bar, which is within the range of silicate melts; its coefficient of thermal expansion is 1.8 (±0.5)×10^–4 K^–1 at 800 °C. Although the volumes of carbonate liquids mix linearly with respect to carbonate components, they do not mix linearly with silicate liquids. Our data are used with those in the literature to estimate the value of in alkaline silicate magmas (20 cm³/mol at 1400 °C and 20 kbar), where CO₂ is dissolved as carbonate in close association with Ca. Our volume measurements are combined with sound speed data in the literature to derive the compressibility of the end-member liquids Li₂CO₃, Na₂CO₃, and K₂CO₃. These results are combined with calorimetric data to calculate the fusion curves for Li₂CO₃, Na₂CO₃, and K₂CO₃ to 5 kbar; the calculations are in excellent agreement with experimental determinations of the respective melting reactions.Editorial responsibility: I Carmichael     

Argon retention properties of silicate glasses and implications for <Superscript>40</Superscript>Ar/<Superscript>39</Superscript>Ar age and noble gas diffusion studies

Sized aggregates of glasses (47–84 wt% SiO₂) were fused from igneous-derived cohesive fault rock and igneous rock, and step-heated from ~400 to >1,200 °C to obtain their ³⁹Ar diffusion properties (average E=33,400 cal mol^?1; D _o=4.63×10^?3 cm² s^?1). At T<~1,000 °C, glasses containing <~69 wt% SiO₂ and abundant network-forming cations (Ca, Fe, Mg) reveal moderate to strong non-linear increases in D and E, reflecting structural modifications as the solid transitions to melt. Extrapolation of these Arrhenius properties down to typical geologic T-t conditions could result in a 1.5 log₁₀ unit underestimation in the diffusion rate of Ar in similar materials. Numerical simulations based upon the diffusion results caution that some common geologic glasses will likely yield ⁴⁰Ar/³⁹Ar cooling ages rather than formation ages. However, if cooling rates are sufficiently high, ambient temperatures are sufficiently low (e.g., <65–175 °C), and coarse particles (e.g., radius (r) >~1 mm) are analyzed, glasses with compositions similar to ours may preserve their formation ages.     

Dynamic stress concentration and scattering of SH-wave by interface elliptic cylindrical cavity

In this paper, the dynamic stress concentration and scattering of SH-waves by bi-naterial structures that possess an interface elliptic cavity are investigated. First, by using the complex function method, the Green‘s function is constructed. This yields the solution of the displacement field for an elastic half space with a semi-elliptic canyon impacted by an anti-plane harmonic line source loading on the horizontal surface. Then, the problem is divided into an upper and lower half space along the horizontal interface, regarded as a harmony model. In order to satisfythe integral continuity condition,the unknown anti-plane forces are applied to the interface. The integral equations with unknown forces can be established through the continuity condition, and after transformation, the algebraic equations are solved numerically. Finally, the distribution of the dynamic stress concentration factor (DSCF) around the elliptic cavity is given and the effect of different parameters on DSCF is discussed.     

Remote structural health monitoring with serially multiplexed fiber optic acoustic emission sensors

Development and testing of a serially multiplexed fiber optic sensor system is described. The sensor differs from conventional fiber optic acoustic systems, as it is capable of sensing AE emissions at several points along the length of a single fiber. Multiplexing provides for single channel detection of cracks and their locations in large structural systems. An algorithm was developed for signal recognition and tagging of the AE waveforms for detection of crack locations. Laboratory experiments on plain concrete beams and post-tensioned FRP tendons were performed to evaluate the crack detection capability of the sensor system. The acoustic emission sensor was able to detect initiation, growth and location of the cracks in concrete as well as in the FRP tendons. The AE system is potentially suitable for applications involving health monitoring of structures following an earthquake Supported by: National Science Foundation, Grant number CMS-9900338     

A technique to improve the empirical mode decomposition in the Hilbert-Huang transform

The Hilbert-based time-frequency analysis has promising capacity to reveal the time-variant behaviors of a system. To admit well-behaved Hilbert transforms, component decomposition of signals must be performed beforehand. This was first systematically implemented by the empirical mode decomposition (EMD) in the Hilbert-Huang transform, which can provide a time-frequency representation of the signals. The EMD, however, has limitations in distinguishing different components in narrowband signals commonly found in free-decay vibration signals. In this study, a technique for decomposing components in narrowband signals based on waves’ beating phenomena is proposed to improve the EMD, in which the time scale structure of the signal is unveiled by the Hilbert transform as a result of wave beating, the order of component extraction is reversed from that in the EMD and the end effect is confined. The proposed technique is verified by performing the component decomposition of a simulated signal and a free decay signal actually measured in an instrumented bridge structure. In addition, the adaptability of the technique to time-variant dynamic systems is demonstrated with a simulated time-variant MDOF system.     

Relationships between moment magnitude and fault parameters: theoretical and semi-empirical relationships

Fault parameters are important in earthquake hazard analysis. In this paper, theoretical relationships between moment magnitude and fault parameters including subsurface rupture length, downdip rupture width, rupture area, and average slip over the fault surface are deduced based on seismological theory. These theoretical relationships are further simplified by applying similarity conditions and an unique form is established. Then, combining thc simplified theoretical relationships between moment magnitude and fault parameters with seismic source data selected in this study, a practical semi-empirical relationship is established. The seismic source data selected is also to used to derive empirical relationships between moment magnitude and fault parameters by the ordinary least square regression method. Comparisons between semi-empirical relationships and empirical relationships show that the former depict distribution trends of data better than the latter. It is also observed that downdip rupture widths of strike slip faults are saturated when moment magnitude is more than 7.0, but downdip rupture widths of dip slip faults are not saturated in the moment magnitude ranges of this study.     

Lateral load pattern in pushover analysis

The seismic capacity curves of three types of buildings including frame, frame-shear wall and shear wall obtained by pushover analysis under different lateral load patterns are compared with those from nonlinear time history analysis. Based on the numerical results obtained a two-phase load pattern; an inverted triangle (first mode) load pattern until the base shear force reachesβ times its maximum value, V_max, followed by a (x/H)^α form, hereβ and α being some coefficients depending on the type of the structures considered, is proposed in the paper, which can provide excellent approximation of the seismic capacity curve for low-to-mid-rise shear type buildings. Furthermore, it is shown both the two-phase load pattern proposed and the invariant uniform pattern can be used for low-to-mid-rise shear-bending type and low-rise bending type of buildings. No suitable load patterns have been found for high-rise buildings.