Modal identification of self-adjoint distributed-parameter systems

A new method is introduced for the identification of modal quantities of self-adjoint distributed-parameter systems. The method uses the temporal and spatial orthogonality properties of distributed-parameter systems to form a pseudo-Rayleigh quotient. The stationary values of the pseudo-Rayleigh quotient can be determined by the solution of an eigenvalue problem, where the eigenvalues and eigenfunctions provide the frequencies and natural modes of the distributed-parameter system. By way of formulation, the method is insensitive to zero mean measurement noise and is applicable to continuous as well as discrete systems. Numerical examples are presented in which the modal quantities of a simply-supported beam and a discrete model of a membrane are identified. The results are compared with another modal identification technique, namely, the Ibrahim time domain method.     

The “North American shale composite”: Its compilation,major and trace element characteristics

The compilation and major element composition of the “North American shale composite” (NASC) are reported for the first time, along with redeterminations for the REE and selected other elements by modern, high precision analytical methods. The NASC is not strictly of North American origin; 5 of the constituent samples are from Africa and Antarctica, and 15 are from unspecified locations. The major element composition of the NASC compares quite closely with other average shale compositions. New analyses of the NASC document that significant portions of the REE and some other trace elements are contained in minor phases (zircon and possibly other minerals) and that their uneven distribution in the NASC powder appears to have resulted in heterogeneity among analyzed aliquants. The results of this study show that the REE distributions of detrital sediments can be dependent to some extent on their minor mineral assemblages and the sedimentological factors that control these assemblages. Consequently, caution should be exercised in the interpretation of the REE distributions of sediment samples as they may be variable and biased relative to average REE distribution of the crustal rocks supplying detritus. These effects appear to be largely averaged out in sediment composites, with the result that their REE distributions are more likely to be representative of their provenances.     

Micro Computers Applied to Ground Water Monitoring and Testing

Micro computers have been demonstrated to be a most valuable, cost-effective means of long- and short-term data acquisition for ground water investigations and installations. A system can readily be assembled for the cost of labor saved in the field, or for the same cost as other conventional instruments, which perform only a fraction of the functions of the computer system
Documented in this article are systems which have been developed and used for simultaneous monitoring of several wells during aquifer tests, and systems installed for long-term monitoring of piezometric surface fluctuations. Both systems can be contained in a small suitcase or insulated cooler. Specific features of the systems include multiple channel capacity, one-month maintenance period, variable computer controlled reading intervals, magnetic tape data storage, data reduction and analysis capabilities while maintaining monitoring, graphic display of time and measurements, hard copy capability and barometric pressure change corrections.
Other applications are examined for the complete control of pumping tests, including pumping rate; in situ permeability tests; monitoring changes; and even strain. The pressure transducer system may also be applied for river gauging and current measurement.     

High-Pressure crystal chemistry of spinel (MgAl2O4) and magnetite (Fe3O4): Comparisons with silicate spinels

High-pressure crystal structures and compressibilities have been determined by x-ray methods for MgAl₂O₄ spinel and its isomorph magnetite, Fe₃O₄. The measured bulk moduli, K, of spinel and magnetite (assuming K′=4) are 1.94±0.06 and 1.86±0.05 Mbar, respectively, in accord with previous ultrasonic determinations. The oxygen u parameter, the only variable atomic position coordinate in the spinel structure (Fd3m, Z=8), decreases with pressure in MgAl₂O₄, thus indicating that the magnesium tetrahedron is more compressible than the aluminum octahedron. In magnetite the u parameter is unchanged, and both tetrahedron and octahedron display the 1.9 Mbar bulk modulus characteristic of the entire crystal. This behavior contrasts with that of nickel silicate spinel (γ-Ni₂SiO₄), in which the u parameter increases with pressure because the silicon tetrahedron is relatively incompressible compared to the nickel octahedron.     

Seasonal distributions of suspended particulate material and dissolved nutrients in a coastal plain estuary

The temporal and spatial distributions of salinity, dissolved oxygen, suspended particulate material (SPM), and dissolved nutrients were determined during 1983 in the Choptank River, an estuarine tributary of Chesapeake Bay. During winter and spring freshets, the middle estuary was strongly stratified with changes in salinity of up to 5‰ occurring over 1 m depth intervals. Periodically, the lower estuary was stratified due to the intrusion of higher salinity water from the main channel of Chesapeake Bay. During summer this intrusion caused minimum oxygen and maximum NH₄ ⁺ concentrations at the mouth of the Choptank River estuary. Highest concentrations of SPM, particulate carbon (PC), particulate nitrogen (PN), total nitrogen (TN), total phosphorous (TP) and dissolved inorganic nitrogen (DIN) occurred in the upper estuary during the early spring freshet. In contrast, minimum soluble reactive phosphate (SRP) concentrations were highest in the upper estuary in summer when freshwater discharge was low. In spring, PC:PN ratios were >13, indicating a strong influence by allochthonous plant detritus on PC and PN concentrations. However, high concentrations of PC and PN in fall coincided with maximum chlorophyll a concentrations and PC:PN ratios were <8, indicating in situ productivity controlled PC and PN levels. During late spring and summer, DIN concentrations decreased from >100 to <10 μg-at l^?1, resulting mainly from the nonconservative behavior of NO₃ ^?, which dominated the DIN pool. Atomic ratios of both the inorganic and total forms of N and P exceeded 100 in spring, but by summer, ratios decreased to <5 and <15, respectively. The seasonal and spatial changes in both absolute concentrations and ratios of N and P reflect the strong influence of allochthonous inputs on nutrient distributions in spring, followed by the effects of internal processes in summer and fall.     

An electrochemical study of Ni2+, Co2+, and Zn2+ ions in melts of composition CaMgSi2O6

Cyclic voltammetry has been done for Ni²⁺, Co²⁺, and Zn²⁺ in melts of diopside composition in the temperature range 1425 to 1575°C. Voltammetric curves for all three ions excellently match theoretical curves for uncomplicated, reversible charge transfer at the Pt electrode. This implies that the neutral metal atoms remain dissolved in the melt. The reference electrode is a form of oxygen electrode. Relative to that reference assigned a reduction potential of 0.00 volt, the values of standard reduction potential for the ions are $\text{E}{}^1\text{(}\text{Ni}{}^{\mathrm{2+}}\text{Ni}{}^0\text{,}\text{diopside}\text{, 1500°C) = ?0.32 ± .01}\text{V}$, $\text{E}{}^1\text{(}\text{Co}{}^{\mathrm{2+}}\text{Co}{}^0\text{,}\text{diopside}\text{, 1500°C) = ?0.45 ± .02}\text{V}$, and $\text{E}{}^1\text{(}\text{Zn}{}^{\mathrm{2+}}\text{Zn}{}^0\text{,}\text{diopside}\text{, 1500°C) = ?0.53 ± .01}\text{V}$. The electrode reactions are rapid, with first order rate constants of the order of 10^?2 cm/sec. Diffusion coefficients were found to be 2.6 × 10^?6 cm²/sec for Ni²⁺, 3.4 × 10^?6 cm²/sec for Co²⁺, and 3.8 × 10^?6 cm²/sec for Zn²⁺ at 1500°C. The value of $\text{E1}$ ($\text{Ni}{}^{\mathrm{2+}}\text{Ni}{}^0$, diopside) is a linear function of temperature over the range studied, with values of ?0.35 V at 1425°C and ?0.29 V at 1575°C. At constant temperature the value of $\text{E}{}^1\text{(}\text{Ni}{}^{\mathrm{2+}}\text{Ni}{}^0\text{, 1525°C}$) was not observed to vary with composition over the range CaO · MgO · 2SiO₂ to CaO·MgO·3SiO₂ or from 1.67 CaO·0.33MgO·2SiO₂ to 0.5 CaO·1.5MgO·2SiO₂. The value for the diffusion coefficient for Ni²⁺ decreased by an order of magnitude at 1525°C over the compositional range CaO · MgO · 1.25SiO₂ to CaO · MgO · 3SiO₂. This is consistent with a mechanism by which Ni²⁺ ions diffuse by moving from one octahedral coordination site to another in the melt, with the same Ni²⁺ species discharging at the cathode regardless of the SiO₂ concentration in the melt.     

Seismic coupling and uncoupling at subduction zones

Seismic coupling has been used as a qualitative measure of the “interaction” between the two plates at subduction zones. Kanamori (1971) introduced seismic coupling after noting that the characteristic size of earthquakes varies systematically for the northern Pacific subduction zones. A quantitative global comparison of many subduction zones reveals a strong correlation of earthquake size with two other variables: age of the subducting lithosphere and convergence rate. The largest earthquakes occur in zones with young lithosphere and fast convergence rates, while zones with old lithosphere and slow rates are relatively aseismic for large earthquakes. Results from a study of the rupture process of three great earthquakes indicate that maximum earthquake size is directly related to the asperity distribution on the fault plane (asperities are strong regions that resist the motion between the two plates). The zones with the largest earthquakes have very large asperities, while the zones with smaller earthquakes have small scattered asperities. This observation can be translated into a simple model of seismic coupling, where the horizontal compressive stress between the two plates is proportional to the ratio of the summed asperity area to the total area of the contact surface. While the variation in asperity size is used to establish a connection between earthquake size and tectonic stress, it also implies that plate age and rate affect the asperity distribution. Plate age and rate can control asperity distribution directly by use of the horizontal compressive stress associated with the “preferred trajectory” (i.e. the vertical and horizontal velocities of subducting slabs are determined by the plate age and convergence velocity). Indirect influences are many, including oceanic plate topography and the amount of subducted sediments.All subduction zones are apparently uncoupled below a depth of about 40 km, and we propose that the basalt to eclogite phase change in the down-going oceanic crust may be largely responsible. This phase change should start at a depth of 30–35 km, and could at least partially uncouple the plates by superplastic deformation throughout the oceanic crust during the phase change.     

Surface study of HF- and HFH2SO4-treated feldspar using Auger electron spectroscopy

Auger electron spectroscopy has been used to study K-feldspar that has been reacted with both aqueous 10% HF and a 50% mixture of a 10% HF/0.1 N H₂SO₄ solution. In the feldspar/HF system, the resulting feldspar surface was shown to have been fluorinated; depth profiling, using argon ion sputtering, showed the fluorination to have occurred substantially into the mineral bulk. In the feldspar/ $\text{HF}\text{H}{}_2\text{SO}{}_4$ system, the resulting surface contained both fluorine and sulfur. The fluorination had again penetrated into the bulk, but the sulfur could be removed with mild argon ion sputtering. The $\text{Al}\text{F}$ signal ratio was much lower on the feldspar surface treated with the 10% HF/0.1 N H₂SO₄ solution than the feldspar surface treated with the weaker 10% HF acid solution.     

Hybrid Estimation of Semivariogram Parameters

Two widely used methods of semivariogram estimation are weighted least squares estimation and maximum likelihood estimation. The former have certain computational advantages, whereas the latter are more statistically efficient. We introduce and study a “hybrid” semivariogram estimation procedure that combines weighted least squares estimation of the range parameter with maximum likelihood estimation of the sill (and nugget) assuming known range, in such a way that the sill-to-range ratio in an exponential semivariogram is estimated consistently under an infill asymptotic regime. We show empirically that such a procedure is nearly as efficient computationally, and more efficient statistically for some parameters, than weighted least squares estimation of all of the semivariogram’s parameters. Furthermore, we demonstrate that standard plug-in (or empirical) spatial predictors and prediction error variances, obtained by replacing the unknown semivariogram parameters with estimates in expressions for the ordinary kriging predictor and kriging variance, respectively, perform better when hybrid estimates are plugged in than when weighted least squares estimates are plugged in. In view of these results and the simplicity of computing the hybrid estimates from weighted least squares estimates, we suggest that software that currently estimates the semivariogram by weighted least squares methods be amended to include hybrid estimation as an option.