A comparison of methods used in measuring finite strains from ellipsoidal objects

The available methods for measuring strains in two and three dimensions from passive ellipsoidal objects are compared in an attempt to determine the most useful and precise procedure for the structural geologist. A comparison of data collection techniques showed that the use of thin orthogonally cut slabs or mylar overlays used with a monocomparater provides the most reproducible data. Lisle's theta-curve and Shimamoto and Ikeda's algebraic methods provided the most precise, and probably most accurate, two-dimensional data while Miller and Oertel's procedure and possibly Dunnet's PHASE 5 program gave the best three-dimensional results.An examination of errors encountered in strain analyses suggests that all of the available methods give accurate orientations of the finite strain ellipsoid. However, the magnitudes of strain ratios show large variations that are dependent on the sample size and procedure used. Shimamoto and Ikeda's method again proved to be the most precise, giving reproducible results with as few as ten elliptical objects.The samples used in the above comparison are part of a larger analysis of strains occurring in southeastern Maine. Structural elements observed in four selected areas of Avalonian belt rocks and the strain data collected suggest that the region has undergone at least three non-coaxial deformations with D₁ >D₂ >D₃.     

Geochemistry of Archean shales from the Pilbara Supergroup,Western Australia

Archean clastic sedimentary rocks are well exposed in the Pilbara Block of Western Australia. Shales from turbidites in the Gorge Creek Group (ca. 3.4 Ae) and shales from the Whim Creek Group (ca. 2.7 Ae) have been examined. The Gorge Creek Group samples, characterized by muscovite-quartzchlorite mineralogy, are enriched in incompatible elements (K, Th, U, LREE) by factors of about two, when compared to younger Archean shales from the Yilgarn Block. Alkali and alkaline earth elements are depleted in a systematic fashion, according to size, when compared with an estimate of Archean upper crust abundances. This depletion is less notable in the Whim Creek Group. Such a pattern indicates the source of these rocks underwent a rather severe episode of weathering. The Gorge Creek Group also has fairly high B content (85 ± 29 ppm) which may indicate normal marine conditions during deposition.Rare earth element (REE) patterns for the Pilbara samples are characterized by light REE enrichment ($\text{La}{}_{\mathrm{N}}\text{Yb}{}_{\mathrm{N}}\text{≥ 7.5}$) and no or very slight Eu depletion ($\text{Eu}\text{Eu}{}^1\text{= 0.82 – 0.99}$). A source comprised of about 80% felsic igneous rocks without large negative Eu-anomalies (felsic volcanics, tonalites, trondhjemites) and 20% mafic-ultramafic volcanics is indicated by the trace element data. Very high abundances of Cr and Ni cannot be explained by any reasonable provenance model and a secondary enrichment process is called for.     

On the relationship of thunderstorm ice hydrometeor characteristics and total lightning measurements

Satellite-borne and ground-based devices for the detection of lightning offer the opportunity to explore relationships–on all significant scales up to global–between lightning frequency, f, and other thundercloud parameters. Calculations predict that f is proportional to the product of the downflux p of solid precipitation and the upward mass flux, I, of ice crystals. This prediction has received support from limited computational studies. The physical reasons for such a relationship are explained in terms of the paramount role of ice in the electrification of thunderstorms. Herein, this prediction is subjected to further, preliminary examination through analysis of lightning and dual-polarimetric radar data collected during the STERAO experiment conducted in Northern Colorado during the summer of 1996. The analysis has yielded some highly provisional support for this flux hypothesis. Computed trends of radar derived hydrometeor fractions of solid precipitation and small ice show correlation to the total lightning frequency and raise the possibility of determining values of p and/or I from lightning measurements.It is shown that the extent to which the observed correlations between f and both solid precipitation and small ice trends are or are not strong can provide an indication as to whether the lightning activity is limited by the available concentrations of precipitating or non-precipitating ice in the upper regions of the charging zone of the thundercloud, where most of the charge transfer occurs. It is demonstrated that the most accurate determinations of precipitation rate p from measurements of lighting frequency f are likely to be for conditions where the field-growth is limited by the availability of graupel pellets. It is shown that the simultaneous time variations of f and solid precipitation trends of the type obtained in the STERAO experiment could enable us to determine the nature of the dominant glaciation process operative in the thunderclouds studied.     

Reducing model complexity for explanation and prediction

Numerical models can be useful for explaining poorly understood phenomena or for reliable quantitative predictions. When modeling a multi-scale system, a ‘top-down’ approach—basing models on emergent variables and interactions, rather than explicitly on the much faster and smaller scale processes that give rise to them—facilitates both goals. Parameterizations representing emergent interactions range from highly simplified and abstracted to more quantitatively accurate. Empirically based large-scale parameterizations lead more reliably to accurate large-scale behavior than do parameterizations of much smaller scale processes. Conversely, purposefully simplified representations of model interactions can enhance a model's utility for explanation, clarifying the key feedbacks leading to an enigmatic behavior. For such potential insights to be relevant, the interactions in the model need to correspond to those in the ‘real’ system in some straightforward way. Such a correspondence usually holds for models constructed for predictive purposes, although this is not a requirement. The goals motivating a modeling endeavor help determine the most appropriate modeling strategies, as well as the most appropriate criteria for judging model usefulness.     

A 3.5 Ga record of water-limited, acidic weathering conditions on Mars

The secondary mineral budget on Earth is dominated by clay minerals, Al-hydroxides, and Fe-oxides, which are formed under the moderate pH, high water-to-rock ratio conditions typical of Earth's near-surface environment. In contrast, geochemical analyses of rocks and soils from landed missions to Mars indicate that secondary mineralogy is dominated by Mg (± Fe, Ca)-sulfates and Fe-oxides. This discrepancy can be explained as resulting from differences in the chemical weathering environment of Earth and Mars. We suggest that chemical weathering processes on Mars are dominated by: (1) a low-pH, sulfuric acid-rich environment in which the stoichiometric dissolution of labile mineral phases such as olivine and apatite (± Fe–Ti oxides) is promoted; and (2) relatively low water-to-rock ratio, such that other silicate phases with slower dissolution rates (e.g., plagioclase, pyroxene) do not contribute substantially to the secondary mineral budget at the Martian surface. Under these conditions, Al-mobilization is limited, and the formation of significant Al-bearing secondary phases (e.g., clays, Al-hydroxides, Al-sulfates) is inhibited. The antiquity of rock samples analyzed in-situ on Mars suggest that water-limited acidic weathering conditions have more than likely been the defining characteristic of the Martian aqueous environment for billions of years.     

An analytical solution to multi-component NAPL dissolution equations

This note presents a novel method for determining the changing composition of a multi-component NAPL body dissolving into moving groundwater, and the consequent changes in the aqueous phase solute concentrations in the surrounding pore water. A canonical system of coupled non-linear governing equations is derived which is suitable for representation of both pooled and residual configurations, and this is solved. Whereas previous authors have handled such problems numerically, it is shown that these governing equations succumb to analytical solution. By a suitable substitution, the equations become decoupled, and the problem collapses to a single first-order equation. The final result is expressed implicitly, with time as a function of the number of moles of the least soluble component, m₁. The number of moles of each other component is expressed explicitly in terms of m₁. It is shown that the time-m₁ relationship has a well behaved inverse. An example is given in which the analytic solution is verified against traditional finite difference analysis, and its computational efficiency is shown.     

The geomorphology of planetary calderas

Satellite-derived observations of the geomorphology of calderas on Earth, Mars and Venus can be used to learn more about shield volcanoes. Examples of terrestrial basaltic volcanoes from the Galapagos Islands, Hawaii, and the Comoro Islands show how these volcanoes contrast with examples found on Mars and Venus. Caldera structure, degree of infilling, and the location of vents on the flanks are used to interpret each volcano's recent history. The geometry of the caldera floor can be used to infer some of the characteristics of the magma storage system, and the orientation of the deep magma conduits. The formation of benches within the caldera and the effects of the caldera on the distribution of flank eruptions are considered, and it is evident that most calderas on the planets are/were dynamic features. Presently, deep calderas, with evidence of overflowing lavas and ponded lavas high in the caldera wall, show that these calderas were once shallow. Similarly, shallow calderas filled with ponded lavas are evidence that they were once deeper. It is probably a mistake, therefore, to place great significance on caldera depth with regard to the position, shape, or size of subsurface plumbing.     

Determination of Geopotential Differences between Local Vertical Datums and Realization of a World Height System

The methodology developed for connecting Local Vertical Datums (LVD) was applied to the Australian Height Datum (AHD) and the North American Vertical Datum (NAVD88). The geopotential values at AHD and NAVD88 were computed and the corresponding vertical offset of 974 mm with rms 51 mm was obtained between the zero reference surfaces defined by AHD and NAVD88. The solution is based on the four primary geodetic parameters, the GPS/levelling sites and the geopotential model EGM96. The Global Height System (or the Major Vertical Datum) can be defined by a geoidal geopotential value used in the solution as the reference value, or by the geopotential value of the LVD, e.g. NAVD88.