Tensor structure and the least squares

It is shown that for linear parametric adjustment models all the least-squares equations can be obtained from a commutative diagram, where the observation and parameter spaces are regarded as covariant. Their contravariant counterparts are defined through the metric property of the covariance matrix of the observations.     

Long base line tilt and strain measurement

Two types of noise afflict strain and tilt measurement. They may be categorized as “active” noise, which is due to atmospheric pressure variations, temperature variations, water-table variations and so forth; and “passive” or signal-generated noise which is a consequence of the interaction of the strain field of interest with inhomogeneities of material properties local to the measurement site.The reason why both types of noise are normally reduced by the use of long base line instruments is explained and a simple, practical long base line tiltmeter is described.     

Recent crustal movements in the Sierra Nevada—Walker lane region of California—Nevada: Part i, rate and style of deformation

This review of geological, seismological, geochronological and paleobotanical data is made to compare historic and geologic rates and styles of deformation of the Sierra Nevada and western Basin and Range Provinces. The main uplift of this region began about 17 m.y. ago, with slow uplift of the central Sierra Nevada summit region at rates estimated at about 0.012 mm/yr and of western Basin and Range Province at about 0.01 mm/yr. Many Mesozoic faults of the Foothills fault system were reactivated with normal slip in mid-Tertiary time and have continued to be active with slow slip rates. Sparse data indicate acceleration of rates of uplift and faulting during the Late Cenozoic. The Basin and Range faulting appears to have extended westward during this period with a reduction in width of the Sierra Nevada.The eastern boundary zone of the Sierra Nevada has an irregular en-echelon pattern of normal and right-oblique faults. The area between the Sierra Nevada and the Walker Lane is a complex zone of irregular patterns of hörst and graben blocks and conjugate normal-to right- and left-slip faults of NW and NE trend, respectively. The Walker Lane has at least five main strands near Walker Lake, with total right-slip separation estimated at 48 km. The NE-trending left-slip faults are much shorter than the Walker Lane fault zone and have maximum separations of no more than a few kilometers. Examples include the 1948 and 1966 fault zone northeast of Truckee, California, the Olinghouse fault (Part III) and possibly the almost 200-km-long Carson Lineament.Historic geologic evidence of faulting, seismologic evidence for focal mechanisms, geodetic measurements and strain measurements confirm continued regional uplift and tilting of the Sierra Nevada, with minor internal local faulting and deformation, smaller uplift of the western Basin and Range Province, conjugate focal mechanisms for faults of diverse orientations and types, and a NS to NE—SW compression axis (σ₁) and an EW to NW—SE extension axis (σ₃).     

A geochemical study of magmatism associated with the initial stages of back-arc spreading

Bransfield Strait is a narrow basin separating the South Shetland Islands from the Antarctic Peninsula and is attributed to recent back-arc extension behind the South Shetland volcanic arc. The volcanic islands of Deception and Bridgeman are situated close to the axis of spreading, whereas Penguin Island lies slightly to the north of this axis. The mineralogy, petrology and geochemistry of the lavas of the three volcanoes have been studied in order to provide information on the nature of magmatism associated with the initial stages of back-arc spreading.Deception Island lavas range from olivine basalt to dacite, and all are highly sodic, with high Na/K, K/Rb, Ba/Rb and Zr/Nb ratios and with Ce_N/Yb_N = 2. Incompatible elements increase systematically between basalt and rhyodacite, while Sr decreases, suggesting that fractional crystallisation is the dominant process relating lava compositions. The rhyodacites have high concentrations of Zr, Y and the REE and negative Eu anomalies and are compositionally similar to oceanic plagiogranite. Bridgeman Island lavas are mostly basaltic andesites, but the levels of many incompatible elements, including REE, are significantly lower than those of Deception lavas, although Ce_N/Yb_N ratios and ⁸⁷Sr/⁸⁶Sr ratios (0.7035) are the same. Penguin Island lavas are magnesian, mildly alkaline olivine basalts with a small range of composition that can be accommodated by fractional crystallisation of olivine, clinopyroxene and/or chromite. Penguin lavas have higher ⁸⁷Sr/⁸⁶Sr (0.7039) and Ce_N/ Yb_N (4) ratios than Deception and Bridgeman lavas. The Rb/Sr ratios of Deception and Penguin basalts (ca. 0.01) are much too low to account for their present ⁸⁷Sr/⁸⁶Sr ratios.Modelling suggests that the source regions of the lavas of the three volcanoes share many geochemical features, but there are also some significant differences, which probably reflects the complex nature of the mantle under an active island arc combined with complex melting relationships attending the initial stages of back-arc spreading. Favoured models suggest that Bridgeman lavas represent 10–20% melting and the more primitive Deception lavas 5–10% melting of spinel-peridotite, whereas Penguin lavas represent less then 5% melting of a garnet-peridotite source. The mantle source for Bridgeman lavas seems to have undergone short-term enrichment in K, Rb and Ba, possibly resulting from dewatering of the subducted slab. Hydrous melting conditions may also account for the more siliceous, high-alumina nature and low trace element contents of Bridgeman lavas.     

The geochemistry and petrogenesis of dolerites and gabbros from the Tertiary central volcanic complex of Slieve Gullion,North East Ireland

Basaltic magmas emplaced into the root zone of the Slieve Gullion volcano have crystallised to rocks varying in texture from dolerite to gabbro. A mineralogical variation from olivine bearing to quartz bearing varieties has been recorded and with the presence of coexisting Ca-rich and Ca-poor pyroxenes, a tholeiitic assemblage is indicated.Geochemical data confirm this prognosis and a continuous spread of compositions from basalt to tholeiitic andesite are interpreted in terms of fractional crystallisation. Modelling of the fractional crystallisation processes indicate an approach to cotectic conditions with fractionation at low pressures involving olivine, plagioclase, clinopyroxene and Ti-magnetite. Primitive magma compositions, indicated by low values of D.I. and 100 Mg/Mg + Fe²⁺ (atomic)>61, show low concentrations of the large ion lithophile elements such as Rb, Ba, Zr, Y, and K. The relatively high CaO content (>11 %) of these rocks invite comparison with high-calcium low-alkali tholeiitic liquids recognised in extrusive and intrusive magmas elsewhere in the North Atlantic Tertiary volcanic province and with magmas currently erupted at active spreading ridges.In north west Britain the field and stratigraphic distribution of these high-calcium low-alkali magmas suggests that they occupy a distinct chronological niche towards the top of the Palaeocene-Eocene volcanic succession succeeding eruption of mildly alkali and transitional basalts. As such, the refractory (high CaO, MgO, etc.) and large ion lithophile depleted geochemistry can be explained either by differential partial melting in the upper mantle source region or melting of a depleted and refractory mantle source which has already contributed to basalt genesis.     

Finite-element analysis of the transport of water and solutes in title-drained soils

The finite-element method based on a Galerkin technique was used to formulate the problem of simulating the two-dimensional (cross-sectional) transient movement of water and solute in saturated or partially saturated nonuniform porous media. The numerical model utilizes linear triangular elements. Nonreactive, as well as reactive solutes whose behaviour can be described by a distribution coefficient or first-order reaction term were considered. The flow portion of the model was tested by comparison of the model results with experimental and finite-difference results for transient flow in an unsaturated sand column and the solute transport portion of the model was tested by comparison with analytical solution results. The model was applied to a hypothetical case involving movement of water and solutes in tile-drained soils. The simulation results showed the development of distinct solute leaching patterns in the soil as drainage proceeded. Although applied to a tile drainage problem in this study, the model should be equally useful in the study of a wide range of two-dimensional water and solute migration problems.     

Morphology of the Wadati-Benioff zone,andesitic volcanism,and active fracture zones in Central America

Summary The morphology of the Wadati-Benioff zone in the region of Central America, based on the distribution of 1377 earthquake foci, verified the existence of an intermediate aseismic gap and its relation to active andesitic volcanism, and the non-uniformity of subduction due to the hampering effect of the main structural features of the subducting Cocos plate. Four deep seismically active fracture zones, genetically connected with the process of subduction, and three fracture zones manifesting the possible boundary between the Americas and Caribbean plates were identified in the continental wedge.     

Cyclic triaxial tests on frozen sand

Strain-controlled cyclic triaxial tests were performed on a one-size silica (Ottawa) sand artificially frozen into 71.1-mm-diameter cylindrical samples. Ice-saturated samples with three different sand contents were tested under the following conditions: axial strains ranging from 3 × 10⁻³ to 3 X 10⁻²%, confining pressures from zero to 1.378 MPa, frequencies of 0.05–5.0 cps and temperatures from −1 to −10 °C.

Test equipment included (1) an MTS electrohydraulic closed-loop testing system which applies the load to the sample, (2) a triaxial cell completely immersed in a low-temperature coolant for temperature control, (3) a refrigeration unit for control of the coolant temperature and constant coolant circulation and (4) measuring devices including an LVDT and load cell, together with recording devices such as a digital multimeter, an oscilloscope, a strip-chart recorder and a minicomputer.

Test results indicate that the dynamic Young's modulus increases with increasing frequency, confining pressure and sand content, but decreases with increasing strain and temperature. The damping ratio decreases with increasing frequency, sand content and lower temperatures. The influence of confining pressures and axial strain on the damping ratio are less explicit for the ranges considered. The experimental results are compared with data from other sources.