Variograms with zonal anisotropies and noninvertible kriging systems

Zonal anisotropies are usually simply defined as those that are not geometric (i.e., that cannot be removed by an affine transformation). Such anisotropies have often been associated with zonations and models have been proposed to reflect that association. It is shown by example that such models can lead to noninvertible coefficient matrices in kriging systems, because the models are only (conditionally) semidefinite instead of positive definite. The relationship to the construction used in turning bands algorithm and also to spatial-temporal models is discussed.     

Age and paleoclimatic significance of the Stansbury shoreline of Lake Bonneville, Northeastern Great Basin

The Stansbury shoreline, one of the conspicuous late Pleistocene shorelines of Lake Bonneville, consists of tufa-cemented gravel and barrier beaches within a vertical zone of about 45 m, the lower limit of which is 70 m above the modern average level of Great Salt Lake. Stratigraphic evidence at a number of localities, including new evidence from Crater Island on the west side of the Great Salt Lake Desert, shows that the Stansbury shoreline formed during the transgressive phase of late Pleistocene Lake bonneville (sometime between about 22,000 and 20,000 yr B.P.). Tufa-cemented gravel and barrier beaches were deposited in the Stansbury shorezone during one or more fluctuations in water level with a maximum total amplitude of 45 m. We refer to the fluctuations as the Stansbury oscillation. The Stansbury oscillation cannot have been caused by basin-hypsometric factors, such as stabilization of lake level at an external overflow threshold or by expansion into an interior subbasin, or by changes in drainage basin size. Therefore, changes in climate must have caused the lake level to reverse its general rise, to drop about 45 m in altitude (reducing its surface area by about 18%, 5000 km²), and later to resume its rise. If the sizes of Great Basin lakes are controlled by the mean position of storm tracks and the jetstream, which as recently postulated may be controlled by the size of the continental ice sheets, the Stansbury oscillation may have been caused by a shift in the jetstream during a major interstade of the Laurentide ice sheet.     

Estimating Geohydrologic Properties from Borehole-Geophysical Logs

Borehole-geophysical logs can be used to estimate geohydrologic properties based on in situ measurement of rock and water properties. Estimates of properties of both formation and water, such as coefficient of diffusion, formation factor, cementation exponent, hydraulic conductivity, irreducible water content and specific yield can be assessed from borehole-geophysical data and selected algorithms and graphs.
Water properties, such as resistivity, sodium chloride concentration, viscosity and density, can also be estimated using data from borehole-geophysical logs. Water resistivity using the spontaneous-potential method can be estimated if an empirical correction for fresh water is applied.
Estimates of formation properties, such as porosity and permeability, can also be made using borehole-geophysical data.     

Genesis and solvus relations of submicroscopically intergrown paragonite and phengite in a blueschist from northern California

Electron microbeam techniques have been used to examine submicroscopically intergrown paragonite, phengite and chlorite from the South Fork Mountain Schist of the Franciscan Terrane of northern California, which was subjected to blueschist facies metamorphism. The sample also contains quartz, albite, lawsonite, and rutile. The subassemblage albite-lawsonite-rutile requires metamorphic conditions on the low-temperature side of the equilibrium albite+lawsonite+rutile=paragonite+sphene+quartz+H₂O (T<200° C and P<7.4 kbars based on thermodynamic data of Holland and Powell 1990). The white micas appear to be optically homogeneous, but back-scattered electron images can distinguish two different micas by their slight difference in contrast. Electron microprobe analyses (EMPA) of micas show Na/(Na+K) ranging from 0.2 to 0.8. The two micas are resolved by transmission electron microscopy (TEM) as packets of phengite and paragonite that range from 20 to several hundred nm in thickness. The compositions, determined by analytical electron microscopy (AEM), constrain the limbs of the phengite-paragonite solvus to values of Na/(Na+K)=<0.02 and 0.97, representing less mutual solid solution than ever reported by EMPA. The textural relations imply that the sheet silicates were derived from reactions between fluids and detrital clays and that they are in an intermediate stage of textural development. We caution that microprobe analyses of apparently homogeneous sheet silicates may yield erroneous data and lead to faulty conclusions using phengite barometry and paragonite-muscovite thermometry, especially in fine-grained rocks that formed at relatively low temperatures. Contribution no. 473 from the Mineralogical Laboratory, Department of Geological Sciences, The University of Michigan, Ann Arbor, Michigan, USA     

The Batu Hijau porphyry copper-gold deposit, Sumbawa Island, Indonesia

The Batu Hijau porphyry Cu---Au deposit lies in southwest Sumbawa Island, Indonesia. It is a world-class porphyry Cu deposit in an island are setting, and is typical of this deposit type in most features, including igneous association, morphology, hydrothermal alteration and mineralisation style.The region was not previously recognised as a porphyry Cu province; disseminated Cu sulphides were first recognised in float samples in southwest Sumbawa in 1987. Associated stream sediment sampling identified a broad area of anomalous Au and Cu in an area of greater than 5 km² around Batu Hijau, including 169 ppb Au in BLEG samples and 580 ppm Cu in stream silts 1 km from the deposit. Mineralisation in bedrock at surface contains > 0.1 wt % Cu and > 0.1 ppm Au over an area of 0.6 km × 1.2 km, including a zone 300 m × 900 m containing > 0.3 wt % Cu. Areas with elevated Mo (> 30 ppm) form a distinctive annulus around this Cu-rich zone.Batu Hijau mineralisation is hosted in a tonalite intrusive complex, and diorite and metavolcanic wallrocks. There are no post-mineralisation igneous intrusions or breccia pipes within the deposit. The main tonalite intrusion forms a stock in the centre of the deposit, where it generally displays intensely pervasive potassic (biotite with magnetite-quartz) alteration and hosts most of the higher grade mineralisation. Younger tonalite dykes intruding the centre of this stock are generally less altered and mineralised than the older tonalite.The core zone of potassic alteration grades outward into extensive propylitic alteration (chlorite-epidote), with both variably overprinted by widespread fracture controlled intermediate argillic alteration (sericite-chlorite), and minor phyllic (sericite-pyrite) and sodic (albite) alteration. Argillic (sericite-kaolinite) and advanced argillic (kaolinite-alunite-pyrophyllite) assemblages occur near surface.Copper and Au grades within the orebody show a positive correlation with quartz stockwork intensity, although disseminated Cu sulphides are also common. Chalcopyrite and bornite are the principle hypogenal minerals, with minor chalcocite. Oxidation extends to a depth of 5 m to 85 m below surface across the deposit, and is underlain by weak supergene mineralisation. Drill testing of the deposit down to 650 m below surface reveals a single cylindrical to conical orebody of 334 million tonnes grading 0.8 wt % Cu and 0.69 gm per tonne Au; the depth extent of mineralisation is unknown.     

The geochemistry of Ca,Sr, Ba and Ra sulfates in some deep brines from the Palo Duro Basin,Texas

The geochemistry of Ca, Sr, Ba and Ra sulfates in some deep brines from the Palo Duro Basin of north Texas, was studied to define geochemical controls on radionuclides such as ⁹⁰Sr and ²²⁶Ra. Published solubility data for gypsum, anhydrite, celestite, barite and RaSO₄ were first reevaluated, in most cases using the ion interaction approach of Pitzer, to determine solubility products of the sulfates as a function of temperature and pressure. Ionic strengths of the brines were from 2.9 to 4.8 m, their temperatures and pressures up to 40°C and 130 bars. Saturation indices of the sulfates were computed with the ion-interaction approach in one brine from the arkosic granite wash fades and four from the carbonate Wolfcamp Formation. All five brines are saturated with respect to gypsum, anhydrite and celestite, and three of the five with respect to barite. All are undersaturated by from 5 to 6 orders of magnitude with respect to pure RaSO₄. ²²⁶Ra concentrations in the brines, which ranged from 10^?11.3 to 10^?12.7 m, are not controlled by RaSO₄ solubility or adsorption, but possibly by the solubility of trace Ra solid solutions in sulfates including celestite and barite.     

Hydrologic and geochemical properties of the San Andreas fault at the Stone Canyon well

The Stone Canyon well penetrates 600 m of highly fractured and severely altered quartz diorite intimately associated with the creeping segment of the San Andreas fault of central California. Geophysical logs reveal a complex hydrology dominated by major fractures. Fluid pressure in some fractures is sufficient to prevent invasion of the formation by heavy drilling mud, implying pore pressures at least 10% higher than hydrostatic ones. At least three chemically distinct waters are encountered, including a chloride brine clearly segregated from the shallow, potable groundwater. Chemical alteration of the quartz diorite persists throughout the well, far below the depth where the water-rock reactions responsible for the ubiquitous chlorite and mixed-layer clays can be considered weathering. Whole-rock ¹⁸O analyses indicate significant interaction of the rocks with a low ¹⁸O fluid within some of the fractured and altered zones, whereas a deeper sample shows¹⁸O enrichment. High pore pressures encountered in Stone Canyon may be due to tectonic compression. Measurements of temporal variations in the pore pressure at the well may provide a means of predicting earthquakes along this segment of the San Andreas fault.     

A study of the depth of weathering and its relationship to the mechanical properties of near-surface rocks in the Mojave Desert

Weathered granite extends 70 m deep at Hi Vista in the arid central Mojave Desert of southern California. The low strength of this granite is due to the alteration of biotite and chlorite montmorillonite. Deep weathering probably occurs in most granites, although we cannot rule out some anomalous mechanisms at Hi Vista. Geophysical instruments set in these slightly altered rocks are limited by the unstable behavior of the rocks. Thus, tectonic signals from instruments placed in shallow boreholes give vague results. Geophysical measurements of these weathered rocks resemble measurements of granitic rocks near major faults. The rheology of the rocks in which instruments are placed limits the useful sensitivity of the instruments.     

Spatial variability in soil moisture as predicted from airborne thematic mapper (ATM) data

In the first part of this project, the extent to which moisture content of alluvial soils could be predicted from imagery derived from an airborne thematic mapper (ATM) was investigated. From sampling done on the same day as the flight, it was found that digital numbers derived from the thermal channel (waveband 11) were strongly correlated with gravimetric moisture content. From sampling three fields of contrasting land cover, the relationship between waveband 11 values and moisture content was found to be independent of land cover type. Spatial variation in waveband 11 values and thus moisture content were related to palaeochannel patterns on the alluvial land. This was investigated by deriving variograms for long transects from each of the three investigated fields. The range and sills of the variograms are shown to express the nature and pattern of palaeochannels. By the application of such geostatistical techniques, high resolution imagery can thus be used to quantify palaeochannel characteristics on alluvial land.     

Applying Higher Order DIRK Time Steps to the "Modified Picard" Method

The “modified Picard” iteration method, which offers global mass conservation, can also be described as a form of Newton's iteration with lagged nonlinear coefficients. It converges to a time step with first-order discretization error. This paper applies second- and third-order diagonally implicit Runge Kutta (DIRK) time steps to the modified Picard method in one example. It demonstrates improvements over the first-order time step in rms error and error-times-effort model quality by factors ranging from two to over two orders of magnitude, showing that the “modified Picard” and DIRK methods are compatible.