Bias in estimating fractal dimension with the rescaled-range (R/S) technique

Fractal geostatistics are being applied to subsurface geological data as a way of predicting the spatial distribution of hydrocarbon reservoir properties. The fractal dimension is the controlling parameter in stochastic methods to produce random fields of porosity and permeability. Rescaled range (R/S)analysis has become a popular way of estimating the fractal dimension, via determination of the Hurst exponent (H). A systematic investigation has been undertaken of the bias to be expected due to a range of factors commonly inherent in borehole data, particularly downhole wireline logs. The results are integrated with a review of previous work in this area. Small datasets. overlapping samples, drift and nonstationariry of means can produce a very large bias, and convergence of estimates of H around 0.85–0.90 regardless of original fractal dimension. Nonstationarity can also account for H>1, which has been reported in the literature but which is theoretically impossible for fractal time series. These results call into question the validity of fractal stochastic models built using fractal dimensions estimated with the R/Smethod.     

On the kinetics of textural equilibration in forsterite marbles

In the aureole of the Beinn an Dubhaich granite, Skye, the minimum observed median forsterite-calcite-calcite dihedral angle varies from 110° at the olivinein isograd to about 165° (the equilibrium value) at the granite-limestone contact. Laboratory experiments were performed to investigate the kinetics of this textural change. It was found that the rate of change of the forsterite-calcite-calcite dihedral angle followed approximately first-order kinetics with an activation energy of 48±4 kJ mol^-1 for fluid-present conditions, and 90 ±4 kJ mol^-1 for fluid-absent conditions. Scanning ion imaging demonstrated that, at least in the early stages of textural change, solution-reprecipitation of the calcite was the rate determining step in the fluid-present runs. The latter result and the value of the activation energy are both consistent with the activation energy found by previous authors for (albeit zeroth order) silicate-aqueous solution solution-reprecipitation reactions. The value of activation energy for the dry data does not correspond to those for either grain boundary or volume diffusion of oxygen or magnesium in forsterite. The mechanism for textural equilibration in the fluid-absent runs is uncertain. Application of the experimentally-derived rate equation to the Beinn an Dubhaich marbles gave activation energies higher than those obtained experimentally. It is concluded from consideration of grain growth effects that activation energies derived from the Beinn an Dubhaich marbles probably reflect textural equilibration under predominantly fluid-absent conditions.     

Pollen representation,source area,and basin size: Toward a unified theory of pollen analysis

The concepts of pollen source area and of production and dispersal biases in pollen representation are quantified by means of a simple theoretical model. Source areas and relative pollen representation are shown to depend on basin size according to functions that describe the amount of pollen remaining airborne at increasing distances from single pollen sources. The form of these functions is determined by physical processes. Standard formulas for elevated sources do not apply, but the integrated form of Sutton's equation for particle dispersal from a ground-level source gives useful approximations applicable to pollen transport over a forest canopy. Simulations using this equation yielded source areas that increased realistically with basin size, showed substantial differences between source areas for pollen grains with different deposition velocities, and predicted that lighter pollen grains should become better represented with increasing basin size. All of these predictions are qualitatively consistent with present knowledge of the characteristics of pollen assemblages in different depositional environments. The model further allows parameters that can be estimated by statistical calibration methods to be predicted from underlying physical quantities. This extension suggests procedures for testing the theory with quantitative data on surface pollen and forest composition. Preliminary results showed reasonable agreement between estimated and predicted values of dispersal indices for the most abundant taxa in pollen spectra from the northern midwestern United States.     

Permo-Triassic tectonic evolution and metallogenesis of the Rockhampton—Maryborough area, Queensland — A photogeological investigation

Structural analysis of remotely sensed data provides a method of assessing the tectonic significance of regional metallogenic lineaments in the New England Orogen of southeastern Queensland. Photogeological analysis of Landsat imagery and small-scale aerial photography reveals a pattern of WNW—NNW-oriented structures, which were apparently generated in response to Mesozoic crustal extension and reactivated during Early Tertiary block faulting. These structures tend to overprint arcuate late Palaeozoic to early Mesozoic trends and batholith belts, and exert a control over Middle to Late Triassic rifting and epizonal plutonism. The distribution of epigenetic base and precious metal deposits in the Rockhampton—Maryborough area is locally but not regionally related to identifiable structural lineaments.     

Some Biases in Sampling Multilevel Piezometers for Volatile Organics

Multilevel piezometers are cost-effective monitoring devices for determining the three-dimensional distribution of solutes in ground water. Construction includes flexible tubing (plastic or Teflon®). Their sampling is subject to a number of'potential biases, particularly: (1) losses of volatile organic solutes via volatilization, (2) sorption onto the flexible tubing of the piezometers, (3) leaching of organics from this tubing, and (4) collection of unrepresentative samples due to inadequate piezometer flushing. It is shown that these biases are minimal or are easily controlled in most situations.
Another source of bias has been recognized. Organic solutes present in ground water above the screened level can penetrate the flexible plastic or Teflon tubing and contaminate the sampled water being drawn through this tubing. Laboratory tests and field results indicate this transmission causes low organic contaminant concentrations to be erroneously attributed to ground water which is free of such contaminants. The transmitted organics apparently desorb from the plastic tubing during flushing of even 40 piezometer volumes.
Recognition of this transmission problem provides for a better interpretation of existing organic contaminant distribution data. Caution is advised when considering the use of these monitoring devices in organic solute contaminant studies.     

Rhyolites contaminated with metapelite and gabbro,Lipari, Aeolian Islands,Italy: products of lower crustal fusion or of assimilation plus fractional crystallization?

Pleistocene lavas from Monte S. Angelo and Chiesa Vecchia volcanoes on Lipari contain two suites of inclusions. A metapelitic suite consists of gneisses and granulites with combinations of cordierite, garnet, corundum, hercynite, andalusite, sillimanite, orthopyroxene, ilmenite, magnetite, biotite, plagioclase, and quartz. A gabbroic suite has cumulus texture and contains plagioclase, orthopyroxene, clinopyroxene, and magnetite. All megacryst phases in the lavas appear to be derived from rock fragments, with the exception of euhedral strongly zoned calcic plagioclase, and none has grown by homogeneous nucleation from liquid represented by the groundmass, which is peraluminous rhyolite (>70 wt% SiO₂, >6 wt% K₂O). Ground-mass microcrysts were nearly all derived from disaggregated metapelites; overgrowths of alkali feldspar on plagioclase and of orthopyroxene on clinopyroxene, and quartz intergrown with alkali feldspar, are the only phases that grew from the rhyolitic liquid. Euhedral cordierite, hercynite, and plagioclase at the margins of some rock fragments grew by reaction of metapelite with liquid.For grains in contact within metapelite inclusions, geothermometers and geobarometers yield estimates of equilibration conditions in the range of 800±100° C and 5±1 kbar. Compositions of phases in the same thin section, but not in the same inclusion, yield broadly erratic P and T estimates indicating disequilibrium among metapelite inclusions. Pyroxene thermometry in the gabbro suite indicates a crystallization temperature of 1020±50° C and a lack of subsequent thermal equilibration with the rhyolitic liquid.The metapelite suite may partly be restite, but much is xenolithic, derived from a vertical interval of perhaps several kilometers, and may have undergone a much earlier episode of melting. The gabbro fragments are accidental xenoliths incorporated as the magma rose. Contaminants (metapelite and gabbro) account for 50 vol.% of the lavas, and cause them to be classified as high-K andesite according to whole-rock major element analysis.The rhyolitic liquid may have originated by partial fusion of metapelites in the lower crust, or by fractional crystallization of mafic mantle-derived magma combined with assimilation of metapelite; the bulk of the evidence favors assimilation-fractional crystallization. Miocene and younger metapelite-contaminated rhyolites also occur in Tuscany, SE Spain, E Morocco, and NW Tunisia, and are associated in each region with mafic silica-undersaturated lavas, implying crustal underplating around the western Mediterranean before, during, and after formation of the Tyrrhenian basin.     

Asymmetry in the time-lapse seismic response to injection and depletion

Large changes in seismic reflection amplitude have been observed around injectors, and result from the decrease in elastic‐wave velocity due to the increase in pore pressure in the reservoir. In contrast, the velocity change resulting from the decrease in pore pressure in depleting reservoirs is observed to be smaller in magnitude. Elastic‐wave velocities in sandstones vary with stress due to the presence of stress‐sensitive grain boundaries within the rock. Grain‐boundary stiffness increases non‐linearly with increasing compressive stress, due to increased contact between opposing faces of the boundary. This results in a change in velocity due to a decrease in pore pressure that is smaller than the change in velocity caused by an increase in pore pressure, in agreement with time‐lapse seismic observations. The decrease in porosity resulting from depletion is not fully recovered upon re‐pressurization, and this leads to an additional steepening of the velocity vs. effective stress curve for injection relative to depletion. This difference is enhanced by any breakage of cement or weakening of grain contacts that may occur during depletion and by the reopening or formation of fractures or joints and dilation of grain boundaries that may occur during injection.