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.     

THE RESOLUTION OF NARROW LOW-VELOCITY ZONES WITH THE GENERALIZED RECIPROCAL METHOD1

The depth to the surface of a refractor and the seismic velocity within the refractor are very often intimately related. In the shallow environment, increased thicknesses of weathering occur in areas of jointing, shearing or lithological variations, and these zones of deeper weathering can have lower subweathering refractor velocities. This association is important in geotechnical investigations and in the measurement of weathering thicknesses and sub-weathering velocities for statics corrections for reflection seismic surveys. Algorithms, which employ forward and reverse traveltime data and which explicitly accommodate the offset distance through the process known as refraction migration, are necessary if detailed structure on a refractor and rapid lateral variations of the seismic velocity within it are to be resolved. These requirements are satisfied with wavefront construction techniques, Hales’ method and the generalized reciprocal method (GRM). However, these methods employ refraction migration in fundamentally different manners. Most methods compute an offset distance with an often imprecise knowledge of the seismic velocities of the overlying layers. In contrast, the GRM uses a range of offset distances from less than to greater than the optimum value, with the optimum value being selected with a minimum-variance criterion. The approach of the GRM is essential where there are undetected layers and where there are rapid variations in the depth to a refractor and the seismic velocity within it. In the latter situations the offset distance necessary to define the seismic velocities can differ considerably from the value required to define depths. The efficacy of the GRM in resolving structure and seismic velocity is demonstrated with three model studies and two field examples.     

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.     

X-Ray Fluorescence Determination of Trace Elements in 6 B.C.S. and 5 P.R.E. Reference Materials

The concentrations of 20 trace elements in 6 British Chemical Standards (BCS) reference materials and 5 European Federation of Refractories Producers (PRE) reference materials have been determined by X-ray fluorescence spectrometry.     

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.     

Late Quaternary clay minerals off Middle Vietnam in the western South China Sea: Implications for source analysis and East Asian monsoon evolution

High-resolution clay mineral records combined with oxygen isotopic stratigraphy over the past 450 ka during late Quaternary from Core MD05-2901 off Middle Vietnam in the western South China Sea are re-ported to reconstruct a history of East Asian monsoon evolution. Variations in Illite, chlorite, and kaolinite contents indicate a strong glacial-interglacial cyclicity, while changes in smectite content present a higher frequency cyclicity. The provenance analysis indicates a mixture of individual clay minerals from various sources surrounding the South China Sea. Smectite derived mainly from the Sunda shelf and its major source area of the Indonesian islands. Illite and chlorite originated mainly from the Mekong and Red rivers. Kaolinite was provided mainly by the Pearl River. Spectral analysis of the kaolin-ite/(illite chlorite) ratio displays a strong eccentricity period of 100 ka, implying the ice sheet-forced win-ter monsoon evolution; whereas higher frequency changes in the smectite content show an ice sheet-forced obliquity period of 41 ka, and precession periods of 23 and 19 ka and a semi-precession period of 13 ka as well, implying the tropical-forced summer monsoon evolution. The winter monsoon evolution is generally in coherence with the glacial-interglacial cyclicity, with intensified winter monsoon winds during glacials and weakened winter monsoon winds during interglacials; whereas the summer monsoon evolution provides an almost linear response to the summer insolation of low latitude in the Northern Hemisphere, with strengthened summer monsoon during higher insolation and weakened summer monsoon during lower insolation. The result suggests that the high-latitude ice sheet and low-latitude tropical factor could drive the late Quaternary evolution of East Asian winter and summer monsoons, respectively, implying their diplex and self-contained forcing mechanism.