Stochastic geometry in petroleum geology

Many aspects of the generation, migration, trapping, and discovery of petroleum, as well as its primary and enhanced recovery, depend upon geometry. The scale of the relevant geometric features varies all the way from that of continental margins and basins down to the pores and fissures in reservoir rocks. Because the spatial complexity is so great for each of these processes, it is reasonable to describe them statistically. The primary purpose of this paper is to survey possible ways in which statistical or stochastic geometry enters and might be used in petroleum geology and engineering. While it offers some new theory, this paper does not directly suggest any specific new methods for the estimation of hydrocarbon resources or reserves. This deficiency is mainly due to the current lack of relevant data. When data are available the point of view explained herein will be fruitful. The survey ties together many topics in a novel way.     

Sub-micron scale distributions of trace elements in zircon

Sub-micron scale zoning of Ti concentrations and correlations between concentrations of Ti and other trace elements (P, Ce, and Y) and cathodoluminescent (CL) banding is observed in natural zircons. Ion images were made using the Caltech Microanalysis Center’s CAMECA NanoSIMS 50L with an O⁻ primary beam focused to ~300 nm on the sample surface. The high spatial resolution of this technique allows for interrogation of chemical variations at or below the scale of CL banding in natural zircons. Images produced in this manner display two types of correlations among Ti, P, Ce, and Y (which appears to be a proxy for CL intensity): strong (correlation coefficients >0.8) and subtle (correlation coefficients ~0.15–0.4). Strongly correlated images, which display Ti variations of ca. a factor of 3 between adjacent CL bands and overall elevated trace element concentrations in CL-dark bands, were found within an oscillatory-zoned, trace element enriched sector of a CL sector-zoned zircon. Three possible causes for such correlations include: temperature-dependent equilibrium partitioning, trace element partitioning limited by diffusion in the host melt and surface-controlled, non-equilibrium growth. Comparison of our data with the expected results of these processes suggests that: (1) Ti partitioning in zircon is dependent upon non-equilibrium effects in addition to temperature and/or (2) the incorporation of elements that co-vary with Ti in zircon (e.g., Y, P and Ce) is also temperature-dependent. Sub-micron scale, high-Ti regions are also found within Proterozoic Adirondack and >4 Ga Jack Hills zircons as well as trace element enrichments (including Ti) along cracks within Jack Hills zircons.     

Experimental calibration of oxygen isotope fractionation between quartz and zircon

We report the results of an experimental calibration of oxygen isotope fractionation between quartz and zircon. Data were collected from 700 to 1000 °C, 10–20 kbar, and in some experiments the oxygen fugacity was buffered at the fayalite–magnetite–quartz equilibrium. Oxygen isotope fractionation shows no clear dependence on oxygen fugacity or pressure. Unexpectedly, some high-temperature data (900–1000 °C) show evidence for disequilibrium oxygen isotope partitioning. This is based in part on ion microprobe data from these samples that indicate some high-temperature quartz grains may be isotopically zoned. Excluding data that probably represent non-equilibrium conditions, our preferred calibration for oxygen isotope fractionation between quartz and zircon can be described by:

This relationship can be used to calculate fractionation factors between zircon and other minerals. In addition, results have been used to calculate WR/melt–zircon fractionations during magma differentiation. Modeling demonstrates that silicic magmas show relatively small changes in δ¹⁸O values during differentiation, though late-stage mafic residuals capable of zircon saturation contain elevated δ¹⁸O values. However, residuals also have larger predicted melt–zircon fractionations meaning zircons will not record enriched δ¹⁸O values generally attributed to a granitic protolith. These results agree with data from natural samples if the zircon fractionation factor presented here or from natural studies is applied.     

MAGNETISM OF METEORITES: A REVIEW OF RUSSIAN STUDIES

We present here a summary review of the work of Russian scientists, primarily Gus'kova and Pochtarev, on the magnetism of meteorites. They have measured the initial natural remanent magnetization and the magnetic susceptibility in more than 900 meteorite samples from collections throughout the Soviet Union. More sophisticated studies, involving both thermal and alternating field demagnetization experiments, were also conducted on a few samples. Meteorites almost invariably retain evidence of ancient magnetic fields in their pre-terrestrial history     

Non-linear motions of Australian geodetic stations induced by non-tidal ocean loading and the passage of tropical cyclones

We investigate daily and sub-daily non-tidal oceanic and atmospheric loading (NTOAL) in the Australian region and put an upper bound on potential site motion examining the effects of tropical cyclone Yasi that crossed the Australian coast in January/February 2011. The dynamic nature of the ocean is important, particularly for northern Australia where the long-term scatter due to daily and sub-daily oceanic changes increases by 20–55 % compared to that estimated using the inverted barometer (IB) assumption. Correcting the daily Global Positioning System (GPS) time series for NTOAL employing either a dynamic ocean model or the IB assumption leads to a reduction of up to 52 % in the weighted scatter of daily coordinate estimates. Differences between the approaches are obscured by seasonal variations in the GPS precision along the northern coast. Two compensating signals during the cyclone require modelling at high spatial and temporal resolution: uplift induced by the atmospheric depression, and subsidence induced by storm surge. The latter dominates ( \(>\) 135 %) the combined net effect that reaches a maximum of 14 mm, and 10 mm near the closest GPS site TOW2. Here, 96 % of the displacement is reached within 15 h due to the rapid transit of cyclones and the quasi-linear nature of the coastline. Consequently, estimating sub-daily NTOAL is necessary to properly account for such a signal that can be 3.5 times larger than its daily-averaged value. We were unable to detect the deformation signal in 2-hourly GPS processing and show that seasonal noise in the Austral summer dominates and precludes GPS detection of the cyclone-related subsidence.     

Phytoplankton and iron: validation of a global three-dimensional ocean biogeochemical model

The JGOFS program and NASA ocean-color satellites have provided a wealth of data that can be used to test and validate models of ocean biogeochemistry. A coupled three-dimensional general circulation, biogeochemical, and radiative model of the global oceans was validated using these in situ data sources and satellite data sets. Biogeochemical processes in the model were determined from the influences of circulation and turbulence dynamics, irradiance availability, and the interactions among four phytoplankton functional groups (diatoms, chlorophytes, cyanobacteria, and coccolithophores) and four nutrients (nitrate, ammonium, silica, and dissolved iron).Annual mean log-transformed dissolved iron concentrations in the model were statistically positively correlated on basin scale with observations (P<0.05) over the eight (out of 12) major oceanographic basins where data were available. The model tended to overestimate in situ observations, except in the Antarctic where a large underestimate occurred. Inadequate scavenging and excessive remineralization and/or regeneration were possible reasons for the overestimation.Basin scale model chlorophyll seasonal distributions were positively correlated with SeaWiFS chlorophyll in each of the 12 oceanographic basins (P<0.05). The global mean difference was 3.9% (model higher than SeaWiFS).The four phytoplankton groups were initialized as homogeneous and equal distributions throughout the model domain. After 26 years of simulation, they arrived at reasonable distributions throughout the global oceans: diatoms predominated high latitudes, coastal, and equatorial upwelling areas, cyanobacteria predominated the mid-ocean gyres, and chlorophytes and coccolithophores represented transitional assemblages. Seasonal patterns exhibited a range of relative responses: from a seasonal succession in the North Atlantic with coccolithophores replacing diatoms as the dominant group in mid-summer, to successional patterns with cyanobacteria replacing diatoms in mid-summer in the central North Pacific. Diatoms were associated with regions where nutrient availability was high. Cyanobacteria predominated in quiescent regions with low nutrients.While the overall patterns of phytoplankton functional group distributions exhibited broad qualitative agreement with in situ data, quantitative comparisons were mixed. Three of the four phytoplankton groups exhibited statistically significant correspondence across basins. Diatoms did not. Some basins exhibited excellent correspondence, while most showed moderate agreement, with two functional groups in agreement with data and the other two in disagreement. The results are encouraging for a first attempt at simulating functional groups in a global coupled three-dimensional model but many issues remain.     

A Practical Measurement Strategy to Estimate Nonlinear Chlorinated Solvent Sorption in Low foc Sediments

In this study, we tested a practical strategy useful for accurate chlorinated volatile organic compound (cVOC) sorption prediction. Corresponding to the feature of the superposition of adsorption due to thermally altered carbonaceous matter (TACM) with organic carbon‐water partitioning, a nonlinear Freundlich sorption isotherm covering a wide range of aqueous concentrations was defined by equilibrium sorption measurement at one or a few low concentration points with extrapolation to the empirical organic carbon‐water partition coefficient (K_oc,e) near compound solubility. We applied this approach to obtain perchloroethene equilibrium sorption isotherm parameters for TACM‐containing glacial sand and gravel subsoil samples from a field site in New York. Sorption and associated K_oc,c applicable to low (5–500 µg/L) and high (>100,000 µg/L) aqueous concentrations were determined in batch experiments. (The K_oc,c is the organic carbon‐normalized sorption partition coefficient corresponding to aqueous concentration C_w.) The K_oc,c measurements at low concentration (~5 µg/L) were 6 to 34 times greater than the K_oc,e. The importance of this type of data is illustrated through presentation of its substantial impact on the site remedy. In so doing, we provide an approach that is broadly applicable to cVOC field sites with similar circumstances (low carbon content glacial sand and gravel with TACM).     

The effect of El Niño Southern Oscillation cycles on the decadal scale suspended sediment behavior of a coastal dry‐summer subtropical catchment

Rivers display temporal dependence in suspended sediment–water discharge relationships. Although most work has focused on multi‐decadal trends, river sediment behavior often displays sub‐decadal scale fluctuations that have received little attention. The objectives of this study were to identify inter‐annual to decadal scale fluctuations in the suspended sediment–discharge relationship of a dry‐summer subtropical river, infer the mechanisms behind these fluctuations, and examine the role of El Niño Southern Oscillation climate cycles. The Salinas River (California) is a moderate sized (11 000 km²), coastal dry‐summer subtropical catchment with a mean discharge (Q_mean) of 11.6 m³ s^?1. This watershed is located at the northern most extent of the Pacific coastal North America region that experiences increased storm frequency during El Niño years. Event to inter‐annual scale suspended sediment behavior in this system was known to be influenced by antecedent hydrologic conditions, whereby previous hydrologic activity regulates the suspended sediment concentration–water discharge relationship. Fine and sand suspended sediment in the lower Salinas River exhibited persistent, decadal scale periods of positive and negative discharge corrected concentrations. The decadal scale variability in suspended sediment behavior was influenced by inter‐annual to decadal scale fluctuations in hydrologic characteristics, including: elapsed time since small (~0.1 × Q_mean), and moderate (~10 × Q_mean) threshold discharge values, the number of preceding days that low/no flow occurred, and annual water yield. El Niño climatic activity was found to have little effect on decadal‐scale fluctuations in the fine suspended sediment–discharge relationship due to low or no effect on the frequency of moderate to low discharge magnitudes, annual precipitation, and water yield. However, sand concentrations generally increased in El Niño years due to the increased frequency of moderate to high magnitude discharge events, which generally increase sand supply. Copyright © 2014 John Wiley & Sons, Ltd.