The Proportional Effect

Many regionalized variables encountered in geostatistical application show a proportional effect, that is, greater variability in high valued areas. The proportional effect is a consequence of the univariate distribution of the variable being considered. This presents several challenges including inference of variograms and conditional distributions. The correlogram and relative variogram were devised to mitigate challenges with variography. Other techniques such as normalization, direct simulation, and indicators provide a means to characterize conditional distributions. A review of these tools is given along with several examples to provide an explanation of the proportional effect.     

Integrating Large-Scale Soft Data by Simulated Annealing and Probability Constraints

Interpretation of geophysical data or other indirect measurements provides large-scale soft secondary data for modeling hard primary data variables. Calibration allows such soft data to be expressed as prior probability distributions of nonlinear block averages of the primary variable; poorer quality soft data leads to prior distributions with large variance, better quality soft data leads to prior distributions with low variance. Another important feature of most soft data is that the quality is spatially variable; soft data may be very good in some areas while poorer in other areas. The main aim of this paper is to propose a new method of integrating such soft data, which is large-scale and has locally variable precision. The technique of simulated annealing is used to construct stochastic realizations that reflect the uncertainty in the soft data. This is done by constraining the cumulative probability values of the block average values to follow a specified distribution. These probability values are determined by the local soft prior distribution and a nonlinear average of the small-scale simulated values within the block, which are all known. For each realization to accurately capture the information contained in the soft data distributions, we show that the probability values should be uniformly distributed between 0 and 1. An objective function is then proposed for a simulated annealing based approach to enforce this uniform probability constraint. The theoretical justification of this approach is discussed, implementation details are considered, and an example is presented.     

Dating terrestrial impact events

Abstract— Systematic examination of dating results from various craters indicates that about 90% of the rocks affected by an impact preserve their pre-shock ages because shock and post-shock conditions are not sufficient to disturb isotopic dating systems. In the other 10% of target lithologies, various geochronometers show significant shock-induced effects. Major problems in dating impactites are caused by their non-equlibrated character. They often display complex textures, where differently shocked and unshocked phases interfinger on the sub-mm scale. Due to this, dating on whole rock samples or insufficiently pure mineral fractions often yielded ambiguous results that set broad age limits but are not sufficient to answer reliably questions such as a possible periodicity in cratering on Earth, or correlation of impact events with mass extinctions. Dating results from shock recovery experiments indicate that post-shock annealing plays the most important role in resetting isotopic clocks. Therefore, the major criterion for sample selection in and around craters is the post-shock thermal regime. Based on their different thermal evolution, the following geological impact formations can be distinguished: (1) the coherent impact melt layer, (2) allochthonous breccia deposits, (3) the crater basement, and (4) distant ejecta deposits. Samples of the coherent impact melt layer are the most suitable candidates for dating. Excellent ages of high precision can be obtained by internal Rb-Sr, and Sm-Nd isochrons, U-Pb analyses on newly crystallized accessory minerals, and K-Ar (³⁹Ar-⁴⁰Ar) dating of clast-free melt rocks. Fission track counting on glassy material has yielded correct ages, and paleomagnetic measurements have been successfully applied to post-Triassic craters. In the ideal case of a fast-cooling impact melt layer, all these different techniques should give identical ages. Allochthonous breccias contain shocked, unshocked, and/or glassy components in various proportions; and, hence, each of these ejecta deposits has its own individual thermal history, making sample evaluation difficult Glassy melt particles in suevitic breccias are well suited for fission track and Ar-Ar dating. Weakly shocked material may yield reliable Ar-Ar and fission track ages, if formation temperatures were high, and cooling rates moderate. In contrast, highly shocked but rapidly cooled lithologies show only disturbed and not reset isotopic systems. For ejecta deposits and the crater wall of young craters, dating with cosmogenic nuclides is a new and powerful technique. Crater basement lithologies have a high potential in impact dating, although it has not been exploited so far. A prerequisite for resetting of isotopic clocks in these lithologies is the presence of an overlaying impact melt layer, which causes thermal metamorphism. Fission track and K-Ar techniques are most promising, because both systems are easily reset at low temperatures. Good candidates for impact dating are long-term annealed rocks, even if shock metamorphic overprint is very weak. In addition, Ar-Ar dating dating of pseudotachylites appears promising. In large impact structures, where high temperatures persist for long times, polymict “footwall” breccias beneath the melt sheet are also appropriate for dating, using the isochron approach and U-Pb on accessory minerals. Distant ejecta material have undergone very fast cooling, and the ejecta deposits have ambient formation temperatures. Among this material, tektites and impact melt glass are ideal objects for Ar-Ar and fission track impact dating. Dating on other material from distant ejecta deposits, such as U-Pb analyses on zircons, offers new possibilities. Efforts to correlate distant ejecta with distinct craters critically depend on proper error assignment to a specific age. This aspect is illustrated on the K/T boundary example.     

Magmatic 87Sr/86Sr relicts in hydrothermally altered quartz diorites (Brabant Massif,Belgium) and the role of epidote as a Sr filter

The porphyritic quartz diorites of the Caledonian Brabant Massif have been totally altered. Ca, Rb, Sr, Zr, Ce, Y measurements and Sr-Nd isotopic analyses were performed on the Quenast plug and the Lessines sill, in an attempt to study the relative mobility of Sr and evaluate the extent, direction and magnitude of the ⁸⁷Sr/⁸⁶Sr alterations. Sr electron microprobe analyses of epidote were also carried out to assess its role in the Sr distribution.The initial ⁸⁷Sr/⁸⁶Sr ratio is shown to have had an unsteady behaviour during the studied water/rock interactions since it has been sometimes enhanced, sometimes depressed and occasionally not modified. The possibility and magnitude of the ⁸⁷Sr contamination turn out to be strictly related to the degree of Sr accommodation in the secondary minerals. Epidote in particular has proved to be the main trap for the hydrothermal Sr and this mineral is thus regarded as the major controlling factor of ⁸⁷Sr hydrothermal contamination. The epidote-poor rocks (albite+chlorite-rich rocks) seem to have been unaffected by any Sr interchange with the aqueous solutions. Therefore, as alteration quickly follows the crystallization of the magma, their initial ⁸⁷Sr/ ⁸⁶Sr ratio, which is deduced from an isochron, might be a primary petrogenetic feature enabling interpretation of the genesis of their parental magmas. On the other hand, in the epidote-rich rocks, this ratio has been readily altered; it could thus generally be used only to trace the origin of the hydrothermal solutions. As a consequence, these rocks should not be selected for dating an alteration event by the Rb-Sr method.     

Hierarchical object-based stochastic modeling of fluvial reservoirs

This paper describes a novel approach to modeling braided stream fluvial reservoirs. The approach is based on a hierarchical set of coordinate transformations involving relative straingraphic coordinates, translations, rotations, and straightening functions. The emphasis is placed on geologically sound geometric concepts and realistically-attainable conditioning statistics including areal and vertical facies proportions. Modeling proceeds in a hierarchical fashion, that is (1) a stratigraphic coordinate system is established for each reservoir layer, (2) a number of channel complexes are positioned within each layer, and then (3) channels are positioned within each channel complex. The geometric specification of each sand-filled channel within the background of floodplain shales is a marked point process. Each channel is marked with a starting location, size parameters, and sinuosity parameters. We present the hierarchy of eight coordinate transformations, introduce an analytical expression for the channel cross-section shape, describe the simulation algorithm, and demonstrate how the realizations are made to honor local conditioning data from wells and global conditioning data such as areal and vertical proportions.     

Response of Nereis diversicolor (Polychaeta, Nereidae) populations to reduced wastewater discharge in the polluted estuary of Oued Souss, Bay of Agadir, Morocco

Field investigations on the population dynamics of Nereis diversicolor were carried out from January 2002 to December 2003 in the estuary of Oued Souss (southwestern Morocco) to determine the changes caused by setting up of a domestic and industrial wastewater purification plant (M'zar) before and after by the end of wastewater discharges in November 2002 on the structure of the ecosystem. Samples of N. diversicolor were collected monthly in the intertidal zone at low tide before (during 2002) and after (during 2003) the end of wastewater discharges.Separation of cohorts using the Algorithm EM method (McLachlan, G.J., Krishnan, T., 1997. The EM algorithm and extensions. Wiley Series in Probability and Statistics. Wiley, New York, 274 pp.) allowed determination of the growth rate (mm day⁻¹) by cohort and the annual production. The data showed significant differences between populations of Nereis diversicolor before and after the end of wastewater discharges. During the wastewater discharge period (2002), the population had a mean annual density of 1992 ind m⁻², a mean annual biomass of 75.52 g DW m⁻² and an annual secondary production of 141.3 g DW m⁻² with a P/B ratio of 1.87. After the end of discharges (2003), density, biomass and secondary production decreased significantly. The annual averages for these parameters were 740 ind m⁻², 14.16 g DW m⁻² and 23.83 g DW m⁻², respectively, with a P/B ratio of 1.68.The important decrease observed in density, biomass and secondary production of Nereis diversicolor may be attributed (a) to the environmental changes observed after the end of wastewater discharges in the estuary of Oued Souss, namely the increase of salinity and the decrease of organic matter content, and (b) to the migration of this species towards other areas.     

Multiple-Point Statistics for Training Image Selection

Selecting a training image (TI) that is representative of the target spatial phenomenon (reservoir, mineral deposit, soil type, etc.) is essential for an effective application of multiple-point statistics (MPS) simulation. It is often possible to narrow potential TIs to a general subset based on the available geological knowledge; however, this is largely subjective. A method is presented that compares the distribution of runs and the multiple-point density function from available exploration data and TIs. The difference in the MPS can be used to select the TI that is most representative of the data set. This tool may be applied to further narrow a suite of TIs for a more realistic model of spatial uncertainty. In addition, significant differences between the spatial statistics of local conditioning data and a TI may lead to artifacts in MPS. The utilization of this tool will identify contradictions between conditioning data and TIs. TI selection is demonstrated for a deepwater reservoir with 32 wells.