Comparison of Two Methods Used to Model Shape Parameters of Pareto Distributions

Two methods are compared for estimating the shape parameters of Pareto field-size (or pool-size) distributions for petroleum resource assessment. Both methods assume mature exploration in which most of the larger fields have been discovered. Both methods use the sizes of larger discovered fields to estimate the numbers and sizes of smaller fields: (1) the tail-truncated method uses a plot of field size versus size rank, and (2) the log–geometric method uses data binned in field-size classes and the ratios of adjacent bin counts. Simulation experiments were conducted using discovered oil and gas pool-size distributions from four petroleum systems in Alberta, Canada and using Pareto distributions generated by Monte Carlo simulation. The estimates of the shape parameters of the Pareto distributions, calculated by both the tail-truncated and log–geometric methods, generally stabilize where discovered pool numbers are greater than 100. However, with fewer than 100 discoveries, these estimates can vary greatly with each new discovery. The estimated shape parameters of the tail-truncated method are more stable and larger than those of the log–geometric method where the number of discovered pools is more than 100. Both methods, however, tend to underestimate the shape parameter. Monte Carlo simulation was also used to create sequences of discovered pool sizes by sampling from a Pareto distribution with a discovery process model using a defined exploration efficiency (in order to show how biased the sampling was in favor of larger fields being discovered first). A higher (more biased) exploration efficiency gives better estimates of the Pareto shape parameters.     

New Generation of Probabilistic Seismic Hazard Assessment for the Area Cologne/Aachen Considering the Uncertainties of the Input Data

A new earthquake catalogue for central, northern and northwestern Europe with unified M_w magnitudes, in part derived from chi-square maximum likelihood regressions, forms the basis for seismic hazard calculations for the Lower Rhine Embayment. Uncertainties in the various input parameters are introduced, a detailed seismic zonation is performed and a recently developed technique for maximum expected magnitude estimation is adopted and quantified. Applying the logic tree algorithm, resulting hazard values with error estimates are obtained as fractile curves (median, 16% and 84% fractiles and mean) plotted for pga (peak ground acceleration; median values for Cologne 0.7 and 1.2 m/s² for probabilities of exceedence of 10% and 2%, respectively, in 50 years), 0.4 s (0.8 and 1.5 m/s²) and 1.0 s (0.3 and 0.5 m/s²) pseudoacclerations, and intensity (I₀ = 6.5 and 7.2). For the ground motion parameters, rock foundation is assumed. For the area near Cologne and Aachen, maps show the median and 84% fractile hazard for 2% probability of exceedence in 50 years based on pga (maximum median value about 1.5 m/s²), and 0.4 s (>2 m/s²) and 1.0 s (about 0.8 m/s²) pseudoaccelerations, all for rock. The pga 84% fractile map also has a maximum value above 2 m/s² and shows similarities with the median map for 0.4 s. In all maps, the maximum values fall within the area 6.2–6.3° E and 50.8–50.9° N, i.e., east of Aachen.     

Fayalitic olivine in matrix of the Krymka LL3.1 chondrite: Vapor-solid growth in the solar nebula

Abstract— Fayalitic olivine (Fa_54–94) is a ubiquitous component in the matrix of Krymka (LL3.1) as well as in other highly unequilibrated chondrites (ordinary and carbonaceous). In Krymka, the fayalitic olivine has an unusual anisotropic platy morphology that occurs in at least five types of textural settings that can be characterized as: (1) isolated platelets, (2) clusters of platelets, (3) euhedral to subhedral crystals, (4) overgrowths of platelets on forsteritic olivine, and (5) fluffy (porous) aggregates. From transmission electron microscope (TEM) investigation, the direction of elongation of the platy olivine overgrowths on forsteritic olivine substrates is along the c axis and in most cases it corresponds with the c axis of the substrate olivine, which suggests that the fayalitic olivine grew in this unusual morphology and is not a replacement product of preexisting material. The fayalitic olivine in the matrix of Krymka is compositionally similar to olivine with platy morphology in the matrix of some CV3 chondrites and both have similar Fe/Mn ratios, but important morphological differences indicate that their relationship needs to be explored further. Textural and compositional data indicate that the fayalitic olivine in the matrix of Krymka, as well as in some other unequilibrated ordinary chondrites, formed prior to final lithification of the meteorite and probably prior to parent body accretion. We find that formation of the fayalitic olivine by vapor-solid growth provides the best explanation for our observations and data and is the only feasible mechanism for the formation of fayalitic olivine in the matrix of Krymka. We propose that the fayalitic olivine formed by vaporization and recondensation of olivine rich-dust, during a period of enhanced dust/gas ratio in the nebula.     

Distribution of early-type stars and dusty matter in the direction of the stellar cluster NGC 1893

The distribution of 255 O-B9-A2, K-G stars and interstellar dust in the direction of the stellar cluster NGC 1893 is studied using V, B-V, and U-B photometric data. Sixteen groups of stars (associations) are discovered at various distances. The first group includes 9 stars of different spectral classes of later types in the sun’s neighborhood lying at a distance of 110 pc. The next 3 groups, at distances of 420, 890, and 14300 pc, are type B associations and the remaining twelve groups are OB associations. They are designated as Aur 0.11, Aur B 0.43, Aur B 0.89, Aur OB 1.4, Aur OB 2.6, AurOB 3.8, Aur OB 4.6, Aur OB 5.4, Aur OB 6.1, Aur OB 7.4, Aur OB 9.3, Aur OB11.6, Aur OB14.3, Aur OB 17.9, Aur OB 25.9, and Aur OB 31.3. For most of these stars the absorption lies within the range from 0m.45 to 5m.41. Such high absorption may be caused by circumstellar absorption as well as by the diffuse nebula IC 410. The dusty matter is distributed nonuniformly in the Aur 0.11, Aur B 0.43, and Aur B 0.89 associations. There is no dust in the space between the associations. There is essentially no dust within the groups (associations) at distances greater than 0.9 kpc. (See Table 2.) __________ Translated from Astrofizika, Vol. 50, No. 2, pp. 243–251 (May 2007).     

Observed daily large-scale rainfall patterns during BOBMEX-1999

A daily rainfall dataset and the corresponding rainfall maps have been produced by objective analysis of rainfall data. The satellite estimate of rainfall and the raingauge values are merged to form the final analysis. Associated with epochs of monsoon these rainfall maps are able to show the rainfall activities over India and the Bay of Bengal region during the BOBMEX period. The intra-seasonal variations of rainfall during BOBMEX are also seen using these data. This dataset over the oceanic region compares well with other available popular datasets like GPCP and CMAP. Over land this dataset brings out the features of monsoon in more detail due to the availability of more local raingauge stations.     

Cosmic‐ray exposure history of two Frontier Mountain H‐chondrite showers from spallation and neutron‐capture products

Abstract— We measured the concentrations of ¹⁰Be, ²⁶Al, ³⁶Cl, ⁴¹Ca and ¹⁴C in the metal and/or stone fractions of 27 Antarctic chondrites from Frontier Mountain (FRO), including two large H‐chondrite showers. To estimate the pre‐atmospheric size of the two showers, we determined the contribution of neutron‐capture produced ³⁶Cl (half‐life = 3.01 times 10⁵ years) and ⁴¹Ca (1.04 times 10⁵ years) in the stone fraction. The measured activities of neutron‐capture ³⁶Cl and ⁴¹Ca, as well as spallation produced ¹⁰Be and ²⁶Al, were compared with Monte Carlo‐based model calculations. The largest shower, FRO 90174, includes eight fragments with an average terrestrial age of (100 ± 30) × 10³ years; the neutron‐capture saturation activities extend to 27 dpm/kg stone for ³⁶Cl and 19 dpm/kg stone for ⁴¹Ca. The concentrations of spallation produced ¹⁰Be, ²⁶Al and ³⁶Cl constrain the radius (R) to 80–100 cm, while the neutron‐capture ⁴¹Ca activities indicate that the samples originated from the outer 25 cm. With a pre‐atmospheric radius of 80–100 cm, FRO 90174 is among the largest of the Antarctic stony meteorites. The large pre‐atmospheric size supports our hypothesis that at least 50 of the ～150 classified H5/H6‐chondrites from the Frontier Mountain stranding area belong to this single fall; this hypothesis does not entirely account for the high H/L ratio at Frontier Mountain. The smaller shower, FRO 90001, includes four fragments with an average terrestrial age of (40 ± 10) × 10³ years; they contain small contributions of neutron‐capture ³⁶Cl, but no excess of ⁴¹Ca. FRO 90001 experienced a complex exposure history with high shielding conditions in the first stage (150 < R < 300 cm) and much lower shielding in the second stage (R < 30 cm), the latter starting ～1.0 million years (Ma) ago. Based on the measured ¹⁰Be/²¹Ne and ²⁶Al/²¹Ne ratios, the cosmic‐ray exposure ages of the two showers are 7.2 ± 0.5 Ma for FRO 90174 and 8 ± 1 Ma for FRO 90001. These ages coincide with the well‐established H‐chondrite peak and corroborate the observation that the exposure age distribution of FRO H‐chondrites is similar to that of non‐Antarctic falls. In addition, we found that corrections for neutron‐capture ³⁶Ar (from decay of ³⁶Cl) result in concordant ²¹Ne and ³⁸Ar exposure ages.