Kriging with strings of data

The concept of a random function and, consequently, the application of kriging cells for the implicit assumption that the data locations are embedded within an infinite domain. An implication of this assumption is that, all else being equal, outlying data locations will receive greater weight because they are seen as less redundant, hence, more informative of the infinite domain. A two- step kriging procedure is proposed for correcting this siring effect. The first step is to establish the total kriging weight attributable to each string. The distribution of that total weight to the samples in the string is accomplished by a second stage of kriging. In the second stage, a spatial redundancy measure r_(n) is used in place of the covariance measure in the data-data kriging matrix. This measure is constructed such that each datum has the same redundancy with the (n)data of the string to which it belongs. This paper documents the problem of kriging with strings of data, develops the redundancy measure r_(n),and presents a number of examples.     

Urban Seismic Risk Evaluation: A Holistic Approach

Risk has been defined, for management purposes, as the potential economic, social and environmental consequences of hazardous events that may occur in a specified period of time. However, in the past, the concept of risk has been defined in a fragmentary way in many cases, according to each scientific discipline involved in its appraisal. From the perspective of this article, risk requires a multidisciplinary evaluation that takes into account not only the expected physical damage, the number and type of casualties or economic losses, but also the conditions related to social fragility and lack of resilience conditions, which favour the second order effects (indirect effects) when a hazard event strikes an urban centre. The proposed general method of urban risk evaluation is multi hazard and holistic, that is, an integrated and comprehensive approach to guide decision-making. The evaluation of the potential physical damage (hard approach) as the result of the convolution of hazard and physical vulnerability of buildings and infrastructure is the first step of this method. Subsequently, a set of social context conditions that aggravate the physical effects are also considered (soft approach). In the method here proposed, the holistic risk evaluation is based on urban risk indicators. According to this procedure, a physical risk index is obtained, for each unit of analysis, from existing loss scenarios, whereas the total risk index is obtained by factoring the former index by an impact factor or aggravating coefficient, based on variables associated with the socio-economic conditions of each unit of analysis. Finally, the proposed method is applied in its single hazard form to the holistic seismic risk evaluation for the cities of Bogota (Colombia) and Barcelona (Spain).     

Nullarbor 018: A new L6 chondrite from Australia

Abstract— A new meteorite find from the Nullarbor Plain in Australia was studied using optical, SEM, and electron microprobe techniques. The meteorite, Nullarbor 018, is an orthodox L6 chondrite that experienced minor-to-moderate alteration of metal during terrestrial weathering (grade A–B to B). During weathering, troilite was preferentially altered, and roughly 20% of the original complement of S in the meteorite was removed. Shock metamorphic effects corresponding to shock stage S4 (or shock facies d) are found, including the presence of some diaplectic feldspar (maskelynite). The meteorite is not obviously paired with other finds from the Nullarbor region, but the possibility that it is paired cannot be excluded.     

Saturn's satellites: Nuar-infrared spectrophotometry (0.6–2.5 μm) of the leading and trailing sides and compositional implications

Near-infrared spectra, 0.65–2.5 μm, are presented for Tethys, Dione, Rhea, Iapetus, and Hyperion. Water ice absorptions at 2.0, 1.5, and 1.25 μm are seen in the spectra of all five objects (except the 1.25-μm band was not detected in spectra of Hyperion) and the weak 1.04-μm ice absorption is detected on the leading and trailing sides of Rhea, and the trailing side of Dione. Upper limits to the 1.04-μm ice band depth are <0.3% for the leading side of Dione; <0.7% for the leading side of Iapetus, and the trailing side of Tethys; <1% on the trailing side of Iapetus; and <5% on the leading side of Tethys. The leading-trailing side ice band depth differences on Saturn's satellites are similar to those for the Galilean satellites, indicating possible surface modification by magnetospheric charged particle bombardment. Limits are determined for the amount of particulates, trapped gases, and amonium hydroxide on the surface. The surfaces of Saturn's satellites (except the dark side of Iapetus) are nearly pure water ice, with probably less than about 1 wt% particulate minerals. The ice could be clathrates with as much as a few weight percent trapped gases. The upper limit of amonium hydroxide depends on the spectral data precision and varies from ～ 1 wt% NH₃ for the leading side of Rhea to ～ 10 wt% NH₃ for Dione.     

Calculation of Uncertainty in the Variogram

There are often limited data available in early stages of geostatistical modeling. This leads to considerable uncertainty in statistical parameters including the variogram. This article presents an approach to calculate the uncertainty in the variogram. A methodology to transfer this uncertainty through geostatistical simulation and decision making is also presented.The experimental variogram value for a separation lag vector h is a mean of squared differences. The variance of a mean can be calculated with a model of the correlation between the pairs of data used in the calculation. The data here are squared differences; therefore, we need a measure of a 4-point correlation. A theoretical multi-Gaussian approach is presented for this uncertainty assessment together with a number of examples. The theoretical results are validated by numerical simulation. The simulation approach permits generalization to non-Gaussian situations.Multiple plausible variograms may be fit knowing the uncertainty at each variogram point, . Multiple geostatistical realizations may then be constructed and subjected to process assessment to measure the impact of this uncertainty.     

Observing with SIRTF: Opportunities for the Scientific Community

The Space InfraRed Telescope Facility (SIRTF) is the fourth and finalelement in NASA's family of orbiting Great Observatories. SIRTFconsists of a 0.85-meter diameter telescope and three cryogenically-cooledscience instruments capable of observing from the near- to the far-infrared,between 3 and 180 m. Incorporating the latest in large-format infrareddetector arrays, SIRTF offers orders-of-magnitude improvements in capabilityover existing facilities. Launch is scheduled for December 2001, with ananticipated lifetime of up to 5 years. SIRTF will observe targets rangingfrom small, icy bodies in the outer Solar System to the most luminousknown objects in the distant reaches of the Universe. SIRTF representsan important scientific and technical bridge to NASA's new Origins program,and is managed for NASA by the Jet Propulsion Laboratory, CaliforniaInstitute of Technology.     

Deriving Constraints on Small-Scale Variograms due to Variograms of Large-Scale Data

The application of kriging-based geostatistical algorithms to integrate large-scale seismic data calls for direct and cross variograms of the seismic variable and primary variable (e.g., porosity) at the modeling scale, which is typically much smaller than the seismic data resolution. In order to ensure positive definiteness of the cokriging matrix, a licit small-scale coregionalization model has to be built. Since there are no small-scale secondary data, an analytical method is presented to infer small-scale seismic variograms. The method is applied to estimate the 3-D porosity distribution of a West Texas oil field given seismic data and porosity data at 62 wells.