Parameterization of Pilot Point Methodology for Supplementing Sparse Transmissivity Data

Pilot point methodology (PPM) permits estimation of transmissivity at unsampled pilot points by solving the hydraulic head based inverse problem. Especially relevant to areas with sparse transmissivity data, the methodology supplements the limited field data. Presented herein is an approach for estimating parameters of PPM honoring the objectives of refinement of the transmissivity (T) interpolation and the model calibration. The parameters are the locations and number of pilot transmissivity points. The location parameter is estimated by defining a qualifying matrix Q comprising weighted sum of the hydraulic head-sensitivity and the kriging variance fields. Whereas the former component of Q promotes the model calibration, the latter one leads to improved T interpolation by locating pilot points in un-sampled tracts. Further, a three-stage methodology is proposed for an objective determination of the number of pilot points. It is based upon sequential upgradation of the Variogram as the pilot points are added to the data base, ensuring its convergence with the head-based optimal Variogram. The model has been illustrated by applying it to Satluj-Beas interbasin wherein the pumping test data is not only sparse, but also unevenly distributed.

Planning a geostatistical survey for mapping soil micronutrients: eliciting sampling densities

<p>When planning a geochemical survey, it is necessary to make decisions about the sampling density. Sampling density determines both the quality of predictions and the cost of field work. In geostatistical surveys, the relationship between sampling density and map quality, as measured by the kriging variance (mean square error of the prediction) can be computed. When the variogram is known, then the kriging variance at an unsampled site depends only on the spatial distribution of sampling points around that site. It is therefore possible to find the sample density such that the kriging variance is limited to acceptable values. However, the implications of kriging variances are not always straightforward for decision makers or sponsors of survey to understand. Here we present an alternative method to help end-users assess the implications of uncertainty in spatial prediction in so far as this is controlled by sampling.  It is called the offset correlation and is a measure of how far the mapped spatial variation depends on the positioning of a reqular square sampling grid.  The offset correlation increases as the uncertainty in the map, attributable to sample density, decreases.  It is bounded on the interval [0,1], which makes it intuitively easy to interpret as an uncertainty measure.  In this presentation we shall explain the offset correlation concept, illustrate it with some test cases, and provide session participants with an opportunity to join an elicitation of sampling density for a hypothetical survey of soil micronutrient status.</p><p>The offset correlation is an intuitive measure of the precision of a geostatistical mapping process because people can more easily grasp bounded measures like a correlation than unbounded ones like a variance.</p>

Accounting for Local Geological Variability in Sequential Simulations—Concept and Application

Heterogeneity-preserving property models of subsurface regions are commonly constructed by means of sequential simulations. Sequential Gaussian simulation (SGS) and direct sequential simulation (DSS) draw values from a local probability density function that is described by the simple kriging estimate and the local simple kriging variance at unsampled locations. The local simple kriging variance, however, does not necessarily reflect the geological variability being present at subsets of the target domain. In order to address that issue, we propose a new workflow that implements two modified versions of the popular SGS and DSS algorithms. Both modifications, namely, LVM-DSS and LVM-SGS, aim at simulating values by means of introducing a local variance model (LVM). The LVM is a measurement-constrained and geology-driven global representation of the locally observable variance of a property. The proposed modified algorithms construct the local probability density function with the LVM instead of using the simple kriging variance, while still using the simple kriging estimate as the best linear unbiased estimator. In an outcrop analog study, we can demonstrate that the local simple kriging variance in sequential simulations tends to underestimate the locally observed geological variability in the target domain and certainly does not account for the spatial distribution of the geological heterogeneity. The proposed simulation algorithms reproduce the global histogram, the global heterogeneity, and the considered variogram model in the range of ergodic fluctuations. LVM-SGS outperforms the other algorithms regarding the reproduction of the variogram model. While DSS and SGS generate a randomly distributed heterogeneity, the modified algorithms reproduce a geologically reasonable spatial distribution of heterogeneity instead. The new workflow allows for the integration of continuous geological trends into sequential simulations rather than using class-based approaches such as the indicator simulation technique.

Gridded Monthly Rainfall Estimates Derived from Historical Atoll Observations

To provide an analysis tool for areal rainfall estimates, 1° gridded monthly sea level rainfall estimates have been derived from historical atoll rainfall observations contained in the Pacific Rainfall (PACRAIN) database. The PACRAIN database is a searchable repository of in situ rainfall observations initiated and maintained by the University of Oklahoma and supported by a research grant from the National Oceanic and Atmospheric Administration (NOAA)/Climate Program Office/Ocean Observing and Monitoring. The gridding algorithm employs ordinary kriging, a standard geostatistical technique, and selects for nonnegative estimates and for local estimation neighborhoods yielding minimum kriging variance. This methodology facilitates the selection of fixed-size neighborhoods from available stations beyond simply choosing the closest stations, as it accounts for dependence between estimator stations. The number of stations used for estimation is based on bias and standard error exhibited under cross estimation. A cross validation is conducted, comparing estimated and observed rains, as well as theoretical and observed standard errors for the ordinary kriging estimator. The conditional bias of the kriging estimator and the predictive value of kriging standard errors, with respect to observed standard errors, are discussed. Plots of the gridded rainfall estimates are given for sample El Niño and La Niña cases and standardized differences between the estimates produced here and the merged monthly rainfall estimates published by the Global Precipitation Climatology Project (GPCP) are shown and discussed.

Optimal Mobility Control of Sensors in the Event of a Disaster

Disasters have caused serious damage on human beings throughout their long history. In a major natural disaster such as an earthquake, a key to mitigate the damage is evacuation. Evidently, secondary collateral disasters is account for more casualty than the initial one. In order to have citizens to evacuate safely for the sake of saving their lives, collecting information is vital. However at times of a disaster, it is a difficult task to gain environmental information about the area by conventional way. One of the solutions to this problem is crowd-sensing, which regards citizens as sensors nodes and collect information with their help. We considered a way of controlling the mobility of such sensor nodes under limitation of its mobility, caused by road blockage, for example. Aiming to make a mobility control scheme that enables high-quality information collection, our method uses preceding result of the measurement to control the mobility. Here it uses kriging variance to do that. We evaluated this method by simulating some measurements and it showed better accuracy than baseline. This is expected to be a method to enable a higher-quality input to the agent-based evacuation simulation, which helps to guide people to evacuate more safely.

Geostatistics Application On Uranium Resources Classification: Case Study of Rabau Hulu Sector, Kalan, West Kalimantan

ABSTRACT In resources estimation, geostatistics methods have been widely used with the benefit of additional attribute tools to classify resources category. However, inverse distance weighting (IDW) is the only method used previously for estimating the uranium resources in Indonesia. The IDW method provides no additional attribute that could be used to classify the resources category. The objective of research is to find the best practice on geostatistics application in uranium resource estimation adjusted with geological information and determination of acceptable geostatistics estimation attribute for resources categorization. Geostatistics analysis in Rabau Hulu Sector was started with correlation of the orebody between boreholes. The orebodies in Rabau Hulu Sectors are separated individual domain which further considered has the hard domain. The orebody-15 was selected for further geostatistics analysis due to its wide distribution and penetrated most by borehole. Stages in geostatistics analysis cover downhole composites, basic statistics analysis, outliers determination, variogram analysis, and calculation on the anisotropy ellipsoid. Geostatistics analysis shows the availability of the application for two resources estimation attributes, which are kriging efficiency and kriging variance. Based on technical judgment of the orebody continuity versus the borehole intensity, the kriging efficiency is considered compatible with geological information and could be used as parameter for determination of the resources category. ABSTRAK Pada estimasi sumber daya, metode geostatistik telah banyak digunakan dengan kelebihan adanya alat atribut tambahan untuk mengklasifikasikan kategori sumber daya. Namun demikian, pembobotan inverse distance (IDW) adalah satu-satunya metode yang sebelumnya digunakan untuk mengestimasi sumber daya uranium di Indonesia. Metode IDW tidak memberikan tambahan atribut yang dapat digunakan dalam mengklasifikasikan kategori sumber daya. Tujuan dari penelitian adalah mendapatkan praktek terbaik untuk aplikasi geostatistik pada estimasi sumber daya disesuaikan dengan informasi geologi dan penentuan atribut geostatistik yang dapat digunakan untuk kategorisasi sumber daya. Analisis geostatistik di Sektor Rabau Hulu diawali dengan korelasi tubuh bijih antara lubang bor. Tubuh-tubuh bijih di Sektor Rabau Hulu merupakan domain individual yang selanjutnya dipertimbangkan memiliki domain tegas. Tubuh bijih-15 dipilih untuk digunakan pada analisis geostatistik selanjutnya karena distribusinya yang luas dan paling banyak dipenetrasi bor. Tahapan dalam analisis geostatistik mencakup komposit downhole, analisis statistik dasar, determinasi outliers, analisis variogram, dan perhitungan ellipsoid anisotropi. Analisis geostatistik menghasilkan kemungkinan aplikasi dua atribut estimasi sumber daya, yaitu kriging efisiensi dan kriging varians. Berdasarkan penilaian teknis kemenerusan tubuh bijih terhadap intensitas lubang bor, kriging efisiensi dipertimbangkan sesuai dengan informasi geologi dan dapat digunakan sebagai parameter untuk penentuan kategori sumber daya.

Planning spatial sampling of the soil from an uncertain reconnaissance variogram

An estimated variogram of a soil property can be used to support a rational choice of sampling intensity for geostatistical mapping. However, it is known that estimated variograms are subject to uncertainty. In this paper we address two practical questions. First, how can we make a robust decision on sampling intensity, given the uncertainty in the variogram? Second, what are the costs incurred in terms of oversampling because of uncertainty in the variogram model used to plan sampling? To achieve this we show how samples of the posterior distribution of variogram parameters, from a computational Bayesian analysis, can be used to characterize the effects of variogram parameter uncertainty on sampling decisions. We show how one can select a sample intensity so that a target value of the kriging variance is not exceeded with some specified probability. This will lead to oversampling, relative to the sampling intensity that would be specified if there were no uncertainty in the variogram parameters. One can estimate the magnitude of this oversampling by treating the tolerable grid spacing for the final sample as a random variable, given the target kriging variance and the posterior sample values. We illustrate these concepts with some data on total uranium content in a relatively sparse sample of soil from agricultural land near mine tailings in the Copperbelt Province of Zambia.