Analytic Properties and Covariance Functions of a New Class of Generalized Gibbs Random Fields

Spartan Spatial Random Fields (SSRFs) are generalized Gibbs random fields, equipped with a coarse-graining kernel that acts as a low-pass filter for the fluctuations. SSRFs are defined by means of physically motivated spatial interactions and a small set of free parameters (interaction couplings). This paper focuses on the FGC-SSRF model, which is defined on the Euclidean space $\mathbb{R}^{d}$ by means of interactions proportional to the squares of the field realizations, as well as their gradient and curvature. The permissibility criteria of FGC-SSRFs are extended by considering the impact of a finite-bandwidth kernel. It is proved that the FGC-SSRFs are almost surely differentiable in the case of finite bandwidth. Asymptotic explicit expressions for the Spartan covariance function are derived for $d=1$ and $d=3$; both known and new covariance functions are obtained depending on the value of the FGC-SSRF shape parameter. Nonlinear dependence of the covariance integral scale on the FGC-SSRF characteristic length is established, and it is shown that the relation becomes linear asymptotically. The results presented in this paper are useful in random field parameter inference, as well as in spatial interpolation of irregularly-spaced samples.Comment: 24 pages; 4 figures Submitted for publication to IEEE Transactions on Information Theor

Macro-Scale Underground Geomechanical and Thermal Mapping for Very Shallow Geothermal Applications

The document is an extended abstract presented at "GeoENV 2016", the 11th International Conference on Geostatistics for Environmental Application Conference, 6-8 July 2016, Lisbon, Portugal

Analisis Variography pada Estimasi Ordinary Kriging Endapan Batubara Di Kecamatan Murung Pudak, Kabupaten Tabalong, Provinsi Kalimantan Selatan

A functional analysis of the determination of the variogram value is very influential on the coal model formed (variography analysis). Variography is a series of activities ranging from data searching, modeling to analysis reports. Coal quality estimation is an activity to get a proper distribution of coal quality values, and the results can contribute as one of the control processes in coal mining activities. This research aims to estimate coal parameters (Ash Content, Calorific Value, Total Moisture, and Total Sulfur) using Ordinary Kriging. Comparison of Ordinary Kriging estimation variogram model with omnidirectional and omnidirectional-vertical model variogram results in the conclusion that the vertical variogram is quite capable of giving a positive effect on the Ordinary Kriging estimation results seen from the residual value of the results of cross-validation, although in general, the distribution of Ordinary Kriging results is not too much different

PENGGUNAAN BOOTSTRAP PENGGUNAAN BOOTSTRAP

Bootstrap dikembangkan untuk data tak berkorelasi, jika berkorelasi maka diperlukan suatu transformasi yaitu dekomposisi Cholesky sehingga menjadi menjadi tak berkorelasi. Bootstrap merupakan resampling untuk mengukur keakuratan estimator. Data spatial merupakan salah satu jenis data berkorelasi. Kriging merupakan metoda estimasi data spatial yang hanya memberikan satu nilai taksiran. Standar eror kriging tidak bergantung pada data tetapi bergantung pada konfigurasi/ukuran dispersi titik sampel. Kata Kunci: Bootstrap, Dekomposisi Coleski, krigin

Spatial variability change of MgO content in Jelsava magnesite deposit (Slovakia)

The presented paper deals with the study of the spatial variability changes of MgO content within the Jelšava magnesite deposit in Slovakia. The geostatistical structural analysis was used to study the spatial variability changes of the MgO content within three mining sectors A, B and C, localised in different parts of the deposit. The results show some important connections between the variability of MgO content and the structure setting of the deposit with utilization for the magnesite processing in the metallurgy

Seam Modelling and Reserve Calculation for Lignite Field in Adana-Tufanbeyli (Turkey)

Since the first investment in mining operations is very high, so, it is absolutely important to model the field inthree dimensions for appropriate planning and cost analysis. The whole data set belonging to the geological, geophysicaland drilling exploration studies carried out in the field should be evaluated as a package. In the modelling phase, thecomputer-aided tri-dimensional mining software has been used instead of the classical reserve calculation methods beingutilized in previous years. Thus, more realistic and shorter results are achieved. In the present work, three-dimensionalseam modelling of the Adana-Tufanbeyli (Turkey) lignite field was carried out. In modelling, the coal horizon of thefield was examined. Then, the sub-seam levels in the horizon were determined and after examining their geometricrelationships with each other, three sub-seams were defined. Seam composites were prepared by the downhole methodto make the analysis results of different sizes uniform. It is possible to make block quality estimations, which will be thebasis for reserve calculations, by creating variograms in different directions. Variograms are first created in the verticaldirection and then in the horizontal direction respectively, to obtain the necessary parameters. The nugget effect andstructural distance parameters were obtained from the created variogram models. To assign quality estimation values onthe block model, the Kriging method was used when the number of data was sufficient, and the inverse distance methodwas applied, when it was insufficient. As a result of this modelling study, a total of 355.617.194 tons of lignite reserveswith an average calorific value of 1.153 Kcal/kg were determined in the field

PENERAPAN METODE COKRIGING UNTUK MENGESTIMASI JUMLAH ZAT PADAT TERLARUT PADA AIR DI PERMUKIMAN KOTA PONTIANAK

The aim of this study is to apply cokriging method in estimating solid substance from water sample in the city of Pontianak. Cokriging is a method to estimate a variable using cross correlation among severa variables. The sample is water from 41 location in housing areas in Pontianak. Measurement of dissolved solid substance level and colors in a laboratory. Based on the result, a theoretical semivariogram model is developed of dissolved solid substance level and spherical model for color. Cross semivariogram model between content of dissolved solid substance and coloris spherical model. The study also showed estimation value of dissolved solid substance for ten new location in housing area of Pontianak city which are not studied previously. The estimation showed that the largest dissolved solid sbubstance is 155,4 mg/L and the smallest is 11,7 mg/L. A visualization of the locations are shown in a map by Geographical Information System. Metode cokriging adalah metode yang digunakan untuk mengestimasi suatu variabel dengan dengan memanfaatkan korelasi silang antara beberapa variabel. Penelitan ini bertujuan untuk mengaplikasikan metode cokriging dalam mengestimasi kandungan jumlah zat padat terlarut dari kandungan warna air di kawasan permukiman Kota Pontianak. Data yang digunakan adalah sampel air dari 41 lokasi di kawasan permukiman Kota Pontianak. Setiap sampel air dilakukan pengukuran nilai jumlah zat padat terlarut dan warna di laboratorium. Hasil analisis diperoleh model semivariogram teoritis untuk jumlah zat padat terlarut yang digunakan adalah model eksponensial, sedangkan untuk warna adalah model spherical. Model cross semivariogram antara jumlah zat padat terlarut dan warna yang digunakan adalah model spherical. Selanjutnya diperoleh nilai estimasi dari jumlah zat padat terlarut untuk sepuluh titik lokasi baru di kawasan permukiman Kota Pontianak yang belum tersampel. Hasil estimasi menunjukkan nilai jumlah zat padat terlarut terbesar sebesar 155,4 mg/L dan terkecil di parit sebesar 11,7 mg/L. Titik-titik lokasi divisualisasikan dalam bentuk peta melalui Sistem Informasi Geografis