Статті в журналах: "Geostatistical estimation"

1

Lebrenz, Henning, and András Bárdossy. "Geostatistical interpolation by quantile kriging." Hydrology and Earth System Sciences 23, no. 3 (March 20, 2019): 1633–48. http://dx.doi.org/10.5194/hess-23-1633-2019.

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Abstract. The widely applied geostatistical interpolation methods of ordinary kriging (OK) or external drift kriging (EDK) interpolate the variable of interest to the unknown location, providing a linear estimator and an estimation variance as measure of uncertainty. The methods implicitly pose the assumption of Gaussianity on the observations, which is not given for many variables. The resulting “best linear and unbiased estimator” from the subsequent interpolation optimizes the mean error over many realizations for the entire spatial domain and, therefore, allows a systematic under-(over-)estimation of the variable in regions of relatively high (low) observations. In case of a variable with observed time series, the spatial marginal distributions are estimated separately for one time step after the other, and the errors from the interpolations might accumulate over time in regions of relatively extreme observations. Therefore, we propose the interpolation method of quantile kriging (QK) with a two-step procedure prior to interpolation: we firstly estimate distributions of the variable over time at the observation locations and then estimate the marginal distributions over space for every given time step. For this purpose, a distribution function is selected and fitted to the observed time series at every observation location, thus converting the variable into quantiles and defining parameters. At a given time step, the quantiles from all observation locations are then transformed into a Gaussian-distributed variable by a 2-fold quantile–quantile transformation with the beta- and normal-distribution function. The spatio-temporal description of the proposed method accommodates skewed marginal distributions and resolves the spatial non-stationarity of the original variable. The Gaussian-distributed variable and the distribution parameters are now interpolated by OK and EDK. At the unknown location, the resulting outcomes are reconverted back into the estimator and the estimation variance of the original variable. As a summary, QK newly incorporates information from the temporal axis for its spatial marginal distribution and subsequent interpolation and, therefore, could be interpreted as a space–time version of probability kriging. In this study, QK is applied for the variable of observed monthly precipitation from raingauges in South Africa. The estimators and estimation variances from the interpolation are compared to the respective outcomes from OK and EDK. The cross-validations show that QK improves the estimator and the estimation variance for most of the selected objective functions. QK further enables the reduction of the temporal bias at locations of extreme observations. The performance of QK, however, declines when many zero-value observations are present in the input data. It is further revealed that QK relates the magnitude of its estimator with the magnitude of the respective estimation variance as opposed to the traditional methods of OK and EDK, whose estimation variances do only depend on the spatial configuration of the observation locations and the model settings.

2

Thorson, James T., Andrew O. Shelton, Eric J. Ward, and Hans J. Skaug. "Geostatistical delta-generalized linear mixed models improve precision for estimated abundance indices for West Coast groundfishes." ICES Journal of Marine Science 72, no. 5 (January 14, 2015): 1297–310. http://dx.doi.org/10.1093/icesjms/fsu243.

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AbstractIndices of abundance are the bedrock for stock assessments or empirical management procedures used to manage fishery catches for fish populations worldwide, and are generally obtained by processing catch-rate data. Recent research suggests that geostatistical models can explain a substantial portion of variability in catch rates via the location of samples (i.e. whether located in high- or low-density habitats), and thus use available catch-rate data more efficiently than conventional “design-based” or stratified estimators. However, the generality of this conclusion is currently unknown because geostatistical models are computationally challenging to simulation-test and have not previously been evaluated using multiple species. We develop a new maximum likelihood estimator for geostatistical index standardization, which uses recent improvements in estimation for Gaussian random fields. We apply the model to data for 28 groundfish species off the U.S. West Coast and compare results to a previous “stratified” index standardization model, which accounts for spatial variation using post-stratification of available data. This demonstrates that the stratified model generates a relative index with 60% larger estimation intervals than the geostatistical model. We also apply both models to simulated data and demonstrate (i) that the geostatistical model has well-calibrated confidence intervals (they include the true value at approximately the nominal rate), (ii) that neither model on average under- or overestimates changes in abundance, and (iii) that the geostatistical model has on average 20% lower estimation errors than a stratified model. We therefore conclude that the geostatistical model uses survey data more efficiently than the stratified model, and therefore provides a more cost-efficient treatment for historical and ongoing fish sampling data.

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Brom, Aleksander, and Adrianna Natonik. "Estimation of geotechnical parameters on the basis of geophysical methods and geostatistics." Contemporary Trends in Geoscience 6, no. 2 (December 1, 2017): 70–79. http://dx.doi.org/10.1515/ctg-2017-0006.

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AbstractThe paper presents possible implementation of ordinary cokriging and geophysical investigation on humidity data acquired in geotechnical studies. The Author describes concept of geostatistics, terminology of geostatistical modelling, spatial correlation functions, principles of solving cokriging systems, advantages of (co-)kriging in comparison with other interpolation methods, obstacles in this type of attempt. Cross validation and discussion of results was performed with an indication of prospect of applying similar procedures in various researches..

4

Nowak, Wolfgang. "Measures of Parameter Uncertainty in Geostatistical Estimation and Geostatistical Optimal Design." Mathematical Geosciences 42, no. 2 (October 10, 2009): 199–221. http://dx.doi.org/10.1007/s11004-009-9245-1.

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Mälicke, Mirko. "SciKit-GStat 1.0: a SciPy-flavored geostatistical variogram estimation toolbox written in Python." Geoscientific Model Development 15, no. 6 (March 25, 2022): 2505–32. http://dx.doi.org/10.5194/gmd-15-2505-2022.

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Abstract. Geostatistical methods are widely used in almost all geoscientific disciplines, i.e., for interpolation, rescaling, data assimilation or modeling. At its core, geostatistics aims to detect, quantify, describe, analyze and model spatial covariance of observations. The variogram, a tool to describe this spatial covariance in a formalized way, is at the heart of every such method. Unfortunately, many applications of geostatistics focus on the interpolation method or the result rather than the quality of the estimated variogram. Not least because estimating a variogram is commonly left as a task for computers, and some software implementations do not even show a variogram to the user. This is a miss, because the quality of the variogram largely determines whether the application of geostatistics makes sense at all. Furthermore, the Python programming language was missing a mature, well-established and tested package for variogram estimation a couple of years ago. Here I present SciKit-GStat, an open-source Python package for variogram estimation that fits well into established frameworks for scientific computing and puts the focus on the variogram before more sophisticated methods are about to be applied. SciKit-GStat is written in a mutable, object-oriented way that mimics the typical geostatistical analysis workflow. Its main strength is the ease of use and interactivity, and it is therefore usable with only a little or even no knowledge of Python. During the last few years, other libraries covering geostatistics for Python developed along with SciKit-GStat. Today, the most important ones can be interfaced by SciKit-GStat. Additionally, established data structures for scientific computing are reused internally, to keep the user from learning complex data models, just for using SciKit-GStat. Common data structures along with powerful interfaces enable the user to use SciKit-GStat along with other packages in established workflows rather than forcing the user to stick to the author's programming paradigms. SciKit-GStat ships with a large number of predefined procedures, algorithms and models, such as variogram estimators, theoretical spatial models or binning algorithms. Common approaches to estimate variograms are covered and can be used out of the box. At the same time, the base class is very flexible and can be adjusted to less common problems, as well. Last but not least, it was made sure that a user is aided in implementing new procedures or even extending the core functionality as much as possible, to extend SciKit-GStat to uncovered use cases. With broad documentation, a user guide, tutorials and good unit-test coverage, SciKit-GStat enables the user to focus on variogram estimation rather than implementation details.

6

Delbari, M., P. Afrasiab, and W. Loiskandl. "Geostatistical analysis of soil texture fractions on the field scale." Soil and Water Research 6, No. 4 (November 28, 2011): 173–89. http://dx.doi.org/10.17221/9/2010-swr.

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  Geostatistical estimation methods including ordinary kriging (OK), lognormal ordinary kriging (LOK), cokriging (COK), and indicator kriging (IK) are compared for the purposes of prediction and, in particular, uncertainty assessment of the soil texture fractions, i.e. sand, silt, and clay proportions, in an erosion experimental field in Lower Austria. The soil samples were taken on 136 sites, about 30-m apart. The validation technique was cross-validation, and the comparison criteria were the mean bias error (MBE) and root mean squared error (RMSE). Statistical analysis revealed that the sand content is positively skewed, thus persuading us to use LOK for the estimation. COK was also used due to a good negative correlation seen between the texture fractions. The autocorrelation analysis showed that the soil texture fractions in the study area are strongly to moderately correlated in space. Cross-validation indicated that COK is the most accurate method for estimating the silt and clay contents; RMSE equalling to 3.17% and 1.85%, respectively. For the sand content, IK with RMSE (12%) slightly smaller than COK (RMSE = 14%) was the best estimation method. However, COK maps presented the true variability of the soil texture fractions much better than the other approaches, i.e. they achieved the smallest smoothness. Regarding the local uncertainty, the estimation variance maps produced by OK, LOK, and COK methods similarly indicated that the lowest uncertainty occurred near the data locations, and that the highest uncertainty was seen in the areas of sparse sampling. The uncertainty, however, varied much less across the study area compared to conditional variance for IK. The IK conditional variance maps showed, in contrast, some relations to the data values. The estimation uncertainty needs to be evaluated for the incorporation into the risk analysis in the soil management.

7

Philip, Ross D., and Peter K. Kitanidis. "Geostatistical Estimation of Hydraulic Head Gradients." Ground Water 27, no. 6 (November 1989): 855–65. http://dx.doi.org/10.1111/j.1745-6584.1989.tb01049.x.

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8

Soares, Amilcar. "Geostatistical estimation of multi-phase structures." Mathematical Geology 24, no. 2 (February 1992): 149–60. http://dx.doi.org/10.1007/bf00897028.

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Lindner, Anabele, Cira Souza Pitombo, Lucas Assirati, Jorge Ubirajara Pedreira Junior, and Ana Rita Salgueiro. "Estimation of Travel Mode Choice Using Geostatistics: a Brazilian Case Study." Revista Brasileira de Cartografia 73, no. 1 (February 19, 2021): 182–97. http://dx.doi.org/10.14393/rbcv73n1-54210.

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Traditional methods for travel demand estimation are often built on socioeconomic and travel information. The information required to conduct such studies is costly and rarely available in developing countries. Besides, some conventional methods do not consider the spatial relationship of variables and, in general, a large amount of socioeconomic and individual travel data is required. The key aim of this paper is to evaluate the importance of considering spatial information when estimating travel mode choices especially considering the lack of available data. The study area is the São Paulo Metropolitan Area (Brazil) and the dataset refers to an Origin-Destination Survey, conducted in 2007. This research paper analyzes the use of Geostatistics when estimating discrete travel mode choices. The results demonstrated a satisfactory outcome for the geostatistical approach. Finally, although socioeconomic and travel variables have greater explanatory power in predicting travel mode choices, spatial factors contribute to better understand the travel behavior and to provide further information when estimating spatially correlated data.

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Müller, Sebastian, Lennart Schüler, Alraune Zech, and Falk Heße. "GSTools v1.3: a toolbox for geostatistical modelling in Python." Geoscientific Model Development 15, no. 7 (April 12, 2022): 3161–82. http://dx.doi.org/10.5194/gmd-15-3161-2022.

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Abstract. Geostatistics as a subfield of statistics accounts for the spatial correlations encountered in many applications of, for example, earth sciences. Valuable information can be extracted from these correlations, also helping to address the often encountered burden of data scarcity. Despite the value of additional data, the use of geostatistics still falls short of its potential. This problem is often connected to the lack of user-friendly software hampering the use and application of geostatistics. We therefore present GSTools, a Python-based software suite for solving a wide range of geostatistical problems. We chose Python due to its unique balance between usability, flexibility, and efficiency and due to its adoption in the scientific community. GSTools provides methods for generating random fields; it can perform kriging, variogram estimation and much more. We demonstrate its abilities by virtue of a series of example applications detailing their use.

11

Thiesen, Stephanie, Diego M. Vieira, Mirko Mälicke, Ralf Loritz, J. Florian Wellmann, and Uwe Ehret. "Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics." Hydrology and Earth System Sciences 24, no. 9 (September 17, 2020): 4523–40. http://dx.doi.org/10.5194/hess-24-4523-2020.

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Abstract. Interpolation of spatial data has been regarded in many different forms, varying from deterministic to stochastic, parametric to nonparametric, and purely data-driven to geostatistical methods. In this study, we propose a nonparametric interpolator, which combines information theory with probability aggregation methods in a geostatistical framework for the stochastic estimation of unsampled points. Histogram via entropy reduction (HER) predicts conditional distributions based on empirical probabilities, relaxing parameterizations and, therefore, avoiding the risk of adding information not present in data. By construction, it provides a proper framework for uncertainty estimation since it accounts for both spatial configuration and data values, while allowing one to introduce or infer properties of the field through the aggregation method. We investigate the framework using synthetically generated data sets and demonstrate its efficacy in ascertaining the underlying field with varying sample densities and data properties. HER shows a comparable performance to popular benchmark models, with the additional advantage of higher generality. The novel method brings a new perspective of spatial interpolation and uncertainty analysis to geostatistics and statistical learning, using the lens of information theory.

12

Michalak, A. M. "Technical Note: Adapting a fixed-lag Kalman smoother to a geostatistical atmospheric inversion framework." Atmospheric Chemistry and Physics 8, no. 22 (November 26, 2008): 6789–99. http://dx.doi.org/10.5194/acp-8-6789-2008.

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Abstract. Inverse modeling methods are now commonly used for estimating surface fluxes of carbon dioxide, using atmospheric mass fraction measurements combined with a numerical atmospheric transport model. The geostatistical approach to flux estimation takes advantage of the spatial and/or temporal correlation in fluxes and does not require prior flux estimates. In this work, a previously-developed, computationally-efficient, fixed-lag Kalman smoother is adapted for application with a geostatistical approach to atmospheric inversions. This method makes it feasible to perform multi-year geostatistical inversions, at fine resolutions, and with large amounts of data. The new method is applied to the recovery of global gridscale carbon dioxide fluxes for 1997 to 2001 using pseudodata representative of a subset of the NOAA-ESRL Cooperative Air Sampling Network.

13

Wang, Yu, Deji Wang, Jianghai Zhao, and Changan Zhu. "Wind speed spatial estimation using geostatistical kriging." IOP Conference Series: Earth and Environmental Science 619 (December 22, 2020): 012049. http://dx.doi.org/10.1088/1755-1315/619/1/012049.

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JIANG, Xiaowei, Li WAN, Qiang DU, and B. X. HU. "Estimation of NDVI Images Using Geostatistical Methods." Earth Science Frontiers 15, no. 4 (July 2008): 71–80. http://dx.doi.org/10.1016/s1872-5791(08)60040-8.

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Ordoñez, José A., Dipankar Bandyopadhyay, Victor H. Lachos, and Celso R. B. Cabral. "Geostatistical estimation and prediction for censored responses." Spatial Statistics 23 (March 2018): 109–23. http://dx.doi.org/10.1016/j.spasta.2017.12.001.

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Soares, Amilcar. "Geostatistical estimation of orebody geometry: Morphological kriging." Mathematical Geology 22, no. 7 (October 1990): 787–802. http://dx.doi.org/10.1007/bf00890663.

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Murakami, H., X. Chen, M. S. Hahn, Y. Liu, M. L. Rockhold, V. R. Vermeul, J. M. Zachara, and Y. Rubin. "Bayesian approach for three-dimensional aquifer characterization at the Hanford 300 Area." Hydrology and Earth System Sciences 14, no. 10 (October 21, 2010): 1989–2001. http://dx.doi.org/10.5194/hess-14-1989-2010.

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Abstract. This study presents a stochastic, three-dimensional characterization of a heterogeneous hydraulic conductivity field within the Hanford 300 Area, Washington, USA, by assimilating large-scale, constant-rate injection test data with small-scale, three-dimensional electromagnetic borehole flowmeter (EBF) measurement data. We first inverted the injection test data to estimate the transmissivity field, using zeroth-order temporal moments of pressure buildup curves. We applied a newly developed Bayesian geostatistical inversion framework, the method of anchored distributions (MAD), to obtain a joint posterior distribution of geostatistical parameters and local log-transmissivities at multiple locations. The unique aspects of MAD that make it suitable for this purpose are its ability to integrate multi-scale, multi-type data within a Bayesian framework and to compute a nonparametric posterior distribution. After we combined the distribution of transmissivities with depth-discrete relative-conductivity profile from the EBF data, we inferred the three-dimensional geostatistical parameters of the log-conductivity field, using the Bayesian model-based geostatistics. Such consistent use of the Bayesian approach throughout the procedure enabled us to systematically incorporate data uncertainty into the final posterior distribution. The method was tested in a synthetic study and validated using the actual data that was not part of the estimation. Results showed broader and skewed posterior distributions of geostatistical parameters except for the mean, which suggests the importance of inferring the entire distribution to quantify the parameter uncertainty.

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Murakami, H., X. Chen, M. S. Hahn, Y. Liu, M. L. Rockhold, V. R. Vermeul, J. M. Zachara, and Y. Rubin. "Bayesian approach for three-dimensional aquifer characterization at the hanford 300 area." Hydrology and Earth System Sciences Discussions 7, no. 2 (March 23, 2010): 2017–52. http://dx.doi.org/10.5194/hessd-7-2017-2010.

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Abstract. This study presents a stochastic, three-dimensional characterization of a heterogeneous hydraulic conductivity field within DOE's Hanford 300 Area site, Washington, by assimilating large-scale, constant-rate injection test data with small-scale, three-dimensional electromagnetic borehole flowmeter (EBF) measurement data. We first inverted the injection test data to estimate the transmissivity field, using zeroth-order temporal moments of pressure buildup curves. We applied a newly developed Bayesian geostatistical inversion framework, the method of anchored distributions (MAD), to obtain a joint posterior distribution of geostatistical parameters and local log-transmissivities at multiple locations. The unique aspects of MAD that make it suitable for this purpose are its ability to integrate multi-scale, multi-type data within a Bayesian framework and to compute a nonparametric posterior distribution. After we combined the distribution of transmissivities with depth-discrete relative-conductivity profile from the EBF data, we inferred the three-dimensional geostatistical parameters of the log-conductivity field, using the Bayesian model-based geostatistics. Such consistent use of the Bayesian approach throughout the procedure enabled us to systematically incorporate data uncertainty into the final posterior distribution. The method was tested in a synthetic study and validated using the actual data that was not part of the estimation. Results showed broader and skewed posterior distributions of geostatistical parameters except for the mean, which suggests the importance of inferring the entire distribution to quantify the parameter uncertainty.

19

Nikou, Melpomeni, and Panagiotis Tziachris. "Prediction and Uncertainty Capabilities of Quantile Regression Forests in Estimating Spatial Distribution of Soil Organic Matter." ISPRS International Journal of Geo-Information 11, no. 2 (February 11, 2022): 130. http://dx.doi.org/10.3390/ijgi11020130.

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One of the core tasks in digital soil mapping (DSM) studies is the estimation of the spatial distribution of different soil variables. In addition, however, assessing the uncertainty of these estimations is equally important, something that a lot of current DSM studies lack. Machine learning (ML) methods are increasingly used in this scientific field, the majority of which do not have intrinsic uncertainty estimation capabilities. A solution to this is the use of specific ML methods that provide advanced prediction capabilities, along with innate uncertainty estimation metrics, like Quantile Regression Forests (QRF). In the current paper, the prediction and the uncertainty capabilities of QRF, Random Forests (RF) and geostatistical methods were assessed. It was confirmed that QRF exhibited outstanding results at predicting soil organic matter (OM) in the study area. In particular, R2 was much higher than the geostatistical methods, signifying that more variation is explained by the specific model. Moreover, its uncertainty capabilities as presented in the uncertainty maps, shows that it can also provide a good estimation of the uncertainty with distinct representation of the local variation in specific parts of the area, something that is considered a significant advantage, especially for decision support purposes.

20

Borssoi, Joelmir André, Miguel Angel Uribe-Opazo, and Manuel Galea Rojas. "Diagnostic techniques applied in geostatistics for agricultural data analysis." Revista Brasileira de Ciência do Solo 33, no. 6 (December 2009): 1561–70. http://dx.doi.org/10.1590/s0100-06832009000600005.

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The structural modeling of spatial dependence, using a geostatistical approach, is an indispensable tool to determine parameters that define this structure, applied on interpolation of values at unsampled points by kriging techniques. However, the estimation of parameters can be greatly affected by the presence of atypical observations in sampled data. The purpose of this study was to use diagnostic techniques in Gaussian spatial linear models in geostatistics to evaluate the sensitivity of maximum likelihood and restrict maximum likelihood estimators to small perturbations in these data. For this purpose, studies with simulated and experimental data were conducted. Results with simulated data showed that the diagnostic techniques were efficient to identify the perturbation in data. The results with real data indicated that atypical values among the sampled data may have a strong influence on thematic maps, thus changing the spatial dependence structure. The application of diagnostic techniques should be part of any geostatistical analysis, to ensure a better quality of the information from thematic maps.

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Chihi, Hayet, Michel Tesson, Alain Galli, Ghislain de Marsily, and Christian Ravenne. "Geostatistical modelling (3D) of the stratigraphic unit surfaces of the Gulf of Lion western margin (Mediterranean Sea) based on seismic profiles." Bulletin de la Société Géologique de France 178, no. 1 (January 1, 2007): 25–38. http://dx.doi.org/10.2113/gssgfbull.178.1.25.

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Abstract The purpose of this study is to build efficiently and automatically a three-dimensional geometric model of the stratigraphic units of the Gulf of Lion margin on the basis of geophysical investigations by a network of seismic profiles, using geostatistics. We want to show that geostatistics can produce unbiased maps of the morphology of submarine stratigraphic units, and furthermore that some specific features of these units can be found, that classical manual mapping may ignore. Depth charts of each surface identified by seismic profiling describe the geometry of these units. The geostatistical approach starts with a statistical analysis to determine the type and parameters of the variograms of the variable “depth” of each identified surface. The variograms of these surfaces show that they are mostly non-stationary. We therefore tried the following two non-stationary methods to map the desired surfaces : (i) the method of universal kriging in case the underlying variogram was directly accessible; (ii) the method of increments if the underlying variogram was not directly accessible. After having modelled the variograms of the increments and of the variable itself, we calculated the surfaces by kriging the variable “depth” on a small-mesh estimation grid. The depth charts of each surface calculated with the geostatistical model are then interpreted in terms of their geological significance, which makes it possible to suggest hypotheses on the influence of major processes, such as tectonics and rivers (Rhône, Hérault, etc.) on the sedimentary structure of the gulf of Lion margin. The added value of geostatistics for this interpretation is emphasized. These unusual geostatistical methods are capable of being widely used in earth sciences for automatic mapping of “non-stationary” geometric surfaces, i.e. surfaces that possess a gradient or a trend developing systematically in space, such as piezometric or concentrations surfaces.

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Amanipoor, Hakimeh. "PROVIDING A SUBSURFACE RESERVOIR QUALITY MAPS IN OIL FIELDS BY GEOSTATISTICAL METHODS." Geodesy and Cartography 39, no. 4 (December 18, 2013): 145–48. http://dx.doi.org/10.3846/20296991.2013.859779.

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Under study reservoir oilfield is located south-west of Iran. This field is comprised of naturally fractured Asmari and Bangestan formation. Reservoir management and characteristic evaluation of this field requires good knowledge of reservoir rock and fluid properties. One of main methods to get such information is using known parameter and estimates this property in unknown area of reservoir by geostatistics and kriging method. In this research used the porosity parameter data from 36 oil wells that taken by well logging to estimate porosity parameter in unknown part of reservoir by geostatistics and kriging method. The porosity parameter had normal distribution. After surveyed the distribution of data varioghraphy was done and strength of structure was proved and kriging parameters including characteristic of search ellipse determined for estimation. Then porosity parameter was estimated with the use of geostatistical method in reservoir.

23

Montes, Fernando, María José Hernández, and Isabel Cañellas. "A geostatistical approach to cork production sampling estimation in Quercus suber forests." Canadian Journal of Forest Research 35, no. 12 (December 1, 2005): 2787–96. http://dx.doi.org/10.1139/x05-197.

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The estimation of cork production in cork oak (Quercus suber L.) forests is complex because of the high heterogeneity of stripped surface distribution (the variable used to quantify cork production) and the importance of cork thickness estimation as a determining factor of cork quality. In this study, the different sources of variation in stripped surface ([Formula: see text]d) estimation and the effects of the spatial structure of the variance were analysed. When indicator kriging was used to determine the cork productive area, ordinary kriging and kriging with measurement errors gave better estimations of [Formula: see text]d (ordinary block kriging estimation of 156.16 m2/ha and standard errors (SE) of 16.40 and 15.7 m2/ha, respectively) than the design-based approach for the whole forest area (66.37 m2/ha, SE = 11.34 m2/ha). The SE lying in the second-stage design was 4.93 m2/ha. The ordinary kriging prediction of cork thickness using an XY(λZ) variogram, where λ is the anisotropy coefficient of the Z axis, gives a smaller SE and less bias than the kriging prediction with the XY variogram (for a mean estimation of 21.91 mm, SE = 3.90 and 4.16 mm, respectively, and sum of errors of 0.42 and 0.85 respectively).

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Dimitrakopoulos, R. "Towards intelligent systems for geostatistical ore reserve estimation." International Journal of Surface Mining, Reclamation and Environment 4, no. 1 (January 1990): 37–41. http://dx.doi.org/10.1080/09208119008944165.

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25

Ferrari, F., T. Apuani, and G. P. Giani. "Rock Mass Rating spatial estimation by geostatistical analysis." International Journal of Rock Mechanics and Mining Sciences 70 (September 2014): 162–76. http://dx.doi.org/10.1016/j.ijrmms.2014.04.016.

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26

Downes, Peter M. "Handbook of applied advanced geostatistical ore reserve estimation." Ore Geology Reviews 5, no. 1-2 (December 1989): 147–48. http://dx.doi.org/10.1016/0169-1368(89)90005-x.

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27

Breitkreuz, H. "Handbook of applied advances Geostatistical Ore Reserve Estimation." Ore Geology Reviews 6, no. 1 (February 1991): 77. http://dx.doi.org/10.1016/0169-1368(91)90033-4.

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Breikreuz, H. "Handbook of applied advanced geostatistical ore reserve estimation." Earth-Science Reviews 32, no. 3 (April 1992): 222–23. http://dx.doi.org/10.1016/0012-8252(92)90052-u.

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Srivastava, R. Mohan. "Handbook of Applied Advanced Geostatistical Ore Reserve Estimation." Computers & Geosciences 16, no. 2 (January 1990): 273–74. http://dx.doi.org/10.1016/0098-3004(90)90136-h.

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Marín Ballón, Edgar M., Hugo Jiménez-Pacheco, Máximo O. M. Rondón Rondón, Antonio E. Linares Flores Castro, and Ferly E. Urday Luna. "Review of Matheron’s Kriging Method and its Application at the Estimation of Mineral Deposits." Veritas 20, no. 1 (October 21, 2019): 59. http://dx.doi.org/10.35286/veritas.v20i1.227.

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The Geostatistics provides effective tools for the solution of many problems of engineering in which the location in the space of the variable under study is considered, based on definitions of mathematics that provide the necessary foundation for its application. In particular, the Geostatistics are applied in the spatial estimation of the recoverable reserves of mineral deposits. The geostatistical methods that are used in the estimation of mineral deposits are implemented in industrial software and consider the evaluation of the complex geological structure, but these softwares only display the obtained results with an input data and do not exhibit the concepts thatthey use during the process or the methodology of its application. This happens particularly with the Kriging method, which is based on the assumption of strict stationarity, taking into account changes in the mean and local variations, therefore unreliable. In this study is established to review the Kriging method, its application in the estimation of the recoverable reserves of mining deposits and the relevance of the developed model established particularly in mines ofPeru, which use this method as part of the mining exploration for the evaluation of the feasibility of exploitation.

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Bhowmik, A. K., and P. Cabral. "Spatially shifting temporal points: estimating pooled within-time series variograms for scarce hydrological data." Hydrology and Earth System Sciences Discussions 12, no. 2 (February 20, 2015): 2243–65. http://dx.doi.org/10.5194/hessd-12-2243-2015.

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Abstract. Estimation of pooled within-time series (PTS) variograms is a frequently used technique for geostatistical interpolation of continuous hydrological variables in spatial data-scarce regions conditional that time series are available. The only available method for estimating PTS variograms averages semivariances, which are computed for individual time steps, over each spatial lag within a pooled time series. However, semivariances computed by a few paired comparisons for individual time steps are erratic and hence they may hamper precision of PTS variogram estimation. Here, we outlined an alternative method for estimating PTS variograms by spatializing temporal data points and shifting them. The data were pooled by ensuring consistency of spatial structure and stationarity within a time series, while pooling sufficient number of data points for reliable variogram estimation. The pooled spatial data point sets from different time steps were assigned to different coordinate sets on the same space. Then a semivariance was computed for each spatial lag within a pooled time series by comparing all point pairs separable by that spatial lag, and a PTS variogram was estimated by controlling the lower and upper boundary of spatial lags. Our method showed higher precision than the available method for PTS variogram estimation and was developed by using the freely available R open source software environment. The method will reduce uncertainty for spatial variability modeling while preserving spatiotemporal properties of data for geostatistical interpolation of hydrological variables in spatial data-scarce developing countries.

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Michalak, A. M. "Technical note: A geostatistical fixed-lag Kalman smoother for atmospheric inversions." Atmospheric Chemistry and Physics Discussions 8, no. 2 (April 21, 2008): 7755–79. http://dx.doi.org/10.5194/acpd-8-7755-2008.

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Abstract. Inverse modeling methods are now commonly used for estimating surface fluxes of carbon dioxide, using atmospheric mass fraction measurements combined with a numerical atmospheric transport model. The geostatistical approach to flux estimation takes advantage of the spatial and/or temporal correlation in fluxes and does not require prior flux estimates. In this work, a geostatistical implementation of a fixed-lag Kalman smoother is developed to improve the computational efficiency of the inverse problem. This method makes it feasible to perform multi-year inversions, at fine resolutions, and with large amounts of data. The new method is applied to the recovery of global gridscale carbon dioxide fluxes for 1997 to 2001 using pseudodata representative of a subset of the NOAA-ESRL Cooperative Air Sampling Network.

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Davidovic, Nebojsa, Verka Prolovic, and Dragoslav Stojic. "Modeling of soil parameters spatial uncertainty by geostatistics." Facta universitatis - series: Architecture and Civil Engineering 8, no. 1 (2010): 111–18. http://dx.doi.org/10.2298/fuace1001111d.

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Geotechnical performance of 'soil-structure' systems is strongly dependent on the properties of the soil and prediction of the performance of these systems in real conditions requires accurate modeling of soil parameters. With the help of high-speed computers, now it is possible to create advanced constitutive models, but large uncertainties and variations in soil properties could reduce the advantages gained by using such models. In this paper sources and types of uncertainty in geotechnical engineering practice are first presented, followed by a review of the basic concepts and terminology of geostatistics. Finally, procedures for quantification of uncertainty and for geostatistical estimation and simulation of spatially variable soil properties are presented.

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Mallick, Manas K., Bhanwar S. Choudhary, and Gnananandh Budi. "Geological Reserve Estimation of Limestone Deposit: A Comparative Study Between ISDW and OK." Modelling, Measurement and Control C 81, no. 1-4 (December 31, 2020): 72–77. http://dx.doi.org/10.18280/mmc_c.811-413.

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Geostatistics plays an important role for reserve estimation in mining industry. Geostatistical tools became popular because of its high degree of accuracy and time saving process for estimation. The uncertainty of geological deposit can be populated by geo-statistical tools. The limestone ore deposit was studied in this paper. The assay value of individual constituents of limestone ore i.e CaO, SiO2, Al2O3 and Fe2O3 were determined for a block by using Inverse Square Distance Weighting (ISDW) method. The average assay value of those individual constituents were 45.85, 15.94, 1.56 and 0.82 percentage respectively. The assay value of CaO was also estimated by two linear method of estimation i.e ISDW and Ordinary Kriging (OK). The assay value of CaO were determined 45.85 and 44.67 percentage respectively. The assay values were properly validated and concluded accordingly. The application of ISDW and OK were implemented to build the resource model together in order to assess the uncertainty of the deposit. Grade estimation by using different geo-statistical techniques are done by SURPAC mine planning software.

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Gutierrez, Edgar Andres, Ivan Fernando Mondragon, Julian D. Colorado, and Diego Mendez Ch. "Optimal Deployment of WSN Nodes for Crop Monitoring Based on Geostatistical Interpolations." Plants 11, no. 13 (June 21, 2022): 1636. http://dx.doi.org/10.3390/plants11131636.

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This paper proposes an integrated method for the estimation of soil moisture in potato crops that uses a low-cost wireless sensor network (WSN). Soil moisture estimation maps were created by applying the Kriging technique over a WSN composed of 11×11 nodes. Our goal is to estimate the soil moisture of the crop with a small-scale WSN. Using a perfect mesh approach on a potato crop, experimental results demonstrated that 25 WSN nodes were optimal and sufficient for soil moisture characterization, achieving estimations errors <2%. We provide a strategy to select the number of nodes to use in a WSN, to characterize the moisture behavior for spatio-temporal analysis of soil moisture in the crop. Finally, the implementation cost of this strategy is shown, considering the number of nodes and the corresponding margin of error.

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Roa-Ureta, Rubén, and Edwin Niklitschek. "Biomass estimation from surveys with likelihood-based geostatistics." ICES Journal of Marine Science 64, no. 9 (October 4, 2007): 1723–34. http://dx.doi.org/10.1093/icesjms/fsm149.

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Abstract Roa-Ureta, R., and Niklitschek, E. 2007. Biomass estimation from surveys with likelihood-based geostatistics. – ICES Journal of Marine Science, 64. A likelihood-based geostatistical method for estimating fish biomass from survey data is presented. Biomass estimates from analysis of a positive random variable with an additional discrete probability mass at zero means that the method accommodates null observations and positive fish density. The positive fish density data were used to estimate mean fish density in the subareas where the stock was present. A presence/absence representation of the data in the survey area was modelled with a generalized linear spatial model of the binomial family, leading to an estimate of the area effectively occupied by the stock. As an extension, a procedure is proposed to accommodate extra sources of correlation, such as multiple surveys or multiple vessels. The new methodology was applied to three cases. The simplest case is a scallop trawl survey for which only the positive density data need to be analysed. The intermediate case is a trawl survey of highly mobile squid where the stock area and the mean density inside the stock area are analysed. The most complex case is in estimating the biomass of very localized orange roughy, for which repeat surveys create dependence in the data in addition to spatial correlation.

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De Benedetto, Daniela, Francesco Montemurro, and Mariangela Diacono. "Mapping an Agricultural Field Experiment by Electromagnetic Induction and Ground Penetrating Radar to Improve Soil Water Content Estimation." Agronomy 9, no. 10 (October 15, 2019): 638. http://dx.doi.org/10.3390/agronomy9100638.

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A growing interest in proximal sensing technologies for estimating soil water content (SWC) will be highlighted. On this matter the objectives of this study were: (1) to use both the combined electromagnetic induction (EMI) sensor and Ground Penetrating Radar (GPR) to characterize an innovative field experiment located in southern Italy, in which different agricultural practices are tested, including a soil hydraulic arrangement; (2) to implement a geostatistical approach in order to merge different geophysical sensor data as auxiliary variables for SWC estimation. The multi-sensor recorded data were: (1) SWC data measured by gravimetric method; (2) Differential Global Positioning System height; (3) apparent electrical conductivity measured by an EMI sensor; (4) depths of soil discontinuities individuated by GPR radargrams interpretation; and (5) amplitude of GPR signal data at two different frequencies. Geostatistical techniques were used both to map all variables and improve the SWC estimation. The findings of this research indicate that: (1) the GPR radargrams identified four reflection events as a consequence of interfaces; (2) the EMI and GPR mapping provided identification of areas with high potential for water stagnation; and (3) the outputs of geophysical sensors can be effectively used as auxiliary tools to supplement the sampling of the target variable and to improve water content estimation.

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Ponte, Flávia Braz, Francisco Fábio de Araújo Ponte, Adalberto Silva, and Alberto Garcia Figueiredo. "WELL-SEISMIC INTEGRATION TO PORE PRESSURE PREDICTION USING MULTIVARIATE GEOSTATISTICS: A CASE STUDY IN A BRAZILIAN EQUATORIAL MARGIN BASIN." Brazilian Journal of Geophysics 38, no. 1 (March 1, 2020): 32. http://dx.doi.org/10.22564/rbgf.v38i1.2033.

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ABSTRACT. Pore pressure modeling has been fundamental on several applications and stages of hydrocarbon exploration, evaluation, development and production. Pore pressure estimation is generally obtained from seismic velocity data and pore pressure analysis on wells. There are many methods available for pore pressure analysis, although more recently the application of the geostatistical approach is increasing in popularity and proving to be an important method for pore pressure gradient prediction in challenging areas where pore pressure prediction is difficult using deterministic methods. In this case study on a new frontier area in the Brazilian Equatorial Margin, multivariate geostatistics allowed integration of data at different scales and spatial variations of seismic and well variables produce pore pressure gradient models. The final result is a geopressure model where one can easily extract well-conditioned pore pressure information at any location.Keywords: geostatistical approach, different scales, pore pressure gradient models. INTEGRAÇÃO POÇO-SÍSMICA PARA PREDIÇÃO DE PRESSÃO DE POROS USANDO A GEOSTATÍSTICA MULTIVARIADA: UM ESTUDO DE CASO EM UMA BACIA DA MARGEM EQUATORIAL BRASILEIRARESUMO. A modelagem de pressão de poros tem sido fundamental em diversas aplicações e etapas da exploração, avaliação, desenvolvimento e produção de hidrocarbonetos. Em geral, a estimativa de pressão de poros é obtida a partir da integração de dados de velocidade sísmica e análise de pressão em poços. Existem diversos métodos para análise de pressão de poros, entretanto, atualmente, a aplicação da abordagem geoestatística está crescendo em popularidade e provando ser um importante método para predição de gradiente de pressão de poros em áreas de fronteiras onde a previsão de pressão de poros usando métodos determinísticos não é bem sucedida. Neste estudo de caso, localizado em uma área de nova fronteira na Margem Equatorial Brasileira, a geoestatística multivariada permitiu a integração das variáveis sísmicas e de poço em diferentes escalas e variações espaciais e a obtenção de modelos de gradiente de pressão de poros. Os resultados geraram um modelo de geopressão no qual a extração de valores de pressão de poros bem condicionados é simples em qualquer parte da área.Palavras-chave: abordagem geostatistica, diferentes escalas, modelos de gradiente depressão de poros.

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Wälder, Konrad, Olga Wälder, Jörg Rinklebe, and Joachim Menz. "Estimation of soil properties with geostatistical methods in floodplains." Archives of Agronomy and Soil Science 54, no. 3 (June 2008): 275–95. http://dx.doi.org/10.1080/03650340701488485.

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40

Danilov, Aleksandr, Inna Pivovarova, and Svetlana Krotova. "Geostatistical Analysis Methods for Estimation of Environmental Data Homogeneity." Scientific World Journal 2018 (June 3, 2018): 1–7. http://dx.doi.org/10.1155/2018/7424818.

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The methodology for assessing the spatial homogeneity of ecosystems with the possibility of subsequent zoning of territories in terms of the degree of disturbance of the environment is considered in the study. The degree of pollution of the water body was reconstructed on the basis of hydrochemical monitoring data and information on the level of the technogenic load in one year. As a result, the greatest environmental stress zones were isolated and correct zoning using geostatistical analysis techniques was proved. Mathematical algorithm computing system was implemented in an object-oriented programming C #. A software application has been obtained that allows quickly assessing the scale and spatial localization of pollution during the initial analysis of the environmental situation.

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Kuznetsova, Ya V. "Object methods of geostatistical analysis for facies modeling." Oil and Gas Studies, no. 1 (March 19, 2021): 20–29. http://dx.doi.org/10.31660/0445-0108-2021-1-20-29.

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Facies cube is a required part of a static model, especially concerning fields characterized by complicated geological structure. The important quantitative limitations for modeling are facies proportions in the formation volume. Nowadays these proportions are calculated using standard geostatistical methods without considering particular properties of facies data. These properties are specific geometrical characteristics of sedimentological units. The consequences are significant differences between calculated and actual data and unreliable hydrocarbon reserves estimation.In order to enhance reliability of reserves estimation on the basis of 3D static models, this article is devoted to special methods of geostatistical analysis for facies data: object geometrization and object clustering. These methods allow taking into account specific geometrical parameters of formations deposited in different environments, therefore, allow reducing differences between calculated and actual facies data and enhancing reliability of reserves estimation.

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Namysłowska-Wilczyńska, Barbara, and Janusz Wynalek. "Geostatistical Investigations of Displacements on the Basis of Data from the Geodetic Monitoring of a Hydrotechnical Object." Studia Geotechnica et Mechanica 39, no. 4 (December 1, 2017): 59–75. http://dx.doi.org/10.1515/sgem-2017-0037.

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Abstract Geostatistical methods make the analysis of measurement data possible. This article presents the problems directed towards the use of geostatistics in spatial analysis of displacements based on geodetic monitoring. Using methods of applied (spatial) statistics, the research deals with interesting and current issues connected to space-time analysis, modeling displacements and deformations, as applied to any large-area objects on which geodetic monitoring is conducted (e.g., water dams, urban areas in the vicinity of deep excavations, areas at a macro-regional scale subject to anthropogenic influences caused by mining, etc.). These problems are very crucial, especially for safety assessment of important hydrotechnical constructions, as well as for modeling and estimating mining damage. Based on the geodetic monitoring data, a substantial basic empirical material was created, comprising many years of research results concerning displacements of controlled points situated on the crown and foreland of an exemplary earth dam, and used to assess the behaviour and safety of the object during its whole operating period. A research method at a macro-regional scale was applied to investigate some phenomena connected with the operation of the analysed big hydrotechnical construction. Applying a semivariogram function enabled the spatial variability analysis of displacements. Isotropic empirical semivariograms were calculated and then, theoretical parameters of analytical functions were determined, which approximated the courses of the mentioned empirical variability measure. Using ordinary (block) kriging at the grid nodes of an elementary spatial grid covering the analysed object, the values of the Z* estimated means of displacements were calculated together with the accompanying assessment of uncertainty estimation – a standard deviation of estimation σk. Raster maps of the distribution of estimated averages Z* and raster maps of deviations of estimation σk (in perspective) were obtained for selected years (1995 and 2007), taking the ground height 136 m a.s.l. into calculation. To calculate raster maps of Z* interpolated values, methods of quick interpolation were also used, such as the technique of the inverse distance squares, a linear model of kriging, a spline kriging, which made the recognition of the general background of displacements possible, without the accuracy assessment of Z* value estimation, i.e., the value of σk. These maps are also related to 1995 and 2007 and the elevation. As a result of applying these techniques, clear boundaries of subsiding areas, upthrusting and also horizontal displacements on the examined hydrotechnical object were marked out, which can be interpreted as areas of local deformations of the object, important for the safety of the construction. The effect of geostatistical research conducted, including the structural analysis, semivariograms modeling, estimating the displacements of the hydrotechnical object, are rich cartographic characteristic (semivariograms, raster maps, block diagrams), which present the spatial visualization of the conducted various analyses of the monitored displacements. The prepared geostatistical model (3D) of displacement variability (analysed within the area of the dam, during its operating period and including its height) will be useful not only in the correct assessment of displacements and deformations, but it will also make it possible to forecast these phenomena, which is crucial when the operating safety of such constructions is taken into account.

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Erfanian, Hamid Reza, and Samaneh Barati. "Estimation method of spatial geostatistical data : Application to rainfall data." International Journal of Advanced Statistics and Probability 5, no. 2 (September 16, 2017): 91. http://dx.doi.org/10.14419/ijasp.v5i2.7824.

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Restriction of water resources for agricultural and non-agricultural purposes has caused major difficulties and rainfall is considered as one of the most important water resources. Therefore, predicting rainfall and estimating its rate monthly or annually for each region as one of the most important atmospheric parameters, is of particular importance in optimized usage of water resources.In this paper in addition to the presenting application of novel statistical methods, prediction of rainfall amount has been performed for the entire map of Iran. In this analysis, data of average rainfall of 108 pluviometry stations in different cities of Iran have been used and zoning of rainfall has been prepared for the country.

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Rosen, Lars, and Gunnar Gustafson. "A Bayesian Markov Geostatistical Model for Estimation of Hydrogeological Properties." Ground Water 34, no. 5 (September 1996): 865–75. http://dx.doi.org/10.1111/j.1745-6584.1996.tb02081.x.

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45

Nathanail, C. P., and M. S. Rosenbaum. "The use of low cost geostatistical software in reserve estimation." Geological Society, London, Special Publications 63, no. 1 (1992): 169–77. http://dx.doi.org/10.1144/gsl.sp.1992.063.01.17.

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46

Al-Hassan, S., and A. E. Annels. "Geostatistical estimation of manganese oxide resources at the Nsuta Mine." Geological Society, London, Special Publications 79, no. 1 (1994): 157–69. http://dx.doi.org/10.1144/gsl.sp.1994.079.01.15.

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Zhang, Xuesong, and Raghavan Srinivasan. "GIS-Based Spatial Precipitation Estimation: A Comparison of Geostatistical Approaches." JAWRA Journal of the American Water Resources Association 45, no. 4 (August 2009): 894–906. http://dx.doi.org/10.1111/j.1752-1688.2009.00335.x.

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48

Aguilar-Velázquez, Manuel J., Nelson Alejandro Gil-Vargas, Xyoli Pérez-Campos, Marcela Baena-Rivera, and Leonardo Ramirez-Guzman. "Spatial estimation of fundamental mode dispersion curves using geostatistical techniques." Geophysical Journal International 228, no. 3 (October 28, 2021): 1946–61. http://dx.doi.org/10.1093/gji/ggab446.

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SUMMARY This paper proposes the use of geostatistical techniques to estimate dispersion curves between other known ones. To do it, we introduce two novel methodologies: the stacking method and the group-velocity mapping method. We obtain our set of group-velocity fundamental mode dispersion curves from seismic noise correlation. Consequently, we first assign their attribution point at the mid-distance between the stations used for the dispersion curves calculation. The stacking method uses the range of the omnidirectional semivariogram of a regionalized variable that quantifies the similarity between dispersion curves to stack them according to their spatial correlation. We test this technique with dispersion curves obtained in Mexico City and get a range of ∼400 m for the omnidirectional semivariogram. We also calculate directional semivariograms and observe a maximum range (∼500 m) in the NW-SE direction, agreeing with the city's spatial distribution of natural periods. On the other hand, the group-velocity mapping method uses the ordinary kriging estimator in the group velocities for all the ranges of periods to generate maps and then dispersion curves. Estimated dispersion curves retrieved from both, the stacking and the group-velocity mapping method, were compared with those obtained with the fast marching tomographic method. We also establish analogies between getting group-velocity maps with the tomographic method and with the group-velocity mapping method. Finally, we observe that the range of the omnidirectional semivariogram used in the stacking method may be related to the tomographic method resolution.

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Minkwitz, D., K. G. van den Boogaart, T. Gerzen, and M. Hoque. "Tomography of the ionospheric electron density with geostatistical inversion." Annales Geophysicae 33, no. 8 (August 31, 2015): 1071–79. http://dx.doi.org/10.5194/angeo-33-1071-2015.

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Abstract. In relation to satellite applications like global navigation satellite systems (GNSS) and remote sensing, the electron density distribution of the ionosphere has significant influence on trans-ionospheric radio signal propagation. In this paper, we develop a novel ionospheric tomography approach providing the estimation of the electron density's spatial covariance and based on a best linear unbiased estimator of the 3-D electron density. Therefore a non-stationary and anisotropic covariance model is set up and its parameters are determined within a maximum-likelihood approach incorporating GNSS total electron content measurements and the NeQuick model as background. As a first assessment this 3-D simple kriging approach is applied to a part of Europe. We illustrate the estimated covariance model revealing the different correlation lengths in latitude and longitude direction and its non-stationarity. Furthermore, we show promising improvements of the reconstructed electron densities compared to the background model through the validation of the ionosondes Rome, Italy (RO041), and Dourbes, Belgium (DB049), with electron density profiles for 1 day.

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Bez, Nicolas. "Global fish abundance estimation from regular sampling: the geostatistical transitive method." Canadian Journal of Fisheries and Aquatic Sciences 59, no. 12 (December 1, 2002): 1921–31. http://dx.doi.org/10.1139/f02-155.

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This article deals with the estimation of fish biomass based on regular samplings. The geostatistical transitive method is a design-based spatially explicit method based on few and falsifiable assumptions concerning the sampling strategy. The falsifiability of a hypothesis corresponds to our capacity to control its adequacy to field data in practice. We first describe the basics of the method, mention the questions relative to the covariogram estimation, the units, and the projections of the coordinates, and explain how to fit the model to the experimental covariogram. We then apply the method to an ICES (International Council for the Exploration of the Sea) triennial mackerel egg survey, with regular sampling, and to a Moroccan octopus survey, with regular stratified sampling. To compare the present technique with existing methods, the number and the falsifiability of their respective hypotheses are considered in addition to the bias, the convergence, and the estimation variance. As is often the case, data are assumed to be synoptic, and we discuss two examples of spatiotemporal methods.

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