Improved spatial modeling by merging multiple secondary data for intrinsic collocated cokriging

Babak, Olena; Deutsch, Clayton V.

doi:10.1016/j.petrol.2009.08.001

Cited by 22 publications

(10 citation statements)

References 4 publications

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“…All secondary variables can be merged into a single secondary variable (merged or super‐secondary) using the linear combination (Babak and Deutsch ) provided in the following equation:

Y_{\begin{matrix} italicsuper \\ italicsecondary \end{matrix}} = \frac{0true \sum_{j = 1}^{n_{\sec}} β_{j} Y_{j}}{ρ_{\begin{matrix} 2false super \\ 2false secondary \end{matrix}}},

where the weights

β_{j}, j = 1, \dots, n_{\sec},

are calculated from the system of equations of the multiple linear regression:

0true \sum_{m = 1}^{n_{\sec}} β_{m} ρ_{Y_{j}, Y_{m}} = ρ_{Y_{j}, Z}, j = 1, \dots, n_{\sec},

where

ρ_{Y_{j}, Y_{m}}

j, m = 1, \dots, n_{\sec},

are correlations between secondary data (data redundancy) and

ρ_{Y_{j}, Z},

j = 1, \dots, n_{\sec},

are correlations between each secondary variable and the primary variable being predicted; and

ρ_{\begin{matrix} 2false super \\ 2false secondary \end{matrix}}

is the correlation coefficient of the merged/super‐secondary variable with the primary variable being estimated given by the following equation: …”

Section: Methodology and Approachmentioning

confidence: 99%

“…All secondary variables can be merged into a single secondary variable (merged or super-secondary) using the linear combination (Babak and Deutsch 2009b) provided in the following equation:…”

Section: Merging Secondary Variables For Intrinsic Collocated Co-krigingmentioning

confidence: 99%

“…A recent study (Barnett and Deutsch ) has shown that the proposed technique is superior to the Bayesian updating/p‐field approach because it does not produce covariance bias, which translates into a significant inflation of global uncertainty. Other reasons for selecting SGS with intrinsic collocated co‐kriging over other approaches include the simplicity of implementation as well as the ensured reproduction of each modelled variable's distribution and the correlations between all variables (Babak and Deutsch ,b).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimizing compaction calculation for improved probabilistic 2D mapping

Babak

Liu

Gallop

2019

Geophysical Prospecting

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Integration of all available data in reservoir characterization is critically important. 2D mapping is a reliable and robust technique that allows integration of multiple secondary data, including geological and geophysical surfaces and maps, to generate realistic summaries of reservoir quality at each location in an area of interest with an associated measure of uncertainty. This is achieved in 2D mapping with a more straightforward implementation, requiring significantly less time and fewer resources than three‐dimensional modelling. In this paper, we propose an approach for the empirical calculation and optimization of differential compaction maps by leveraging existing well control for the use in 2D mapping. Success of the proposal is demonstrated through tests of accuracy, precision and fairness of the local uncertainty distributions for 100 new stratigraphical wells drilled in the Christina Lake and Kirby East area.

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“…All secondary variables can be merged into a single secondary variable (merged or super‐secondary) using the linear combination (Babak and Deutsch ) provided in the following equation:

Y_{\begin{matrix} italicsuper \\ italicsecondary \end{matrix}} = \frac{0true \sum_{j = 1}^{n_{\sec}} β_{j} Y_{j}}{ρ_{\begin{matrix} 2false super \\ 2false secondary \end{matrix}}},

where the weights

β_{j}, j = 1, \dots, n_{\sec},

are calculated from the system of equations of the multiple linear regression:

0true \sum_{m = 1}^{n_{\sec}} β_{m} ρ_{Y_{j}, Y_{m}} = ρ_{Y_{j}, Z}, j = 1, \dots, n_{\sec},

where

ρ_{Y_{j}, Y_{m}}

j, m = 1, \dots, n_{\sec},

are correlations between secondary data (data redundancy) and

ρ_{Y_{j}, Z},

j = 1, \dots, n_{\sec},

are correlations between each secondary variable and the primary variable being predicted; and

ρ_{\begin{matrix} 2false super \\ 2false secondary \end{matrix}}

is the correlation coefficient of the merged/super‐secondary variable with the primary variable being estimated given by the following equation: …”

Section: Methodology and Approachmentioning

confidence: 99%

Section: Merging Secondary Variables For Intrinsic Collocated Co-krigingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimizing compaction calculation for improved probabilistic 2D mapping

Babak

Liu

Gallop

2019

Geophysical Prospecting

Self Cite

View full text Add to dashboard Cite

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“…To reveal the spatiotemporal distribution and evolution characteristics of groundwater salinization, geostatistical methods prove to be of great power to predict and display the distribution, variation and relevancy of different variants by interpolation from points data, especially for ordinary kriging (OK) [47,48]. However, recent studies have shown that the interpolation results by OK were not accurate with relatively few data, and co-kriging (COK) could improve the predict results notably, while the independent variable was highly-correlated with the coordination variables [49][50][51]. Based on the CT results of major ions and TDS and comparing the results of the mean error (ME), mean-squared error (MSE) and mean-square standard error (MSSE) of interpolation results in cross-validation by OK and COK, COK is finally used to display the spatial distribution of groundwater TDS among decades to reflect the variation tendency of groundwater quality in the study area.…”

Section: Data Analysis Methodsmentioning

confidence: 99%

Assessment of Long-Term Evolution of Groundwater Hydrochemical Characteristics Using Multiple Approaches: A Case Study in Cangzhou, Northern China

Wang

Liu³

et al. 2015

Water

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Water shortage is severe in the North China Plain (NCP). In addition to a deficiency of water resources, deterioration of groundwater quality should be of great concern. In this study, hydrogeological analysis was conducted in combination with principal component analysis, correlation analysis and the co-kriging method to identify factors controlling the content of major ions and total dissolved solids (TDS) in areal shallow and deep groundwater and to assess groundwater evolution in Cangzhou, China. The results suggested that groundwater quality degradation occurred and developed in the study area, as indicated by increasing concentrations of major ions, TDS and hardness in both shallow and deep groundwater. In shallow groundwater, whose hydrochemical water types changed from HCO3-Ca.Na.Mg and HCO3.Cl-Na in the west (Zone II) to Cl.SO4-Na and Cl-Na in the east (Zone III). Areas with TDS concentrations between 1500 and 2000 mg/L occupied 79.76% of the total in the 1980s, while areas with a TDS concentration ranging from 2500 to 3000 mg/L comprised 59.11% of the total in the 2010s. In deep groundwater, the area with TDS over 1000 mg/L expanded from 5366.39 km groundwater. Dissolution of dolomite, calcite, feldspar and gypsum were the primary sources of major ions in groundwater, and the ion exchange reaction had a strong effect on the cation content, especially for deep groundwater.

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“…We account for this dichotomy by using secondary variables in the SGS or DS (Babak, 2009a;Babak & Deutsch, 2009b;Mariethoz et al, 2012). The main signal results from tropospheric perturbations due to variations of water vapor, pressure, and temperature.…”

Section: 1029/2018ea000533mentioning

confidence: 99%

Generative Modeling of InSAR Interferograms

Rongier

Rude

Herring

et al. 2019

Earth and Space Science

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Interferometric synthetic aperture radar (InSAR) has become an essential technique to detect surface variations due to volcanoes, earthquakes, landslides, glaciers, and aquifers. However, Earth's ionosphere, atmosphere, vegetation, surface runoff, etc., introduce noise that requires post-processing to separate its components. This work defines a generator to create interferograms that include each of those components. Our approach leverages deformation models with real data, either directly or through machine learning using geostatistical methods. These methods result from previous developments to more efficiently and better simulate spatial variables and could replace some statistical approaches used in InSAR processing. We illustrate the use of the generator to simulate an artificial interferogram based on the 2015 Illapel earthquake and discuss the improved performance offered by geostatistical approaches compared with classical statistical ones. The generator establishes a tool for multiple applications (1) to evaluate InSAR correction workflows in controlled scenarios with known ground truth; (2) to develop training sets and generative methods for machine learning algorithms; and (3) to educate on InSAR and its principles.

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Improved spatial modeling by merging multiple secondary data for intrinsic collocated cokriging

Cited by 22 publications

References 4 publications

Optimizing compaction calculation for improved probabilistic 2D mapping

Optimizing compaction calculation for improved probabilistic 2D mapping

Assessment of Long-Term Evolution of Groundwater Hydrochemical Characteristics Using Multiple Approaches: A Case Study in Cangzhou, Northern China

Generative Modeling of InSAR Interferograms

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