Abstract
The empirical variogram is a measure of spatial data correlation in geostatistical modeling and simulations. Typically, the empirical variogram is estimated for some defined lag intervals by applying method of moments on an underlying variogram cloud. Depending on the distribution of pair-wise lag values, the variogram cloud of an irregularly-sampled field may exhibit clusteredness. Issues of noisy, uninterpretable and inconsistent empirical variogram plots are commonly encountered in cases of irregularly-sampled fields with clustered variogram clouds. An insightful diagnosis of these problems and a practical solution are the subject of this paper. This research establishes the fact that these problems are caused by the neglect of variogram cloud cluster configurations when defining lag intervals. It is here shown that such neglect hinders the optimal use of spatial correlation information present in variogram clouds. Specifically, four sub-optimal effects are articulated in this paper as the consequence of the neglect.
Consequently, this research presents an efficient cluster-analysis – driven technique for variogram estimation in cases of irregularly-sampled fields with clustered variogram clouds. The cluster analysis required for this technique is implemented using an unsupervised machine learning algorithm known as Density-based Spatial Clustering of Applications with Noise (DBSCAN). This technique has been applied to a real field to obtain a stable, interpretable and geologically consistent variogram plot. It has also been applied to a synthetic field and was found to give the lowest estimation error among other techniques. This technique would find usefulness in geo-modeling of natural resource deposits wherein irregular sampling is prevalent.
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Abbreviations
- CID:
-
Cluster Identifier
- \( \vec{h} \) :
-
Lag vector, m
- \( \Delta h \) :
-
Lag distance tolerance, m
- i:
-
Loop counter
- N:
-
Number of clusters
- \( Z\left( {u_{i} } \right) \) :
-
Value of a random variable attribute at location \( \varvec{u}_{\varvec{i}} \)
- \( Z\left( {u_{i} + \vec{h}} \right) \) :
-
Value of a random variable attribute at location \( u_{i} + \vec{h} \)
- \( \gamma \left( {\vec{h}} \right) \) :
-
Variogram, squared unit of attribute
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Acknowledgements
Inspirations from the only wise God are acknowledged. Dr. A. A. Adepelumi facilitated access to previous report of the Geological Consultancy Unit of Obafemi Awolowo University. Publication support from Covenant University Centre for Research, Innovation and Discovery (CUCRID) is also appreciated.
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Mosobalaje, O.O., Orodu, O.D., Ogbe, D. (2020). The Application of DBSCAN Algorithm to Improve Variogram Estimation and Interpretation in Irregularly-Sampled Fields. In: Florez, H., Misra, S. (eds) Applied Informatics. ICAI 2020. Communications in Computer and Information Science, vol 1277. Springer, Cham. https://doi.org/10.1007/978-3-030-61702-8_20
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