Programs for kriging and sequential Gaussian simulation with locally varying anisotropy using non-Euclidean distances

Boisvert, Jeff B.; Deutsch, Clayton V.

doi:10.1016/j.cageo.2010.03.021

Cited by 69 publications

(39 citation statements)

References 23 publications

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“…A spatial process may also vary with direction, and in this respect, anisotropic processes can be represented using non-ED metrics (e.g. Boisvert and Deutsch 2011). In particular, Páez (2004) found GWR models calibrated with anisotropic kernels to outperform their isotropic (standard) counterparts.…”

Section: Introductionmentioning

confidence: 99%

The Minkowski approach for choosing the distance metric in geographically weighted regression

Charlton

Brunsdon

et al. 2015

International Journal of Geographical Information Science

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In this study, the geographically weighted regression (GWR) model is adapted to benefit from a broad range of distance metrics, where it is demonstrated that a well-chosen distance metric can improve model performance. How to choose or define such a distance metric is key, and in this respect, a 'Minkowski approach' is proposed that enables the selection of an optimum distance metric for a given GWR model. This approach is evaluated within a simulation experiment consisting of three scenarios. The results are twofold: (1) a well-chosen distance metric can significantly improve the predictive accuracy of a GWR model; and (2) the approach allows a good approximation of the underlying 'optimal distance metric', which is considered useful when the 'true' distance metric is unknown. ARTICLE HISTORY

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Section: Introductionmentioning

confidence: 99%

The Minkowski approach for choosing the distance metric in geographically weighted regression

Charlton

Brunsdon

et al. 2015

International Journal of Geographical Information Science

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“…We therefore wish to take an arbitrary image which we believe has spatial features that our model should also exhibit, and derive from the image a covariance matrix whose corresponding prior probability distribution will yield models with the desired spatial properties. To do this, we follow the method of Boisvert (2010;Boisvert and Deutsch, 2011) who defines a distance function, on an image, whose "shortest paths" between points follow curved lines parallel to any structure in the image.…”

Section: Methods and Resultsmentioning

confidence: 99%

“…Our method, following work by Boisvert (2010) divides the image into cells, in each of which a local anisotropy is estimated. This allows a distance function to be defined, whose shortest paths follow the directions of spatial structure in the image.…”

Section: Introductionmentioning

confidence: 99%

Constraining an inversion to follow curving trends in an image

King¹

2018

ASEG Extended Abstracts

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SUMMARYThis paper addresses the question of how to include structural information, for example from a magnetic image, into an airborne electromagnetic (AEM) inversion. The kind of information we are interested in is the trend directions seen in the magnetic image, such as strike directions of dipping bodies, or the shape of palaeochannels.A commonly-used technique for including prior information is to use a model covariance matrix, describing the spatial covariance between different model points. However, these covariances are usually constructed from a stationary covariance function which is dependent on the vector distance between two points, but is the same for the entire model. However, if a palaeochannel is visible in the magnetics, then we know that the AEM model is more likely to be similar along the channel than away from the channel. We therefore wish to construct a covariance matrix that can take curved and branching structure into account.We construct an inhomogeneous covariance matrix from an image by breaking the image up into multiple windows, and then computing an elliptical distance metric in each window, such that distances in the direction of the features in that window are shorter than distances across those features. This collection of distance metrics then allows us to compute, between any two points in the image, a shortest path that curves to follow the directions of trends in the image. Using this curved-path distance allows us to generate a covariance matrix that encourages the inverted model to follow the trends in the image.

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“…The accessory minerals are zircon, rutile, ilmenite, magnetite, and apatite. The plagioclase (An 30-47) has normal zoning with a common narrow albite-oligoclase (An [8][9][10][11][12][13][14][15][16][17][18][19][20] rim. The skarn is at the contact between the monzogranite and the carbonate rock, where a Cu-Au-Mo calcic skarn developed.…”

Section: Geological Characteristics and Constraintsmentioning

confidence: 99%

“…Advances have been made in the modeling of local anisotropy in complex geological structures, see [11], but this method does not include mining parameters such as the minimum thickness values or the dilution. This paper uses a new method to model tabular deposits, as exemplified by the "Zona M" seam of the northern side of the Carlés deposit, in Spain.…”

Section: Introductionmentioning

confidence: 99%

Resource and Reserve Calculation in Seam-Shaped Mineral Deposits; A New Approach: “The Pentahedral Method”

et al. 2017

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Abstract:In recent years, the introduction of specific software for the evaluation of geological resources and mineral reserves has increased significantly thanks to the use of block models capable of working with large databases and applicable to virtually all types of deposits. It is only in layered, tabular-shaped deposits where the use of block models poses certain drawbacks, not only in terms of visual representation but also during the process of interpolation. Other calculation methods for tabular bodies such as sections, polygons, and triangles work with 2D projections but not with 3D. The "Pentahedral" method described here is undoubtedly an innovative method that allows work to always be conducted in 3D, providing a fairly accurate representation of tabular bodies and making it possible to carry out calculations of resources and reserves using any interpolation method. It is demonstrated with figures and tables of the Carlés mineral deposit, a well-developed exoskarn gold deposit in northwestern Spain (Asturias) where the authors have worked extensively. The pentahedral method takes into account not only geological and stratigraphic data from the model interpolation, but also mining concepts such as "minimum thickness," related to the minimum seam size that can be economically and technically mined, and "overbreak," related to the dilution effect that appears during the mining process due to over-excavation.

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Programs for kriging and sequential Gaussian simulation with locally varying anisotropy using non-Euclidean distances

Cited by 69 publications

References 23 publications

The Minkowski approach for choosing the distance metric in geographically weighted regression

The Minkowski approach for choosing the distance metric in geographically weighted regression

Constraining an inversion to follow curving trends in an image

Resource and Reserve Calculation in Seam-Shaped Mineral Deposits; A New Approach: “The Pentahedral Method”

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