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Abstract We develop a new methodology for the multi‐resolution assimilation of electric fields by extending a Gaussian process model (Lattice Kriging) used for scalar field originally to vector field. This method takes the background empirical model as “a priori” knowledge and fuses real observations under the Gaussian process framework. The comparison of assimilated results under two different background models and three different resolutions suggests that (a) the new method significantly reduces fitting errors compared with the global spherical harmonic fitting (SHF) because it uses range‐limited basis functions ideal for the local fitting and (b) the fitting resolution, determined by the number of basis functions, is adjustable and higher resolution leads to smaller errors, indicating that more structures in the data are captured. We also test the sensitivity of the fitting results to the total amount of input data: (a) as the data amount increases, the fitting results deviate from the background model and become more determined by data and (b) the impacts of data can reach remote regions with no data available. The assimilation also better captures short‐period variations in local PFISR measurements than the SHF and maintains a coherent pattern with the surrounding. The multi‐resolution Lattice Kriging is examined via attributing basis functions into multiple levels with different resolutions (fine level is located in the region with observations). Such multi‐resolution fitting has the smallest error and shortest computation time, making the regional high‐resolution modeling efficient. Our method can be modified to achieve the multi‐resolution assimilation for other vector fields from unevenly distributed observations.
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Traditional kriging versus modern Gaussian processes for large‐scale mining data
The canonical technique for nonlinear modeling of spatial/point‐referenced data is known as kriging in geostatistics, and as Gaussian Process (GP) regression for surrogate modeling and statistical learning. This article reviews many similarities shared between kriging and GPs, but also highlights some important differences. One is that GPs impose a process that can be used to automate kernel/variogram inference, thus removing the human from the loop. The GP framework also suggests a probabilistically valid means of scaling to handle a large corpus of training data, that is, an alternative to ordinary kriging. Finally, recent GP implementations are tailored to make the most of modern computing architectures, such as multi‐core workstations and multi‐node supercomputers. We argue that such distinctions are important even in classically geostatistical settings. To back that up, we present out‐of‐sample validation exercises using two, real, large‐scale borehole data sets acquired in the mining of gold and other minerals. We compare classic kriging with several variations of modern GPs and conclude that the latter is more economical (fewer human and compute resources), more accurate and offers better uncertainty quantification. We go on to show how the fully generative modeling apparatus provided by GPs can gracefully accommodate left‐censoring of small measurements, as commonly occurs in mining data and other borehole assays.
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- Award ID(s):
- 1822108
- PAR ID:
- 10652343
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Statistical Analysis and Data Mining: The ASA Data Science Journal
- Volume:
- 16
- Issue:
- 5
- ISSN:
- 1932-1864
- Page Range / eLocation ID:
- 488 to 506
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1002/sam.11635
