Statistics of spatio-temporal processes



Kircher’s model of the seismic systems of the earth

The dynamics of spatial processes evolving in time.

Tools

geostack

…is a toolkit for high performance geospatial processing, modelling and analysis.

Some highlights of Geostack include:

  • Range of programmable geospatial operations based on OpenCL, including map algebra, distance mapping and rasterisation.
  • Data IO for common geospatial types such as geotiff and shapefiles with no dependencies.
  • Implicit handling geospatial alignment and projections, allowing easier coding of geospatial models.
  • Python bindings for interoperability with GDAL/RasterIO/xarray/NetCDF.
  • Built-in computational solvers including level set and network flow models.

More information and build guides are on our wiki.

Geostack can be installed for Python using conda.

gstat does certain R stats.

References

Baisch, Stefan, and Götz H. R. Bokelmann. 1999. Spectral Analysis with Incomplete Time Series: An Example from Seismology.” Computers & Geosciences 25 (7): 739–50.
Bárdossy, András. 2006. Copula-Based Geostatistical Models for Groundwater Quality Parameters.” Water Resources Research 42 (11).
Diggle, Peter, and Paulo J. Ribeiro. 2007. Model-Based Geostatistics. Springer Series in Statistics. New York, NY: Springer.
Hoffimann, Júlio, Maciel Zortea, Breno de Carvalho, and Bianca Zadrozny. 2021. Geostatistical Learning: Challenges and Opportunities.” Frontiers in Applied Mathematics and Statistics 7.
Lewis, Adam, Simon Oliver, Leo Lymburner, Ben Evans, Lesley Wyborn, Norman Mueller, Gregory Raevksi, et al. 2017. The Australian Geoscience Data Cube — Foundations and Lessons Learned.” Remote Sensing of Environment 202 (December): 276–92.
Matheron, Georges. 1963. Principles of Geostatistics.” Economic Geology 58 (8): 1246–66.
Peruzzi, Michele, Sudipto Banerjee, and Andrew O. Finley. 2020. Highly Scalable Bayesian Geostatistical Modeling via Meshed Gaussian Processes on Partitioned Domains.” Journal of the American Statistical Association 0 (0): 1–14.
Pluch, Philipp. 2007. Some Theory for the Analysis of Random Fields - With Applications to Geostatistics.” arXiv:math/0701323, January.
Roberts, Dale, Norman Mueller, and Alexis Mcintyre. 2017. High-Dimensional Pixel Composites From Earth Observation Time Series.” IEEE Transactions on Geoscience and Remote Sensing 55 (11): 6254–64.
Scalzo, Richard, Mark Lindsay, Mark Jessell, Guillaume Pirot, Jeremie Giraud, Edward Cripps, and Sally Cripps. 2022. Blockworlds 0.1.0: a demonstration of anti-aliased geophysics for probabilistic inversions of implicit and kinematic geological models.” Geoscientific Model Development 15 (9): 3641–62.
Sun, Alexander Y., Hongkyu Yoon, Chung-Yan Shih, and Zhi Zhong. 2021. Applications of Physics-Informed Scientific Machine Learning in Subsurface Science: A Survey.” arXiv:2104.04764 [Physics], April.

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