VarioCorreKrigE: Variogram, Correlation and Krigging Estimation

This repository was created to perform the estimation of variogram and correlation models, which are essential for many engineering uses. In particular, variogram and correlation models form the backbone for Kriging, by which values can be estimated at unknown locations. There are several available packages (see References), whilst some are thorough and fairly robust, they are largely niche in most cases and not tailored to specific use cases without additional modifications. In this regard, this repository focuses mainly on engineering applications such as:

1. Spatial Correlation Models (SCMs) for parameter and residual estimation (e.g., Vs30, $\delta W$)
2. Kriging Estimates of values at unknown locations
3. Sequential Gaussian Simulation (SGS) for statistically robust estimates at unknown locations

Refer to Theory for getting a quick overview of the process for estimating semivariance and correlation whereby models are developed. Theory also provides an overview of the available kernels and some of the underlying assumptions required to conduct robust geostatistical analyses.

Installation

Option A

1. Clone the repository:

   git clone https://github.com/AaronJR474/VarioCorreKrigE.git
   cd VarioCorreKrigE

2. Install the required dependencies:

   pip install -r requirements.txt

Option B

pip install git+https://github.com/AaronJR474/VarioCorreKrigE.git

Utilizing the package

The package is broken down into three main functions as follows:

1. variofit.py: Estimation of Semivariance and fitting of variogram models

     from VarioCorreKrigE.variofit import variofit
     from VarioCorreKrigE.variofit import VARIOGRAM_MODELS

2. correfit.py: Estimation of correlation coefficients and fitting of correlation models

     from VarioCorreKrigE.correfit import correfit
     from VarioCorreKrigE.correfit import CORRELATION_MODELS

3. skrig.py: Estimation of Simple Kriging (including Sequential Gaussian Simulation)

     from VarioCorreKrigE.skrig import simple_kriging, sgs_simple_kriging
     from VarioCorreKrigE.correfit import CORRELATION_MODELS
     from VarioCorreKrigE.variofit import VARIOGRAM_MODELS
     from VarioCorreKrigE.utils import theta_from_params, LatLongToPolar, sample_points_from_geotiff

In the folder Examples, there are detailed examples for each of the mentioned functions, including the ability to utilize custom correlation/variogram models not currently within the package. The examples also demonstrate the creation of custom covariance matrices and corresponding pairwise distances for a user-tailored Kriging analysis.

Future versions will be extended to include:

• Ordinary and Universal Kriging
• Bayesian Markov Chain Monte Carlo estimation of Variogram/Correlation model parameters

References

Learning Resources

Myers, Donald. (1997). Multivariate geostatistics By Hans Wackernagel. Mathematical Geology. 29. 307-310. 10.1007/BF02769635.

Pyrcz, M.J., 2024, Applied Geostatistics in Python: a Hands-on Guide with GeostatsPy [e-book]. Zenodo. doi:10.5281/zenodo.15169133

Other Python Geostatistical Packages

Mirko Mälicke, Egil Möller, Helge David Schneider, & Sebastian Müller. (2021, May 28). mmaelicke/scikit-gstat: A scipy flavoured geostatistical variogram analysis toolbox (Version v0.6.0). Zenodo. http://doi.org/10.5281/zenodo.4835779

Müller, S., Schüler, L., Zech, A., and Heße, F.: GSTools v1.3: a toolbox for geostatistical modelling in Python, Geosci. Model Dev., 15, 3161–3182, https://doi.org/10.5194/gmd-15-3161-2022, 2022.