Area-to-point kriging (A2PK)
This MATLAS package allows you to generate fine-scale stocastic Gaussian simulation based on a known coarse scale image of the same domain. This is done through area-to-point kriging, a co-kriging estimation where the coase-scale is considered as a secondary variable so that the cross-covariance can be computed easily.
Area-to-point kriging
The main function is A2PK.m, and an example script is provided in script.mlx.
Examples
The following two scripts give a step-by-step instruction to run area-to-point kriging:
A2PK _gaussian.mlxis the easiest place to start. It will guide you through the computation of a simulation based on a synthetic example.A2PK_cond_gaussian.mlxexpends the previous example with a conditional case.
Application to Electrical Resistivity Tomography (ERT)
During my PhD, I applied A2PK to the simulation of a fine-scale scale electrical conductivity field, based on the smooth result of a deterministic inversion of an electrical resistivity tomography (ERT). The code used for this can be found in the ERT folder, and, in particular, the published script script_ERT.mlx.
- Nussbaumer, R., Linde, N., Mariethoz, G., & Holliger, K. (2019). simulation of fine-scale electrical conductivity fields using resolution-limited tomograms and area-to-point kriging. Geophysical Journal International, 218(2), 1322–1335. 10.1093/gji/ggz185
Application to Hydraulic tomography (HT)
We also worked on an adaptation of a similar technique for hydraulic tomography. Refer to the HT folder, and more precisely to the main script. Despite promising results, I did not finish this work because of time constraint.
References
- Nussbaumer, R., Mariethoz, G., Linde N., & Holliger, K. (2018). Simulation of fine-scale electrical conductivity fields using tomograms and area-to-point kriging, GeoEnv2018, Belfast. DOI: 10.13140/RG.2.2.31712.12801
- Kyriakidis, Phaedon C. (2004). A Geostatistical Framework for Area-to-Point Spatial Interpolation.Geographical Analysis 36(3):259. DOI: 10.1353/geo.2004.0009.