Random Fields (WebR Version)

PPOL 6805 / DSAN 6750: GIS for Spatial Data Science
Fall 2026

Jeff Jacobs

jj1088@georgetown.edu

Wednesday, October 7, 2026

Geostatistical Data: Dumping Sand onto a Table!

  • Domain \(D\): tabletop; Random process: dumping sand onto the tabletop
  • \(\Omega\): All possible realizations of process. \(\omega_i \in \Omega\) Particular realization
Figure 1: \(\omega_1 \in \Omega\)
Figure 2: \(\omega_2 \in \Omega\)
Figure 3: \(\omega_3 \in \Omega\)
Figure 4: \(\omega_4 \in \Omega\)

Example: Water Coverage in Bhola, Bangladesh

@parenti_tropic_2011

Geostatistical Modeling: Terrains Are Not Spiky Chaotic Landscapes!

(If they were… we’d have to worry about suddenly plunging 1000km with each step!)

Geostatistical Data \(\rightarrow\) Point Pattern

(Example “event”: Discovery of a point higher than Washington Monument)

Indicator function: \(\mathbb{1}\left[Z(\mathbf{s}) > 860\text{m}\right]\)