Geostatistics

Geostatistics
By OgbonLab

Spatial estimation and uncertainty, from variograms to multipoint.

From experimental variograms to multipoint simulation, with full reservoir-characterization capstones, kriging done right, simulation done right.

13 parts 74 sections Free, browser-native
Start reading → First up: What makes data spatial?

Table of contents

Every section is a working session: text, math, code, interactive widgets. Click any title to jump in.

Part 1: Part 0, Spatial data fundamentals

  1. What makes data spatial?
  2. Stationarity, ergodicity, and the practical compromise
  3. Support and scale: the volume problem
  4. Coordinate systems and spatial reference
  5. Spatial sampling and its biases
  6. Exploratory data analysis for spatial data

Part 2: Part 1, Univariate statistics for geo-data

  1. Histograms, CDFs, and quantile-quantile plots
  2. Normal-score transform
  3. Why your sample histogram is biased
  4. Robust descriptive statistics for clustered data
  5. From global statistics to local: blocks and panels

Part 3: Part 2, Declustering

  1. Cell declustering
  2. Polygonal declustering
  3. Comparing methods on the same dataset
  4. What declustering changes downstream

Part 4: Part 3, Experimental variograms

  1. Covariance, correlogram, and variogram, three views of the same thing
  2. h-scatterplots and lag binning
  3. Isotropic and directional variograms
  4. Anisotropy: range, sill, geometric vs zonal
  5. Indicator variograms
  6. Robust variogram estimators

Part 5: Part 4, Variogram modeling

  1. Permissible model families (spherical, exponential, Gaussian)
  2. Nugget effect and short-scale variability
  3. Anisotropic ellipsoids and the search ellipse
  4. Nested structures and additive sills
  5. Fitting strategies: by eye, by WLS, by likelihood

Part 6: Part 5, Kriging

  1. Simple kriging from first principles
  2. Ordinary kriging and the unbiasedness constraint
  3. Universal kriging and kriging with external drift
  4. The kriging variance, what it means and what it doesn't
  5. Block kriging and change-of-support
  6. Neighbourhood selection and search ellipsoids
  7. Cokriging with secondary data
  8. Common kriging pathologies and how to spot them

Part 7: Part 6, Cross-validation and QC

  1. Leave-one-out cross-validation for kriging
  2. Accuracy plots and reliability diagnostics
  3. Calibration of the kriging variance
  4. Jackknife and split-sample validation
  5. Debiasing checks and conditional bias

Part 8: Part 7, Sequential Gaussian simulation

  1. From kriging to simulation: why one map is never enough
  2. The LU decomposition approach to simulation
  3. Sequential Gaussian Simulation (SGS)
  4. Conditioning on hard data
  5. Multiple realisations and uncertainty maps
  6. Post-processing realisations into decision metrics

Part 9: Part 8, Indicator methods

  1. Indicator variograms revisited
  2. Indicator kriging for facies probabilities
  3. Sequential Indicator Simulation (SISIM)
  4. Categorical facies modeling
  5. Indicator methods: strengths and known pitfalls

Part 10: Part 9, Multipoint statistics and modern methods

  1. From two-point to multipoint: motivation
  2. SNESIM and the role of training images
  3. FILTERSIM and pattern-based simulation
  4. Generative models for geostatistics (GANs, diffusion)
  5. Choosing between two-point and multipoint methods

Part 11: Part 10, Reservoir-characterization capstones

  1. Capstone 1: Clastic shelf reservoir characterization
  2. Capstone 2: Carbonate reservoir with facies modeling
  3. Capstone 3: Fluvial channel reservoir (multipoint statistics)
  4. Capstone 4: Tight-gas reservoir with fracture overprint
  5. Capstone 5: Heavy-oil reservoir under WAG flood
  6. Capstone 6: CO₂-storage site characterization

Part 12: Part 11, Self-assessment quizzes

  1. Quiz, Part 0: Spatial data fundamentals
  2. Quiz, Part 1: Univariate stats
  3. Quiz, Part 2: Declustering
  4. Quiz, Part 3: Experimental variograms
  5. Quiz, Part 4: Variogram modeling
  6. Quiz, Part 5: Kriging
  7. Quiz, Part 6: Cross-validation and QC
  8. Quiz, Part 7: Sequential Gaussian simulation
  9. Quiz, Part 8: Indicator methods
  10. Quiz, Part 9: Multipoint and modern
  11. Quiz, Part 10: Capstones
  12. Final exam, integrated assessment

Part 13: Part 12, Master geostatistical workflow

  1. Master geostatistical workflow card

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