NO. 34 · Petrophysics & Reservoir

Geostatistics for Reservoir Characterization

From spatial data hygiene to kriging, simulation, and a full reservoir capstone. The statistical spine of every property model you will ever build or QC.

You can decluster a biased dataset, model its variogram, choose and defend a kriging or simulation method, and read uncertainty maps like a reservoir geologist.

29 competencies · 6 interactive widget challenges · 25 to 36 hours of guided study

For geoscientists moving into reservoir modeling teams

Draws on: Geostatistics

Spatial data

Thinking in space

Stationarity is the quiet contract behind every map you will ever krige; learn what it promises and when it breaks.

Reads: What makes data spatial? Stationarity, ergodicity, and the practical compromise

Support, scale, and sampling

A core plug and a seismic voxel measure different Earths; support and sampling decide what your numbers even mean.

Reads: Support and scale: the volume problem Spatial sampling and its biases

Coordinates and first looks

Most geostatistical disasters are visible in the first hour of honest exploratory analysis, if you plot the right things in the right coordinates.

Reads: Coordinate systems and spatial reference Exploratory data analysis for spatial data

Distributions and the normal score

Simulation lives and dies in Gaussian space; the normal-score transform is the doorway and you need to walk it in both directions.

Reads: Histograms, CDFs, and quantile-quantile plots Normal-score transform

Bias, robustness, and local statisticswidget challenge

Wells are drilled where rock is good, so every raw statistic flatters the reservoir; robustness is how you stop believing your own advertising.

Reads: Why your sample histogram is biased Robust descriptive statistics for clustered data From global statistics to local: blocks and panels

Declustering

Declustering, two wayswidget challenge

Cell and polygonal declustering are the two standard cures for preferential drilling; you should be able to run both and say why they disagree.

Reads: Cell declustering Polygonal declustering

Choosing and defending weights

Declustering is a judgment call with reserves on the line; this is where you learn to defend the cell size you picked.

Reads: Comparing methods on the same dataset What declustering changes downstream

Variograms

The variogram as a spatial contractwidget challenge

Every kriging weight and every simulated map is downstream of this one function; if you cannot read a variogram you cannot QC a model.

Reads: Covariance, correlogram, and variogram, three views of the same thing h-scatterplots and lag binning

Anisotropy and direction

Reservoirs are longer than they are thick; a variogram that ignores direction models a reservoir that does not exist.

Reads: Isotropic and directional variograms Anisotropy: range, sill, geometric vs zonal

Indicator and robust variograms

Outliers and skewed grades can wreck an experimental variogram; indicator and robust estimators keep the structure visible when the data fight you.

Reads: Indicator variograms Robust variogram estimators

Permissible models and the nugget

Only a handful of curves are mathematically legal to krige with, and the nugget you choose quietly sets how much your maps smooth.

Reads: Permissible model families (spherical, exponential, Gaussian) Nugget effect and short-scale variability

Nested and anisotropic models

Real reservoirs carry structure at more than one scale and direction; nested anisotropic models are how a variogram tells that truth.

Reads: Anisotropic ellipsoids and the search ellipse Nested structures and additive sills

Fitting, three ways

By eye, by weighted least squares, by likelihood: each fitting strategy fails differently, and knowing which to trust is the skill.

Reads: Fitting strategies: by eye, by WLS, by likelihood

Kriging

Simple kriging from first principles

Simple kriging is the clean derivation everything else amends; get the weights-from-covariance logic here and the rest of the family is bookkeeping.

Reads: Simple kriging from first principles

Ordinary kriging and drift

Ordinary kriging is the industry workhorse, and kriging with external drift is how you let seismic into a well-data map; together they cover most maps you will ship.

Reads: Ordinary kriging and the unbiasedness constraint Universal kriging and kriging with external drift

What the kriging variance means

The most misread number in geostatistics; it prices data geometry, not local reality, and interviews love it.

Reads: The kriging variance, what it means and what it doesn't

Blocks, support, and the search

Block kriging answers the support question deliberately, and the search neighbourhood is the dial that most changes your map in practice.

Reads: Block kriging and change-of-support Neighbourhood selection and search ellipsoids

Cokriging with secondary data

When seismic covers what wells cannot, cokriging is the principled way to let a secondary variable speak without letting it shout.

Reads: Cokriging with secondary data

Kriging pathologies

Negative weights, string effects, and screening artifacts are how kriging tells you the setup is wrong; learn to read the symptoms before the client does.

Reads: Common kriging pathologies and how to spot them

Cross-validation

Leave-one-out and jackknife are the cheapest honest tests a kriging model ever gets; run them before anyone else can.

Reads: Leave-one-out cross-validation for kriging Jackknife and split-sample validation

QC and calibrationwidget challenge

Accuracy plots and variance calibration turn "the map looks right" into a defensible statement about uncertainty.

Reads: Accuracy plots and reliability diagnostics Calibration of the kriging variance Debiasing checks and conditional bias

Simulation

From kriging to simulation

Kriging gives the best single map and quietly deletes the heterogeneity that controls flow; simulation is how you get it back.

Reads: From kriging to simulation: why one map is never enough The LU decomposition approach to simulation

Sequential Gaussian simulationwidget challenge

SGS is the industry's default simulation engine; know the sequential logic well enough to predict what conditioning will do before you click run.

Reads: Sequential Gaussian Simulation (SGS) Conditioning on hard data

Realisations into decisions

A stack of realisations is not an answer; percentile maps and decision metrics are how uncertainty earns its seat in a development plan.

Reads: Multiple realisations and uncertainty maps Post-processing realisations into decision metrics

Indicator kriging and SISIM

Facies do not obey Gaussian rules; indicator methods let categories carry their own spatial law into the model.

Reads: Indicator variograms revisited Indicator kriging for facies probabilities Sequential Indicator Simulation (SISIM)

Facies models and their traps

Categorical models fail in characteristic ways, from order relations to patchwork artifacts; knowing the pitfalls is half the method.

Reads: Categorical facies modeling Indicator methods: strengths and known pitfalls

Multipoint and modern methods

When channels and lobes matter, two-point statistics run out of words; training images and multipoint simulation are the vocabulary upgrade, used with judgment.

Reads: From two-point to multipoint: motivation SNESIM and the role of training images Choosing between two-point and multipoint methods

Capstone

Capstone: clastic shelf reservoirwidget challenge

One dataset, the full workflow, decisions at the end; this is the rehearsal for the job.

Reads: Capstone 1: Clastic shelf reservoir characterization

The master workflow card

The whole path compressed onto one card you can carry into any project review.

Reads: Master geostatistical workflow card