Gaussian Collocated Cosimulation

Gaussian collocated cosimulation is a sequential Gaussian simulation algorithm that incorporates secondary data (such as seismic attributes) at every simulation grid node by exploiting a Markov-type screening hypothesis — the assumption that the primary variable (such as porosity) at unsampled locations is conditionally independent of all secondary data at distant locations, given knowledge of the collocated secondary value at the same location — which reduces the full co-kriging system to a computationally tractable simple kriging co-kriging equation that uses only the collocated secondary datum and the primary variable's spatial covariance structure; the algorithm produces stochastic realizations of the primary variable (porosity, net-to-gross, permeability) that honor all available primary data (well measurements), reproduce the primary variable's histogram and variogram, and locally integrate the spatial information provided by the secondary variable (seismic impedance, attribute cubes), making Gaussian collocated cosimulation the standard geostatistical technique for generating reservoir property models that are constrained by both well data and 3D seismic attributes in petroleum reservoir characterization workflows.

What Is Gaussian Collocated Cosimulation?

Building a reservoir model requires populating a three-dimensional grid — often containing millions of cells — with estimates of properties like porosity, permeability, and fluid saturations. The challenge is that direct measurements (from wells) are sparse, while indirect measurements (from seismic) are dense but imprecise. Reservoir modelers want to use both: the accurate but sparse well data and the spatially comprehensive but noisy seismic data.

Gaussian collocated cosimulation is the algorithm that accomplishes this integration efficiently. The "Gaussian" part means the simulation works by drawing random values from normal distributions defined by the local statistics of the data. The "collocated" part refers to the Markov screening trick: instead of considering all the seismic data points across the entire model when simulating porosity at any given cell, the algorithm uses only the seismic value at that same cell location — the observation that a nearby seismic value tells you far less about the porosity at a point once you already know the seismic value at that exact point. This simplification makes the algorithm computationally feasible for million-cell grids while producing results that are nearly as good as the theoretically rigorous full co-kriging approach.

The result is a set of realizations — multiple equally probable reservoir property models — that all honor the well data, reproduce the expected geological variability (encoded in the variogram), and follow the spatial trends implied by the seismic. Running flow simulation on many such realizations quantifies how geological uncertainty translates into production forecast uncertainty, which is the information needed for risk-adjusted investment decisions in field development.

Gaussian Collocated Cosimulation in Reservoir Modeling Practice

Variogram modeling for the primary variable is a critical pre-processing step that defines the spatial continuity model used in the collocated cosimulation — the experimental variogram (a function describing how rapidly the primary variable becomes dissimilar with increasing separation distance in different directions) is computed from the available well data, typically by calculating the average squared difference between porosity values at well pairs separated by increasing lag distances in multiple azimuthal directions; the modeled variogram (a permissible covariance model such as a spherical, exponential, or Gaussian function fitted to the experimental variogram) provides the spatial continuity parameters (range, sill, nugget) in each principal direction (horizontal maximum continuity, horizontal minimum continuity, vertical) that control the size and shape of simulated spatial features; in reservoir settings with directional depositional fabrics (fluvial channels, turbidite lobes, deltaic systems), the variogram is anisotropic with much longer horizontal range in the depositional transport direction than perpendicular to it, and the variogram azimuth must be aligned with the geological interpretation of depositional strike.

Simulation validation uses the Q-Q plot of simulated versus input data distributions, variogram reproduction checks (do the simulated realizations reproduce the input variogram model within sampling uncertainty?), and cross-validation at well locations removed from the conditioning data to assess whether the simulation honors data at new locations with appropriate uncertainty; poor variogram reproduction in realizations typically indicates that the search neighborhood (number of conditioning data and search radius) is too small to adequately constrain the simulation at each node, requiring enlargement of the neighborhood parameters; over-smoothing (realizations that look too homogeneous compared to expected geological variability) typically indicates over-conditioning to secondary data (correlation coefficient too high) or a variogram range that is too long, requiring recalibration of the collocated correlation coefficient or variogram model against the actual data scatter.

Gaussian Collocated Cosimulation Across International Jurisdictions

Canada (AER / WCSB): WCSB reservoir modeling for oil sands and deep conventional reservoirs routinely uses Gaussian collocated cosimulation to integrate 3D seismic with well data in McMurray, Montney, and Duvernay formation reservoir models; AER requires that resource estimates and development plans for in situ oil sands projects include probabilistic reservoir descriptions that reflect geological uncertainty, and cosimulation-based modeling satisfies this requirement by producing multiple realizations that quantify porosity and bitumen saturation uncertainty at the lease scale; companies including Suncor, CNRL, Cenovus, and Imperial Oil use Petrel or RMS-based cosimulation workflows as the standard for McMurray oil sands reservoir characterization, with the seismic acoustic impedance inversion providing the secondary variable for cosimulated bitumen saturation and net-pay thickness used in SAGD well spacing design.