PETE 404 Exam 2

To model the condition of geometric anisotropy, we have to use the same combination of linear models in both directions except with different sills.

The maximum size of the search neighborhood for kriging should be based on the range of the variogram model.

In ordinary kriging, the sum of the weights is forced to be zero.

Because λ0 is forced to be zero in ordinary kriging, there are only n unknowns to solve for instead of n+1 unknowns as for simple kriging.

Weights can be negative in ordinary kriging.

The presence of a high nugget effect reduces spatial information, which results in higher error variance.

One common application of cross variograms is using high-density seismic data to help estimate permeability at undrilled well locations.

In variogram modeling for two variables, the x variogram, y variogram, and x-y cross variogram must all have the same linear combination of structures and must all have the same sill.

In variogram modeling with multiple variables and anisotropy, if all the variograms cannot be modeled well, it is critical to model the cross variograms well while the other models can be sacrificed somewhat.

The cross variogram provides a quantitative measure of the spatial relationship between two variables.

Additional information from the covariable in cokriging should reduce the error variance as compared to just kriging of the primary variable.

Simple cokriging with one secondary variable requires the inversion of a (n+m+2)-size matrix, where n is the number of samples of the primary variable and m is the number of samples of the covariable.

Collocated cokriging requires the covariable sample to be available at every location where the primary variable is to be estimated, which increases the matrix size compared to regular (non-collocated) cokriging.

The kriging error variance is a good measure of the local uncertainty at the unsampled location.

The estimated value from kriging is dependent on the values of the surrounding samples, while the error variance is independent.

Estimation by kriging does not reproduce extreme values observed in the sample data because the weights associated with individual samples are nearly always less than one, thus reducing the effects of extreme values.

A variogram based on estimated values from kriging will have higher sill than the variogram based on sample data.

One of the advantages of conditional simulation is that if we create multiple equiprobable realizations and these realizations correctly represent the multivariate distribution, they will bound the true realization.

A major disadvantage of grid-based simulation methods is that they do not honor the spatial relationships of reservoir properties.

A major disadvantage of object-based simulation methods is that it is difficult to condition data at individual well locations.

Estimation using conventional kriging techniques is dependent on the order in which unsampled locations are visited, while simulation using sequential conditional simulation methods is independent of the order in which unsampled locations are visited.

In the sequential simulation technique, in addition to selecting the sampled points within the search neighborhood, previously simulated points within the search neighborhood are also selected.

The ability to closely reproduce the basic univariate statistics of the conditioning data is one of the best properties of sequential Gaussian simulation.

The five-step sequential simulation process is as follows: (1) model variograms, (2) transform the original data into a new domain, (3) determine a random path to visit all the unsampled locations, (4) sequentially estimate values at the unsampled locations, and (5) back-transform the values to the original domain.

Grid-based conditional simulation methods employ kriging as part of the simulation process.

In a typical reservoir characterization involving cosimulation, geological facies are dependent on porosity and permeability while seismic attributes are dependent on facies and porosity.

The primary advantage of sequential cosimulation is its ability to honor the local relationships between multiple attributes, as well as the individual spatial relationships of the multiple attributes.

In sequential cosimulation of multiple attributes, at each unsampled location, all the unknown attributes are simulated in sequential order from least independent to most independent to preserve their relationships.

If cokriging is used in cosimulation, then the local relationships among the attributes must be linear in the transformed domain.

Geostatistical estimation, or kriging, is based on minimizing the variance between the estimation point and the available samples.

The variability of a regionalized variable is always zero for distance zero.

Estimating the values at unsampled points requires knowledge about the relationship between sampled and unsampled locations.

Geological features are randomly distributed in a spatial context.

Reservoirs are heterogeneous and have directions of continuity because of their specific depositional, structural, and digenetic histories.

Two different reservoir models with similar statistics can be very different in geological features.

For a given direction, spatial covariance depends only on the distance and not location.

By assuming stationarity, we can use observations from one part of the reservoir to construct variograms for other parts.

A Variogram is a measure of similarity between two random variables.

The range in variogram is the distance at which the variogram value becomes constant with respect to lag.

Kriging allows for production uncertainty analysis.

Both Kriging and simulation methods can honor hard data.

Both Kriging and simulation methods can honor the local variogram model.

Relative to Kriging, the sequential Gaussian simulation is locally accurate.

If the random path in sequential Gaussian simulation is not changed, the generated realizations will be identical.

Similar to variance, covariance is defined in units that depend on the units of x and y but the correlation coefficient is dimensionless, and its value always falls between the limits of 1 and -1.

When the square of the correlation coefficient is used to describe the relationship between two variables, whether the two variables are negatively or positively related cannot be exhibited, but it is a common way in describing the "goodness of fit" in a linear regression between two variables.

A Q-Q plot is a scattered plot based on ranked pair data, so two samples with equal size are always required.

SGEMS Objects are files with numerical information and there are two types, Data and Grid, both of which specify the location in the file.

Geostatistics represents a set of mathematical tools which have deterministic or stochastic components, may represent different types of data at different scales, but cannot fill the interwell space properly.

The SGEMS grid(s) has to be specified before attempting any processing that will result in the generation of a grid variable such as Kriging.

In SGEMS, grids can only be displayed in graphical form and grid values are stored in binary form.

The semivariogram is related to the covariance by the difference between the variance and the spatial covariance regardless of the stationarity of the mean.

The spatial covariance always starts with a zero value and increases as the lag distance between the two values increases.

Kriging is a form of linear regression and works best for estimation inside a convex hull of the data.

The most frequently used types of semi-variogram models are Gaussian, Spherical, and Exponential models.

Conditional simulation reproduces the value and location of observations.

Kriging method accounts for local variations.

Kriging estimation method is appropriate for flow simulation.

Sequential Gaussian simulation requires transformation of data to normal scores.

Geo-statistical simulation method cannot use secondary data.

For collocated cokriging method, the secondary data points have to be at the same locations as the primary data points.