Which of the following are valid guidelines, or rules of thumb, for constructing variograms?
a. it is best to start with isotropic variograms before proceeding to investigation of anisotropic variograms
b. estimation of variograms should begin with large tolerances, and should be decreased as needed to achieve a clearly defined structure
c. use half the maximum possible distance within a region of interest as the maximum lag distance at the which the variogram is calculated
d. at least 15 to 20 data pairs are needed for a reliable estimate of the variogram for a given lag distance
Which of the following are true statements about variogram models?
a. the spherical model is probably the most commonly used model
b. any linear combination of nugget, exponential, spherical and Gaussian models is a valid variogram model
c. the simplest model is the exponential model
d. the Gaussian model is more robust than the exponential model
To model the condition of geometric anisotropy, we have to use the same combination of linear models in both directions except with different sills.
Which of the following are reasons why we restrict the number of samples to a smaller neighborhood for estimation using kriging?
a. Because kriging requires inverting a matrix, using a large number of data points can require an excessive amount of memory and computation time requirements
b. If too many sample points are used, there is a possibility the matrix will become close to singular
c. If we use data points at large distances, we may have to extrapolate beyond the available data in the variogram model
d. Restricting the search to closer samples results in a more representative estimate, because of local variations due to a lack of stationarity in practice
e. Use of sample points farther away tend to screen sample points that are closer, reducing the accuracy of the estimation
The maximum size of the search neighborhood for kriging should be based on the range of the variogram model.
Which of the following are true statements about kriging cross validation?
a. Cross validation involves the estimation of values at unsampled locations so they can be compared with values at sampled locations
b. Cross validation can identify glaring errors in estimation, but it does not guarantee a successful kriging operation
c. "Jackknifing" is the most common version of cross validation
d. Heteroscedasticity of error variance is a desirable outcome of a cross validation exercise
Which of the following are true statements about kriging?
a. The maximum kriging error variance is the data variance
b. Simple kriging is the most popular kriging procedure
c. Kriging is a weighted average of values at sampled locations
d. Kriging weights assigned to sample values are directly proportional to the covariances among the sample points
e. Kriging weights assigned to sample values are directly proportional to the covariances between sample points and the unsampled location
Ordinary kriging overcomes which of the following problems that can occur with simple kriging?
a. the true global mean is rarely known
b. all of the other choices
c. the local mean within the search neighborhood may vary over the region of interest
d. the assumption of first-order stationarity may not be strictly valid
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.
Which of the following are true statements about cross variograms?
a. the cross covariance is symmetric.
b. the cross variogram is symmetric.
c. the cross variogram is always non-negative.
d. estimation of the cross variogram requires that both variable values be available at locations ui and ui+L.
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.
Which of the following factors, if favorable, support use of cokriging?
a. there is a physical basis for the relationship between the primary variable and covariable
b. the primary variable is considerably undersampled
c. the relationship between the primary variable and covariable is strong
d. the covariable has been used successfully in the past for estimation of the primary variable
e. the primary variable and covariable are linearly related
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.
Which of the following characterize the differences between conventional estimation and conditional simulation techniques?
a. Conventional estimation does not reproduce extreme values in the sample data, while conditional simulation is able to.
b. Conventional estimation does not provide a good estimation of local uncertainty, while conditional simulation is able to.
c. Conventional estimation preserves the spatial relationship among the estimated values while conditional simulation does not.
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.
If full cokriging is used in sequential cosimulation, the following variograms are required for modeling:
a. cross-variograms for all pairs of attributes in the original domain
b. variograms for each attribute in the transformed domain
c. cross-variograms for all pairs of attributes in the transformed domain
d. cross-variograms for all pairs of attributes for which there are dependencies in the original domain
e. cross-variograms for all pairs of attributes for which there are dependencies in the transformed domain
f. variograms for each attribute in the original domain
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.
A semivariogram model is:
A polynomial expression representing sample variance
A mathematical approximation of sample variability
A determinate trend in sample values
None of the above
Assume we have two porosity models generated with the same parameters using Gaussian and exponential models. Identify the variogram model for porosity map given in Figure (1).
Gaussian Model
Exponential Model
Assume we have two porosity models generated with the same parameters using Gaussian and exponential models. Identify the variogram model for porosity map given in Figure (2).
For the following three basic variogram models, which one has the highest growth at the origin? (i.e. the biggest slope at origin)
1
2
3
For the following three basic variogram models, which one has the lowest growth at the origin? (i.e. the smallest slope at origin)
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.
We have the following variogram model, what is C(0)?
5.87
3.14
2.73
We have the following variogram model, what is C(3.7)?
3.64
2.07
2.23
3.78
In the following drawing, we know the attributes at S1, S2, and S3. What is Z(S0)?
As shown, we know the distances in between, e.g. the distance between S1 and S2 is 20. We also know the variogram model.
21.69
21.83
22.83
23.34
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