HPGL: Solved Problems Scripts

This document provide set of examples for HPGL scripts on "Solved Problems in Geostatistics" by O. Leuangthong, K.Daniel Khan, and Clayton V. Deutsch book.



2.3. Standartization and Probability Intervals
3.1. Basic Declustering
4.1. Central limit theorem
4.2. Bootstrap and Spatial Bootstrap
4.3. Transfer of Uncertainty
5.2. Variogram Calculation
5.3. Variogram Modeling and Volume Variance
7.2. Conditioning by Kriging
7.3. Gaussian Simulation
8.3. Indicator Simulation for Categorical Data

2.3. Standartization and Probability Intervals

Program output:

----------------------------------------------------
Probability interval is: [ 4.16014400549 , 19.8398559945 ]
----------------------------------------------------
Probability interval for standartized normal data is: [ -1.95996399863 , 1.95996399863 ]
----------------------------------------------------
Variance of standartized data in presense of corellation is: 0.154686035265
Probability interval for standartized data in presense of corellation is: [ -7.68516995924 , 7.99454202977 ]
----------------------------------------------------
Variance of data in presense of corellation is: 2.47497656424
Probability interval for data in presense of corellation is: [ -5.36487943027 , 10.3148325587 ]

3.1. Basic Declustering

Program output:

    ---------------------------------------------------

    Original data mean is:  2.28333333333

    Original data variance is:  1.39088301289

    ---------------------------------------------------

    Weights: 


    [  993.01065958   373.60679775  1290.24604696   905.17560067   697.2135955

    903.11288741   802.10095283   453.22475511  1002.18336591   432.84271247

    1409.99414493   834.1619253   1358.58995672   453.22475511   823.39636687]

    ---------------------------------------------------

    Weighted data mean is:  1.7969204512

    Weighted data variance is:  1.25755053183

    ---------------------------------------------------

4.1. Central limit theorem

a) Program output:

    ---------------------------------------------------

    One random realization mean is:  0.5501317718

    One random realization var is:  0.121800789196

    ---------------------------------------------------

    Summary mean is:  5.03416472703

    Summary variance is: 0.0790254982388

    ---------------------------------------------------
b) Histogram of random variables:

c) Histogram of summary random variables statistics:

4.2. Bootstrap and Spatial Bootstrap

a) Program output:

 ----------------------------------------------------

 Porosity mean = 8.40197517019

 Porosity mean with cell declustering = 8.20568171395

 Porosity variance with cell declustering = 1.85087882609

 Difference between means =  0.196293456243

 ----------------------------------------------------

 

 ----------------------------------------------------

 Correlation between porosity and seismic:  0.627627936802

 Weighted correlation between porosity and seismic:  0.570620708566

 ----------------------------------------------------

 Doing boostrap for poro mean and correlation with seismic data... 

 Number of random realizations:  1000

 Bootstrap calculation completed.

 ----------------------------------------------------
b) Bootstrapped correlation between porosity and collocated seismic:

c) Bootstrapped correlation between weighted porosity and collocated seismic:

d) Cross plot porosity vs seismic:

e) Distribution of bootstrapped mean for porosity:

f) Distribution of mean porosity considering spatial correlation between the data:

4.3. Transfer of Uncertainty

a) Program output: 

 NPVs result:

 -----------------------------

 P10 =  3.77887084616

 P50 =  8.51502639745

 P90 =  13.1389507745

 Probability of negative NPV =  0.012


 

 Correlated NPVs result:

 -----------------------------

 P10 =  6.17564708413

 P50 =  8.29905237775

 P90 =  10.4664660712

 Probability of negative NPV =  0.0
b) Cumulative histogram of simulated NPVs:

c) Histogram of simulated NPVs:

e) Cumulative histogram of NPVs (Correlated):

f) Histogram of NPVs (Correlated):

5.2. Variogram Calculation

a) Program output: 

 2D-Vertical semivariogram: [  0.           7.22204065  12.21773338  11.72054482  13.21637726
 15.12846851  19.08102226  23.91016388]

 Horizontal semovariogram: [  0.           7.3053236   13.54503155]



 3D-Vertical Variogram: [  0.46787289   3.67752957   6.19086933   6.27916288   6.78850794
 8.19655132   9.4901104   10.41752148  10.44062805  10.32573032
 12.14958477]
b) Experimental horizontal semivariogram:

c) Experimental vertical semivariogram:

e) Vertical semivariogram (3D):

5.3. Variogram Modeling and Volume Variance

a) Program output: 

 Vertical Variogram:

 [  0.46787289   3.67752957   6.19086933   6.27916288   6.78850794

 8.19655132   9.4901104   10.41752148  10.44062805  10.32573032

 12.14958477]


 XLagDistance:  [ 0  4  8 12 16 20 24 28 32 36 40]


 Gamma for vartical semivariogram:  [  0.           0.90357918   1.73293519   2.49416494   3.19286442

 3.83417034   4.4227972    4.96307182   5.45896673   5.91412687

 6.33189869   6.71535301   7.06730938   7.39035463   7.6868639

 7.95901632   8.20881367   8.43809128   8.64853573   8.84169388

 9.01898479   9.18171215   9.33107281   9.46816444   9.59399509

 9.70948887   9.81549644   9.91279602  10.00210285  10.08407307

 10.15931129  10.22836781  10.29175282  10.34993076  10.40332985

 10.45234203  10.49732876  10.53862     10.57651901  10.61130524]
b) Variogram modeling results in vertical direction:

7.2. Conditioning by Kriging

a) Program output:

 SK result: [-1.22333932 -1.45956635 -1.88999999 -1.20342791 -0.61605299  0.09

 -0.42059055 -0.74000001 -1.08000004 -1.01502895 -0.97937196 -0.99411529

 -1.01281166 -1.05999994 -1.00405264 -0.97334808 -0.95649707 -0.947249

 -0.9421736  -0.93599999]


 SGS result: [-1.88999999 -1.0674969  -1.06365824 -1.07050645 -0.74000001 -1.88999999

 -0.97683221 -0.92199361 -0.79168916 -0.74000001 -0.75715584 -0.74000001

 -0.93187928 -1.17170084 -1.84693933 -1.88999999 -1.88999999 -1.06650364

 -0.74000001 -0.74000001]


 Simple Kriging result: [-1.13643897 -1.11064959 -1.06365824 -1.27064908 -1.51578677 -1.88999999

 -1.36873245 -0.92199361 -0.79168916 -0.96138978 -1.05452347 -1.11227918

 -1.14602923 -1.17170084 -1.16994464 -1.16898084 -1.16845179 -1.16816151

 -1.16800225 -1.16780841]


 Error Field: [ 0.75356102 -0.04315269  0.         -0.20014262 -0.77578676  0.

 -0.39190024  0.          0.         -0.22138977 -0.29736763 -0.37227917

 -0.21414995  0.          0.67699468  0.72101915  0.7215482  -0.10165787

 -0.42800224 -0.4278084 ]


 Cond.Sim: [-0.4697783  -1.50271904 -1.88999999 -1.40357053 -1.39183974  0.09

 -0.81249082 -0.74000001 -1.08000004 -1.23641872 -1.2767396  -1.36639452

 -1.22696161 -1.05999994 -0.32705796 -0.25232893 -0.23494887 -1.0489068

 -1.37017584 -1.36380839]
b) Plots:



7.3. Gaussian Simulation

Problem 1:








Problem 2:

a) Program output: 

 Arithmetic variance: 3.23284634677

 Geometric variance: 3.26164002852

 Harmonic variance: 3.29291846535

 Point scale variance: 3.61991197546

 var_back_krigged_transformed_data: 3.82252807617

 The diff_variance between point scale and kriged values: -0.202616100712

 Sgs on arithmetic data variance: 2.6416104126

 The differential variance between point scale and simulated values: 0.978301562862

 12.9032258065 % of the data lies above the threshold

 4.0 % value of the kriged model falls above the threshold

 10.0 % value of the simulated model falls above the threshold
b) Plots:







8.3. Indicator Simulation for Categorical Data



Note, that more scripts can be added at download section.