Svug models J. W. Jennings Introduction to Data Processing Flows with Scons and Geostatistics with Madagascar Jim Jennings and Sergey Fomel Carbonate Reservoir Characterization Research Laboratory Bureau of Economic Geology Jackson School of Geosciences The University of Texas at Austin April 20, 2007 January 2, 2019

Introduction to data processing flows with Scons two simple examples Svug models Outline J. W. Jennings Introduction to data processing flows with Scons two simple examples Variograms with Madagascar what is a variogram? how to compute a variogram with FFTs implementation in Madagascar examples Random Fields with Madagascar what is stochastic simulation? how to make random field with FFTs implementation in Madagascar examples 2 J. W. Jennings Geostatistics with Madagascar January 2, 2019

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Variogram Array Svug models J. W. Jennings January 2, 2019 8 Geostatistics with Madagascar January 2, 2019

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Variogram Computation with FFTs Svug models Variogram Computation with FFTs J. W. Jennings The trick is to think of an FFT not as an approximation to the Fourier integral transform, but as a tool for exact and efficient computation of the discrete product sum: … for all possible values of the discrete lag vector h. 10 J. W. Jennings Geostatistics with Madagascar January 2, 2019

Variogram Computation with FFTs Svug models Variogram Computation with FFTs J. W. Jennings Then, expand the variogram definition into a collection of product sums: 11 J. W. Jennings Geostatistics with Madagascar January 2, 2019

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Variogram Computation with FFTs Svug models Variogram Computation with FFTs J. W. Jennings Then, expand the variogram definition into a collection of product sums: 13 J. W. Jennings Geostatistics with Madagascar January 2, 2019

Variogram Computation with FFTs Svug models Variogram Computation with FFTs J. W. Jennings … that can be computed efficiently with FFTs: 14 J. W. Jennings Geostatistics with Madagascar January 2, 2019

Variogram Computation with FFTs Svug models Variogram Computation with FFTs J. W. Jennings … that can be computed efficiently with FFTs: Marcotte, D., 1996, Fast variogram computation with FFT, Computers & Geosciences, v 22, n 10, pp. 1175–1186. 15 J. W. Jennings Geostatistics with Madagascar January 2, 2019

Implementation in Madagascar Svug models J. W. Jennings 16 J. W. Jennings Geostatistics with Madagascar January 2, 2019

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Implementation in Madagascar Svug models J. W. Jennings 18 J. W. Jennings Geostatistics with Madagascar January 2, 2019

Example Application Svug models J. W. Jennings January 2, 2019 19 Geostatistics with Madagascar January 2, 2019

Data Array Svug models J. W. Jennings January 2, 2019 20 Geostatistics with Madagascar January 2, 2019

Indicator Array Svug models J. W. Jennings January 2, 2019 21 Geostatistics with Madagascar January 2, 2019

Pair-Count Array Svug models J. W. Jennings January 2, 2019 22 Geostatistics with Madagascar January 2, 2019

Variogram Array Svug models J. W. Jennings January 2, 2019 23 Geostatistics with Madagascar January 2, 2019

Data Array Svug models J. W. Jennings January 2, 2019 24 Geostatistics with Madagascar January 2, 2019

Data Array, Matrix Only Svug models J. W. Jennings January 2, 2019 25 Geostatistics with Madagascar January 2, 2019

Indicator Array, Matrix Only Svug models J. W. Jennings 26 J. W. Jennings Geostatistics with Madagascar January 2, 2019

Pair-Count Array, Matrix Only Svug models J. W. Jennings 27 J. W. Jennings Geostatistics with Madagascar January 2, 2019

Variogram Array, Matrix Only Svug models J. W. Jennings 28 J. W. Jennings Geostatistics with Madagascar January 2, 2019

Variogram Array Svug models J. W. Jennings January 2, 2019 29 Geostatistics with Madagascar January 2, 2019

Stochastic Simulation Svug models Stochastic Simulation J. W. Jennings Unconditional stochastic simulation in geostatistics is the process of generating a random field with a specified variogram model. Unconditional stochastic simulation is like variography in reverse. Conditional stochastic simulation makes random fields that have a specified variogram and have specified values at given control points. 30 J. W. Jennings Geostatistics with Madagascar January 2, 2019

Stochastic Gaussian Simulation Svug models J. W. Jennings 31 J. W. Jennings Geostatistics with Madagascar January 2, 2019

Stochastic Gaussian Simulation with FFTs Svug models J. W. Jennings 32 J. W. Jennings Geostatistics with Madagascar January 2, 2019

Implementation in Madagascar Svug models J. W. Jennings 33 J. W. Jennings Geostatistics with Madagascar January 2, 2019

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Example Application Svug models J. W. Jennings January 2, 2019 35 Geostatistics with Madagascar January 2, 2019

Example Application Svug models J. W. Jennings January 2, 2019 36 Geostatistics with Madagascar January 2, 2019

1D Random Field Svug models J. W. Jennings January 2, 2019 37 Geostatistics with Madagascar January 2, 2019

2D Random Field Svug models J. W. Jennings January 2, 2019 38 Geostatistics with Madagascar January 2, 2019

3D Random Field Svug models J. W. Jennings January 2, 2019 39 Geostatistics with Madagascar January 2, 2019

Deep-Water Channels with Background Noise Svug models J. W. Jennings 40 J. W. Jennings Geostatistics with Madagascar January 2, 2019