AMARILLO BY MORNING: DATA VISUALIZATION IN GEOSTATISTICS

William V. Harper, Otterbein College, USA wharper@otterbein.edu

Isobel Clark, Geostokos, ScotlandEnvironmental Statistics, Session 6A2

ICOTS8, Ljubljana, Slovenia11 – 16 July 2010

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Amarillo by Morning – a Haunting Country Song

Amarillo by morning, up from San Antone.Everything that I’ve got is just what I’ve got on.When that sun is high in that Texas skyI’ll be bucking it to county fair.Amarillo by morning, Amarillo I’ll be there.

They took my saddle in Houston, broke my leg in Santa Fe.

Lost my wife and a girlfriend somewhere along the way.

Well I’ll be looking for eight when they pull that gate,And I’m hoping that judge ain’t blind.Amarillo by morning, Amarillo’s on my mind.

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Amarillo, Wolfcamp Aquifer, and Nuclear Waste Repository

In the United States in 1987, the possible nuclear waste sites were reduced to: Salt bed in Texas Basalt formation in Washington state Tuff formation near Las Vegas, Nevada

Wolfcamp Aquifer underlies salt site Briny (salty) slow moving water Modeled as 2-D plane using geostatistics

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Geostatistics

Geostatistics Spatial statistics used for continuous data Each data value has a location in space Roots in Mining, not Statistics Observations close have similar values Goals of Geostatistics

Estimate spatial correlation structure Predict values at un-sampled locations

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Wolfcamp Potentiometric Data: 85 values

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Wolfcamp Initial Assessment

Higher values in Southwest, Lower in Northeast

Travel path from Deaf Smith county toward Amarillo in lower Potter County

If a breach, flow is toward Amarillo

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Kriging, Universal Kriging

Universal Kriging (combines trend, kriging) Many possible iterative steps to produce

minimum variance linear unbiased estimates Distribution Analysis, Data Transformation Trend, Isotropy/Anisotropy analysis Semi-variogram modeling of spatial variability Cross-Validation to partially validate model Kriged expected value map at un-sampled locations Kriged standard error map

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Will you be my Neighbor?

Nearest Neighbor Analysis

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Empirical Semi-variogram, Semi-variogram Cloud

2*

Empirical Semi-Variogram

1( )

2i j

hh

h x xN

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Directional Semi-variograms

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Directional Shaded Plot Semi-variograms

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Directional Semi-variograms on Regression Residuals

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Omni-directional Semi-variogram on Residuals

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Universal Kriging Potentiometric Surface

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Universal Kriging Standard Error Map