A methodology for quantifying the value of spatial information for dynamic Earth problems

  • Whitney J. Trainor-Guitton
  • Tapan Mukerji
  • Rosemary Knight
Original Paper

Abstract

We develop a methodology for assessing the value of information (VOI) from spatial data for groundwater decisions. Two sources of uncertainty are the focus of this VOI methodology: the spatial heterogeneity (how it influences the hydrogeologic response of interest) and the reliability of geophysical data (how they provide information about the spatial heterogeneity). An existing groundwater situation motivates and in turn determines the scope of this research. The objectives of this work are to (1) represent the uncertainty of the dynamic hydrogeologic response due to spatial heterogeneity, (2) provide a quantitative measure for how well a particular information reveals this heterogeneity (the uncertainty of the information) and (3) use both of these to propose a VOI workflow for spatial decisions and spatial data. The uncertainty of the hydraulic response is calculated using many Earth models that are consistent with the a priori geologic information. The information uncertainty is achieved quantitatively through Monte Carlo integration and geostatistical simulation. Two VOI results are calculated which demonstrate that a higher VOI occurs when the geophysical attribute (the data) better discriminates between geological indicators. Although geophysical data can only indirectly measure static properties that may influence the dynamic response, this transferable methodology provides a framework to estimate the value of spatial data given a particular decision scenario.

List of symbols

\( {{\theta}} \)

Geologic Input Parameter (e.g. training image)

i

Index of training images

N

Total number of training images

z

Vector of Earth parameters

t

Index of realizations

\( T_{\theta i} \)

Total number of realizations for training image i

s

Aquifer vulnerability

\( \ell \)

Surface location

a

Decision alternative

\( g_{a} \)

Decision predictor (e.g. flow simulation)

v

Value: metric to define outcome of decision

d

Synthetic data

y

Soft probability (pre-posterior)

Ρ, ρ

Electrical resistivity

Litho

Lithology

c

Decision alternative combinations

Notes

Acknowledgments

This work was possible because of the support from the Affiliates of Stanford Center for Reservoir Forecasting and Schlumberger Water Services. We thank professor Jef Caers for his early participation in this work. Esben Auken and Nikolaj Foged of the University of Århus, Denmark provided helpful insights about the TEM measurement. Thomas Nyholm and Stine Rasmussen of the Danish Ministry of the Environment provided useful information about aquifer vulnerability issues. Prepared by LLNL under Contract DE-AC52-158 07NA27344

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Whitney J. Trainor-Guitton
    • 1
  • Tapan Mukerji
    • 2
  • Rosemary Knight
    • 3
  1. 1.Lawrence Livermore National LaboratoryLivermoreUSA
  2. 2.Energy Resources EngineeringStanford UniversityStanfordUSA
  3. 3.Department of GeophysicsStanford UniversityStanfordUSA

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