Algorithms for Geoinformatics: Where Do We Come From? What Are We? Where Are We Going?

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Algorithms for GeoinformaticsWhere Do We Come
From? What Are We? Where Are We Going?

• Vladik Kreinovich
• University of Texas at El Paso

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Algorithms for Geoinformatics

• We start with measured data (gravity,
  traveltimes, etc.)
• Preliminary data processing (duplicates,
  outliers, merging)
• Inversion
• Uncertainty estimation
• Fusion of several inversion results
• Ideally, joint inversion

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Preliminary Data Processing

• This was our main focus so far
• Detecting outliers (Q. Wen, J. Beck) algorithms,
  results for gravity data
• Detecting duplicates (R. Torres) algorithms,
  results for gravity data
• Registering multi-spectral images
  (R. Araiza)

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Inversion Problems

• Takes too long many guesses are needed before
  success
• Does not take geological knowledge into
  consideration
• The resulting values are approximate, but what is
  the accuracy?
• Impossible to take other data into account

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Estimating Inversion Uncertainty

• Preliminary results reasonable (D. Doser,
• M. Baker)
• In general, results qualitatively reasonable but
  quantitatively wrong (M. Averill, K. Miller,
• J. Beck)
• Problem we do not take geophysical knowledge
  into consideration
• Solution take this knowledge into account

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New Approaches to Inversion

• For geophysically unreasobale profiles, least
  square errors are small, but individual large
  
• Piece-wise smoothness instead of smoothness
• Geophysical constraints and fuzzy
• Faster shortest-path-type algorithms
• Use the geologically simplest (symmetrical) model
  (R. Keller)

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Data Fusion

• Successful, e.g., in earthquake localization
• Problem fusion is very problem-specific
• Solution select fusion techniques that are
  optimal for different types of data
• Approach take seismic and gravity data with
  wells, use wells results as benchmarks for
  different fusion techniques

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Uncertainty Revisited

• What is the best way to visualize uncertainty (R.
  Arrowsmith, J. Beck)?
• How to describe expert uncertainty?
• How to describe uncertainty of the interface
  rules (B. Ludascher, M. Ceberio, E. Saad)?
• Probabilistic, uncertainty (I. Zaslasky)
• Use experience of astronomers (D. Bizyaev)

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Quo Vadis Dreams of the Future

• What we need is integration of different
  techniques
• We need joint inversion methods that would take
  all the data and incorporate all the geophysical
  knowledge, formal informal
• Dialogue if a geophysicist finds something wrong
  s/he should tell the system what is wrong
• It must automatically produce the accuracy