1. Algorithms for Geoinformatics: Where Do We Come From? What Are We? Where Are We Going? Vladik Kreinovich University of Texas at El Paso

2. Algorithms for Geoinformatics We start with measured data (gravity etc.) Preliminary data processing (duplicates, outliers, merging) Inversion Uncertainty estimation Fusion of several inversion results Ideally: joint inversion

3. 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)

4. 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

5. 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

6. New Approaches to Inversion For non-physical profiles, least square errors are small, but individual large [ ] Piece-wise smoothness instead of smoothness Geophysical constraints: [ ] and fuzzy Faster shortest-path-type algorithms Using geometric symmetries (R. Keller)

7. 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 sesmic and gravity data w/o well known wells, use wells results as benchmarks for different fusion techniques

8. 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)

9. 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