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

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

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

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

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

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

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

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

Quo Vadis: Dreams of the Future What we need is integration of different techniques 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 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 Dialogue: if a geophysicist finds something wrong s/he should tell the system what is wrong It must automatically produce the accuracy It must automatically produce the accuracy