Representing spatial uncertainty using distances and kernels

Mathematical Geosciences

Volumn 41, Issue 4, 2009, Pages 397-419

  Scheidt, Céline ^a   Caers, Jef ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Distance; Geostatistics; Kernel methods; Ranking; Uncertainty quantification

Indexed keywords

DISTANCE; GEOSTATISTICS; KERNEL METHODS; RANKING; UNCERTAINTY QUANTIFICATION;

PETROLEUM RESERVOIR ENGINEERING; PETROLEUM RESERVOIRS; PRINCIPAL COMPONENT ANALYSIS; SET THEORY; UNCERTAINTY ANALYSIS;

TRANSFER FUNCTIONS;

ALGORITHM; GEOSTATISTICS; MODELING; OIL FIELD; PRINCIPAL COMPONENT ANALYSIS; PROBABILITY; RANKING; STOCHASTICITY; TRANSFER FUNCTION; UNCERTAINTY ANALYSIS;

EID: 67349161808     PISSN: 18748961     EISSN: 18748953     Source Type: Journal    
DOI: 10.1007/s11004-008-9186-0     Document Type: Article

References (25)

1. Arpat BG (2005) Sequential Simulation with patterns. PhD dissertation, Stanford University, USA, 166 p
2. Arpat BG, Caers J (2007) Stochastic simulation with patterns. Math Geol 39(202):177-203
3. Ballin PR, Journel AG, Aziz K (1992) Prediction of uncertainty in reservoir performance forecast. JCPT 31(4):52-62
4. Batycky RP, Blunt MJ, Thiele MR (1997) A 3D field-scale streamline-based reservoir simulator. SPERE 12(4):246-254
5. Borg I, Groenen P (1997) Modern multidimensional scaling: Theory and applications. Springer, New York, 614 p
6. Bowman AW, Azzalini A (1997) Applied smoothing techniques for data analysis. Oxford University Press, London, 204 p
7. Buhmann JM (1995) Data clustering and learning. In: Arbib M (ed) The handbook of brain theory and neural networks. MIT Press, Cambridge, pp 278-281
8. Box GEP, Draper NR (1975) Robust designs. Biometrica 62(2):347-352
9. Cox TF, Cox MAA (1994) Multidimensional scaling. Chapman and Hall, London, 213 p
10. Damslet E, Hage A, Volder R (1992) Maximum information at minimum cost! A north field development study with an experimental design. JPT 44(12):1350-1356
11. Dubuisson M-P, Jain AK (1994) A modified Hausdorff distance for object matching. In: Proceeding of the international conference on pattern recognition, Jerusalem, vol A, pp 566-568
12. Gilman JR, Meng H-Z, Uland MJ, Dzurman PJ, Cosic S (2002) Statistical ranking of stochastic geomodels using streamline simulation: A field application. In: SPE annual technical conference and exhibition. SPE 77374
13. Journel A, Alabert F (1990) New method for reservoir mapping. JPT 42(2):212-218
14. Keerthi SS, Lin C-J (2003) Asymptotic behaviors of support vector machines with Gaussian kernel. Neural Comput 15(7):1667-1689
15. Manceau E, Zabalza-Mezghani I, Roggero F (2001) Use of experimental design to make decisions in an uncertain reservoir environment - from reservoir uncertainties to economic risk analysis. In: OAPEC conference, Rueil, France, 26-28 June 2001
16. McLennan JA, Deutsch CV (2005) Ranking geostatistical realizations by measures of connectivity. In: SPE/PS-CIM/CHOA, international thermal operations and heavy oil symposium, Calgary, Canada. SPE 98168-MS
17. Park K, Caers J (2007) History matching in low-dimensional connectivity-vector space. Unpublished SCRF report 20, Stanford University
18. Sarma P (2006) Efficient closed-loop optimal control of petroleum reservoirs under uncertainty. PhD dissertation, Stanford University, USA, 201 p
19. Scheidt C, Caers J (2008) A new method for uncertainty quantification using distances and kernel methods - application to a deepwater turbidite reservoir. SPE J (submitted)
20. Schöelkopf B, Smola A (2002) Learning with kernels. MIT Press, Cambridge, 664 p
21. Schöelkopf B, Smola A, Muller K-R (1998) Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput 10(5):1299-1318
22. Shawe-Taylor J, Cristianni N (2004) Kernel methods for pattern analysis. Cambridge University Press, Cambridge, 462 p
23. Shi J, Malik J (2000) Normalized-cut and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888-905
24. Suzuki S, Caers J (2008) A distance based prior model parameterization for constraining solution of spatial inverse problems. Math Geosci 40(4):445-469
25. Vapnick VN (1998) Statistical learning theory. Wiley, New York, 736 p