High-order stochastic simulation of complex Spatially distributed natural phenomena

Mathematical Geosciences

Volumn 42, Issue 5, 2010, Pages 457-485

  Mustapha, Hussein ^a   Dimitrakopoulos, Roussos ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

Conditional sequential simulation; High order spatial cumulants; Legendre polynomials

Indexed keywords

COMPUTER SIMULATION; DATA SET; EARTH SCIENCE; GAUSSIAN METHOD; GEOMECHANICS; GEOSTATISTICS; IMAGE ANALYSIS; NUMERICAL MODEL; SPATIAL DISTRIBUTION; STOCHASTICITY; VARIOGRAM;

EID: 77954088598     PISSN: 18748961     EISSN: 18748953     Source Type: Journal    
DOI: 10.1007/s11004-010-9291-8     Document Type: Article

References (52)

1. Alabert FG (1987) Stochastic imaging of spatial distributions using hard and soft information. MSc thesis, Stanford University.
2. Arpat B, Caers J (2007) Stochastic simulation with patterns. Math Geosci 39: 177-203.
3. Bernardeau F, Colombi S, Gaztanaga E, Scoccimarro R (2002) Large-scale structure of the universe and cosmological perturbation theory. Phys Rep 367(1): 1-248.
4. Billinger DR, Rosenblatt M (1966) Asymptotic theory of kth-order spectra. In: Harris B (ed) Spectral analysis of time series. Wiley, New York, pp 189-232.
5. Boucher A (2009) Considering complex training images with search tree partitioning. Comput Geosci 35: 1151-1158.
6. Chatterjee S, Dimitrakopoulos R, Mustapha H (2009) Three-dimensional wavelet based conditional co-simulation using training image. COSMO Res Rep 3(2): 143-181.
7. Chilès JP, Delfiner P (1999) Geostatistics-modeling spatial uncertainty. Wiley, New York.
8. Chugunova TL, Hu LY (2008) Multiple point simulations constrained by continuous auxiliary data. Math Geosci 40: 133-146.
9. Daly C (2004) Higher order models using entropy, Markov random fields and sequential simulation. In: Geostatistics Banff. Springer, Berlin, pp 215-225.
10. Daniels HE (1954) Saddlepoint approximations in statistics. Ann Math Stat 25: 631-650.
11. David M (1988) Handbook of applied advanced geostatistical ore reserve estimation. Elsevier, Amsterdam.
12. Delopoulos A, Giannakis GB (1996) Cumulant based identification of noisy closed loop systems. Int J Adapt Control Signal Process 10(2/3): 303-317.
13. Dimitrakopoulos R, Mustapha H, Gloaguen E (2010) High-order statistics of spatial random fields: exploring spatial cumulants for modelling complex, non-Gaussian and non-linear phenomena. Math Geosci 42: 65-99.
14. Dimitrakopoulos R (1990) Conditional simulation of intrinsic random functions of order k. Math Geosci 22: 361-380.
15. Dimitrakopoulos R, Luo X (2004) Generalized sequential Gaussian simulation. Math Geosci 36: 567-591.
16. Edgeworth FY (1905) The law of error. Trans Camb Philos Soc 20: 113-141.
17. Edgeworth FY (1907) On the representation of a statistical frequency by a series. J R Stat Soc 70: 102-106.
18. Gaztanaga EP, Fosalba P, Elizalde E (2000) Gravitational evolution of the large-scale probability density distribution. Astrophys J 539: 522-531.
19. Goovaerts P (1998) Geostatistics for natural resources evaluation. Oxford, New York.
20. Gloaguen E, Dimitrakopoulos R (2009) Two-dimensional conditional simulations based on the wavelet decomposition of training images. Math Geol 41: 679-701.
21. Guardiano J, Srivastava RM (1993) Multivariate geostatistics: beyond bivariate moments. In: Soares A (ed) Geosatistics Tróia '92, vol 1. Kluwer, Dordrecht, pp 133-144.
22. Hille E (1926) On Laguerre's Series: First note. Proc Natl Acad Sci USA 12: 261-265.
23. Hosny KM (2007) Exact Legendre moment computation for gray level images. Pattern Recogn 40: 3597-3605.
24. Journel AG (1994) Modelling uncertainty: some conceptual thoughts. In: Dimitrakopoulos R (ed) Geostatistics for the next century. Kluwer Academic Press, Dordrecht, pp 30-43.
25. Journel AG (1997) Deterministic geostatistics: a new visit. In: Baafy E, Shofield N (eds) Geostatistics Woolongong '96. Kluwer, Dordrecht, pp 213-224.
26. Journel AG, Alabert F (1989) Non-Gaussian data expansion in the earth sciences. Terra Nova 1: 123-134.
27. Kendall MG, Stuart A (1977) The advanced theory of statistics, 4th edn, vol 1. Macmillan, New York.
28. Law AM, Kelton WD (1999) Simulation modelling and analysis. McGraw-Hill Higher Education, Singhapore.
29. Lebedev NN (1965) Special functions and their applications. Prentice-Hall Inc., New York.
30. Liao SX, Pawlak M (1996) On image analysis by moments. IEEE Trans Pattern Anal Mach Intell 18: 254-266.
31. Mao S, Journel AG (1999) Generation of a reference petrophysical and seismic 3D data set: the Stanford V reservoir. In: Stanford Center for Reservoir Forecasting Annual Meeting. Available at: http://ekofisk. stanford. edu/SCRF. html.
32. Mirowski PW, Trtzlaff DM, Davies RC, McCormick DS, Williams N, Signer C (2008) Stationary scores on training images for multipoint geostatistics. Math Geosci 41: 447-474.
33. Mustapha H, Dimitrakopoulos R (2010) A new approach for geological pattern recognition using high-order spatial cumulants. Comput Geosci 36: 313-343.
34. Nikias CL, Petropulu AP (1993) Higher-order spectra analysis: a nonlinear signal processing framework. PTR Prentice Hall, Upper Saddle River.
35. Pan J Szapudi I (2005) Conditional cumulants in a weakly non-linear regime. Mon Not R Astron Soc 361: 357-361.
36. Remy N, Boucher A, Wu J (2009) Applied geostatistics with SGeMs: a users's guide. Cambridge University Press, Cambridge.
37. Ripley BD (1987) Stochastic simulation. John Wiley & Sons, New York.
38. Rosenblatt M (1985) Stationary sequences and random fields. Birkhaüser, Boston.
39. Rubinstein R (1981) Simulation and the Monte Carlo method. John Wiley & Sons, New York.
40. Sadler B, Giannakis GB, Shamsunder S (1995) Noise subspace techniques in non-Gaussian noise using cumulants. IEEE Trans Aerosp Electron Syst 31: 1009-1018.
41. Scheidt C, Caers J (2009) Representing spatial uncertainty using distances and kernels. Math Geosci 41: 397-419.
42. Spiegel MR (1968) Mathematical handbook of formulas and tables. Schaum's outline series. McGraw-Hill Book Co., New York.
43. Strebelle S (2002) Conditional simulation of complex geological structures using multiple point statistics. Math Geosci 34: 1-22.
44. Tjelmeland H (1998) Markov random fields with higher order interactions. Scand J Stat 25: 415-433.
45. Tjelmeland H, Eidsvik J (2004) Directional metropolis: hastings updates for conditionals with nonlinear likelihoods. In: Geostatistics Banff, vol 1. Springer, Berlin, pp 95-104.
46. Volker O, Dimitrakopoulos R (2007) Simulation of wireframes and geometric features with multiple point techniques: application at Yandi Iron Ore deposit, Australia. Orebody modelling and strategic mine planning, The Australasian Institute of Mining and Metallurgy, Spectrum Series, vol 14, pp 51-60.
47. Welling M (1999) Robust series expansions for probability density estimation. Technical report, California Institute of Technology, Computational Vision Lab.
48. Wilson GA, Wragg A (1973) Numerical methods for approximating continuous probability density functions over [0,) using moments. IMA J Appl Math 12: 165-173.
49. Wu J, Boucher A, Zhang T (2008) SGeMS code for pattern simulation of continuous and categorical variables: FILTERSIM. Comput Geosci 34: 1863-1876.
50. Yap PT, Paramesran R (2005) An efficient method for the computation of Legendre moments. IEEE Trans Pattern Anal Mach Intell 27: 1996-2002.
51. Zhang F (2005) A high order cumulants based multivariate nonlinear blind source separation method source. Mach Learn J 61105-61127.
52. Zhang T, Switzer P, Journel AG (2006) Filter-based classification of training image patterns for spatial simulation. Math Geol 38: 63-80.