New anisotropic covariance models and estimation of anisotropic parameters based on the covariance tensor identity

Stochastic Environmental Research and Risk Assessment

Volumn 16, Issue 1, 2002, Pages 43-62

  Hristopulos, D T ^a  

^a PAPRICAN   (Canada)

Author keywords

Anisotropy; Covariance tensor; Power law; Random fields; Simulation

Indexed keywords

EID: 23044529084     PISSN: 14363240     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00477-001-0084-y     Document Type: Article

References (48)

1. Abrahamsen P (1997) A review of Gaussian random fields and correlation functions. Rapport No. 917, SAND, Norwegian Computing Center, Oslo, Norway
2. Adler RJ (1981) The Geometry of Random Fields. John Wiley & Sons, New York, NY, USA
3. Bochner S (1959) Lectures on Fourier Integrals. Princeton University Press, Princeton, NJ, USA
4. Bouchaud JP, Georges A (1990) Anomalous diffusion in disordered media, Statistical mechanics, models and physical applications. Phys. Rep. 195: 127-293
5. Chaikin PM, Lubensky TC (1995) Principles of Condensed Matter Physics. Cambridge University Press, New York, NY, USA
6. Choy D, Chen S (2000) Clipped random wave analysis of isomeric lamellar microemulsions. Phys. Rev. E 61(4): 4148-4155
7. Christakos G (1992) Random Field Models in Earth Sciences. Academic Press, San Diego, CA, USA
8. Christakos G (2000) Modern Spatiotemporal Geostatistics. Oxford University Press, New York, NY, USA
9. Christakos G, Hristopulos DT (1998) Spatiotemporal Environmental Health Modelling: A Tractatus Stochasticus. Kluwer Academic Publishers, Boston, MA, USA
10. Christakos G, Hristopulos DT, Bogaert P (2000) On the physical geometry concept at the basis of space/time geostatistical hydrology. Adv. Water Resour. 23(8): 799-810
11. Cushman JH (1984) On unifying the concepts of scale, instrumentation and stochastics in the development of multiphase transport theory. Water Resour. Res. 20(11): 1668-1676
12. Cushman JH (1986) On measurement, scale and scaling. Water Resour. Res. 22(2): 129-134
13. Drummond IT, Horgan RR (1987) The effective permeability of a random medium. J. Phys. A 20: 4661-4672
14. Di Federico V, Neuman SP (1997) Scaling of random fields by means of truncated power variograms and associated spectra. Water Resour. Res. 33(5): 1075-1085
15. Di Federico V, Neuman SP (1998) Flow in multiscale log-conductivity fields with truncated power variograms. Water Resour. Res. 34(5): 975-987
16. Erikson M, Siska P (2000) Understanding anisotropy computations. Math. Geol. 32(6): 683-700
17. Feder J (1988) Fractals. Plenum Press, New York, NY, USA
18. Gelhar LW (1993) Stochastic Subsurface Hydrology. Prentice Hall, Englewood Cliffs, NJ, USA
19. Gradshteyn IS, Ryzhik IM (1994) Tables of Integrals, Series, and Products (5th edn). Academic Press, New York, NY, USA
20. Henriette A, Jacquin CG, Adler PM (1989) The effective permeability of heterogeneous porous media. PhysicoCh. Hydrodyn. 11(1): 63-79
21. Isichenko MB (1992) Percolation, statistical topography, and transport in porous media. Rev. Mod. Phys. 64(4): 961-1043
22. Jinnai H, Nishikawa Y, Spontak SD, Smith RJ, Agard DA, Hashimoto T (2000a) Direct measurement of interfacial curvature distributions in a bicontinuous block copolymer morphology. Phys. Rev. Let. 84(3): 518-521
23. Jinnai H, Nishikawa Y, Chen S, Koizumi S, Hashimoto T (2000b) Morphological characterization of bicontinuous structures in polymer blends and microemulsions by the inverse-clipping method in the context of the clipped-random-wave model. Phys. Rev. E 61(6): 6773-6780
24. Kikkinides ES, Burganos VN (1999) Structural and flow properties of binary media generated by fractional Brownian motion models. Phys. Rev. E 59(6): 7185-7194
25. Kikkinides ES, Burganos VN (2000) "Permeation properties of three-dimensional self-affine reconstructions of porous materials. Phys. Rev. E 62(5): 6906-6915
26. Kitanidis PK (1983) Statistical estimation of polynomial generalized covariance functions and hydrologic applications. Water Resour. Res. 19: 909-921
27. Koch DL, Brady JF (1988) Anomalous diffusion in heterogeneous porous media. Phys. Fluids A 31(1): 965-973
28. Le Ravalec M, Noettinger B, Hu LY (2000) The FFT Moving Average (FFT-MA) Generator: an efficient numerical method for generating and conditioning Gaussian simulations. Math. Geol. 32(6): 701-724
29. Liu HH, Molz FJ (1997) Comment on 'Evidence for non-Gaussian scaling behavior in heterogeneous sedimentary formations' by S. Painter. Water Resour. Res. 33(4): 907-908
30. Molz FJ, Liu HH, Szulga J (1997) Fractional Brownian motion and fractional Gaussian noise in subsurface hydrology: a review, presentation of fundamental properties, and extensions. Water Resour. Res. 33(10): 2273-2286
31. Lovejoy S, Schertzer D (1995) Multifractals and rain. In Kundzevicz AW (ed) New Uncertainty Concepts in Hydrology and Hydrological Modeling, pp. 61-103. Cambridge University Press, New York, NY, USA
32. Makse HA, Davies GW, Havlin S, Ivanov PC, King PR, Stanley HE (1996a) Long-range correlations in permeability fluctuations in porous rock. Phys. Rev. E 54(4): 3129-3134
33. Makse HA, Havlin S, Schwartz M, Stanley HE (1996b) Method for generating long-range correlations for large systems. Phys. Rev. E 53(5): 5445-5449
34. Mandelbrot BB (1982) The Fractal Geometry of Nature. Freeman and Company, New York, NY, USA
35. Mandelbrot BB, Van Ness JW (1968) Fractional Brownian motions, fractional noises and applications. SIAM Review 10(4): 422-437
36. Menadbe M, Seed A, Harris D, Austin G (1999) Multiaffine random field model of rainfall. Water Resour. Res. 35(2): 509-514
37. Neuman SP (1990) Universal scaling of hydraulic conductivities and dispersivities in geologic media. Water Resour. Res. 26(8): 1749-1758
38. Neuman SP (1994) Generalized scaling of permeabilities, validation and effect of support scale. Geoph. Rev. Let. 21(5): 349-352
39. Olea RA (1999) Geostatistics for Engineers and Earth Scientists. Kluwer Academic Publishers, Boston, MA, USA
40. Painter S (1996) Evidence for non-Gaussian scaling behavior in heterogeneous sedimentary formations. Water Resour. Res. 32(5): 1323-1332
41. Provatas N, Alava MJ, Ala-Nissila T (1996) Density correlations in paper. Phys. Rev. E 54(1): R36-R38
42. Press WH, Flannery BP, Teukolsky SA, Vettering WT (1986) Numerical Recipes. Cambridge University Press, New York, NY, USA
43. Schertzer D, Lovejoy S (1987) Physically based rain and cloud modeling by anisotropic, multiplicative turbulent cascades. J. Geophys. Res. 92: 9692-9714
44. Schoenberg IJ (1938) Metric spaces and positive definite functions. Trans. Amer. Math. Soc. 44(3): 522-536
45. Swerling P (1962) Statistical properties of the contours of random surfaces. IRE Trans. Infor. Th. IT-8: 315-321
46. Veneziano D, Bras RL, Niemann JD (1996) Nonlinearity and self-similarity of rainfall in time and a stochastic model. J. Geophys. Res. Atmos. 101 (D21): 26371-26392
47. Wallace A (1968) Differential Topology. Benjamin/Cummings, Reading, MA, USA
48. Yaglom AM (1987) Correlation Theory of Stationary and Related Random Functions I. Springer Series in Statistics, Springer, New York, NY, USA