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Quantitative Information Fusion for Hydrological Sciences pp 69–103Cite as

Trajectory-Based Methods for Modeling and Characterization

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 79))

Given the increasing data flow associated with characterizing and modeling natural hydrological systems there is a need for efficient data analysis tools. New experimental techniques such as multi-level samplers and crosswell pressure tomography produce extensive sets of hydrologic observations. Furthermore, integrating geophysical and remote sensing data can produce a massive array of measurements. Relating these data to flow properties in the subsurface and using them for characterization can be a computational challenge. In this chapter I discuss trajectory-based methods for integrating transient head, tracer, multi-phase flow, and associated geophysical data. The techniques, which are similar to ray methods in geophysics, are motivated by two methodologies outlined in this chapter. The first methodology, implemented in the frequency-domain, is along the lines of methods associated with elastic and electromagnetic wave propagation [26, 28, 30]. The second approach, the method of multiple scales is somewhat more general, applicable to nonlinear and diffusive propagation, and has been applied to gas dynamics and shock propagation [2]. The techniques described have connections with other methods used in the modeling of fluid flow. For example asymptotic approaches have been used to describe solute transport in the limit of long times, giving for example traveling wave solutions [19, 22, 46, 47].

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References

  1. K. Aki and P. G. Richards. Quantitative Seismology. Freeman and Sons, 1980.

    Google Scholar 

  2. A. M. Anile, J. K. Hunter, P. Pantano, and G. Russo. Ray Methods for Nonlinear Waves in Fluids and Plasmas. Longman Scientific and Technical, 1993.

    Google Scholar 

  3. J. Bear. Dynamics of Fluids in Porous Media. Dover Publications, 1972.

    Google Scholar 

  4. R. N. Bracewell. The Fourier Transform and Its Applications. McGraw-Hill, New York, 1978.

    MATH  Google Scholar 

  5. J. Carrera. State of the art of the inverse problem applied to the flow and solute transport problems. In Groundwater Flow and Quality Modeling, pages 549–585. NATO ASI Ser., 1987.

    Google Scholar 

  6. H. S. Carslaw and J. C. Jaeger. Conduction of Heat in Solids. Oxford University Press, Oxford, 1959.

    Google Scholar 

  7. H. Cheng, A. Datta-Gupta, and Z. He. A comparison of travel-time and amplitude matching for field-scale production data integration: Sensitivity, non-linearity, and practical implications. SPE Annual Meeting, 84570:1–15, 2003.

    Google Scholar 

  8. R. Courant and D. Hilbert. Methods of Mathematical Physics. Interscience, New York, 1962.

    MATH  Google Scholar 

  9. M. J. Crane and M. J. Blunt. Streamline-based simulation of solute transport. Water Resour. Res., 35:3061–3078, 1999.

    Article  Google Scholar 

  10. A. Datta-Gupta and M. J. King. A semianalytic approach to tracer flow modeling in heterogeneous permeable media. Advan. Water Resour., 18:9–24, 1995.

    Article  Google Scholar 

  11. A. Datta-Gupta, L. W. Lake, G. A. Pope, K. Sepehrnoori, and M. J. King. High-resolution monotonic schemes for reservoir fluid flow simulation. In Situ, 15:289–317, 1991.

    Google Scholar 

  12. A. Datta-Gupta, D. W. Vasco, J. C. S. Long, P. S. D’Onfro, and W. D. Rizer. Detailed characterization of a fractured limestone formation by use of stochastic inverse approaches. SPE Form. Eval., 10:133–140, 1995.

    Google Scholar 

  13. G. de Marsily. Quantitative Hydrogeology. Academic Press, San Diego, 1986.

    Google Scholar 

  14. S. N. Domenico. Effect of water saturation on seismic reflectivity of sand reservoirs encased in shale. Geophysics, 39:759–769, 1974.

    Article  Google Scholar 

  15. F. G. Friedlander and J. B. Keller. Asymptotic expansions of solutions of (∇2 + k 2)u = 0. Comm. Pure Appl. Math., 8:387, 1955.

    Article  MATH  MathSciNet  Google Scholar 

  16. C. S. Gardner and G. K. Morikawa. Similarity in the asymptotic behavior of collision-free hydromagnetic waves and water waves. Courant Inst. Math. Sci. Rep., 90:9082, 1960.

    Google Scholar 

  17. F. Gassmann. Elastic waves through a packing of spheres. Geophysics, 16:673–685, 1951.

    Article  Google Scholar 

  18. L. W. Gelhar and M. A. Collins. General analysis of longitudinal dispersion in nonuniform flow. Water Resour. Res., pages 1511–1521, 1971.

    Google Scholar 

  19. R. E. Grundy, C. J. van Duijn, and Dawson C. N. Asymptotic profiles with finite mass in one-dimensional contaminant transport through porous media: The fast reaction case. Q. J. Mech. Appl. Math., 47:69–106, 1994.

    Article  MATH  Google Scholar 

  20. Z. He, A. Datta-Gupta, and D. W. Vasco. Rapid inverse modeling of pressure interference tests using trajectory-based traveltime and amplitude sensitivities. Water Resources Research, 42:1–15, 2006.

    Google Scholar 

  21. G. M. Hoversten, R. Gritto, J. Washbourne, and T. Daley. Pressure and fluid saturation prediction in a multicomponent reservoir using combined seismic and electromagnetic imaging. Geophysics, 68:1580–1591, 2003.

    Article  Google Scholar 

  22. U. Jaekel, A. Georgescu, and H. Vereecken. Asymptotic analysis of nonlinear equilibrium solute transport in porous media. Water Resour. Res., 32:3093–3098, 1996.

    Article  Google Scholar 

  23. K. Karasaki, B. Freifeld, A. Cohen, K. Grossenbacher, P. Cook, and D. Vasco. A multidisciplinary fractured rock characterization study at the Raymond field site, Raymond, California. J. Hydrol., 236:17–34, 2000.

    Article  Google Scholar 

  24. J. B. Keller and R. M. Lewis. Asymptotic methods for partial differential equations: The reduced wave equation, and Maxwell’s equations. In J. P. Keller, D. W. McLaughlin, and G. C. Papanicolaou, editors, Surveys in Applied Mathematics, volume 1, chapter 1. Plenum Press, 1995.

    Google Scholar 

  25. M. J. King and A. Datta-Gupta. Streamline simulation: A current perspective. In Situ, 22:91–140, 1998.

    Google Scholar 

  26. M. Kline and I. W. Kay. Electromagnetic Theory and Geometrical Optics. Robert E. Krieger Publishing, Huntington, NY, 1979.

    Google Scholar 

  27. S. Korsunsky. Nonlinear Waves in Dispersive and Dissipative Systems with Coupled Fields. Addison Wesley Longman Ltd., Essex, 1997.

    MATH  Google Scholar 

  28. Y. A. Kravtsov and Y. I. Orlov. Geometrical Optics of Inhomogeneous Media. Springer-Verlag, 1990.

    Google Scholar 

  29. M. Landro. Discrimination between pressure and fluid saturation changes from time-lapse seismic data. Geophysics, 66:836–844, 2001.

    Article  Google Scholar 

  30. R. K. Luneburg. Mathematical Theory of Optics. University of California Press, Berkeley, 1966.

    Google Scholar 

  31. T. N. Narasimhan and P. A. Witherspoon. An integrated finite difference method for analyzing fluid flow in porous media. Water Resour. Res., 12:57–64, 1976.

    Article  Google Scholar 

  32. B. Noble and J. W. Daniel. Applied Linear Algebra. Prentice-Hall, Englewood Cliffs, NJ, 1977.

    MATH  Google Scholar 

  33. A. Nur. Four-dimensional seismology and (true) direct detection of hydrocarbon: The petrophysical basis. The Leading Edge, 8:30–36, 1989.

    Article  Google Scholar 

  34. C. C. Paige and M. A. Saunders. LSQR: An algorithm for sparse linear equations and sparse linear systems. ACM Trans. Math. Software, 8:195–209, 1982.

    Article  MathSciNet  Google Scholar 

  35. R. L. Parker. Geophysical Inverse Theory. Princeton University Press, Princeton, 1994.

    MATH  Google Scholar 

  36. D. W. Peaceman. Fundamentals of Numerical Reservoir Simulation. Elsevier Scientific Publishing, 1977.

    Google Scholar 

  37. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes. Cambridge University Press, Cambridge, 1992.

    Google Scholar 

  38. K. Pruess, C. Oldenburg, and G. Moridis. Tough2 user’s guide, version 2.0. LBNL Report, Berkeley, 43134, 1999.

    Google Scholar 

  39. J. R. Rice and M. P. Cleary. Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Rev. Geophys. Space. Phys., 14:227–241, 1976.

    Article  Google Scholar 

  40. P. Segall. Stress and subsidence resulting from subsurface fluid withdrawal in the epicentral region of the 1983 Coalinga earthquake. J. Geophys. Res., 90:6801–6816, 1985.

    Article  Google Scholar 

  41. J. A. Sethian. Level Set and Fast Marching Methods. Cambridge University Press, Cambridge, 1999.

    MATH  Google Scholar 

  42. N.-Z. Sun and W.-G. Yeh. Coupled inverse problems in groundwater modeling, 1, sensitivity analysis and parameter identification. Water Resour. Res., 26:2507–2525, 1990.

    Google Scholar 

  43. T. Taniuti and Nishihara K. Nonlinear Waves. Pitman Publishing Inc., Marshfield, MA, 1983.

    MATH  Google Scholar 

  44. A. Tarantola. Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Elsevier Sci., 1987.

    Google Scholar 

  45. A. Tura and D. E. Lumley. Estimating pressure and saturation changes from time-lapse avo data. 61st Ann. Conf. Eur. Assoc. Geosci. Eng., Extended Abstracts:1–38, 1999.

    Google Scholar 

  46. S. E. van der Zee. Analytical traveling wave solutions for transport with nonlinear and nonequilibrium adsorption. Water Resour. Res., 26:2563–2578, 1990.

    Google Scholar 

  47. C. J. van Duijn and P. Knabner. Traveling waves in the transport of reactive solutes through porous media: Adsorption and binary ion exchange, 1. Trans. Porous. Media, 8:167–194, 1992.

    Article  Google Scholar 

  48. D. W. Vasco, S. Yoon, and A. Datta-Gupta. Integrating dynamic data into high-resolution reservoir models using streamline-based analytic sensitivity coefficients. SPE Journal, 4:389–399, 1999.

    Article  Google Scholar 

  49. D. W. Vasco. An asymptotic solution for two-phase flow in the presence of capillary forces. Water Resources Research, 40:W12407, 2004.

    Article  Google Scholar 

  50. D. W. Vasco. Estimation of flow properties using surface deformation and head data: A trajectory-based approach. Water Resources Research, 40:1–14, 2004.

    Google Scholar 

  51. D. W. Vasco. Trajectory-based modeling of broadband electromagnetic wavefields. Geophysical Journal International, 168:949–963, 2007.

    Article  Google Scholar 

  52. D. W. Vasco and A. Datta-Gupta. Asymptotic solutions for solute transport: A formalism for tracer tomography. Water Resources Research, 35:1–16, 1999.

    Article  Google Scholar 

  53. D. W. Vasco and A. Datta-Gupta. Asymptotics, saturation fronts, and high resolution reservoir characterization. Transport in Porous Media, 42:315–350, 2001.

    Article  MathSciNet  Google Scholar 

  54. D. W. Vasco, A. Datta-Gupta, R. Behrens, P. Condon, and J. Rickett. Seismic imaging of reservoir flow properties: Time-lapse amplitude changes. Geophsics, 69:1425–1442, 2004.

    Article  Google Scholar 

  55. D. W. Vasco and S. Finsterle. Numerical trajectory calculations for the efficient inversion of transient flow and tracer observations. Water Resources Research, 40:W01507, 2004.

    Article  Google Scholar 

  56. D. W. Vasco, K. Karasaki, and H. Keers. Estimation of reservoir properties using transient pressure: An asymptotic approach. Water Resources Research, 36:3447–3465, 2000.

    Article  Google Scholar 

  57. D. W. Vasco, K. Karasaki, and K. Kishida. A coupled inversion of pressure and surface displacement. Water Resources Research, 37:3071–3089, 2001.

    Article  Google Scholar 

  58. J. Virieux, C. Flores-Luna, and D. Gibert. Asymptotic theory for diffusive electromagnetic imaging. Geophys. J. Int., 119:857–868, 1994.

    Article  Google Scholar 

  59. G. B. Whitham. Linear and Nonlinear Waves. Wiley, New York, 1974.

    MATH  Google Scholar 

  60. W.-G. Yeh. Review of parameter identification procedures in groundwater hydrology: The inverse problem. Water Resour. Res., 22:95–108, 1986.

    Article  Google Scholar 

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Authors and Affiliations

  1. Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA

    D. W. Vasco

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  1. D. W. Vasco
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Editors and Affiliations

  1. Simula Research Laboratory, 134, 1325, Lysaker, Norway

    Xing Cai

  2. Department of Informatics, University of Oslo, 1080 Blindern, 0316, Oslo, Norway

    Xing Cai

  3. Department of Hydrology and Water Resources, The University of Arizona, Tucson, Arizona, 85721, USA

    T. -C. Jim Yeh

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Vasco, D.W. (2008). Trajectory-Based Methods for Modeling and Characterization. In: Cai, X., Yeh, T.C.J. (eds) Quantitative Information Fusion for Hydrological Sciences. Studies in Computational Intelligence, vol 79. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75384-1_4

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  • DOI: https://doi.org/10.1007/978-3-540-75384-1_4

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