A Kalman filter powered by H2 -matrices for quasi-continuous data assimilation problems

Water Resources Research

Volumn 50, Issue 5, 2014, Pages 3734-3749

  Li, Judith Yue ^a   Ambikasaran, Sivaram ^a   Darve, Eric F ^a   Kitanidis, Peter K ^a,b  

^a Stanford University   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

data assimilation; large scale problems; numerical linear algebra; stochastic inverse modeling; subsurface monitoring; time series analysis

Indexed keywords

CARBON DIOXIDE; DATA PROCESSING; INVERSE PROBLEMS; KALMAN FILTERS; LINEAR ALGEBRA; RANDOM PROCESSES; STOCHASTIC SYSTEMS; TIME SERIES ANALYSIS; WATER INJECTION;

DATA ASSIMILATION; LARGE-SCALE PROBLEM; NUMERICAL LINEAR ALGEBRA; STOCHASTIC INVERSE MODELING; SUBSURFACE MONITORING;

COST REDUCTION;

DATA ASSIMILATION; FLUID FLOW; IMAGE RESOLUTION; INVERSE ANALYSIS; KALMAN FILTER; PLUME; STOCHASTICITY; SUBSURFACE FLOW; TIME SERIES;

EID: 84902368701     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/2013WR014607     Document Type: Article

References (57)

1. Ajo-Franklin, J. B., (2009), Optimal experiment design for time-lapse traveltime tomography, Geophysics, 74 (4), Q27-Q40.
2. Ambikasaran, S., and, E. Darve, (2013), An O (N log â?¡ N) fast direct solver for partial hierarchically semi-separable matrices, J. Sci. Comput., 57 (3), 1-25.
3. Ambikasaran, S., J. Li, E. Darve, and, P. K. Kitanidis, (2013a), Large-scale stochastic linear inversion using hierarchical matrices, Comput. Geosci., 17, 913-927.
4. Ambikasaran, S., A. K. Saibaba, E. Darve, and, P. K. Kitanidis, (2013b), Fast algorithms for Bayesian inversion, in The IMA Volumes in Mathematics and its Applications, vol. 156, Springer, New York.
5. Anderson, J. L., (2001), An ensemble adjustment Kalman filter for data assimilation, Mon. Weather Rev., 129 (12), 2884-2903. (Pubitemid 34004796)
6. Anderson, J. L., (2007), Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter, Physica D, 230 (1), 99-111. (Pubitemid 46776901)
7. Anderson, B., and, J. Moore, (1979), Optimal Filtering, vol. 11, Prentice Hall, Englewood Cliffs, N. J.
8. Arogunmati, A., and, J. M. Harris, (2009), An approach for quasi-continuous time-lapse seismic monitoring with sparse data, in 79th Annual Meeting and International Exposition, Curran Assoc., Inc., New York.
9. Bebendorf, M., (2000), Approximation of boundary element matrices, Numer. Math., 86 (4), 565-589.
10. Bebendorf, M., (2008), Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems, vol. 63, Springer, New York.
11. Benson, S., (2006), Monitoring carbon dioxide sequestration in deep geological formations for inventory verification and carbon credits, in Annual Technical Conference and Exhibition, Soc. of Pet. Eng., Richardson, Tex.
12. Bishop, C. H., B. J. Etherton, and, S. J. Majumdar, (2001), Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects, Mon. Weather Rev., 129 (3), 420-436. (Pubitemid 32418366)
13. Börm, S., L. Grasedyck, and, W. Hackbusch, (2003a), Introduction to hierarchical matrices with applications, Eng. Anal. Boundary Elem., 27 (5), 405-422.
14. Börm, S., L. Grasedyck, and, W. Hackbusch, (2003b), Hierarchical matrices, Lecture Notes, 21, Max Planck Institute for Mathematics in the Sciences, Leipzig.
15. Burgers, G., P. van Leeuwen, and, G. Evensen, (1998), Analysis scheme in the ensemble Kalman filter, Mon. Weather Rev., 126, 1719-1724. (Pubitemid 128597660)
16. Chandrasekaran, S., M. Gu, and, T. Pals, (2006a), A fast ULV decomposition solver for hierarchically semiseparable representations, SIAM J. Matrix Anal. Appl., 28 (3), 603-622. (Pubitemid 47109352)
17. Chandrasekaran, S., P. Dewilde, M. Gu, W. Lyons, and, T. Pals, (2006b), A fast solver for HSS representations via sparse matrices, SIAM J. Matrix Anal. Appl., 29 (1), 67-81. (Pubitemid 351269885)
18. Daily, W., A. Ramirez, D. LaBrecque, and, J. Nitao, (1992), Electrical resistivity tomography of vadose water movement, Water Resour. Res., 28 (5), 1429-1442. (Pubitemid 23372229)
19. Daley, T., R. Solbau, J. Ajo-Franklin, and, S. Benson, (2007), Continuous active-source seismic monitoring of injection in a brine aquifer, Geophysics, 72 (5), A57-A61. (Pubitemid 47382164)
20. Evensen, G., (1994), Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99, 10,143-10,162.
21. Evensen, G., (2004), Sampling strategies and square root analysis schemes for the EnKF, Ocean Dyn., 54 (6), 539-560. (Pubitemid 40003080)
22. Fahimuddin, A., S. Aanonsen, and, J.-A. Skjervheim, (2010), Ensemble based 4D seismic history matching: Integration of different levels and types of seismic data, in EUROPEC/EAGE Annual Conference and Exhibition, Soc. of Pet. Eng., Richardson, Tex.
23. Fong, W., and, E. Darve, (2009), The black-box fast multipole method, J. Comput. Phys., 228 (23), 8712-8725.
24. Fritz, J., I. Neuweiler, and, W. Nowak, (2009), Application of FFT-based algorithms for large-scale universal kriging problems, Math. Geosci., 41 (5), 509-533.
25. Fukumori, I., and, P. Malanotte-Rizzoli, (1995), An approximate Kalman filter for ocean data assimilation: An example with an idealized gulf stream model, J. Geophys. Res., 100, 6777-6793.
26. Goreinov, S. A., E. E. Tyrtyshnikov, and, N. L. Zamarashkin, (1997), A theory of pseudoskeleton approximations, Linear Algebra Appl., 261 (1), 1-21. (Pubitemid 127380509)
27. Greengard, L., and, V. Rokhlin, (1987), A fast algorithm for particle simulations, J. Comput. Phys., 73 (2), 325-348.
28. Guivant, J. E., and, E. M. Nebot, (2001), Optimization of the simultaneous localization and map-building algorithm for real-time implementation, IEEE Trans. Robotics Autom., 17 (3), 242-257. (Pubitemid 32829732)
29. Hackbusch, W., (1999), A sparse matrix arithmetic based on H -matrices. Part I: Introduction to H -matrices, Computing, 62 (2), 89-108.
30. Hackbusch, W., and, B. Khoromskij, (2000), A sparse H -matrix arithmetic. Part II: Application to multi-dimensional problems, Computing, 64 (1), 21-47.
31. Hamill, T., J. Whitaker, and, C. Snyder, (2001), Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter, Mon. Weather Rev., 129 (11), 2776-2790. (Pubitemid 33079980)
32. Houtekamer, P., and, H. Mitchell, (1998), Data assimilation using an ensemble Kalman filter technique, Mon. Weather Rev., 126 (3), 796-811. (Pubitemid 128581567)
33. Houtekamer, P., and, H. Mitchell, (2001), A sequential ensemble Kalman filter for atmospheric data assimilation, Mon. Weather Rev., 129, 123-137. (Pubitemid 32180439)
34. Hubbard, S., J. Chen, J. Peterson, E. Majer, K. Williams, D. Swift, B. Mailloux, and, Y. Rubin, (2001), Hydrogeological characterization of the south oyster bacterial transport site using geophysical data, Water Resour. Res., 37, 2431-2456. (Pubitemid 32908195)
35. Kalman, R., (1960), A new approach to linear filtering and prediction problems, J. Basic Eng., 82 (1), 35-45.
36. Kepert, J. D., (2004), On ensemble representation of the observation-error covariance in the ensemble Kalman filter, Ocean Dyn., 54 (6), 561-569. (Pubitemid 40003081)
37. Kim, J., M. Yi, S. Park, and, J. Kim, (2009), 4-D inversion of DC resistivity monitoring data acquired over a dynamically changing earth model, J. Appl. Geophys., 68 (4), 522-532.
38. Kitanidis, P. K., (1983), Statistical estimation of polynomial generalized covariance functions and hydrologic applications, Water Resour. Res., 19, 909-921. (Pubitemid 15253093)
39. Kitanidis, P. K., (1993), Generalized covariance functions in estimation, Math. Geol., 25 (5), 525-540. (Pubitemid 23394845)
40. Kitanidis, P., (1997), Introduction to Geostatistics: Applications in Hydrogeology, Cambridge Univ. Press, Cambridge, U. K.
41. Kitanidis, P. K., (1999), Generalized covariance functions associated with the Laplace equation and their use in interpolation and inverse problems, Water Resour. Res., 35 (5), 1361-1367. (Pubitemid 29207972)
42. 2 injection, Leading Edge, 16 (9), 1300-1308.
43. Martinsson, P.-G., and, V. Rokhlin, (2005), A fast direct solver for boundary integral equations in two dimensions, J. Comput. Phys., 205 (1), 1-23.
44. Nenna, V., A. Pidlisecky, and, R. Knight, (2011), Application of an extended Kalman filter approach to inversion of time-lapse electrical resistivity imaging data for monitoring recharge, Water Resour. Res., 47, W10525, doi: 10.1029/2010WR010120.
45. Neumaier, A., (1998), Solving ill-conditioned and singular linear systems: A tutorial on regularization, SIAM Rev., 40 (3), 636-666. (Pubitemid 128619822)
46. Nowak, W., S. Tenkleve, and, O. Cirpka, (2003), Efficient computation of linearized cross-covariance and auto-covariance matrices of interdependent quantities, Math. Geol., 35 (1), 53-66. (Pubitemid 38149279)
47. Pnevmatikakis, E. A., K. R. Rad, J. Huggins, and, L. Paninski, (2013), Fast Kalman filtering and forward-backward smoothing via a low-rank perturbative approach, J. Comput. Graph. Stat., doi: 10.1080/10618600.2012.760461.
48. Pruess, K., (1991), TOUGH2: A general-purpose numerical simulator for multiphase fluid and heat flow, NASA STI/Recon Tech. Rep. 92(14316), Greenbelt, Md.
49. Quan, Y., and, J. Harris, (2008), Stochastic seismic inversion using both waveform and traveltime data and its application to time-lapse monitoring, paper presented at 2008 Annual Meeting, Soc. of Explor. Geophys., Las Vegas, Nev.
50. Rjasanow, S., (2002), Adaptive cross approximation of dense matrices, paper presented at International Association Boundary Element Methods Conference, Austin, Tex.
51. Saibaba, A., S. Ambikasaran, J. Li, P. Kitanidis, and, E. Darve, (2012), Application of hierarchical matrices to linear inverse problems in geostatistics, Oil Gas Sci. Technol., 67 (5), 857-875, doi: 10.2516/ogst/ 2012064.
52. Starks, T., and, J. Fang, (1982), On the estimation of the generalized covariance function, J. Int. Assoc. Math. Geol., 14 (1), 57-64.
53. Tippett, M. K., J. L. Anderson, C. H. Bishop, T. M. Hamill, and, J. S. Whitaker, (2003), Ensemble square root filters, Mon. Weather Rev., 131 (7), 1485-1490. (Pubitemid 36953823)
54. Tuan Pham, D., J. Verron, and, M. C. Roubaud, (1998), A singular evolutive extended Kalman filter for data assimilation in oceanography, J. Mar. Syst., 16 (3-4), 323-340. (Pubitemid 28490324)
55. Vauhkonen, M., P. Karjalainen, and, J. Kaipio, (1998), A Kalman filter approach to track fast impedance changes in electrical impedance tomography, IEEE Trans. Biomed. Eng., 45 (4), 486-493.
56. 2 flood in a carbonate reservoir: A rock physics study, Geophysics, 63 (5), 1604-1617. (Pubitemid 29167528)
57. White, J., (2001), Computed seismic speeds and attenuation in rocks with partial gas saturation, Geophysics, 40 (2), 224-232.