A wavelet approach to adjoint state sensitivity computation for steady state differential equations

Water Resources Research

Volumn 47, Issue 3, 2011, Pages

  Awotunde, Abeeb A ^a,b   Horne, Roland N ^a  

^a STANFORD UNIVERSITY   (United States)

^b KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

Author keywords

[No Author keywords available]

Indexed keywords

ADJOINT EQUATIONS; ADJOINT SENSITIVITY ANALYSIS; ADJOINTS; COMPUTATIONAL COSTS; DATA COMPRESSION TOOLS; DATA SPACE; NUMERICAL EXAMPLE; PARAMETER ESTIMATION ALGORITHM; SENSITIVITY COEFFICIENT; SENSITIVITY COMPUTATION; SENSITIVITY MATRIX; SPATIAL DATA; STEADY STATE; TIME-CONSUMING PARTS;

DATA COMPRESSION; DIFFERENTIAL EQUATIONS; EQUATIONS OF STATE; LINEAR SYSTEMS; METADATA; NUMERICAL METHODS; PARAMETER ESTIMATION; SENSITIVITY ANALYSIS; WAVELET TRANSFORMS;

DATA REDUCTION;

ADJOINT METHOD; ALGORITHM; DATABASE; PARAMETERIZATION; SENSITIVITY ANALYSIS; STEADY-STATE EQUILIBRIUM; WAVELET ANALYSIS;

EID: 79952235812     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2010WR009165     Document Type: Article

References (37)

1. Anterion, F., B. Karcher, and R. Eymard (1989), Use of parameter gradients for reservoir history matching, paper SPE 18433 presented at the SPE Symposium on Reservoir Simulation, Soc. of Pet. Eng., Houston, Tex., 6-8 Feb.
2. Athichanagorn, S., R. N. Horne, and J. Kikani (2002), Processing and interpretation of long-term data acquired from permanent press (Pubitemid 35391675)
3. Awotunde, A. A., and R. N. Horne (2008), A multiresolution analysis of the relationship between spatial distribution of reservoir parameters and time distribution of data measurements, paper SPE 115795 presented at the SPE Annual Technical Conference and Exhibition, Soc. of Pet. Eng., Denver, Colo., 21-24 Sept.
4. Carrera, J., and S. P. Neuman (1986), Estimation of aquifer parameters under transient and steady state conditions: 1. Maximum likelihood method incorporating prior information, Water Resour. Res., 22, 199-210. (Pubitemid 16477839)
5. Carter, R. D., L. F. Kemp, A. C. Piece, and D. L. Williams (1974), Performance matching with constraints, Soc. Pet. Eng. J., 14, 187-196.
6. Chavent, G. M., M. Dupuy, and P. Lemonnier (1975), History matching by use of optimal theory, Soc. Pet. Eng. J., 15, 74-86.
7. Chen, W. H., G. R. Gavalas, J. H. Seinfeld, and M. L. Wasserman (1974), A new algorithm for automatic history matching, Soc. Pet. Eng. J., 14, 593-608.
8. Chui, C. K. (1992), An Introduction to Wavelets, Academic, San Diego, Calif.
9. Daubechies, I. (1992), Ten Lectures on Wavelets, SIAM-CBMS Ser., vol. 61, Soc. for Ind. and Appl. Math., Philadelphia, Pa.
10. Donoho, D. L., and I. M. Johnstone (1994), Ideal spatial adaptation by wavelet shrinkage, Biometrika, 81, 425-455.
11. Jacquard, P., and C. Jain (1965), Permeability distribution from field pressure data, Soc. Pet. Eng. J., 5, 281-294.
12. Jansen, F. E., and M. G. Kelkar (1997), Application of wavelets to production data in describing inter-well relationships, paper SPE 38876 presented at the SPE Annual Technical Conference and Exhibition, Soc. of Pet. Eng., San Antonio, Tex., 5-8 Oct.
13. Kikani, J., and M. He (1998), Multiresolution analysis of long-term pressure transient data using wavelet methods, paper SPE 36517 presented at the SPE Annual Technical Conference and Exhibition, Soc. of Pet. Eng., New Orleans, La., 27-30 Sept.
14. Landa, J. L. (1997), Reservoir parameter estimation constrained to pressure transients, performance history and distributed saturation data, Ph. D. thesis, Stanford Univ., Stanford, Calif.
15. Li, S., and L. Petzold (2004), Adjoint sensitivity analysis for time-dependent partial differential equations with adaptive mesh refinement, J. Comput. Phys., 198, 310-325. (Pubitemid 38881882)
16. Lu, P., and R. N. Horne (2000), A multiresolution approach to reservoir parameter estimation using wavelet analysis, paper SPE 62985 presented at the SPE Annual Technical Conference and Exhibition, Soc. of Pet. Eng., Dallas, Tex., 1-4 Oct.
17. Mallat, S. (1989), A theory for multiresolution signal decomposition: The wavelet representation, IEEE Trans. Pattern Anal. Mach Intell., 11, 674-693.
18. Mallat, S. (1999), A Wavelet Tour of Signal Processing, 2nd ed., Academic, New York.
19. Michalak, A. M., and P. K. Kitanidis (2004), Estimation of historical groundwater contaminant distribution using the adjoint state method applied to geostatistical inverse modeling, Water Resour. Res., 40, W08302, doi:10.1029/2004WR003214. (Pubitemid 39250910)
20. Oldenburg, D. W., P. R. McGillivray, and R. G. Ellis (1993), Generalized subspace methods for large-scale inverse problems, Geophys. J. Int., 114, 12-20. (Pubitemid 23394825)
21. Oppenheim, A. V., and R. W. Schafer (1999), Digital Signal Processing, Prentice Hall, Upper Saddle River, N. J.
22. Panda, M. N., C. C. Mosher, and A. K. Chopra (2000), Application of wavelet transforms to reservoir-data analysis and scaling, SPE J., 5, 92-101. (Pubitemid 32272575)
23. Percival, D., and A. T. Walden (2000), Wavelet Methods for Time Series Analysis, Cambridge Univ. Press, Cambridge, U. K.
24. Plessix, R. E. (2006), A review of adjoint-state method for computing the gradient of a functional with geophysical applications, Geophys. J. Int., 167, 495-503.
25. Reynolds, A. C., N. He, L. Chu, and D. S. Oliver (1996), Reparameterization techniques for generating reservoir descriptions conditioned to variograms and well-test pressure data, SPE J., 1, 413-426. (Pubitemid 126697456)
26. Sahni, I., and R. N. Horne (2006), Generating multiple history-matched realizations using wavelets, SPE Reservoir Eval. Eng., 9, 217-226. (Pubitemid 43984848)
27. Sardy, S., D. B. Percival, A. G. Bruce, H. Gao, and S. Werner (1999), Wavelet shrinkage for unequally spaced data, Stat. Comput., 9, 65-75.
28. Sarma, P., L. J. Durlofsky, and K. Aziz (2008), Kernel principal component analysis for efficient, differentiable parameterization of multipoint geostatiscs, Math. Geosci., 40, 3-32.
29. Shah, P. C., G. R. Gavalas, and J. H. Seinfeld (1978), Error analysis in history matching: The optimal level of parameterization, Soc. Pet. Eng. J., 18, 219-228. (Pubitemid 8613422)
30. Sun, N.-Z., and W. W.-G. Yeh (1985), Identification of parameter structure in groundwater inverse problems, Water Resour. Res., 21, 869-883.
31. Sun, N.-Z., and W. W.-G. Yeh (1990a), Coupled inverse problems in groundwater modeling: 1. Sensitivity analysis and parameter identification, Water Resour. Res., 26, 2507-2525.
32. Sun, N.-Z., and W. W.-G. Yeh (1990b), Coupled inverse problems in groundwater modeling: 2. Identifiability and experimental design, Water Resour. Res., 26, 2507-2525.
33. Tang, Y. N., Y. M. Chen, W. H. Chen, and M. L. Wasserman (1989), Generalized pulse-spectrum technique for 2-D and 2-phase history matching, Appl. Numer. Math., 5, 529-539. (Pubitemid 20655758)
34. Wasserman, M. L., A. S. Emanuel, and J. H. Seinfeld (1975), Practical application of optimal-control theory to history-matching multiphase simulator models, Soc. Pet. Eng. J., 15, 347-355.
35. Wu, Z., A. C. Reynolds, and D. S. Oliver (1999), Conditioning geostatistical models to two-phase production data, SPE J., 4, 142-155.
36. Yeh, W. W.-G. (1986), Review of parameter identification procedure in ground water hydrology, Water Resour. Res., 22, 95-108.
37. Yeh, W. W.-G., and N.-Z. Sun (1990), Variational sensitivity analysis, data requirements, and parameter identification in a leaky aquifer system, Water Resour. Res., 26, 1927-1938.