Cascade Inversion for Tilt Data

Toshifumi Matsuoka; Hirohide Fukamori; Yuzuru Ashida; Eric Davis

doi:10.1071/ASEG2001ab085

ISSN: 2202-0586
E-ISSN:

oa Cascade Inversion for Tilt Data
Authors Toshifumi Matsuoka^a, Hirohide Fukamori^b, Yuzuru Ashida^c and Eric Davis^d
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^a Kyoto University,, Japan, [email protected] ^b Kyoto University,, Japan, [email protected] ^c Kyoto University,, Japan, [email protected] ^d Pinnacle Technologies,, [email protected]
Publisher: Australian Society of Exploration Geophysicists
Source: ASEG Extended Abstracts, Volume 2001, Issue ASEG2001 - 15th Geophysical Conference, Dec 2001, p. 1 - 4
DOI: https://doi.org/10.1071/ASEG2001ab085
- Published online: 01 Dec 2001

Abstract

We investigate an inverse problem for mapping hydraulic fracture geometry using surface tiltmeter data. It is well known that this problem becomes a non-linear inverse problem. If the inversion algorithm can be separated into two stages as: (1) the identification of the fracture plane and (2) the estimation of the fracture aperture distribution, the computation scheme becomes robust and stable. We call this methodology a cascade inversion scheme for tilt data.

In the first stage of the inversion, the fracture plane is estimated by the Nelder-Mead simplex method whereby we obtain the volume of the hydraulic fracture. The fracture aperture distribution is then determined by the successive linear inversion stage. In this second stage, the fracture plane is divided into small rectangular pieces and each piece has a different fracture aperture. The normal equation, where the fracture apertures are unknowns, can be solved by the least squared method with two constraints, which are the smoothness and non-negative values of the fracture apertures.

The proposed methodology was applied to synthetic and field data. The inversion results are quite acceptable and we conclude that this cascade inversion scheme is a robust method and easy to apply to field data.

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References

Davis, P. (1983): Surface Deformation Associated with a Dipping Hydrofracture, J.G.R. Vol.88, 5826-5834
Du, Jin: Geophysical Inversion of Far-field Deformation for Hydraulic Fracture and Reservoir Information, Dissertation, University of Texas at Austin, August, 2000
Okada, Y. (1985): Surface Deformation Due to Shear and Tensile Faults in a Half Space, Bull. Seism. Soc. Am., 75,1135-1154
Okada, Y. (1992): Internal Deformation due to shear and tensile faults in a half-space, Bull. Seism. Soc. Am., 82, 1018-1040
Lagarias, J. C, Reeds, J.A., Wright, M.H., and Wright, P.E. (1998): Convergence Properties of the Nelder-Mead Simplex Algorithm in Low Dimensions, SIAM Journal on Optimization, 9, 112-147
Lawson, CL. and Hanson, R.J. (1974) Solving Least Squares Problems, Prentice-Hall, Chapter 23, 161
Matsuoka, T., Ashida, Y., Fukamori, H., Kuwano, Y., Kurozumi, H., Churei, M., Harada, S., Suzuki, I., Mukai, S., Arai, F., Takasugi, S., Tateno, M., Takahashi, M., and Wright C.A. (1999): Application of High Resolution Tiltmeter for Crustal Movements Associated with Volcanic Activities of Mt. Iwate, �BUTSURI-TANSA, 52, -583-593
Nelder, J.A., and Mead, R., (1965):A simplex method for function minimization, Computer T, 7, 308-313
Wright, C.A., Minner, W.A., Ward, J.F., Schell, E.J., and Hunter, S.P.,(1998): Surface Tiltmeter Fracture Mapping Reaches New Depth - 10,000 feet, and beyond?, SPE 39919
Olson, Jon E., Du, Yijun and Du, Jin: Tiltmeter data inversion with continuous, non-uniform opening distribution: A new method for detecting hydraulic fracture geometry, Int. J. Rock Mech & Min. Sci. Vol. 34, No. 3-4, (1997)
Wright, C.A., Davis, E.J., Weijers, L.,Minner, W.A., Hennigan, CM., and Golich, G.M. (1997) : Horizontal Hydraulic Fractures: Oddball Occurrences of Practical Engineering Concern?, SPE paper 38324, Western Regional Meeting

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Article Type: Research Article

Keyword(s): cascade inversiona; hydraulic fracture; inversion; non-linear; simplex method

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