傾斜計データのインバージョン解析によるフラクチャの推定(<特集>岩石力学)

概要

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We investigate an inverse problem for mapping the hydraulic fracture geometry using surface tilt 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, then the computation scheme becomes robust and stable. We call this methodology as a cascade inversion scheme for tilt data. At the first stage of the inversion, the fracture plane is estimated by the Nelder-Mead simplex method and we can determine the fracture plane. And then the fracture aperture distribution is determined by the successive linear inversion stage. In the second stage, the fracture plane is divided into the small rectangular peaces and each peace has the different fracture aperture. The normal equation, where the fracture apertures are unknowns, can be solved by the least squared methods with two constraints as the smoothness and non-negative values of the fracture apertures. The proposed methodology was applied to the synthetic and field data. The inversion results are quite acceptable and we conclude this cascade inversion scheme is a robust method and easy to handle the field data.
2002-02-15