TY - JOUR
T1 - Sharp boundary inversion in crosswell travel-time tomography
AU - Zhdanov, M. S.
AU - Vignoli, G.
AU - Ueda, T.
PY - 2006
Y1 - 2006
N2 - The reconstruction of seismic images of the medium from crosswell travel-time data is a typical example of the ill-posed inverse problem. In order to obtain a stable solution and to replace an ill-posed problem by a well-posed one, a stabilizing functional (stabilizer) has to be introduced. The role of this functional is to select the desired stable solution from a class of solutions with specific physical and/or geometrical properties. One of these properties is the existence of sharp boundaries separating rocks with different petrophysical parameters, e.g., oil- and water-saturated reservoirs. In this paper, we develop a new tomographic method based on application of a minimum support stabilizer to the crosswell travel-time inverse problem. This stabilizer makes it possible to produce clear and focused images of geological targets with sharp boundaries. We demonstrate that the minimum support stabilizer allows a correct recovery of not only the shape but also the velocity value of the target. We also point out that this stabilizer provides good results even with a low ray density, when the traditional minimum norm stabilizer fails.
AB - The reconstruction of seismic images of the medium from crosswell travel-time data is a typical example of the ill-posed inverse problem. In order to obtain a stable solution and to replace an ill-posed problem by a well-posed one, a stabilizing functional (stabilizer) has to be introduced. The role of this functional is to select the desired stable solution from a class of solutions with specific physical and/or geometrical properties. One of these properties is the existence of sharp boundaries separating rocks with different petrophysical parameters, e.g., oil- and water-saturated reservoirs. In this paper, we develop a new tomographic method based on application of a minimum support stabilizer to the crosswell travel-time inverse problem. This stabilizer makes it possible to produce clear and focused images of geological targets with sharp boundaries. We demonstrate that the minimum support stabilizer allows a correct recovery of not only the shape but also the velocity value of the target. We also point out that this stabilizer provides good results even with a low ray density, when the traditional minimum norm stabilizer fails.
KW - Crosswell
KW - Focusing
KW - Inversion
KW - Travel-time tomography
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U2 - 10.1088/1742-2132/3/2/003
DO - 10.1088/1742-2132/3/2/003
M3 - Article
AN - SCOPUS:33745658842
VL - 3
SP - 122
EP - 134
JO - Journal of Geophysics and Engineering
JF - Journal of Geophysics and Engineering
SN - 1742-2132
IS - 2
M1 - 003
ER -