Abstract
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.
| Original language | English |
|---|---|
| Article number | 003 |
| Pages (from-to) | 122-134 |
| Number of pages | 13 |
| Journal | Journal of Geophysics and Engineering |
| Volume | 3 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2006 |
| Externally published | Yes |
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Keywords
- Crosswell
- Focusing
- Inversion
- Travel-time tomography
ASJC Scopus subject areas
- Geophysics
- Geology
- Management, Monitoring, Policy and Law
- Industrial and Manufacturing Engineering
Cite this
Sharp boundary inversion in crosswell travel-time tomography. / Zhdanov, M. S.; Vignoli, G.; Ueda, Takumi.
In: Journal of Geophysics and Engineering, Vol. 3, No. 2, 003, 2006, p. 122-134.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Sharp boundary inversion in crosswell travel-time tomography
AU - Zhdanov, M. S.
AU - Vignoli, G.
AU - Ueda, Takumi
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
UR - http://www.scopus.com/inward/record.url?scp=33745658842&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33745658842&partnerID=8YFLogxK
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 -