A comparison of the Gauss-Newton and quasi-Newton methods in resistivity imaging inversion
Författare
Summary, in English
The smoothness-constrained least-squares method is widely used for two-dimensional (2D) and three-dimensional (3D) inversion of apparent resistivity data sets. The Gauss-Newton method that recalculates the Jacobian matrix of partial derivatives for all iterations is commonly used to solve the least-squares equation. The quasi-Newton method has also been used to reduce the computer time. In this method. the Jacobian matrix for a homogeneous earth model is used for the first iteration, and the Jacobian matrices for subsequent iterations are estimated by an updating technique. Since the Gauss-Newton method uses the exact partial derivatives, it should require fewer iterations to converge. However, for many data sets, the quasi-Newton method can be significantly faster than the Gauss-Newton method. The effectiveness of a third method that is a combination of the Gauss-Newton and quasi-Newton methods is also examined. In this combined inversion method, the partial derivatives are directly recalculated for the first two or three iterations, and then estimated by a quasi-Newton updating technique for the later iterations. The three different inversion methods are tested with a number of synthetic and field data sets. In areas with moderate (less than 10:1) subsurface resistivity contrasts, the inversion models obtained by the three methods are similar. In areas with large resistivity contrasts, the Gauss-Newton method gives significantly more accurate results than the quasi-Newton method. However, even for large resistivity contrasts, the differences in the models obtained by the Gauss-New-ton method and the combined inversion method are small. As the combined inversion method is faster than the Gauss-Newton method, it represents a satisfactory compromise between speed and accuracy for many data sets.
Avdelning/ar
Publiceringsår
2002
Språk
Engelska
Sidor
149-162
Publikation/Tidskrift/Serie
Journal of Applied Geophysics
Volym
49
Issue
3
Fulltext
- Available as PDF - 816 kB
- Download statistics
Dokumenttyp
Artikel i tidskrift
Förlag
Elsevier
Ämne
- Geotechnical Engineering
Nyckelord
- imaging
- resistivity
- optimisation
- quasi-Newton
- gauss-Newton
- 2D
Status
Published
ISBN/ISSN/Övrigt
- ISSN: 0926-9851