A comparison of the Gauss-Newton and quasi-Newton methods in resistivity imaging inversion
(2002) In Journal of Applied Geophysics 49(3). p.149-162- Abstract
- 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/339568
- author
- Loke, MH and Dahlin, Torleif LU
- organization
- publishing date
- 2002
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- imaging, resistivity, optimisation, quasi-Newton, gauss-Newton, 2D
- in
- Journal of Applied Geophysics
- volume
- 49
- issue
- 3
- pages
- 149 - 162
- publisher
- Elsevier
- external identifiers
-
- wos:000175227100003
- scopus:0036509413
- ISSN
- 0926-9851
- DOI
- 10.1016/S0926-9851(01)00106-9
- language
- English
- LU publication?
- yes
- id
- 567dee15-971c-426e-bf25-e70518fc82e7 (old id 339568)
- date added to LUP
- 2016-04-01 15:22:49
- date last changed
- 2022-04-22 07:15:04
@article{567dee15-971c-426e-bf25-e70518fc82e7, abstract = {{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.}}, author = {{Loke, MH and Dahlin, Torleif}}, issn = {{0926-9851}}, keywords = {{imaging; resistivity; optimisation; quasi-Newton; gauss-Newton; 2D}}, language = {{eng}}, number = {{3}}, pages = {{149--162}}, publisher = {{Elsevier}}, series = {{Journal of Applied Geophysics}}, title = {{A comparison of the Gauss-Newton and quasi-Newton methods in resistivity imaging inversion}}, url = {{https://lup.lub.lu.se/search/files/4380044/4934427.pdf}}, doi = {{10.1016/S0926-9851(01)00106-9}}, volume = {{49}}, year = {{2002}}, }