A comparison of the GaussNewton and quasiNewton methods in resistivity imaging inversion
(2002) In Journal of Applied Geophysics 49(3). p.149162 Abstract
 The smoothnessconstrained leastsquares method is widely used for twodimensional (2D) and threedimensional (3D) inversion of apparent resistivity data sets. The GaussNewton method that recalculates the Jacobian matrix of partial derivatives for all iterations is commonly used to solve the leastsquares equation. The quasiNewton 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 GaussNewton method uses the exact partial derivatives, it should require fewer iterations to converge. However, for many data sets, the quasiNewton method... (More)
 The smoothnessconstrained leastsquares method is widely used for twodimensional (2D) and threedimensional (3D) inversion of apparent resistivity data sets. The GaussNewton method that recalculates the Jacobian matrix of partial derivatives for all iterations is commonly used to solve the leastsquares equation. The quasiNewton 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 GaussNewton method uses the exact partial derivatives, it should require fewer iterations to converge. However, for many data sets, the quasiNewton method can be significantly faster than the GaussNewton method. The effectiveness of a third method that is a combination of the GaussNewton and quasiNewton 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 quasiNewton 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 GaussNewton method gives significantly more accurate results than the quasiNewton method. However, even for large resistivity contrasts, the differences in the models obtained by the GaussNewton method and the combined inversion method are small. As the combined inversion method is faster than the GaussNewton 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:
http://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, quasiNewton, gaussNewton, 2D
 in
 Journal of Applied Geophysics
 volume
 49
 issue
 3
 pages
 149  162
 publisher
 Elsevier
 external identifiers

 wos:000175227100003
 scopus:0036509413
 ISSN
 09269851
 DOI
 10.1016/S09269851(01)001069
 language
 English
 LU publication?
 yes
 id
 567dee15971c426ebf25e70518fc82e7 (old id 339568)
 date added to LUP
 20071123 12:19:26
 date last changed
 20180408 04:15:12
@article{567dee15971c426ebf25e70518fc82e7, abstract = {The smoothnessconstrained leastsquares method is widely used for twodimensional (2D) and threedimensional (3D) inversion of apparent resistivity data sets. The GaussNewton method that recalculates the Jacobian matrix of partial derivatives for all iterations is commonly used to solve the leastsquares equation. The quasiNewton 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 GaussNewton method uses the exact partial derivatives, it should require fewer iterations to converge. However, for many data sets, the quasiNewton method can be significantly faster than the GaussNewton method. The effectiveness of a third method that is a combination of the GaussNewton and quasiNewton 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 quasiNewton 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 GaussNewton method gives significantly more accurate results than the quasiNewton method. However, even for large resistivity contrasts, the differences in the models obtained by the GaussNewton method and the combined inversion method are small. As the combined inversion method is faster than the GaussNewton method, it represents a satisfactory compromise between speed and accuracy for many data sets.}, author = {Loke, MH and Dahlin, Torleif}, issn = {09269851}, keyword = {imaging,resistivity,optimisation,quasiNewton,gaussNewton,2D}, language = {eng}, number = {3}, pages = {149162}, publisher = {Elsevier}, series = {Journal of Applied Geophysics}, title = {A comparison of the GaussNewton and quasiNewton methods in resistivity imaging inversion}, url = {http://dx.doi.org/10.1016/S09269851(01)001069}, volume = {49}, year = {2002}, }