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A comparison of the Gauss-Newton and quasi-Newton methods in resistivity imaging inversion

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Author

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.

Publishing year

2002

Language

English

Pages

149-162

Publication/Series

Journal of Applied Geophysics

Volume

49

Issue

3

Document type

Journal article

Publisher

Elsevier

Topic

  • Geotechnical Engineering

Keywords

  • imaging
  • resistivity
  • optimisation
  • quasi-Newton
  • gauss-Newton
  • 2D

Status

Published

ISBN/ISSN/Other

  • ISSN: 0926-9851