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Smoothness-constrained time-lapse inversion of data from 3D resistivity surveys

Loke, M. H.; Dahlin, Torleif LU and Rucker, D. F. (2014) In Near Surface Geophysics 12(1). p.5-24
Abstract
Three-dimensional resistivity surveys and their associated inversion models are required to accurately resolve structures exhibiting very complex geology. In the same light, 3D resistivity surveys collected at multiple times are required to resolve temporally varying conditions. In this work we present 3D data sets, both synthetic and real, collected at different times. The large spatio-temporal data sets are then inverted simultaneously using a least-squares methodology that incorporates roughness filters in both the space and time domains. The spatial roughness filter constrains the model resistivity to vary smoothly in the x-, y- and z-directions. A temporal roughness filter is also applied that minimizes changes in the resistivity... (More)
Three-dimensional resistivity surveys and their associated inversion models are required to accurately resolve structures exhibiting very complex geology. In the same light, 3D resistivity surveys collected at multiple times are required to resolve temporally varying conditions. In this work we present 3D data sets, both synthetic and real, collected at different times. The large spatio-temporal data sets are then inverted simultaneously using a least-squares methodology that incorporates roughness filters in both the space and time domains. The spatial roughness filter constrains the model resistivity to vary smoothly in the x-, y- and z-directions. A temporal roughness filter is also applied that minimizes changes in the resistivity between successive temporal inversion models and the L-curve method is used to determine the optimum weights for both spatial and temporal roughness filters. We show that the use of the temporal roughness filter can accurately resolve changes in the resistivity even in the presence of noise. The L1- and L2-norm constraints for the temporal roughness filter are first examined using a synthetic model. The synthetic data test shows that the L1-norm temporal constraint produces significantly more accurate results when the resistivity changes abruptly with time. The model obtained with the L1-norm temporal constraint is also less sensitive to random noise compared with independent inversions (i.e., without any temporal constraint) and the L2-norm temporal constraint. Anomalies that are common in models using independent inversions and the L2-norm and L1-norm temporal constraints are likely to be real. In contrast, anomalies present in a model using independent inversions but that are significantly reduced with the L2-norm and L1-norm constraints are likely artefacts. For field data sets, the method successfully recovered temporal changes in the subsurface resistivity from a landfill monitoring survey due to rainwater infiltration, as well as from an experiment to map the migration of sodium cyanide solution from an injection well using surface and borehole electrodes in an area with significant topography. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Near Surface Geophysics
volume
12
issue
1
pages
5 - 24
publisher
EAGE
external identifiers
  • wos:000331668000002
  • scopus:84894118634
ISSN
1873-0604
DOI
10.3997/1873-0604.2013025
language
English
LU publication?
yes
id
a486e016-47a6-484b-81ef-23e3e8bde6f7 (old id 4364195)
date added to LUP
2014-04-16 15:34:07
date last changed
2017-10-22 03:02:16
@article{a486e016-47a6-484b-81ef-23e3e8bde6f7,
  abstract     = {Three-dimensional resistivity surveys and their associated inversion models are required to accurately resolve structures exhibiting very complex geology. In the same light, 3D resistivity surveys collected at multiple times are required to resolve temporally varying conditions. In this work we present 3D data sets, both synthetic and real, collected at different times. The large spatio-temporal data sets are then inverted simultaneously using a least-squares methodology that incorporates roughness filters in both the space and time domains. The spatial roughness filter constrains the model resistivity to vary smoothly in the x-, y- and z-directions. A temporal roughness filter is also applied that minimizes changes in the resistivity between successive temporal inversion models and the L-curve method is used to determine the optimum weights for both spatial and temporal roughness filters. We show that the use of the temporal roughness filter can accurately resolve changes in the resistivity even in the presence of noise. The L1- and L2-norm constraints for the temporal roughness filter are first examined using a synthetic model. The synthetic data test shows that the L1-norm temporal constraint produces significantly more accurate results when the resistivity changes abruptly with time. The model obtained with the L1-norm temporal constraint is also less sensitive to random noise compared with independent inversions (i.e., without any temporal constraint) and the L2-norm temporal constraint. Anomalies that are common in models using independent inversions and the L2-norm and L1-norm temporal constraints are likely to be real. In contrast, anomalies present in a model using independent inversions but that are significantly reduced with the L2-norm and L1-norm constraints are likely artefacts. For field data sets, the method successfully recovered temporal changes in the subsurface resistivity from a landfill monitoring survey due to rainwater infiltration, as well as from an experiment to map the migration of sodium cyanide solution from an injection well using surface and borehole electrodes in an area with significant topography.},
  author       = {Loke, M. H. and Dahlin, Torleif and Rucker, D. F.},
  issn         = {1873-0604},
  language     = {eng},
  number       = {1},
  pages        = {5--24},
  publisher    = {EAGE},
  series       = {Near Surface Geophysics},
  title        = {Smoothness-constrained time-lapse inversion of data from 3D resistivity surveys},
  url          = {http://dx.doi.org/10.3997/1873-0604.2013025},
  volume       = {12},
  year         = {2014},
}