Corrigendum: ‘Upscaling of spectral induced polarization response using random tube networks’, by Maineult et al. (, Geophysical Journal International, 209, pp. 948–960).

Corrigendum: ‘Upscaling of spectral induced polarization response using random tube... Geophysical Journal International Geophys. J. Int. (2018) 213, 1296–1296 doi: 10.1093/gji/ggy052 Advance Access publication 2018 February 9 GJI Marine geosciences and applied geophysics Corrigendum: ‘Upscaling of spectral induced polarization response using random tube networks’, by Maineult et al. (2017, Geophysical Journal International, 209, pp. 948–960). by Alexis Maineult Sorbonne Universite, ´ CNRS, EPHE, UMR 7619 Metis, 4 place Jussieu, 75005 Paris, France. E-mail: alexis.maineult@upmc.fr A correction is given for eqs (2) and (3) of Maineult et al. (2017). Maineult et al. (2017) used the methodology of the random tube networks to study the upscaling of the spectral induced polarization ∗ 2 (SIP) response. In their paper, eq. (2) (Kirchhoff’s law) was applied to the complex current density J (in A m ): it has to be applied to the complex electrical current I (in A) instead (Kirchhoff 1845). Their eq. (2) should therefore be replaced by ∗ ∗ ∗ ∗ I + I + I + I = 0, (1) (x ,y−1)→(x ,y) (x −1,y)→(x ,y) (x +1,y)→(x ,y) (x ,y+1)→(x ,y) where I is the electrical current inside the element made of the tube connecting node p to node q and the surrounding matrix. p→q The local constitutive equation (Ohm’s law) for the current density J also contains an error, since the length l of the tube p→q p→q connecting node p to node q was omitted in the expression of the gradient of the electrical potential V. Their eq. (3) should therefore correctly read as ∗ ∗ V − V p q ∗ ∗ J = σ , (2) p→q p→q p→q where σ is the complex conductivity of each element constituted by the tube connecting node p to node q and the surrounding matrix, p→q and V is the complex electrical potential at node p. Introducing eq. (2) into eq. (1) gives S S S (x ,y−1)→(x ,y) (x −1,y)→(x ,y) (x +1,y)→(x ,y) ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ σ V + σ V +  V + σ V (x ,y−1)→(x ,y) x ,y−1 (x −1,y)→(x ,y) x −1,y x ,y x ,y (x +1,y)→(x ,y) x +1,y l l l (x ,y−1)→(x ,y) (x −1,y)→(x ,y) (x +1,y)→(x ,y) (x ,y+1)→(x ,y) ∗ ∗ + σ V = 0, (3) (x ,y+1)→(x ,y) x ,y+1 (x ,y+1)→(x ,y) with S S S S (x ,y−1)→(x ,y) (x −1,y)→(x ,y) (x +1,y)→(x ,y) (x ,y+1)→(x ,y) ∗ ∗ ∗ ∗ ∗ =− σ + σ + σ + σ , (4) x ,y (x ,y−1)→(x ,y) (x −1,y)→(x ,y) (x +1,y)→(x ,y) (x ,y+1)→(x ,y) l l l l (x ,y−1)→(x ,y) (x −1,y)→(x ,y) (x +1,y)→(x ,y) (x ,y+1)→(x ,y) where S is the section of each element constituted by a tube connecting node p to node q and the surrounding matrix. p→q In their work, Maineult et al. (2017) considered that all the tubes have the same length l. As a consequence, the elementary cross-sections of the elements are also equal (l ), and thus eqs (3) and (4) simplify to ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ σ V + σ V +  V + σ V + σ V = 0, (5) (x ,y−1)→(x ,y) x ,y−1 (x −1,y)→(x ,y) x −1,y x ,y x ,y (x +1,y)→(x ,y) x +1,y (x ,y+1)→(x ,y) x ,y+1 ∗ ∗ ∗ ∗ ∗ =− σ + σ + σ + σ . (6) x ,y (x ,y−1)→(x ,y) (x −1,y)→(x ,y) (x +1,y)→(x ,y) (x ,y+1)→(x ,y) Eqs (5) and (6) are identical to eqs (4) and (5) of Maineult et al. (2017), which are consequently correct. REFERENCES Maineult, A., Revil, A., Camerlynck, C., Florsch, N. & Titov, K., 2017. Upscaling of spectral induced polarization response using random tube Kirchhoff, G., 1845. Ueber den Durchgang eines elektrischen Stromes networks, Geophys. J. Int., 209(2), 948–960. durch eine Ebene, insbesondere durch eine kreisfor ¨ mige, Ann. Phys., 140(4), 497–514. 1296 The Author(s) 2018. Published by Oxford University Press on behalf of The Royal Astronomical Society. Downloaded from https://academic.oup.com/gji/article-abstract/213/2/1296/4847895 by Ed 'DeepDyve' Gillespie user on 16 March 2018 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geophysical Journal International Oxford University Press

Corrigendum: ‘Upscaling of spectral induced polarization response using random tube networks’, by Maineult et al. (, Geophysical Journal International, 209, pp. 948–960).

Free
1 page

Loading next page...
1 Page
 
/lp/ou_press/corrigendum-upscaling-of-spectral-induced-polarization-response-using-88XvBkaONd
Publisher
The Royal Astronomical Society
Copyright
© The Author(s) 2018. Published by Oxford University Press on behalf of The Royal Astronomical Society.
ISSN
0956-540X
eISSN
1365-246X
D.O.I.
10.1093/gji/ggy052
Publisher site
See Article on Publisher Site

Abstract

Geophysical Journal International Geophys. J. Int. (2018) 213, 1296–1296 doi: 10.1093/gji/ggy052 Advance Access publication 2018 February 9 GJI Marine geosciences and applied geophysics Corrigendum: ‘Upscaling of spectral induced polarization response using random tube networks’, by Maineult et al. (2017, Geophysical Journal International, 209, pp. 948–960). by Alexis Maineult Sorbonne Universite, ´ CNRS, EPHE, UMR 7619 Metis, 4 place Jussieu, 75005 Paris, France. E-mail: alexis.maineult@upmc.fr A correction is given for eqs (2) and (3) of Maineult et al. (2017). Maineult et al. (2017) used the methodology of the random tube networks to study the upscaling of the spectral induced polarization ∗ 2 (SIP) response. In their paper, eq. (2) (Kirchhoff’s law) was applied to the complex current density J (in A m ): it has to be applied to the complex electrical current I (in A) instead (Kirchhoff 1845). Their eq. (2) should therefore be replaced by ∗ ∗ ∗ ∗ I + I + I + I = 0, (1) (x ,y−1)→(x ,y) (x −1,y)→(x ,y) (x +1,y)→(x ,y) (x ,y+1)→(x ,y) where I is the electrical current inside the element made of the tube connecting node p to node q and the surrounding matrix. p→q The local constitutive equation (Ohm’s law) for the current density J also contains an error, since the length l of the tube p→q p→q connecting node p to node q was omitted in the expression of the gradient of the electrical potential V. Their eq. (3) should therefore correctly read as ∗ ∗ V − V p q ∗ ∗ J = σ , (2) p→q p→q p→q where σ is the complex conductivity of each element constituted by the tube connecting node p to node q and the surrounding matrix, p→q and V is the complex electrical potential at node p. Introducing eq. (2) into eq. (1) gives S S S (x ,y−1)→(x ,y) (x −1,y)→(x ,y) (x +1,y)→(x ,y) ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ σ V + σ V +  V + σ V (x ,y−1)→(x ,y) x ,y−1 (x −1,y)→(x ,y) x −1,y x ,y x ,y (x +1,y)→(x ,y) x +1,y l l l (x ,y−1)→(x ,y) (x −1,y)→(x ,y) (x +1,y)→(x ,y) (x ,y+1)→(x ,y) ∗ ∗ + σ V = 0, (3) (x ,y+1)→(x ,y) x ,y+1 (x ,y+1)→(x ,y) with S S S S (x ,y−1)→(x ,y) (x −1,y)→(x ,y) (x +1,y)→(x ,y) (x ,y+1)→(x ,y) ∗ ∗ ∗ ∗ ∗ =− σ + σ + σ + σ , (4) x ,y (x ,y−1)→(x ,y) (x −1,y)→(x ,y) (x +1,y)→(x ,y) (x ,y+1)→(x ,y) l l l l (x ,y−1)→(x ,y) (x −1,y)→(x ,y) (x +1,y)→(x ,y) (x ,y+1)→(x ,y) where S is the section of each element constituted by a tube connecting node p to node q and the surrounding matrix. p→q In their work, Maineult et al. (2017) considered that all the tubes have the same length l. As a consequence, the elementary cross-sections of the elements are also equal (l ), and thus eqs (3) and (4) simplify to ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ σ V + σ V +  V + σ V + σ V = 0, (5) (x ,y−1)→(x ,y) x ,y−1 (x −1,y)→(x ,y) x −1,y x ,y x ,y (x +1,y)→(x ,y) x +1,y (x ,y+1)→(x ,y) x ,y+1 ∗ ∗ ∗ ∗ ∗ =− σ + σ + σ + σ . (6) x ,y (x ,y−1)→(x ,y) (x −1,y)→(x ,y) (x +1,y)→(x ,y) (x ,y+1)→(x ,y) Eqs (5) and (6) are identical to eqs (4) and (5) of Maineult et al. (2017), which are consequently correct. REFERENCES Maineult, A., Revil, A., Camerlynck, C., Florsch, N. & Titov, K., 2017. Upscaling of spectral induced polarization response using random tube Kirchhoff, G., 1845. Ueber den Durchgang eines elektrischen Stromes networks, Geophys. J. Int., 209(2), 948–960. durch eine Ebene, insbesondere durch eine kreisfor ¨ mige, Ann. Phys., 140(4), 497–514. 1296 The Author(s) 2018. Published by Oxford University Press on behalf of The Royal Astronomical Society. Downloaded from https://academic.oup.com/gji/article-abstract/213/2/1296/4847895 by Ed 'DeepDyve' Gillespie user on 16 March 2018

Journal

Geophysical Journal InternationalOxford University Press

Published: May 1, 2018

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial