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).

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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

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Geophysical Journal InternationalOxford University Press

Published: May 1, 2018

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