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The inverse problem for electroseismic conversion: Stable recovery of the conductivity and the electrokinetic mobility parameter
1. | 8817 234th St. SW, Edmonds, WA 98026, United States |
2. | Computational and Applied Mathematics, Rice University, Houston, TX 77005, United States |
References:
[1] |
G. Bal and G. Uhlmann, Inverse diffusion theory of photo-acoustics,, Inverse Problems, 26 (2010).
doi: 10.1088/0266-5611/26/8/085010. |
[2] |
G. Bal and T. Zhou, Hybrid inverse problems for a system of Maxwell's equations,, Inverse Problem, 30 (2014).
doi: 10.1088/0266-5611/30/5/055013. |
[3] |
M. A. Biot, Theory of propagation of elastic waves in a fluid-saturated porous solid. I-Low-frequency range,, Journal of the Acoustical Society of America, 28 (1956), 168.
doi: 10.1121/1.1908239. |
[4] |
M. A. Biot, Theory of propagation of elastic waves in a fluid-saturated porous solid. II-High-frequency range,, Journal of the Acoustical Society of America, 28 (1956), 179.
doi: 10.1121/1.1908241. |
[5] |
P. Caro, P. Ola and M. Salo, Inverse boundary value problem for Maxwell equations with local data,, Comm. in PDE, 34 (2009), 1425.
doi: 10.1080/03605300903296272. |
[6] |
J. Chen and Y. Yang, Quantitative photo-acoustic tomography with partial data,, Inverse Problem, 28 (2012).
doi: 10.1088/0266-5611/28/11/115014. |
[7] |
J. Chen and Y. Yang, Inverse problem of electroseismic conversion,, Inverse Problem, 29 (2013).
|
[8] |
D. Colton and L. Paivarinta, The uniqueness of a solution to an inverse scattering problem for electromagnetic waves,, Arch. Rational Mech. Anal., 119 (1992), 59.
doi: 10.1007/BF00376010. |
[9] |
C. Guo and G. Bal, Reconstruction of complex-valued tensors in the Maxwell system from knowledge of internal magnetic fields,, Inverse Problems and Imaging, 8 (2014), 1033.
doi: 10.3934/ipi.2014.8.1033. |
[10] |
M. W. Haartsen, Coupled Electromagnetic and Acoustic Wavefield Modeling in Poro-Elastic Media and Its Application in Geophysical Exploration,, Ph.D. Thesis, (1995). Google Scholar |
[11] |
C. E. Kenig, M. Salo and G. Uhlmann, Inverse problems for the anisotropic maxwell equations,, Duke Math. J., 157 (2011), 369.
doi: 10.1215/00127094-1272903. |
[12] |
P. Ola and E. Somersalo, Electromagnetic inverse problems and generalized sommerfeld potentials,, SIAM J. Appl. Math., 56 (1996), 1129.
doi: 10.1137/S0036139995283948. |
[13] |
P. Ola, L. Päivärinta and E Somersalo, An inverse boundary value problem in electrodynamics,, Duke Mathematical Journal, 70 (1993), 617.
doi: 10.1215/S0012-7094-93-07014-7. |
[14] |
T. Plona, Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies,, Appl. Phys. Lett., 36 (1980), 259.
doi: 10.1063/1.91445. |
[15] |
S. R. Pride, Governing equations for the coupled electro-magnetics and acoustics of porous media,, Phys. Rev., 50 (1994), 15678. Google Scholar |
[16] |
S. R. Pride and M. W. Haartsen, Electroseismic wave properties,, Journal of the Acoustical Society of America, 100 (1996), 1301.
doi: 10.1121/1.416018. |
[17] |
M. D. Schakel, Coupled Seismic and Electromagnetic Wave Propagation,, Ph.D. thesis, (2011). Google Scholar |
[18] |
A. Thompson and G. Gist, Geophysical applications of electro-kinetic conversion,, The Leading Edge, 12 (1993), 1169. Google Scholar |
[19] |
A. Thompson and S. Hornbostel et. al., Field tests of electroseismic hydrocarbon detection,, Geophysics, 72 (2007). Google Scholar |
[20] |
J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem,, Ann. of Math., 125 (1987), 153.
doi: 10.2307/1971291. |
[21] |
B. White, Asymptotic theory of electro-seismic prospecting,, SIAM J. Appl. Math., 65 (2005), 1443.
doi: 10.1137/040604108. |
[22] |
K. L. Williams, An effective density fluid model for acoustic propagation in sediments derived from Biot theory,, J. Acoust. Soc. Am., 110 (2001), 2276.
doi: 10.1121/1.1412449. |
[23] |
Z. Zhu, M. W. Haartsen and M. N. Toksöz, Experimental studies of electro-kinetic conversions in fluid-saturated bore-hole models,, Geophysics, 64 (1999), 1349. Google Scholar |
[24] |
Z. Zhu and M. N. Toksöz, Cross hole seismoelectric measurements in bore-hole models with fractures,, Geophysics, 68 (2003), 1519. Google Scholar |
[25] |
Z. Zhu and M. N. Toksöz, Seismoelectric and seismomagnetic measurements in fractured bore-hole models,, Geophysics, 70 (2005). Google Scholar |
show all references
References:
[1] |
G. Bal and G. Uhlmann, Inverse diffusion theory of photo-acoustics,, Inverse Problems, 26 (2010).
doi: 10.1088/0266-5611/26/8/085010. |
[2] |
G. Bal and T. Zhou, Hybrid inverse problems for a system of Maxwell's equations,, Inverse Problem, 30 (2014).
doi: 10.1088/0266-5611/30/5/055013. |
[3] |
M. A. Biot, Theory of propagation of elastic waves in a fluid-saturated porous solid. I-Low-frequency range,, Journal of the Acoustical Society of America, 28 (1956), 168.
doi: 10.1121/1.1908239. |
[4] |
M. A. Biot, Theory of propagation of elastic waves in a fluid-saturated porous solid. II-High-frequency range,, Journal of the Acoustical Society of America, 28 (1956), 179.
doi: 10.1121/1.1908241. |
[5] |
P. Caro, P. Ola and M. Salo, Inverse boundary value problem for Maxwell equations with local data,, Comm. in PDE, 34 (2009), 1425.
doi: 10.1080/03605300903296272. |
[6] |
J. Chen and Y. Yang, Quantitative photo-acoustic tomography with partial data,, Inverse Problem, 28 (2012).
doi: 10.1088/0266-5611/28/11/115014. |
[7] |
J. Chen and Y. Yang, Inverse problem of electroseismic conversion,, Inverse Problem, 29 (2013).
|
[8] |
D. Colton and L. Paivarinta, The uniqueness of a solution to an inverse scattering problem for electromagnetic waves,, Arch. Rational Mech. Anal., 119 (1992), 59.
doi: 10.1007/BF00376010. |
[9] |
C. Guo and G. Bal, Reconstruction of complex-valued tensors in the Maxwell system from knowledge of internal magnetic fields,, Inverse Problems and Imaging, 8 (2014), 1033.
doi: 10.3934/ipi.2014.8.1033. |
[10] |
M. W. Haartsen, Coupled Electromagnetic and Acoustic Wavefield Modeling in Poro-Elastic Media and Its Application in Geophysical Exploration,, Ph.D. Thesis, (1995). Google Scholar |
[11] |
C. E. Kenig, M. Salo and G. Uhlmann, Inverse problems for the anisotropic maxwell equations,, Duke Math. J., 157 (2011), 369.
doi: 10.1215/00127094-1272903. |
[12] |
P. Ola and E. Somersalo, Electromagnetic inverse problems and generalized sommerfeld potentials,, SIAM J. Appl. Math., 56 (1996), 1129.
doi: 10.1137/S0036139995283948. |
[13] |
P. Ola, L. Päivärinta and E Somersalo, An inverse boundary value problem in electrodynamics,, Duke Mathematical Journal, 70 (1993), 617.
doi: 10.1215/S0012-7094-93-07014-7. |
[14] |
T. Plona, Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies,, Appl. Phys. Lett., 36 (1980), 259.
doi: 10.1063/1.91445. |
[15] |
S. R. Pride, Governing equations for the coupled electro-magnetics and acoustics of porous media,, Phys. Rev., 50 (1994), 15678. Google Scholar |
[16] |
S. R. Pride and M. W. Haartsen, Electroseismic wave properties,, Journal of the Acoustical Society of America, 100 (1996), 1301.
doi: 10.1121/1.416018. |
[17] |
M. D. Schakel, Coupled Seismic and Electromagnetic Wave Propagation,, Ph.D. thesis, (2011). Google Scholar |
[18] |
A. Thompson and G. Gist, Geophysical applications of electro-kinetic conversion,, The Leading Edge, 12 (1993), 1169. Google Scholar |
[19] |
A. Thompson and S. Hornbostel et. al., Field tests of electroseismic hydrocarbon detection,, Geophysics, 72 (2007). Google Scholar |
[20] |
J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem,, Ann. of Math., 125 (1987), 153.
doi: 10.2307/1971291. |
[21] |
B. White, Asymptotic theory of electro-seismic prospecting,, SIAM J. Appl. Math., 65 (2005), 1443.
doi: 10.1137/040604108. |
[22] |
K. L. Williams, An effective density fluid model for acoustic propagation in sediments derived from Biot theory,, J. Acoust. Soc. Am., 110 (2001), 2276.
doi: 10.1121/1.1412449. |
[23] |
Z. Zhu, M. W. Haartsen and M. N. Toksöz, Experimental studies of electro-kinetic conversions in fluid-saturated bore-hole models,, Geophysics, 64 (1999), 1349. Google Scholar |
[24] |
Z. Zhu and M. N. Toksöz, Cross hole seismoelectric measurements in bore-hole models with fractures,, Geophysics, 68 (2003), 1519. Google Scholar |
[25] |
Z. Zhu and M. N. Toksöz, Seismoelectric and seismomagnetic measurements in fractured bore-hole models,, Geophysics, 70 (2005). Google Scholar |
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