3D LBFGS inversion of controlled source extremely low frequency electromagnetic data
Cao Meng1, Tan Han-Dong1, and Wang Kun-Peng1
1. Key Laboratory of Geo-detection Ministry of Education and School of Geophysics and Information Technology, China University of Geosciences, Beijing 100083, China.
Abstract：
The controlled source extremely low frequency (CSELF) electromagnetic method is characterized by extremely long and powerful sources and a huge measurement range. Its electromagnetic field can therefore be affected by the ionosphere and displacement current. Research on 3D forward modeling and inversion of CSELF electromagnetic data is currently in its infancy. This paper makes exploratory attempts to firstly calculate the 1D extremely low frequency electromagnetic field under ionosphere-air-earth coupling circumstances, and secondly analyze the propagation characteristics of the background electromagnetic field. The 3D staggered-grid finite difference scheme for solving for the secondary electric field is adopted and incorporated with the 1D modeling algorithm to complete 3D forward modeling. Considering that surveys can be carried out in the near field and transition zone for lower frequencies, the 3D Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) inversion of CSELF electromagnetic data is presented (in which the sources, or primary fields, are included), with the aim of directly inverting the impedance data, regardless of where it is acquired. Derivation of the objective functional gradient is the core component in the inversion. Synthetic tests indicate that the well-chosen approximation to the Hessian can significantly speed up the inversion. The model responses corresponding to the coexistence of conductive and resistive blocks show that the off-diagonal components of tensor impedance are much more sensitive to the resistivity variation than the diagonal components. In comparison with conventional scalar inversion, tensor inversion is superior in the recoveries of electric anomalies and background resistivity.
Barr, R., Jones, D. L., and Rodger, C. J., 2000, ELF and VLF radio waves: J. Atmos. Sol.-Terr. Phys., 62(17), 1689-1718.
[4]
Bashkuev, Y. B., and Khaptanov, V. B., 2001, Deep radio impedance sounding of the crust using the electromagnetic ?eld of a VLF radio installation: Izv. Phys. Solid Earth, 37(2), 157-165.
[5]
Cummer, S. A., 2000, Modeling electromagnetic propagation in the Earth-ionosphere waveguide: IEEE Trans. Antennas Propag., 48(9), 1420-1429.
[6]
Di, Q. Y., Wang, M. Y., Wang, R., and Wang, G. J., 2008, Study of the long bipole and large power electromagnetic ?eld: Chin. J. Geophys. (in Chinese), 51(6), 1917-1928.
[7]
Farquharson, C. G., Oldenburg, D. W., Haber, E., and Shekhtman, R., 2002, Three-dimensional forward-modeling and inversion algorithms for magnetotelluric data: Proceedings of the 16th Workshop on Electromagnetic Data, Santa Fe, New Mexico, June 16-22.
[8]
Fraser-Smith, A. C., Bernardi, A., McGill, P. R., Ladd, M. E., Helliwell, R. A., and Villard, O. G., 1990, Low-frequency magnetic ?eld measurements near the epicenter of the Ms 7.1 Loma Prieta earthquake: Geophys. Res. Lett., 17(9), 1465-1468.
[9]
Fu, C. M., Di, Q. Y., and Wang, M. Y., 2010, Calculate electromagnetic fields in stratified medium with layer-matrix method: Chin. J. Geophys. (in Chinese), 53(1), 177-188.
[10]
Fu, C. M., Di, Q. Y., Xu, C., et al., 2012, Electromagnetic fields for different type sources with effect of the ionosphere: Chin. J. Geophys. (in Chinese), 55(12), 3958-3968.
[11]
Haber, E., Ascher, U. and Oldenburg, D., 2004, Inversion of 3D electromagnetic data in frequency and time domain using an inexact all-at-once approach: Geophysics, 69, 1216-1228.
[12]
Kong, F. N., 2007, Hankel transform filters for dipole antenna radiation in a conductive medium: Geophysical Prospecting, 55(1), 83-89.
[13]
Kulak, A., Mlynarczyk, J., and Kozakiewicz, J., 2013, An analytical model of ELF radiowave propagation in ground-ionosphere waveguides with a multilayered ground: IEEE Trans. Antennas Propag., 61(9), 4803-4809.
[14]
Li, D. Q., Di, Q. Y., Wang, M. Y., and Nobes, D., 2015, ‘Earth-ionosphere’ mode controlled source electromagnetic method: Geophys. J. Int., 202, 1848-1858.
[15]
Lin, C. H., Tan, H. D., Shu, Q., et al., 2012, Three-dimensional conjugate gradient inversion of CSAMT data: Chin. J. Geophys. (in Chinese), 55(11), 3829-3838.
[16]
Liu, D. C. and Nocedal, J., 1989, On the limited memory BFGS method for large scale optimization: Mathematical Programming, 45(1), 503-528.
[17]
Mackie, R. L., and Madden, T. R., 1993, Three-dimensional magnetotelluric inversion using conjugate gradients: Geophys. J. Int., 115, 215-229.
[18]
Newman, G. A., and Alumbaugh, D. L., 2000, Three-dimensional magnetotelluric inversion using non-linear conjugate gradients: Geophys. J. Int., 140, 410-424.
[19]
Newman, G. A., and Boggs, P. T., 2004, Solution accelerators for large-scale three-dimensional electromagnetic inverse problems: Inverse Problems, 20, s151-s170.
[20]
Porrat, D., and Fraser-Smith, A. C., 2003, Propagation at extremely low frequencies: Wiley Encyclopedia of Electrical and Electronics Engineering, John Wiley and Sons, Inc.
[21]
Saraev, A. K., Pertel, M. I., Parfent’ev, P. A., Prokof’ev, V. E., and Kharlamov, M. M., 1999, Experimental study of the electromagnetic ?eld from a VLF radio set for the purposes of monitoring seismic activity in the North caucasus: Izv. Phys. Solid Earth, 35(2), 101-108.
[22]
Sasaki, Y., 2001, Full 3D inversion of electromagnetic data on PC: J. Appl. Geophys., 46, 45-54.
[23]
Silber, I., Price, C., Galanti, E. and Shuval, A., 2015, Anomalously strong vertical magnetic ?elds from distant ELF/VLF sources: J. Geophys. Res. Space Physics, 120, 6036-6044.
[24]
Simpson, J. J., 2009, Current and future applications of 3-D global Earth-Ionosphere models based on the full-vector Maxwell’s equations FDTD method: Surv. Geophys., 30(2), 105-130.
[25]
Simpson, J. J., Heikes, R. P., and Ta?ove, A., 2006, FDTD modeling of a novel ELF radar for major oil deposits using a three-dimensional geodesic grid of the Earth-ionosphere waveguide: IEEE Trans. Antennas Propag., 54(6), 1734-1741.
[26]
Simpson, J. J., and Ta?ove, A., 2004, Three-dimensional FDTD modeling of impulsive ELF propagation about the Earth-sphere: IEEE Trans. Antennas Propag., 52(2), 443-451.
[27]
Simpson, J. J., and Taflove, A., 2005, Electrokinetic effect of the Loma Prieta earthquake calculated by an entire-Earth FDTD solution of Maxwell’s equations: Geophys. Res. Lett., 32(9), L09302.
[28]
Simpson, J. J., and Taflove, A., 2007, A review of progress in FDTD Maxwell’s equations modeling of impulsive subionospheric propagation below 300 kHz: IEEE Trans. Antennas Propag., 55(6), 1582-1590.
[29]
Siripunvaraporn, W., Egbert, G., Lenbury, Y., and Uyeshima, M., 2005, Three-dimensional magnetotelluric: data space method: Physics of the Earth and Planetary Interiors, 150, 3-14.
[30]
Velikhov, E. P., Zhamaletdinov, A. A., Shevtsov, A. N., et al., 1998, Deep electromagnetic studies with the use of powerful ELF radio installations: Izv. Phys. Solid Earth, 34(8), 615-632.
[31]
Wait, J. R., 1958, An extension to the mode theory of VLF ionospheric propagation: J. Geophys. Res., 63(1), 125-135.
[32]
Wait, J. R., 1970, Electromagnetic Waves in Strati?ed Media: Vol. 147, Pergamon Press, United Kingdom.
[33]
Wang, Y., and Cao, Q. S., 2011, Analysis of seismic electromagnetic phenomena using the FDTD method: IEEE Trans. Antennas Propag., 59(11), 4171-4180.
[34]
Wang, Y. and Cao, Q. S., 2015, Extremely low-frequency surface response caused by underground resource: IET Microw. Antennas Propag., 9(11), 1193-1199.
[35]
Ward, S. H., and Hohmann, G. W., 1988, Electromagnetic theory for geophysical applications: Electromagnetic Methods in Applied Geophysics, SEG, 131-312.
[36]
Weiss, C. J., and Constable, S., 2006, Mapping thin resistors and hydrocarbons with marine EM methods, Part II-Modeling and analysis in 3D: Geophysics, 71, 321-332.
[37]
Zhamaletdinov, A., Semenov, V., Shevtsov, A., et al., 2002, Geoelectrical structure of the baltic shield and its vicinity through the lithosphere and mantle: Acta Geophysica Polonica, 50(4), 583-606.
2016, Vol. 13 
