Three-dimensional conjugate gradient inversion of magnetotelluric impedance tensor data

Abstract

We developed a three-dimensional (3D) conjugate gradient inversion algorithm for inverting magnetotelluric impedance tensor measurements. In order to show the importance of including diagonal components of magnetotelluric impedance tensor in 3D inversion, synthetic data were inverted using the 3D conjugate gradient inversion, and the inversion results were compared and analyzed. The results from the 3D inversion of synthetic data indicate that both the off-diagonal and the diagonal components are required in inversions to obtain better inversion results when there are no enough data sites to recover the target resistivity structure. These examples show that lots of information about 3D structure is also contained in the diagonal components; as a result, diagonal components should be included in 3D inversions. The inversion algorithm was also used to invert the impedance tensor data acquired in the Kayabe area in Japan. Inversions with the synthetic and real data demonstrated the validity and practicability of the inversion algorithm.

Keywords

magnetotelluric / impedance tensor / 3D inversion / conjugate gradients / diagonal components

References

[1] Avdeev D. B., Avdeeva A. D.. A Rigorous Three-Dimensional Magnetotelluric Inversion. Progress in Electromagnetics Research, 2006, 62: 41-48.

[2] Dai S. K.. Geophysical Inversion Using Apparent Model Space Contrast Method. Acta Geophys. Sinica, 1994, 37(Suppl.II): 524-533.

[3] Dai S. K., Xu S. Z.. Rapid Inversion of Magnetotelluric Data for 2-D and 3-D Continuous Media. Oil Geophysical Prospecting, 1997, 32(3): 305-317.

[4] De-Groot-Hedlin C. D., Constable S. C.. Occam’s Inversion to Generate Smooth, Two-Dimensional Models from Magnetotelluric Data. Geophysics, 1990, 55(12): 1613-1624.

[5] Hu Z. Z., Hu X. Y., He Z. X.. Pseudo-Three-Dimensional Magnetotelluric Inversion Using Nonlinear Conjugate Gradients. Chinese J. Geophys., 2006, 49(4): 1226-1234.

[6] Jupp D. L. B., Vozoff K.. Two-Dimensional Magnetotelluric Inversion. Geophys. J. Roy. Astr. Soc., 1977, 50(2): 333-352.

[7] Lin C. H., Tan H. D., Tong T.. Three-Dimensional Conjugate Gradient Inversion of Magnetotelluric Sounding Data. Applied Geophysics, 2008, 5(4): 314-321.

[8] Lin C. H., Tan H. D., Tong T.. Parallel Rapid Relaxation Inversion of 3D Magnetotelluric Data. Applied Geophysics, 2009, 6(1): 77-83.

[9] Lin C. H., Tan H. D., Tong T.. The Possibility of Obtaining nearby 3D Resistivity Structure from Magnetotelluric 2D Profile Data Using 3D Inversion. Chinese J. Geophys., 2011, 54(1): 245-256.

[10] Mackie R. L., Madden T. R.. Three-Dimensional Magnetotelluric Inversion Using Conjugate Gradients. Geophys. J. Int., 1993, 115(1): 215-229.

[11] Madden T. R., Mackie R. L.. Three-Dimensional Magnetotelluric Modeling and Inversion. Proc. IEEE, 1989, 77(2): 318-333.

[12] Newman G. A., Alumbaugh D. L.. Three-Dimensional Massively Parallel Electromagnetic Inversion—I. Theory. Geophys. J. Int., 1997, 128(2): 345-354.

[13] Newman G. A., Alumbaugh D. L.. Three-Dimensional Magnetotelluric Inversion Using Non-linear Conjugate Gradients. Geophys. J. Int., 2000, 140(2): 410-424.

[14] Rodi W., Mackie R. L.. Nonlinear Conjugate Gradients Algorithm for 2-D Magnetotelluric Inversion. Geophysics, 2001, 66(1): 174-187.

[15] Siripunvaraporn W., Egbert G.. An Efficient Data-Subspace Inversion Method for 2-D Magnetotelluric Data. Geophysics, 2000, 65(3): 791-803.

[16] Siripunvaraporn W., Egbert G., Lenbury Y., . Three-Dimensional Magnetotelluric Inversion: Data-Space Method. Physics of the Earth and Planetary Interiors, 2005, 150(1–3): 3-14.

[17] Smith J. T., Booker J. R.. Rapid Inversion of Two- and Three-Dimensional Magnetotelluric Data. J. Geophys. Res., 1991, 96(B3): 3905-3922.

[18] Spichak V., Popova I.. Artificial Neural Network Inversion of Magnetotelluric Data in Terms of Three-Dimensional Earth Macroparameters. Geophys. J. Int., 2000, 142(1): 15-26.

[19] Takasugi S., Tanaka K., Kawakami N., . High Spatial Resolution of the Resistivity Structure Revealed by a Dense Network MT Measurement—A Case Study in the Minamikayabe Area, Hokkaido, Japan. Journal of Geomagnetism and Geoelectricity, 1992, 44(4): 289-308.

[20] Tan H. D., Wei W. B., Deng M., . General Use Formula in MT Tensor Impedance. Oil Geophysical Prospecting, 2004, 39(1): 114-116.

[21] Tan H. D., Yu Q. F., Booker J., . Magnetotelluric Three-Dimensional Modeling Using the Staggered-Grid Finite Difference Method. Chinese J. Geophys., 2003, 46(5): 705-711.

[22] Tan H. D., Yu Q. F., Booker J., . Three-Dimensional Rapid Relaxation Inversion for the Magnetotelluric Method. Chinese J. Geophys., 2003, 46(6): 850-854.

[23] Zhdanov M. S., Fang S., Hursan G.. Electromagnetic Inversion Using Quasi-linear Approximation. Geophysics, 2000, 65(5): 1501-1513.