3D Electromagnetic Low Induction Number Modeling using Integral Equations

Document Type : Research Article


Ph.D. Graduated, Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran


In this paper, a code for 3D forward modeling of electromagnetic low induction number (EM-LIN) data is developed based on the linear integral equations (IE). At first, the code is manipulated for a resistive block immersed in a homogenous background, and the obtained results have RMS errors of 2% comparing with the previously standard published results, which demonstrates the productivity of the 3D forward modeling code. Then, a model composed of two conductive anomalies with different depth ranges and conductivities in a resistive background is considered. IE Forward reposes shows that the shallower block produce larger values in spite of having less conductivity.
Since the forward modeling is linear, the productivity of the forward modeling code depends on the efficiency of the forward operator. Furthermore, linear forward operator plays the key role in the linear inversion procedure, therefore, a real data set of a thick dyke in Bloemfontein Nature Reserve region in South Africa is manipulated. Weighted damped minimum length solution is utilized for the inversion procedure and the inverted model is demonstrative of the forward operator efficiency in practical applications.


Main Subjects

Beamish, D., 2011, Low induction number, ground conductivity meters: A correction procedure in the absence of magnetic effects, Journal of Applied Geophysics 75(2), 244-253.
Carlson, N. R. and Zonge, K. L., 1997, Case histories of electrical and electromagnetic geophysics for environmental applications at active mines. 10th EEGS Symposium on the Application of Geophysics to Engineering and Environmental Problems, European Association of Geoscientists & Engineers.
Constable, S. and Srnka, L. J., 2007, An introduction to marine controlled-source electromagnetic methods for hydrocarbon exploration, Geophysics 72(2), WA3-WA12.
Doolittle, J. A. and Brevik, E. C., 2014, The use of electromagnetic induction techniques in soils studies, Geoderma 223, 33-45.
Fitterman, D. V. and Labson, V. F., 2005, Electromagnetic induction methods for environmental problems. Near-surface geophysics, Society of Exploration Geophysicists, 301-356.
Heil, K. and Schmidhalter, U., 2017, The application of EM38: Determination of soil parameters, selection of soil sampling points and use in agriculture and archaeology, Sensors 17(11), 2540.
Jahandari, H. and Farquharson, C. G., 2013, Forward modeling of gravity data using finite-volume and finite-element methods on unstructured grids, Geophysics 78(3), G69-G80.
Kamm, J., Becken, M. and Pedersen, L. B., 2013, Inversion of slingram electromagnetic induction data using a Born approximation, Geophysics 78(4), E201-E212.
Li, Y. and Oldenburg, D. W., 1996, 3-D inversion of magnetic data, Geophysics 61(2), 394-408.
Makhokha, D. and Fourie, F., 2016, A systematic approach to the interpretation of conductivity anomalies across intrusive dolerite dykes and sills in the Karoo Supergroup, MSc thesis. University of the Free State, Bloemfontein.
McNeill, J. D., 1980, Electromagnetic terrain conductivity measurement at low induction numbers.
Méndez-Delgado, S., Gómez-Treviño, E. and Pérez-Flores, M. A., 1999, Forward modelling of direct current and low-frequency electromagnetic fields using integral equations, Geophysical Journal International 137(2), 336-352.
Menke, W., 2012, Geophysical data analysis: discrete inverse theory: MATLAB edition, Academic press.
Olorunfem, M. O., Dan-Hassan, M. A. and Ojo, J. S., 1995, On the scope and limitations of the electromagnetic method in groundwater prospecting in a Precambrian basement terrain-a Nigerian case study, Journal of African Earth Sciences 20(2), 151-160.
Parnow, S., Oskooi, B. and Florio, G., 2021, Improved linear inversion of low induction number electromagnetic data, Geophysical Journal International 224(3), 1505-1522.
Pellerin, L., 2002), Applications of electrical and electromagnetic methods for environmental and geotechnical investigations, Surveys in Geophysics 23(2), 101-132.
Pérez-Flores, M. A., Antonio-Carpio, R. G., Gómez-Treviño, E., Ferguson, I. and Méndez-Delgado, S., 2012, Imaging of 3D electromagnetic data at low-induction numbers, Geophysics 77(4), WB47-WB57.
Schaller, A., Streich, R., Drijkoningen, G., Ritter, O. and Slob, E., 2018, A land-based controlled-source electromagnetic method for oil field exploration: An example from the Schoonebeek oil field, Geophysics 83(2), WB1-WB17.
Sheriff, R. E., 2002, Encyclopedic dictionary of applied geophysics, Society of exploration geophysicists.
Siemon, B., Christiansen, A. V. and Auken, E., 2009, A review of helicopterā€borne electromagnetic methods for groundwater exploration, Near Surface Geophysics 7(5-6), 629-646.
Simpson, F. and Bahr, K., 2005, Practical magnetotellurics, Cambridge University Press.
Smith, R., 2014, Electromagnetic induction methods in mining geophysics from 2008 to 2012, Surveys in Geophysics 35(1), 123-156.
Song, Y. and Kim, J.-H., 2008, An efficient 2.5 D inversion of loop-loop electromagnetic data, Exploration Geophysics 39(1), 68-77.
Tikhonov, A. N. and Arsenin, V. Y., 1977, Solutions of ill-posed problems, New York 1(30), 487.
Varfinezhad, R., Oskooi, B. and Fedi, M., 2020, Joint Inversion of DC Resistivity and Magnetic Data, Constrained by Cross Gradients, Compactness and Depth Weighting, Pure & Applied Geophysics 177(9).
Yoder, R. E., Freeland, R. S., Ammons, J. T. and Leonard, L. L., 2001, Mapping agricultural fields with GPR and EMI to identify offsite movement of agrochemicals, Journal of Applied Geophysics 47(3-4), 251-259.
Yuan, B., Li, D. and Bayless, R. C., 2017, Wide field electromagnetic method for shale gas exploration in southern China: A case study, Journal of Environmental and Engineering Geophysics 22(3), 279-289.
Zhdanov, M. S., 2002, Geophysical inverse theory and regularization problems, Elsevier.