Abstract
Time domain electromagnetic (TDEM) response of a conductive permeable sphere is a main topic for good understanding and in developing past studies for detection and discrimination of buried metallic objects. Stochastic differential equation model is a valuable tool for stimulating real experience. In this paper, according to an Itô integral, we have obtained a weak approximation of stochastic TDEM response of permeable and nonpermeable sphere. We have used the deterministic solution of TDEM response of conductive permeable sphere by changing one of the variables that have been obtained from the boundary conditions of problem to random variable. By adding white noise to random variable and using stochastic integral, we have displayed stochastic time domain response of conductive permeable sphere. The Itô integral includes a factor that shows infirmity and intensity of noise which has been simply considered constant. Accordingly, we have showed the effect of noise for magnetic and nonmagnetic spheres. Numerical results from step and impulse response of TDEM have shown that the amount of this factor is different for the two types of spheres.
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References
Billings SD, Pasion C, Walker S, Beran L (2006) Magnetic models of unexploded ordnance. IEEE Trans Geosci Remote Sens 44(8):2115–2124
Munschy M, Boulanger D, Ulrich P, Bouiflane M (2007) Magnetic mapping for the detection and characterization of UXO: use of multi-sensor fluxgate 3-axis magnetometers and methods of interpretation. J Appl Geophys 61(3–4):168–183
Butler Dwain K (2003) Implications of magnetic backgrounds for unexploded ordnance detection. J Appl Geophys 54(1–2):111–125
Oru B (2010) Location and depth estimation of point-dipole and line of dipoles using analytic signals of the magnetic gradient tensor and magnitude of vector components. J Appl Geophys 70(1):27–37
Takahashi K, Preetz H, Igel J (2011) Soil properties and performance of landmine detection by metal detector and ground-penetrating radar—soil characterisation and its verification by a field test. J Appl Geophys 73(4):368–377
Shubitidze F, O’Neill K, Shamatava I, Sun K, Paulsen KD (2003) Analysis of GPR scattering by multiple subsurface metallic objects to improve UXO discrimination. In: Geoscience and remote sensing symposium, IGARSS 03, proceedings, IEEE international, vol 7, p 4163
Chen C-C, Higgins MB, O’Neill K, Detsch R. (2001) Ultrawide-bandwidth fully-polarimetric ground penetrating radar classification of subsurface unexploded ordnance. IEEE Trans Geosci Remote Sens 39:1221–1230
Shubitidze F, Barrowes B, O’Neill K, Shamatava I (2006) Advanced EMI modeling and processing approaches for UXO discrimination. In: Proceedings of the 11th international conference on mathematical methods in electromagnetic theory, 26–29 June 2006. Kharkiv, Ukraine, p 126–131
Moss CD, Grzegorczyk TM, O’Neill K, Jin Au Kong BAE Syst, Burlington MA (2006) A hybrid time-domain model of electromagnetic induction from conducting, permeable targets. IEEE Trans Geosci Remote Sens 44(10):2916–2926
Asten MW, Duncan C (2007) Fast approximate EM induction modeling of metallic and UXOnext term targets using a permeable prism. J Appl Geophys 61(3–4):235–242
Wait JR (1951) A conducting sphere in a time varying magnetic-field. Geophysics 16:666–672
Wait JR, Spies KP (1969) Quasi-static transient response of a conducting permeable sphere short note. Geophysics 34:789–792
Smith J, Morrison HF, Becker A (2004) Parametric forms and the inductive response of a permeable conducting sphere. J Environ Eng Geophys 9:213–216
Nabighian MN (1970) Quasi-static transient response of a conducting permeable sphere. Geophysics 35:303–309
Kaufman AA, Keller GV (1985) Inductive mining prospecting. Elsevier (Amsterdam-Oxford-New York- Tokyo:Elsevier)
Hjelt SE (1971) Discussion on quasi-static transient response of a conducting permeable sphere (short note), by Wait, James R et al (GEO-34-05-0789-0792), with reply by author. Geophysics 36:615–616
Bell T, Barrow B, Miller J, Keiswetter D (2001) Time and frequency domain electromagnetic induction signatures of unexploded ordnance. Subsurface Sensing Technologies and Applications 2:153–160
Pasion LR (1999) Detecting unexploded ordnance with time domain electromagnetic induction. Master’s thesis, University of British Columbia
Pasion LR, Billings SD, Oldenburg DW, Walker SE (2007) Application of a library-based method to time domain electromagnetic data for the identification of unexploded ordnance. J Appl Geophys 61:279–291
Munkholm MS, Auken E (1996) Electromagnetic noise contamination on transient electromagnetic soundings in culturally disturbed environments. J Environ Eng Geophys 1(2):119–127
Nabighian MN, Macnae JC (1991) Time domain electromagnetic prospecting methods. In: Nabighian MN (ed) Electromagnetic methods in applied geophysics. Tulsa, OK. Society of Exploration Geophysicists, vol 2, part A, pp 427–520
McNeill JD, Bosnar M (1996) Application of time domain electromagnetic techniques to UXO detection. In: Proceedings of UXO Forum, Williamsburg, Virginia, 26–28 March 1996, pp 34–42
ϕksendal B (2003) Stochastic differential equations: an introduction with applications. Springer-Verlag, Heidelberg
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Molhem, H., Meshinchi-Asl, M. & Jafarizadeh, M.A. A weak approximation of stochastic time domain electromagnetic response of a conductive permeable sphere. Arab J Geosci 6, 2971–2979 (2013). https://doi.org/10.1007/s12517-012-0546-1
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DOI: https://doi.org/10.1007/s12517-012-0546-1