Geodesic
Noise-Produced Patterns in Images Constructed from Magnetic Flux Leakage Data
D. S. Goldobin1, 2, 3 ; A. V. Pimenova1 ; J. Levesley2 ; P. Elkington4 ; M. Bacciarelli4
1 Institute of Continuous Media Mechanics, UB RAS, Perm 614013, Russia
2 Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
3 Department of Theoretical Physics, Perm State University, Perm 614990, Russia
4 Weatherford, East Leake, Loughborough LE12 6JX, UK
Mathematical modelling of natural phenomena, Tome 10 (2015) no. 3, pp. 139-148

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Magnetic flux leakage measurements help identify the position, size and shape of corrosion-related defects in steel casings used to protect boreholes drilled into oil and gas reservoirs. Images constructed from magnetic flux leakage data contain patterns related to noise inherent in the method. We investigate the patterns and their scaling properties for the case of delta-correlated input noise, and consider the implications for the method’s ability to resolve defects. The analytical evaluation of the noise-produced patterns is made possible by model reduction facilitated by large-scale approximation. With appropriate modification, the approach can be employed to analyze noise-produced patterns in other situations where the data of interest are not measured directly, but are related to the measured data by a complex linear transform involving integrations with respect to spatial coordinates.
DOI : 10.1051/mmnp/201510311

D. S. Goldobin 1, 2, 3 ; A. V. Pimenova 1 ; J. Levesley 2 ; P. Elkington 4 ; M. Bacciarelli 4

1 Institute of Continuous Media Mechanics, UB RAS, Perm 614013, Russia
2 Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
3 Department of Theoretical Physics, Perm State University, Perm 614990, Russia
4 Weatherford, East Leake, Loughborough LE12 6JX, UK 
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D. S. Goldobin; A. V. Pimenova; J. Levesley; P. Elkington; M. Bacciarelli. Noise-Produced Patterns in Images Constructed from Magnetic Flux Leakage Data. Mathematical modelling of natural phenomena, Tome 10 (2015) no. 3, pp. 139-148. doi: 10.1051/mmnp/201510311

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