Riding the Right Wavelet

Detecting Fracture and Fault Orientation Scale Transitions Using Morlet Wavelets

Roberto Emanuele Rizzo, David Healy, Natalie Jane Farrell

Research output: Contribution to conferenceAbstract

Abstract

The analysis of images through two-dimensional (2D) continuous wavelet transforms makes it possible to acquire local information at different scales of resolution. This characteristic allows us to use wavelet analysis to quantify anisotropic random fields such as networks of fractures. Previous studies [1] have used 2D anisotropic Mexican hat wavelets to analyse the organisation of fracture networks from cm- to km-scales. However, Antoine et al. [2] explained that this technique can have a relatively poor directional selectivity. This suggests the use of a wavelet whose transform is more sensitive to directions of linear features, i.e. 2D Morlet wavelets [3]. In this work, we use a fully-anisotropic Morlet wavelet as implemented by Neupauer & Powell [4], which is anisotropic in its real and imaginary parts and also in its magnitude. We demonstrate the validity of this analytical technique by application to both synthetic - generated according to known distributions of orientations and lengths - and experimentally produced fracture networks. We have analysed SEM Back Scattered Electron images of thin sections of Hopeman Sandstone (Scotland, UK) deformed under triaxial conditions. We find that the Morlet wavelet, compared to the Mexican hat, is more precise in detecting dominant orientations in fracture scale transition at every scale from intra-grain fractures (μm-scale) up to the faults cutting the whole thin section (cm-scale). Through this analysis we can determine the relationship between the initial orientation of tensile microcracks and the final geometry of the through-going shear fault, with total areal coverage of the analysed image. By comparing thin sections from experiments at different confining pressures, we can quantitatively explore the relationship between the observed geometry and the inferred mechanical processes. [1] Ouillon et al., Nonlinear Processes in Geophysics (1995) 2:158 – 177. [2] Antoine et al., Cambridge University Press (2008) 192-194. [3] Antoine et al., Signal Processing (1993) 31:241 – 272. [4] Neupauer & Powell, Computer & Geosciences (2005) 31:456 – 471.
Original languageEnglish
Publication statusPublished - 2016
Event2016 AGU Fall Meeting - Moscone centre, San Francisco, United States
Duration: 12 Dec 201616 Dec 2016

Conference

Conference2016 AGU Fall Meeting
CountryUnited States
CitySan Francisco
Period12/12/1616/12/16

Fingerprint

wavelet
thin section
fracture network
transform
geometry
microcrack
wavelet analysis
signal processing
confining pressure
geophysics
analytical method
scanning electron microscopy
sandstone
electron
experiment
analysis

Cite this

Rizzo, R. E., Healy, D., & Farrell, N. J. (2016). Riding the Right Wavelet: Detecting Fracture and Fault Orientation Scale Transitions Using Morlet Wavelets. Abstract from 2016 AGU Fall Meeting, San Francisco, United States.

Riding the Right Wavelet : Detecting Fracture and Fault Orientation Scale Transitions Using Morlet Wavelets. / Rizzo, Roberto Emanuele; Healy, David; Farrell, Natalie Jane.

2016. Abstract from 2016 AGU Fall Meeting, San Francisco, United States.

Research output: Contribution to conferenceAbstract

Rizzo, RE, Healy, D & Farrell, NJ 2016, 'Riding the Right Wavelet: Detecting Fracture and Fault Orientation Scale Transitions Using Morlet Wavelets' 2016 AGU Fall Meeting, San Francisco, United States, 12/12/16 - 16/12/16, .
Rizzo RE, Healy D, Farrell NJ. Riding the Right Wavelet: Detecting Fracture and Fault Orientation Scale Transitions Using Morlet Wavelets. 2016. Abstract from 2016 AGU Fall Meeting, San Francisco, United States.
Rizzo, Roberto Emanuele ; Healy, David ; Farrell, Natalie Jane. / Riding the Right Wavelet : Detecting Fracture and Fault Orientation Scale Transitions Using Morlet Wavelets. Abstract from 2016 AGU Fall Meeting, San Francisco, United States.
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N2 - The analysis of images through two-dimensional (2D) continuous wavelet transforms makes it possible to acquire local information at different scales of resolution. This characteristic allows us to use wavelet analysis to quantify anisotropic random fields such as networks of fractures. Previous studies [1] have used 2D anisotropic Mexican hat wavelets to analyse the organisation of fracture networks from cm- to km-scales. However, Antoine et al. [2] explained that this technique can have a relatively poor directional selectivity. This suggests the use of a wavelet whose transform is more sensitive to directions of linear features, i.e. 2D Morlet wavelets [3]. In this work, we use a fully-anisotropic Morlet wavelet as implemented by Neupauer & Powell [4], which is anisotropic in its real and imaginary parts and also in its magnitude. We demonstrate the validity of this analytical technique by application to both synthetic - generated according to known distributions of orientations and lengths - and experimentally produced fracture networks. We have analysed SEM Back Scattered Electron images of thin sections of Hopeman Sandstone (Scotland, UK) deformed under triaxial conditions. We find that the Morlet wavelet, compared to the Mexican hat, is more precise in detecting dominant orientations in fracture scale transition at every scale from intra-grain fractures (μm-scale) up to the faults cutting the whole thin section (cm-scale). Through this analysis we can determine the relationship between the initial orientation of tensile microcracks and the final geometry of the through-going shear fault, with total areal coverage of the analysed image. By comparing thin sections from experiments at different confining pressures, we can quantitatively explore the relationship between the observed geometry and the inferred mechanical processes. [1] Ouillon et al., Nonlinear Processes in Geophysics (1995) 2:158 – 177. [2] Antoine et al., Cambridge University Press (2008) 192-194. [3] Antoine et al., Signal Processing (1993) 31:241 – 272. [4] Neupauer & Powell, Computer & Geosciences (2005) 31:456 – 471.

AB - The analysis of images through two-dimensional (2D) continuous wavelet transforms makes it possible to acquire local information at different scales of resolution. This characteristic allows us to use wavelet analysis to quantify anisotropic random fields such as networks of fractures. Previous studies [1] have used 2D anisotropic Mexican hat wavelets to analyse the organisation of fracture networks from cm- to km-scales. However, Antoine et al. [2] explained that this technique can have a relatively poor directional selectivity. This suggests the use of a wavelet whose transform is more sensitive to directions of linear features, i.e. 2D Morlet wavelets [3]. In this work, we use a fully-anisotropic Morlet wavelet as implemented by Neupauer & Powell [4], which is anisotropic in its real and imaginary parts and also in its magnitude. We demonstrate the validity of this analytical technique by application to both synthetic - generated according to known distributions of orientations and lengths - and experimentally produced fracture networks. We have analysed SEM Back Scattered Electron images of thin sections of Hopeman Sandstone (Scotland, UK) deformed under triaxial conditions. We find that the Morlet wavelet, compared to the Mexican hat, is more precise in detecting dominant orientations in fracture scale transition at every scale from intra-grain fractures (μm-scale) up to the faults cutting the whole thin section (cm-scale). Through this analysis we can determine the relationship between the initial orientation of tensile microcracks and the final geometry of the through-going shear fault, with total areal coverage of the analysed image. By comparing thin sections from experiments at different confining pressures, we can quantitatively explore the relationship between the observed geometry and the inferred mechanical processes. [1] Ouillon et al., Nonlinear Processes in Geophysics (1995) 2:158 – 177. [2] Antoine et al., Cambridge University Press (2008) 192-194. [3] Antoine et al., Signal Processing (1993) 31:241 – 272. [4] Neupauer & Powell, Computer & Geosciences (2005) 31:456 – 471.

M3 - Abstract

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