Multiscale analysis of geomagnetic data using the continuous wavelet transform: A case study from Hoggar (Algeria)

Ouadfeul, Sid‐Ali; Aliouane, Leila; Eladj, Said

doi:10.1190/1.3513065

Cited by 9 publications

(8 citation statements)

References 6 publications

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“…This interest originated in the analogy between the upward continuation and the wavelet transform (Fedi and Cascone, 2008;Ouadfeul et al, 2010). The modulus of the CWT of a potential field F(x, y) with the Poisson kernel as analyzing wavelet is equivalent to the same field upwarded to a level Z = a (Ouadfeul et al, 2012).…”

Section: The 2-d Continuous Wavelet Transformmentioning

confidence: 99%

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Pattern recognition of structural boundaries from aeromagnetic data using the 2-D continuous wavelet transform and the 3-D analytic signal

Ouadfeul

Aliouane

2013

Pattern Recogn. Phys.

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The main goal of this paper is to use the 2-D continuous wavelet transform (CWT) combined with the 3-D analytic signal (AS) for structural boundaries delimitation from aeromagnetic data. The basic idea is based on the mapping of the maxima of the modulus of the 2-D CWT of the amplitude of the 3-D analytic signal (AS) for the full range of scales used to calculate the 2-D CWT. The proposed idea is applied to the synthetic data of a prism and a cylinder; obtained results show the power of this technique for contacts mapping in cases of high vector magnetization direction. Obtained results of the application to real aeromagnetic data of In Ouzzal area located in the west of Hoggar (Algeria) are compared with the 3-D analytic signal solutions. They show robustness of the proposed tool for pattern recognition of structural boundaries from potential geomagnetic data.

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Section: The 2-d Continuous Wavelet Transformmentioning

confidence: 99%

“…This old chain is probably the result of the evolution of both intercontinental basins and accretion of micro plates involving the creation of oceans and island arcs. It is surrounded by a sediment platform of the Paleozoic age (Ouadfeul et al, 2010).…”

Section: Geological Setting Of Hoggarmentioning

confidence: 99%

Pattern recognition of structural boundaries from aeromagnetic data using the 2-D continuous wavelet transform and the 3-D analytic signal

Ouadfeul

Aliouane

2013

Pattern Recogn. Phys.

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“…(, ), Martelet et al . (), and Ouadfeul, Aliouane and Eladj (). Obviously, this list is not exhaustive but provides a good idea about the state of the art of the wavelet analysis in geophysical applications.…”

Section: Introductionmentioning

confidence: 99%

“…The wavelet transform is an easy-to-implement and versatile tool with applications in many scientific fields (see for instance Lang et al (1995) and Tang et al (2000)). In the field of geophysics, we outline the research work of Chamoli (2009) in bathymetry data, the description of wavelet applications by Kumar and Foufoula-Georgiou (1997), or the interpretation of gravity and magnetic data by Moreau et al (1997Moreau et al ( , 1999, Martelet et al (2001), and Ouadfeul, Aliouane and Eladj (2010). Obviously, this list is not exhaustive but provides a good idea about the state of the art of the wavelet analysis in geophysical applications.…”

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confidence: 99%

Linear inversion via the discrete wavelet transform pseudoinverse

Fernández-Muñiz

Cernea

Fernández-Martínez

2017

Geophysical Prospecting

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Classical least‐squares techniques (Moore–Penrose pseudoinverse) are covariance based and are therefore unsuitable for the solution of very large‐scale linear systems in geophysical inversion due to the need of diagonalisation. In this paper, we present a methodology to perform the geophysical inversion of large‐scale linear systems via the discrete wavelet transform. The methodology consists of compressing the linear system matrix using the interesting properties of covariance‐free orthogonal transformations, to design an approximation of the Moore–Penrose pseudoinverse. We show the application of the discrete wavelet transform pseudoinverse to well‐conditioned and ill‐conditioned linear systems. We applied the methodology to a general‐purpose linear problem where the system matrix has been generated using geostatistical simulation techniques and also to a synthetic 2D gravimetric problem with two different geological set‐ups, in the noise‐free and noisy cases. In both cases, the discrete wavelet transform pseudoinverse can be applied to the original linear system and also to the linear systems of normal equations and minimum norm. The results are compared with those obtained via the Moore–Penrose and the discrete cosine transform pseudoinverses. The discrete wavelet transform and the discrete cosine transform pseudoinverses provide similar results and outperform the Moore–Penrose pseudoinverse, mainly in the presence of noise. In the case of well‐conditioned linear systems, this methodology is more efficient when applied to the least‐squares system and minimum norm system due to their higher condition number that allows for a more efficient compression of the system matrix. Also, in the case of ill‐conditioned systems with very high underdetermined character, the application of the discrete cosine transform to the minimum norm solution provides very good results. Both solutions might differ on their regularity, depending on the wavelet family that is adopted. These methods have a general character and can be applied to solve any linear inverse problem arising in technology, particularly in geophysics, and also to non‐linear inversion by linearisation of the forward operator.

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“…We cite for example the paper of Ouadfeul et al (2010), in which application of the 2D CWT for structural boundary mapping (using geomagnetic data) is demonstrated in an area of the Algerian Sahara. We cite for example the paper of Ouadfeul et al (2010), in which application of the 2D CWT for structural boundary mapping (using geomagnetic data) is demonstrated in an area of the Algerian Sahara.…”

Section: Introductionmentioning

confidence: 99%

Structural edge delimitation from gravity anomaly data using the directional continuous wavelet transform with an example from the Basin and Range Province of the United States

Ouadfeul

Aliouane

2013

The Leading Edge

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In this article, we demonstrate the use of the 2D directional continuous wavelet transform (DCWT) for structural boundary delimitation. We include an example of Bouguer gravity anomaly data analysis from the Basin and Range Province of the United States. Our approach is based on mapping maxima in the modulus of the directional continuous wavelet transform for various scales. We initially validate our concept using synthetic gravity anomaly fields generated from cylindrical and prismatic model bodies (source geometries). Subsequent application of our concept to real gravity anomaly data shows that the method is versatile and robust.

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Multiscale analysis of geomagnetic data using the continuous wavelet transform: A case study from Hoggar (Algeria)

Cited by 9 publications

References 6 publications

Pattern recognition of structural boundaries from aeromagnetic data using the 2-D continuous wavelet transform and the 3-D analytic signal

Pattern recognition of structural boundaries from aeromagnetic data using the 2-D continuous wavelet transform and the 3-D analytic signal

Linear inversion via the discrete wavelet transform pseudoinverse

Structural edge delimitation from gravity anomaly data using the directional continuous wavelet transform with an example from the Basin and Range Province of the United States

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