Identification of sources of potential fields with the continuous wavelet transform: Complex wavelets and application to aeromagnetic profiles in French Guiana

Sailhac, Pascal; Galdéano, A.; Gibert, Dominique; Moreau, Frédérique; Delor, Claude

doi:10.1029/2000jb900090

Cited by 84 publications

(107 citation statements)

References 26 publications

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“…However, such a 3-D geometrical procedure needs sophisticated graphical implementations to be useful in a computer-aided interpretation program. As shown in previous papers [Moreau et al, 1999;Sailhac et al, 2000;Martelet et al, 2001], we instead prefer to invert equation (16) along each line defined in the modulus maxima by using a series of linear regressions in log-log plots, and by testing for a range of trial depths z 0 . In practice, this is done by plotting log( W a j j/a g ) versus log(a + z 0 ) and by searching the z 0 .…”

Section: Wavelet Modulus Maxima Interpretationmentioning

confidence: 99%

“…Second, we develop multipole approximations in case of extended sources, and we show application to synthetic potential fields caused by triaxial ellipsoids and rectangular prisms of finite size. The theory is also illustrated to part of a large aeromagnetic data of French Guyana previously analyzed on the basis of profiles [Sailhac et al, 2000]. This last illustration is kept short for the aim of conciseness of the paper; this shows how to characterize depth extension of a sedimentary lens by interpreting scaling behavior of 2-D wavelet transform coefficients.…”

Section: Introductionmentioning

confidence: 99%

“…This has been done for profiles of Sailhac et al, [2000] who give analytical expressions for typical 2-D bodies and exact power laws as in equation (16) for local sources at depth z 0 . The wavelet coefficients above a homogeneous source at depth z 0 scale as (a + z 0 ) Àb where we recall that b depends both on the homogeneity a of the source and on the order g of the wavelet.…”

Section: Question Of Extended Sourcesmentioning

confidence: 99%

“…[15] Like in profile analysis [Moreau et al, 1999;Sailhac et al, 2000;Martelet et al, 2001], let us now consider the modulus maxima of wavelet coefficients (also called ridges or skeleton). They are determined using classical procedures of local maxima detection and have the useful property of being located nearby above the sources and having good signal to noise ratios.…”

Section: Wavelet Modulus Maxima Interpretationmentioning

confidence: 99%

“…Moreau et al [1999] have analyzed the effects of noise and extent of sources on the properties of the wavelet coefficients. Sailhac et al [2000] have used one-dimensional complex wavelet coefficients similar to upward continued analytic signals. They demonstrated, in the case of total field magnetic anomaly profiles, some useful relations between parameters of the wavelet coefficients and the apparent inclination of magnetization, in addition to depth, vertical extent, and dip angle of the sources.…”

Section: Introductionmentioning

confidence: 99%

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Identification of sources of potential fields with the continuous wavelet transform: Two‐dimensional wavelets and multipolar approximations

Sailhac

Gibert

2003

J. Geophys. Res.

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[1] We show new continuous wavelet-based transformation techniques of potential field maps and propose interpretation schemes for characterizing three-dimensional (3-D) sources having some finite extent. As in previous studies, we use wavelets derived from the Poisson kernel which generate a position-altitude representation of potential field data initially measured at one level above the ground. We use first-order or second-order wavelets to obtain wavelet transform parameters related to the 3-D analytic signals or 3 Â 3 tensors of the data. We show how such parameters can be used to characterize the sources, first, by using the assumption of their local homogeneity and, second, by using multipolar expansions to estimate the sizes of the horizontal or vertical extent of the 3-D source. Thus we generalize to 3-D the Taylor expansion of upward continued 2-D analytic signals previously shown for the interpretation of profiles transformed using complex wavelets. Such a 3-D interpretation scheme based upon position-altitude representations has been developed to interpret the maps of scalar potential field anomalies (e.g., magnetic total field anomalies or vertical gravity anomalies) but can be also used for upward continued maps of vector or tensor of potential field anomalies as obtained by new surveys of the full tensor of gravity; this also concerns the interpretation of derived potentials considered in poroelasticity and electrokinetic in porous materials of the Earth. We illustrate the technique on synthetic data; in addition, a first application on aeromagnetic data from French Guyana shows the potential of the technique.INDEX TERMS: 0903 Exploration Geophysics: Computational methods, potential fields; 0920 Exploration Geophysics: Gravity methods; 0925 Exploration Geophysics: Magnetic and electrical methods; 3260 Mathematical Geophysics: Inverse theory; 3299 Mathematical Geophysics: General or miscellaneous; KEYWORDS: wavelets, magnetics, harmonic/multipolar expansion, upward continuation, analytic signals, Guyane Française Citation: Sailhac, P., and D. Gibert, Identification of sources of potential fields with the continuous wavelet transform: Two-dimensional wavelets and multipolar approximations,

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Section: Wavelet Modulus Maxima Interpretationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Question Of Extended Sourcesmentioning

confidence: 99%

Section: Wavelet Modulus Maxima Interpretationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Identification of sources of potential fields with the continuous wavelet transform: Two‐dimensional wavelets and multipolar approximations

Sailhac

Gibert

2003

J. Geophys. Res.

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Enhancing signals from buried Roman structures in Magnetometer data by combining continuous wavelet transform and tensor voting

Jungmann

Dolenz

Clauser

et al. 2017

Archaeological Prospection

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In this paper, a processing chain is proposed for enhancing larger‐scale building structures in magnetometer data using the continuous wavelet transform for extracting the horizontal location, depth, and homogeneity (or shape) of subsurface objects. Even though the values estimated from our data do not clearly describe the archaeological site, they are used as a filter step for removing objects whose depth and homogeneity fall outside a predefined range. This yields a binary map, where valid points represent the horizontal source positions of magnetic anomalies. In a second step, curvilinear subsets of points are identified on a larger scale by the tensor voting framework indicating archaeological relevant structures, such as arcs and lines. Here, a point casts votes on neighbouring points and their values depend on the distance, and relative position of the points. All votes are summed up and the final value discriminates, whether a certain point (and therefore a magnetic source) is part of a salient curve (e.g. arc, line). Thresholding removes points with lower values while keeping those with larger values. Although the result shows many geometric features, it still needs to be combined with other data, e.g. from aerial photography or excavations. In combination, the extracted features continue those structures in the aerial photograph, thus expanding the knowledge about the archaeological site.

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Depth Estimation of Potential Field by Minimum Inversion Fitting Error

Xie

Wang

Liu

2016

Chinese J of Geophysics

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Estimation of source depth plays an important role in quantitative interpretation of magnetic or gravity data. Various methods have been developed to conduct this estimation, especially for magnetic source depth. They include slope, Naudy, Werner deconvolution, Euler deconvolution, analytical signal, source parameter imaging (SPI), the continuous wavelet transform (CWT) and tilt‐depth approaches. We present a new method to estimate the depth of a field source, which is based on equivalent source technology and potential field inversion. A single layer of 2.5D cuboids model is established as an equivalent source with initial physical property parameters. The single equivalent source layer moves from shallow to deep at certain interval and is used as the initial model to invert the data. Then we estimate the field source depth by inversion fitting error. From shallow to deep, the inversion fitting error usually becomes smaller. The minimum inversion fitting error matches the corresponding field source depth. Because only one equivalent source layer is necessary to invert, the inversion is faster than traditional inversion methods and does not require depth weighting. Calculation of theoretical model data shows that this method can obtain accurate depth of the field source. The data processing of a thin plate with an aspect ratio of 7.5 shows that the depth calculation error is about one measured point (25 m). The data processing of a thick plate with an aspect ratio from 0.5 to 1.5 shows that the depth calculation error is less than one measured point (25 m). Processing of measured aeromagnetic gradient data indicates that the central depth of the magnetic source is between 200 m to 250 m. Drilling data show that such anomalies are caused by the diorite at depth from 200 m to 300 m, in agreement well with estimation. These tests demonstrate that the depth estimation method suggested in this paper is applicable to both isolated anomalies and combined anomalies.

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Identification of sources of potential fields with the continuous wavelet transform: Complex wavelets and application to aeromagnetic profiles in French Guiana

Cited by 84 publications

References 26 publications

Identification of sources of potential fields with the continuous wavelet transform: Two‐dimensional wavelets and multipolar approximations

Identification of sources of potential fields with the continuous wavelet transform: Two‐dimensional wavelets and multipolar approximations

Enhancing signals from buried Roman structures in Magnetometer data by combining continuous wavelet transform and tensor voting

Depth Estimation of Potential Field by Minimum Inversion Fitting Error

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