Stratified multifractal magnetization and surface geomagnetic fields-I. Spectral analysis and modelling

Lovejoy, S.; Pecknold, Sean; Schertzer, D.

doi:10.1111/j.1365-246x.2001.00344.x

Cited by 33 publications

(16 citation statements)

References 40 publications

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“…The crust is composed of multiple layers that may be characterized by different magnetic properties (different fractal parameters) yielding a radial power spectrum possibly more complicated than predicted by equation (4). The fractal parameter might vary with the wavelength [e.g., Gettings , 2005; Pecknold et al , 2001] or depend on the direction (i.e., vertical versus horizontal) [e.g., Lovejoy et al , 2001]. The model parameters z t , Δ z , and β might vary within the computational window.…”

Section: Discussionmentioning

confidence: 99%

“…Early methods assumed that crustal magnetization is a completely random function of position characterized by a flat power density spectrum [e.g., Connard et al , 1983; Blakely , 1988; Tanaka et al , 1999; Ross et al , 2006]. However, other studies have suggested that crustal magnetization more closely follows fractal behavior [e.g., Pilkington et al , 1994; Maus and Dimri , 1995, 1996; Lovejoy et al , 2001; Pecknold et al , 2001; Gettings , 2005]. The method used in the present study is derived from a method initially developed by Maus et al [1997] that incorporates a model of fractal random magnetization, thus providing a more realistic representation for crustal magnetization.…”

Section: Introductionmentioning

confidence: 99%

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Mapping Curie temperature depth in the western United States with a fractal model for crustal magnetization

2009

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[1] We have revisited the problem of mapping depth to the Curie temperature isotherm from magnetic anomalies in an attempt to provide a measure of crustal temperatures in the western United States. Such methods are based on the estimation of the depth to the bottom of magnetic sources, which is assumed to correspond to the temperature at which rocks lose their spontaneous magnetization. In this study, we test and apply a method based on the spectral analysis of magnetic anomalies. Early spectral analysis methods assumed that crustal magnetization is a completely uncorrelated function of position. Our method incorporates a more realistic representation where magnetization has a fractal distribution defined by three independent parameters: the depths to the top and bottom of magnetic sources and a fractal parameter related to the geology. The predictions of this model are compatible with radial power spectra obtained from aeromagnetic data in the western United States. Model parameters are mapped by estimating their value within a sliding window swept over the study area. The method works well on synthetic data sets when one of the three parameters is specified in advance. The application of this method to western United States magnetic compilations, assuming a constant fractal parameter, allowed us to detect robust long-wavelength variations in the depth to the bottom of magnetic sources. Depending on the geologic and geophysical context, these features may result from variations in depth to the Curie temperature isotherm, depth to the mantle, depth to the base of volcanic rocks, or geologic settings that affect the value of the fractal parameter. Depth to the bottom of magnetic sources shows several features correlated with prominent heat flow anomalies. It also shows some features absent in the map of heat flow. Independent geophysical and geologic data sets are examined to determine their origin, thereby providing new insights on the thermal and geologic crustal structure of the western United States.Citation: Bouligand, C., J. M. G. Glen, and R. J. Blakely (2009), Mapping Curie temperature depth in the western United States with a fractal model for crustal magnetization,

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mapping Curie temperature depth in the western United States with a fractal model for crustal magnetization

2009

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“…The multifractal distribution of sources is another unexplored area, however some work has been carried out for the multifractal distribution of susceptibility (Fedi 2003;Fedi et al 2005b;Gettings 2005Gettings , 2012 although its use in the estimation of depth of anomalous sources has not yet been explored. Lovejoy et al (2001) suggested that anisotropic scaling is suitable for modelling the stratified earth and its magnetic field at higher and intermediate wavenumber ranges. Pecknold et al (2001) found that assumption of quasi-Gaussian statistics results in isotropic scaling behaviour of the magnetic field, otherwise it is anisotropic multifractal.…”

Section: O N C L U S I O Nmentioning

confidence: 99%

Modelling of magnetic data for scaling geology

Bansal

Dimri

2013

Geophysical Prospecting

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Interpretation of magnetic data can be carried out either in the space or frequency domain. The interpretation in the frequency domain is computationally convenient because convolution becomes multiplication. The frequency domain approach assumes that the magnetic sources distribution has a random and uncorrelated distribution. This approach is modified to include random and fractal distribution of sources on the basis of borehole data. The physical properties of the rocks exhibit scaling behaviour which can be defined as P(k) = Ak−β, where P(k) is the power spectrum as a function of wave number (k), and A and β are the constant and scaling exponent, respectively. A white noise distribution corresponds to β = 0. The high resolution methods of power spectral estimation e.g. maximum entropy method and multi‐taper method produce smooth spectra. Therefore, estimation of scaling exponents is more reliable. The values of β are found to be related to the lithology and heterogeneities in the crust. The modelling of magnetic data for scaling distribution of sources leads to an improved method of interpreting the magnetic data known as the scaling spectral method. The method has found applicability in estimating the basement depth, Curie depth and filtering of magnetic data.

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“…At regional and crustal scales, Maus and Dimri (1994) and Pilkington and Todoeschuck (1995) have shown that distributions of magnetic susceptibilities can be modeled with fractals. Further work by Lovejoy et al (2001) and Pecknold et al (2001) demonstrated that at these scales the distributions are multifractal. At sub-regional scales, drill hole logs of magnetic susceptibility were well modeled with fractals by Pilkington and Todoeschuck (1993) and were shown to be multifractal in general by Gettings (1995), Fedi (2003), Gettings (2005) and Bansal et al (2010).…”

Section: Introductionmentioning

confidence: 99%

Multifractal model of magnetic susceptibility distributions in some igneous rocks

Gettings

2012

Nonlin. Processes Geophys.

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Abstract. Measurements of in-situ magnetic susceptibility were compiled from mainly Precambrian crystalline basement rocks beneath the Colorado Plateau and ranges in Arizona, Colorado, and New Mexico. The susceptibility meter used measures about 30 cm 3 of rock and measures variations in the modal distribution of magnetic minerals that form a minor component volumetrically in these coarsely crystalline granitic to granodioritic rocks. Recent measurements include 50-150 measurements on each outcrop, and show that the distribution of magnetic susceptibilities is highly variable, multimodal and strongly non-Gaussian. Although the distribution of magnetic susceptibility is well known to be multifractal, the small number of data points at an outcrop precludes calculation of the multifractal spectrum by conventional methods. Instead, a brute force approach was adopted using multiplicative cascade models to fit the outcrop scale variability of magnetic minerals. Model segment proportion and length parameters resulted in 26 676 models to span parameter space. Distributions at each outcrop were normalized to unity magnetic susceptibility and added to compare all data for a rock body accounting for variations in petrology and alteration. Once the best-fitting model was found, the equation relating the segment proportion and length parameters was solved numerically to yield the multifractal spectrum estimate. For the best fits, the relative density (the proportion divided by the segment length) of one segment tends to be dominant and the other two densities are smaller and nearly equal. No other consistent relationships between the best fit parameters were identified. The multifractal spectrum estimates appear to distinguish between metamorphic gneiss sites and sites on plutons, even if the plutons have been metamorphosed. In particular, rocks that have undergone multiple tectonic events tend to have a larger range of scaling exponents.

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Stratified multifractal magnetization and surface geomagnetic fields-I. Spectral analysis and modelling

Cited by 33 publications

References 40 publications

Mapping Curie temperature depth in the western United States with a fractal model for crustal magnetization

Mapping Curie temperature depth in the western United States with a fractal model for crustal magnetization

Modelling of magnetic data for scaling geology

Multifractal model of magnetic susceptibility distributions in some igneous rocks

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