Self-affine gravity covariance model for the Bay of Bengal

Bansal, A. R.; Dimri, V. P.

doi:10.1111/j.1365-246x.2005.02545.x

Cited by 12 publications

(6 citation statements)

References 37 publications

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“…More studies from deep boreholes will further enhance our understanding about the source distribution with depth. The fractal behaviour of magnetic fields may also be used for interpolation and filtering using a covariance model (Bansal and Dimri ) and establishing the relation of age of ocean surface with the variation of magnetic field (Bansal ).…”

Section: Resultsmentioning

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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Section: Resultsmentioning

confidence: 99%

Modelling of magnetic data for scaling geology

Bansal

Dimri

2013

Geophysical Prospecting

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“…The fractal model of magnetic and gravity field data has already been exploited in a variety of uses including kriging of aeromagnetic data using a fractal covariance model (Pilkington et al, 1994), inversion for fractally magnetised source distributions (Maus and Dimri, 1995), Curie depth determination (Maus et al, 1997;Bouligand et al, 2009;Bansal et al, 2011), deriving accurate covariance models for satellite gravity data (Bansal and Dimri, 2005) and synthetic model-making to determine filtering parameters (Pilkington and Cowan, 2006). In the following, we outline a further use of fractals in the preparation of gravity and magnetic data grids prior to FFT-based processing and enhancement algorithms.…”

Section: Fractal Description Of Potential Fieldsmentioning

confidence: 99%

Grid preparation for magnetic and gravity data using fractal fields

Pilkington

Keating

2012

Nonlin. Processes Geophys.

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Abstract. Most interpretive methods for potential field (magnetic and gravity) measurements require data in a gridded format. Many are also based on using fast Fourier transforms to improve their computational efficiency. As such, grids need to be full (no undefined values), rectangular and periodic. Since potential field surveys do not usually provide data sets in this form, grids must first be prepared to satisfy these three requirements before any interpretive method can be used. Here, we use a method for grid preparation based on a fractal model for predicting field values where necessary. Using fractal field values ensures that the statistical and spectral character of the measured data is preserved, and that unwanted discontinuities at survey boundaries are minimized. The fractal method compares well with standard extrapolation methods using gridding and maximum entropy filtering. The procedure is demonstrated on a portion of a recently flown aeromagnetic survey over a volcanic terrane in southern British Columbia, Canada.

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“…See also Bansal and Dimri (2005) which includes scaling analyses of the horizontal anisotropy of gravity anomalies. As in the case of the susceptibility/magnetic anomaly relation, there are complications in the vertical so that there appear to be three regimes in the surface gravity field; essentially they are due to a) the mantle (low wavenumbers), b) the variable lithospheric thickness coupled with the strong mantle/lithosphere density gradient (intermediate range), c) the high wavenumber regime dominated by vertical and horizontal lithospheric heterogeneities (scales smaller than a hundred kilometers or so).…”

Section: Combining Horizontal and Vertical Statistics: Geopotential Fmentioning

confidence: 99%

Scaling and multifractal fields in the solid earth and topography

Lovejoy

Schertzer

2007

Nonlin. Processes Geophys.

124

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Abstract. Starting about thirty years ago, new ideas in nonlinear dynamics, particularly fractals and scaling, provoked an explosive growth of research both in modeling and in experimentally characterizing geosystems over wide ranges of scale. In this review we focus on scaling advances in solid earth geophysics including the topography. To reduce the review to manageable proportions, we restrict our attention to scaling fields, i.e. to the discussion of intensive quantities such as ore concentrations, rock densities, susceptibilities, and magnetic and gravitational fields.We discuss the growing body of evidence showing that geofields are scaling (have power law dependencies on spatial scale, resolution), over wide ranges of both horizontal and vertical scale. Focusing on the cases where both horizontal and vertical statistics have both been estimated from proximate data, we argue that the exponents are systematically different, reflecting lithospheric stratification whichwhile very strong at small scales -becomes less and less pronounced at larger and larger scales, but in a scaling manner. We then discuss the necessity for treating the fields as multifractals rather than monofractals, the latter being too restrictive a framework. We discuss the consequences of multifractality for geostatistics, we then discuss cascade processes in which the same dynamical mechanism repeats scale after scale over a range. Using the binomial model first proposed by de Wijs (1951) as an example, we discuss the issues of microcanonical versus canonical conservation, algebraic ("Pareto") versus long tailed (e.g. lognormal) distributions, multifractal universality, conservative and nonconservative multifractal processes, codimension versus dimension formalisms. We compare and contrast different scaling models (fractional Brownian motion, fractional Levy motion, continuous (in scale) cascades), showing that they are all based on fractional integrations of noises built up from singularity Correspondence to: S. Lovejoy (lovejoy@physics.mcgill.ca) basis functions. We show how anisotropic (including stratified) models can be produced simply by replacing the usual distance function by an anisotropic scale function, hence by replacing isotropic singularities by anisotropic ones.

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Self-affine gravity covariance model for the Bay of Bengal

Cited by 12 publications

References 37 publications

Modelling of magnetic data for scaling geology

Modelling of magnetic data for scaling geology

Grid preparation for magnetic and gravity data using fractal fields

Scaling and multifractal fields in the solid earth and topography

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