Jeferson de Souza

A fast MATLAB program to estimate the multifractal spectrum of multidimensional data: Application to fractures

A MATLAB^(R) program based on the Hou algorithm for estimation of fractal dimension and multifractal spectrum of fractures is presented. The program performance was tested with many synthetical fractals and field data. Interpolation and sampling effects on the fractal dimension and multifractal spectrum estimation were also studied. Some common problems related to the fractal dimension and multifractal spectrum are also discussed.

Enhancement of the total horizontal gradient of magnetic anomalies using tilt derivatives: Part II — Application to real data

We propose a new magnetic anomaly enhancement method based on the tilt derivative of the total horizontal gradient. We illustrate the effectiveness of the method in structural mapping by applying it to reduced-to-the-pole aeromagnetic data and comparing the results to those obtained from other methods reported in literature. The anomalies generated by our method show good correlation with geological structures and Euler deconvolution results.

INDISTINGUISHABLE PARTICLES AND HIDDEN VARIABLES: PART II

In a previous work it was shown that it is possible to deal with collections of indistinguishable elementary particles in a set-theoretical framework, by using hidden variables. We propose in the present paper a set-theoretical axiomatics for collections of indiscernibles with no explicit mention to hidden variables. We also show, in this context, the fundamental role of the (micro) state in the process of individuation of classical and quantum particles. Finally, we discuss the importance of the axiom of choice in Zermelo-Fraenkel set theory in the context of quantum distributions of bosons and fermions.

EdgeDetectPFI: An algorithm for automatic edge detection in potential field anomaly images – application to dike-like magnetic structures

Abstract We propose an algorithm to automatically locate the spatial position of anomalies in potential field images, which can be used to estimate the depth and width of causative sources. The magnetic anomaly is firstly enhanced using an edge detection filter based on a simple transformation (the Signum transform) which retains only the signs of the anomalous field. The theoretical edge positions can be recognized from the locations where one of the spatial field derivatives (or a function of them) change its sign: the zero crossover points. These points are easily identified from the Signum transformed spatial derivatives. The actual sources depths and widths are then estimated using the widths of the positive plateaus obtained from two different Signum transformed data: one based on the vertical derivative and the other using the vertical derivative minus the absolute value of the horizontal derivative. Our algorithm finds these widths in an automatic fashion by computing the radius of the largest circles inside the positive plateaus. Numerical experiments with synthetic data show that the proposed approach provides reliable estimates for the target parameters. Additional testing is carried out with aeromagnetic data from Santa Catarina, Southern Brazil, and the resulting parameter maps are compared with Euler deconvolution.

The application of the Signum transform to the interpretation of magnetic anomalies due to prismatic bodies

The Signum transform is a simple derivative-based method for qualitative and quantitative interpretation of magnetic anomalies from discrete sources. The methodology is based on the normalization of a filtering function, which is a derivative of the anomalous field or function of this, by its absolute value. The filtered anomalies have only two values (+1 or -1) and the causative sources are represented by the positive values. The transform has been applied to three different functions, namely the first order vertical derivative of the magnetic anomaly, the first-order vertical derivative minus total horizontal derivative and second-order vertical derivative For a vertical magnetisation the edges of the sources can be recognised from the locations where one or more of the spatial derivatives change its sign: the zero crossover point. The zero cross over point and actual source edge are separated by an amount which depends on the dykes depth and the type of data being transformed. Thus, actual edge locations are easily computed from the Signum transformed data. The method performs well when closely spaced sources cause anomalies to overlap. Imagery based on the Signum transformation of first and second-order derivative based transforms of the magnetic data combines the advantages of the resolution of the second-order transform with the greater stability of the first-order transform.

Components of multifractality in the central England temperature anomaly series

We study the multifractal nature of the Central England Temperature (CET) anomaly, a time series that spans more than 200 years. The data are analyzed in two ways: as a single set and by using a sliding window of 11 years. In both cases, we quantify the width of the multifractal spectrum as well as its components, which are defined by the deviations from the Gaussian distribution and the dependence between measurements. The results of the first approach show that the key contribution to the multifractal structure comes from the dynamical dependencies, mainly weak ones, followed by a residual contribution of the deviations from the Gaussian. The sliding window approach indicates that the peaks in the evolution of the non-Gaussian contribution occur almost at the same dates associated with climate changes that were determined in previous works using component analysis methods. Moreover, the strong non-Gaussian contribution from the 1960 s onwards is in agreement with global results recently presented.

Propriedades fractais de arenitos fraturados do Canyon Guartelá

The statistical and geometrical properties of fracture systems were obtained by analyzing remote sense images and outcrop data, in the Region of Guartela Canyon, in the central-eastern of Parana State. The probability distributions of fractures, with their parameters and attributes, were obtained through extensive statistical exploration of data. These parameters were used as input data for generating 3-D stochastic fractures models through the “discrete fracture network - DFN” method. The modeling is performed by using the code FRED®. To study the persistence of statistical parameters in multiple scales were used remote sensing images (SRTM, Landsat TM7 and aerial photos), covering a scale range from outcrops (few meters) to basin scales (hundreds of kilometers). The results indicated the presence of power-law (fractal) statistics for the spatial and size distributions. Fractals distributions were found for all sets studied, in some cases with different fractal exponents. The implications of fractal behavior for the generation of discrete fracture network, and consequently for the hydraulic properties, are briefly discussed.