Daniel O . B Nuamah

A new robust and resistant, inversion based 2D Fourier transformation is presented where the spectrum is discretized by series expansion using Hermite functions as basis function. The expansion coefficients are given by the solving a linear inverse problem. Taking advantage of the beneficial properties of the Hermite functions, that they are eigen-functions of the inverse Fourier Transformation, the elements of the Jacobian matrix can be calculated fast without integration. The procedure is robustified by using Iteratively Reweighted Least Squares (IRLS) method with Cauchy-Steiner weights. This results in a very efficient robust and resistant inversion procedure. Its applicability is demonstrated in the field of the interpretation of surface measured geomagnetic data. There is a new feature of the inversion based Fourier transform algorithm, namely that it doesn't need the use of regular (equidistant) measurement array. It is shown, that the algorithm gives acceptable results ev...

A new inversion based Fourier transformation technique named as Legendre-Polynomials Least-Squares Fourier Transformation (L-LSQ-FT) and Legendre-Polynomials Iteratively Reweighted Least-Squares Fourier Transformation (L-IRLS-FT) are presented. The introduced L-LSQ-FT algorithm establishes an overdetermined inverse problem from the Fourier transform. The spectrum was approximated by a series expansion limited to a finite number of terms, and the solution of inverse problem, which gives the values of series expansion coefficients, was obtained by the LSQ method. Practically, results from the least square method are responsive to data outliers, thus scattered large errors and the estimated model values may be far from reality. A definitely better option is attained by introducing Steiner’s Most Frequent Value method. By combining the IRLS algorithm with Cauchy-Steiner weights, the Fourier transformation process was robustified to give the L-IRLS-FT method. In both cases Legendre polyn...

Multivariate statistical methods (principal component analysis, cluster analysis, and correlation analysis) have been applied to coastal soils of Akuse, Southeastern Ghana to determine heavy metal sources (Cu, Zn, Ni, Pb, Cr, Co and Ba). Thirty-four Composite soil samples were taken on a grid of 1km × 1km from the study area and analyzed using X-ray fluorescence analytical protocol. The study showed that: (i) Ni, Pb, Co and Ba had anthropogenic sources (ii) Zn and Cu were associated with parent materials and therefore had natural sources whilst (iii) Cr showed varied sources of both natural and anthropogenic. From the statistical mean estimation, Chromium (Cr) showed the highest mean concentration (mean = 442.8 ± 68.658 ppm). It was followed by Barium (Ba) (mean = 261 ± 137.88 ppm) and Nickel (mean = 83.94 ± 59.915 ppm). Elements such as copper, zinc and Cobalt showed average mean values ranging from (70.45 ppm – 47.47 ppm). Significant positive correlations were found between all m...