Application of electrical and magnetic geophysical methods in depth estimation of potential mineral depositat Olabisi Onabanjo University, Ago Iwoye, Southwestern Nigeria

Geophysical techniques are powerful tools in depth estimation of minerals deposits. This survey was carried out to evaluate the nature and depth of mineral deposits near the Sports complex of Olabisi Onabanjo University (OOU), Ago-Iwoye.’. A total of five (5) Vertical Electrical Soundings (VES) points were investigated using Pasi Terrameter. The spread across the area using the Schlumberger configuration was with a maximum current electrode separation of 100m. The results obtained were interpreted quantitatively and qualitatively using partial curve matching and computer iteration programs known as WINRESIST and SURFER 11. Also, forty one (41) survey profiles were taken at a station interval of 5m using the GEM Magnetometer to acquire the Total Magnetic Intensity reading. The Guassian filter-Oasis Montaj was used for the computation of regional field from the observed TMI readings of the area. The geologic andstructural map reveals a few visible fractured zones imbedded in the migmatite-gneiss deposits which spread from the northwest to the southern and eastern part of the study area and the granite gneiss was seen around the Southwestern and Northern parts. The delineated fractures could potentially serve as geologic traps for mineral localization. The 2D radial average power spectrum indicates that, the northeast part of the mapped area has a depth of 4.5mand a depth of 13m at the eastern part. It can be seen that the depth are shallow and there are visible outcrops at the study area.The approximate depth to the mineral deposit was determined using the standard Euler solution to be around 13 m and the elevation range obtained varies between 37 m – 50 m. The correlation of the electrical and magnetic techniques shows that both methods are able to give the estimated depth of shallow mineral deposit which range between 13 m – 18m. Keywords: Euler solution, Geophysical Techniques, Lithology, Total Magnetic Intensity, Vertical Electrical Sounding.

3-D Kernel Density Imaging Based on the Euler Deconvolution of Tensor Gravity Data

Traditional discrimination techniques for Euler deconvolution use only the color spectrums of structural indexes, without considering the spatial distribution characteristics and inherent relationships among the Euler solutions to separate adjacent causative sources. In the present study, a new approach was developed for discriminating uncorrelated Euler solutions from coherent solutions based on the focusing levels indicated by the probability density distributions generated using multivariate kernel density estimations (KDE). A novel multiple coverage technique was proposed by using a series of different sized moving windows over gridded gravity data, which formed tight clusters of Euler solutions for different sized causative sources. The results of the probability density distributions were obtained using a 3-D KDE method for the Euler solution subsets {x, y, z} of synthetical models, and real data from a survey conducted in British Columbia (Canada) which had successfully established more credible and meaningful geological models when compared with three other subsets.

To Investigate the Euler Solution of Differential Equation

For Euler Equations L(y）=∑aixiy(i) =f(x)are Given Special Solution of a Direct Method, and a Special Coefficient Linear Differential Equations L(y)=∑aiy(i)=∑bjejx into Ordinary Differential Equations Euler.

Zero-electron-mass limit of hydrodynamic models for plasmas

This paper is concerned with the limit of the vanishing ratio of the electron mass to the ion mass in the hydrodynamic models for plasmas in critical Besov spaces. We give a new construction of approximation solutions and show that periodic initial-value problems of certain scaled hydrodynamic models have smooth solutions in a (finite) time interval where the Euler solution is known to exist. Furthermore, it is justified that, as the electron mass tends to zero, the smooth solutions converge rigorously to solutions of the incompressible Euler equations, and the definite convergence orders are also obtained.

Solution of Cubic and Quartic Equations

Solution of Cubic and Quartic Equations In this article, the principal n-th root of a complex number is defined, the Vieta's formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan's solution of cubic equations and the Descartes-Euler solution of quartic equations in terms of their complex coefficients are also presented [5].