Calculus of Variations with Classical and Fractional Derivatives

MSC 2010: 49K05, 26A33

Fractional Korovkin Theory Based on Statistical Convergence

2000 Mathematics Subject Classification: 41A25, 41A36, 40G15.

Fractional Trigonometric Korovkin Theory in Statistical Sense

2000 Mathematics Subject Classification: 41A25, 41A36.

Hydrogeophysical characterization of anisotropy in the Biscayne Aquifer using geophysical methods

The anisotropy of the Biscayne Aquifer which serves as the source of potable water for Miami-Dade County was investigated by applying geophysical methods. Electrical resistivity imaging, self potential and ground penetration radar techniques were employed in both regional and site specific studies. In the regional study, electrical anisotropy and resistivity variation with depth were investigated with azimuthal square array measurements at 13 sites. The observed coefficient of electrical anisotropy ranged from 1.01 to 1.36. The general direction of measured anisotropy is uniform for most sites and trends W-E or SE-NW irrespective of depth. Measured electrical properties were used to estimate anisotropic component of the secondary porosity and hydraulic anisotropy which ranged from 1 to 11% and 1.18 to 2.83 respectively. 1-D sounding analysis was used to models the variation of formation resistivity with depth. Resistivities decreased from NW (close to the margins of the everglades) to SE on the shores of Biscayne Bay. Porosity calculated from Archie's law, ranged from 18 to 61% with higher values found along the ridge. Higher anisotropy, porosities and hydraulic conductivities were on the Atlantic Coastal Ridge and lower values at low lying areas west of the ridge. The cause of higher anisotropy and porosity is attributed to higher dissolution rates of the oolitic facies of the Miami Formation composing the ridge. The direction of minimum resistivity from this study is similar to the predevelopment groundwater flow direction indicated in published modeling studies. Detailed investigations were carried out to evaluate higher anisotropy at West Perrine Park located on the ridge and Snapper Creek Municipal well field where the anisotropy trend changes with depth. The higher anisotropy is attributed to the presence of solution cavities oriented in the E-SE direction on the ridge. Similarly, the change in hydraulic anisotropy at the well field might be related to solution cavities, the surface canal and groundwater extraction wells.^

Physical, Geochemical, Geomechanical, Geophysical and Hydrodynamic Characterization and Anisotropy Assessment of Corvio Sandstone

Corvio sandstone is a ~20 m thick unit (Corvio Formation) that appears in the top section of the Frontada Formation (Campoó Group; Lower Cretaceous) located in Northern Spain in the southern margin of the Basque-Cantabrian Basin. Up to 228 plugs were cored from four 0.3 x 0.2 x 0.5 m blocks of Corvio sandstone, to perform a comprehensive characterization of the physical, mineralogical, geomechanical, geophysical and hydrodynamic properties of this geological formation, and the anisotropic assessment of the most relevant parameters. Here we present the first data set obtained on 53 plugs which covers (i) basic physical and chemical properties including density, porosity, specific surface area and elementary analysis (XRF - CHNS); (ii) the curves obtained during unconfined and confined strengths tests, the tensile strengths, the calculated static elastic moduli and the characteristic stress levels describing the brittle behaviour of the rock; (iii) P- and S-wave velocities (and dynamic elastic moduli) and their respective attenuation factors Qp and Qs, electrical resistivity for a wide range of confining stress; and (iv) permeability and transport tracer tests. Furthermore, the geophysical, permeability and transport tests were additionally performed along the three main orthogonal directions of the original blocks, in order to complete a preliminary anisotropic assessment of the Corvio sandstone.

Table 1 Core site, fractional abundance of individual isoprenoid GDGTs and TEX86 values

TEXL86 and TEXH86 are organic palaeothermometers based on the lipids of Group 1 Crenarchaeota, recently proposed as a modified version of the original TEX86 index, but with significantly improved geographical coverage. Since few data from the global core top calibration are from the Pacific, this study was carried out to assess whether the global core top calibration is regionally biased or not. The result of principal components analysis of the fractional abundance of GDGTs, an analysis of variance (ANOVA) and the comparison of the residuals of TEXH 86 derived sea surface temperature (SST) estimates of the Pacific subset with that of the global data set suggest that the Pacific subset has a similar TEXH 86-SST relationship with the global data set. However, the regression line through the Pacific data and an ANOVA on the residuals of TEXL 86 derived SST estimates suggest otherwise. The contradictory findings are likely to stem from the large scatter in the Pacific TEXL 86 values in the mid temperature range. While regionality does not seem to exert a strong bias on TEXL 86 and TEXH 86 calibration, it appears that there is a strong need to resolve the large scatter in the global data set, especially in the mid and high latitudes, in order to improve the calibration for a better SST estimation.