Solar flares associated with singularities in the differential characteristics of magnetic fields

We analyze the flare events of October 28 and May 27, 2003 to examine the possible connection of solar flares with singularities in the differential characteristics of solar magnetic fields. The relation between flares and the behavior of F indicators (which describe structural singularities of the magnetic fields) introduced earlier is analyzed. It is shown that the generation of flares can be associated with self-intersections (or reconnection) of the F = 0 curves, where magnetic reconnection can occur. Consequently, the current sheets generated in such regions can be sources of energy release.     

Rotational and magnetic corrections to the g-mode frequencies in a one-dimensional MHD model

The central magnetic field and rotation of the solar radiative zone are responsible for corrections to the g-mode frequencies. Magnetogravitational spectra are calculated analytically in a simple one-dimensional MHD model that goes beyond the WKB approximation and avoid any cusp resonances that trap the wave within the radiative zone in the presence of a weak magnetic background. The calculations are compared with spacecraft observations of the 1% frequency shifts for candidate g-modes found in the SOHO GOLF experiment. The magnetic correction is the main contribution for a strong magnetic field satisfying the approximation used. It is shown that a constant magnetic field of 700 kG in the radiative zone provides the required frequency shift for the n = ?10 g-mode. The rotational correction, which is due to the Coriolis force in the one-dimensional model used, is much less than a percent (α_Ω ≤ 0.003).     

Simulations of 3D DC borehole resistivity measurements with a goal-oriented <Emphasis Type="Italic">hp</Emphasis> finite-element method. Part II: through-casing resistivity instruments

We simulate direct current (DC) borehole resistivity measurements acquired in steel-cased deviated wells for the assessment of rock formation properties. The assumed data acquisition configuration considers one current (emitter) and three voltage (collector) electrodes that are utilized to measure the second difference of the electric potential along the well trajectory. We assume a homogeneous, 1.27-cm-thick steel casing with resistivity equal to 10^− 5 Ω· m. Simulations are performed with two different numerical methodologies. The first one is based on transferring two-dimensional (2D) axisymmetric optimal grids to a three-dimensional (3D) simulation software. The second one automatically produces optimal 3D grids yielded by a 3D self-adaptive goal-oriented algorithm. Both methodologies utilize high-order finite elements (FE) that are specially well-suited for problems with high-contrast coefficients and rapid spatial variations of the electric field, as it occurs in simulations that involve steel-cased wells. The method based on transferring 2D-optimal grids is efficient in terms of CPU time (few seconds per logging position). Unfortunately, it may produce inaccurate 3D simulations in deviated wells, even though the error remains below 1% for the axisymmetric (vertical) well. The method based on optimal 3D grids, although less efficient in terms of CPU time (few hours per logging position), produces more accurate results that are validated by a built-in a posteriori error estimator. This paper provides the first existing simulations of through-casing resistivity measurements in deviated wells. Simulated resistivity measurements indicate that, for a 30° deviated well, measurements in conductive layers 0.01 Ω· m) are similar to those obtained in vertical wells. However, in resistive layers (10,000 Ω· m), we observe 100% larger readings in the 30° deviated well. This difference becomes 3,000% for the case of a 60° deviated well. For this highly-deviated well, readings corresponding to the conductive formation layer are about 30% smaller in magnitude than those in a vertical well. Shoulder effects significantly vary in deviated wells.