A Note on Harmonic Analysis of Geophysical Data with Special Reference to the Analysis of Geomagnetic Storms

Some geophysical characteristics tend to have a fixed distribution relative to the sun. An example is the distribution of air temperature on an ideal earth that is perfectly symmetrical (e.g., in its pattern of land and water) about its axis of rotation. In such a case the geophysical characteristic at any fixed station on the earth undergoes a daily variation that depends only on local time (and latitude and season). This simple pattern of daily change may be modified by intrinsic changes in the solar influences on the earth. The harmonic components of the daily variation at any station may in this case undergo phase changes, in some respects corresponding to Doppler shifts of frequency in optical or sonic phenomena. Care is then needed if the results of harmonic analysis are to be properly interpreted. Such interpretation is discussed with reference to the parts Dst and DS of the magnetic storm variations. Like caution must be observed in cases where the amplitude of a harmonic variation changes,with fixed phase.Scientific Report No. 1 -- Contract No. AF 19(6o4)-2l63 April 18, I960 -- Geophysics Research Directorate Air Force Cambridge Research Center Air Research and Development Command United States Air Force Bedford, MassachusettsYe

The Onsager--Machlup functional for data assimilation

When taking the model error into account in data assimilation, one needs to evaluate the prior distribution represented by the Onsager--Machlup functional. Through numerical experiments, this study clarifies how the prior distribution should be incorporated into cost functions for discrete-time estimation problems. Consistent with previous theoretical studies, the divergence of the drift term is essential in weak-constraint 4D-Var (w4D-Var), but it is not nec essary in Markov chain Monte Carlo with the Euler scheme. Although the former property may cause difficulties when implementing w4D-Var in large systems, this paper proposes a new technique for estimating the divergence term and its derivative.Comment: Reprint from Nonlin. Processes Geophys. (ver.5). 12 pages, 5 figure

Fermion Mass Generation in the D-dimensional Thirring Model as a Gauge Theory

Based on the Schwinger-Dyson (SD) equation, the fermion mass generation is further studied in the D(2<D<4)-dimensional Thirring model as a gauge theory previously proposed. By using a certain approximation to the kernel, we analytically obtained explicit form of the dynamical mass of fermion and the critical line in (N,1/g) space, where N is the number of fermions and g is the dimensionless vector-type four-fermion coupling constant. This analytical result is confirmed by the numerical solution for the SD equation with exact form of the kernel in (2+1) dimensions.Comment: 21 pages, 2 Postscript figures, LaTe

Some Notes on the Interpretation of Rapid Fluctuations in Earth-Currents Observed in High Latitudes

[PREFACE] This report was prepared as a part of the Interdisciplinary study of the upper atmospheric disturbance in the polar regions that is conducted at the Geophysical Institute under Dr, C. T. Elvey, Director of the Institute. The report is primarily intended for the student of geophysics who is interested in this subject. A part of the mathematical procedure that was previously given by Prof. A. T. Price (reference 9 in end of paper) is included in Sections 4 to 6 with some modifications so as to enable the student to follow, without referring to Prof. Price’s paper, the derivation of the formulae which are used in the present discussion* and to apply the method to similar problems. November 15, 1958 M. S.This paper shows that a periodically varying infinite linear current, or a periodically varying turbulent circular current of small radius (here approximated by a magnetic dipole with a changing dipole moment), in the ionosphere, which will give rise to magnetic variations of observed order of magnitude, is adequate for producing voltage differences in the ground of order 0 .1 to 1 volt per kilometer that are frequently observed in high latitudes during disturbed periods. It appears difficult to interpret the earth-current record in terms of its primary origin, unless the distribution of the perturbing magnetic field and that of electric conductivity of the earth are both adequately known. However, the earth-current record is a good indicator of the upper atmospheric disturbance in the polar regions.Ye

Field-aligned currents observed by the OGO 5 and Triad satellites

The existence of field-aligned currents in the polar cap boundary layer as a permanent feature of the magnetosphere is investigated. Magnetic field observations from Triad at 800 km altitude and from OGO 5 in the high-altitude magnetosphere are examined. Results indicate that in the morning half of the boundary layer, currents flow into the ionosphere, and that the current direction is reversed in the afternoon half of the layer. The Triad data further indicate that the net current is a maximum near 1500 MLT and that there may be a secondary maximum during early morning hours. According to the Isis 2 electron observations, the locations of these maximums of field-aligned net current roughly match those of two maximums in the isointensity contours for 150 ev electrons. It is proposed that the polar cap boundary current is driven by a current generator in the magnetotail, or ultimately in the solar wind. It is suggested that the large scale field-aligned currents in the polar cap boundary layer are associated with the dominance of protons on the morning side and of electrons on the afternoon side near the poleward edge of the precipitation zone along the auroral oval

Identifications of the polar cap boundary and the auroral belt in the high altitude magnetosphere: A model for field aligned currents

Using the OGO-5 fluxgate magnetometer data, the polar cap boundary is identified in the high altitude magnetosphere by a sudden transition from a dipolar field to a more tail like configuration. The basic pattern of the magnetic field variations observed during the satellite's traversal of the auroral belt is presented. This pattern shows the existence of a field aligned current layer on the equator side of the polar cap boundary. Currents flow in the opposite directions in the two field aligned current layers. The current directions in these layers as observed by OGO-5 in the high-altitude magnetosphere are the same as those observed at low altitudes by the polar orbiting TRIAD satellite. The magnetic field in the region where the lower latitude field aligned current layer is situated is essentially meridional. Thus the equatorial current closure of this current system must be via the equatorial current sheet. The two field aligned current systems, one at the polar cap boundary and the other on the low latitude side of the auroral belt, are coupled through the Pedersen current in the ionosphere