The contribution of magnetospheric currents toSq

Since the discovery of the magnetosphere, it has been known that the currents flowing in the magnetosphere contribute toSq, the regular daily variation in the earth's surface magnetic field. The early models, however, were not very accurate in the vicinity of the earth. The magnetospheric contribution toSq has therefore been recalculated by direct integration over the three major magnetospheric current systems; magnetopause, tail and ring. The finite electrical conductivity of the earth, which increases the horizontal and decreases the vertical components of the magnetospheric field at the earth's surface, has been taken into account. The magnetospheric currents are found to contribute 12 nanotesla to the day to night difference in the mid-latitudeSq pattern for steady, quiet magnetospheric conditions. They also contribute to the annual variation in the surface field and must be considered an important source of the observed day to day variation in theSq pattern.     

Least squares and integral methods for the spherical harmonic analysis of theSq-field

Spherical harmonic coefficients (SHCs) for the daily magnetic variation fields (solar and lunar) and the main field of the earth are usually estimated by the method of least squares applied to a truncated spherical harmonic series. In this paper, an integral method for computing the SHCs for the solar quiet daily magnetic variation fieldSq is described and applied toSq data for May and June 1965. TheSq SHCs thus derived are then compared with the results obtained using both unweighted and weighted versions of the least squares method. The weighting used tends to orthogonalize the least squares terms. The integral and weighted least squares results agree closely for terms up to order 4 and degree 30, but both disagree considerably for the higher degree terms with the results of the unweighted least squares. Errors introduced by the numerical integration can be shown to be small, hence the disagreement between integral and unweighted least squares coefficient sets arises from improper weighting. Also, it is concluded that discrepancies between the geomagnetic northward and eastward component-derived coefficient sets arise from either time-dependent external sources that produce non-local-time, based fields or nonpotential sources and not from truncation of the spherical harmonic series as has previously been suggested.Deceased.     

Bemerkungen zur Hypothese zweier Sturmzeitringströme

Summary For several years the theory of the main phase of geomagnetic storms takes into account the existence of two storm time ring currents which are thought to exist in different altitudes. This hypothesis is supported less by satellite data than by the analysis of recovery effects observed in the geomagnetic records, according to that the recovery phase should exist of two seperate single phases. In our opinion however the observational material seems not convincing enough, especially because material of one station only was used for the hitherto made investigations and no elimination of theSq-part was executed. A critical analysis of the observational material is by all means necessary, especially for the reason that already in literature extensive inferences of theDR2 ring current for the formation and the energy behaviour of theDP part were drawn. For the investigation of recovery effects it is necessary to use additionally to records of equatorial stations those of observatories in higher latitudes. TheSq-part has to be eliminated in the analysis. It is referred that new disturbances after the beginning of the recovery phase can feign two separated ring current effects. Some examples of the recovery phase will be discussed. They show that the observational material gives no necessity for the supposition of two separate strom time ring currents. Furthermore some theoretical considerations are opposite to this hypothesis. The charge exchange with thermical atoms of hydrogen is discussed to be a possible loss process. It is taken into account also the possibility to suppose a wide proton energy spectrum for explaining the recovery phase.

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Mitteilung aus dem Geomagnetischen Institut Potsdam, Nr. 226.     

Polar regionSq

Geomagnetically quiet day variations in the polar region are reviewed with respect to geomagnetic field variation, ionospheric plasma convection, electric field and current. Persistently existing field-aligned currents are the main source of the polar regionSq. Consequently, the morphology and variability of the polar regionSq largely depend upon both field-aligned currents and ionospheric conductivity. Since field-aligned currents are the major linkage between the ionosphere and the magnetosphere, the latter is controlled by solar wind state, in particular, the interplanetary magnetic field, the polar regionSq exhibits remarkable IMF dependence.     

Contribution to geomagneticSq-field and equatorial electrojet from the day/night asymmetry of ionospheric current under dawn-to-dusk electric field of magnetospheric origin

If the earth and its ionosphere are immersed in a large-scale dawn-to-dusk electric field (of the order of 0.5 mV/m), the resultant dawn-to-dusk ionospheric currents are much stronger on the dayside than on the nightside. These asymmetric currents over the earth produce a magnetic field detectable on the ground, which will contribute to a considerable extent to theSq-field and equatorial electrojet.This paper was presented at the IAGA General Assembly meeting (Session 9.1) held in Vancouver, Canada, during August 1987.     

Geomagnetic multipoles, 1829 to 1960

Summary Using the results of spherical harmonic analyses of the geomagnetic field for some fourteen different epochs, includingGauss' first analysis for epoch 1835, and theErman-Petersen analysis for epoch 1829, the strength and axes of geomagnetic multipoles have been computed. In particular, a dipole from the three first order spherical harmonic coefficients, a quadrupole from five second order coefficients, and an octupole from seven third order coefficients. The axes of the quadrupole and octupole have moved quite rapidly when compared with movements of the dipole axis, and show a general movement westwards. Although the strength of the dipole has generally diminished, the strengths of the quadrupole and octupole have generally increased.On leave National University of La Plata, Argentina     

Lunar and solar barometric tides at Rarotonga,Cook Islands

Lunar and solar atmospheric tidal oscillations have been determined with reasonable accuracy from a ten-year record of hourly mercury-barometer readings, corrected to mean-sea-level, at Rarotonga (Cook Islands), 21.2°S. For the lunar semidiurnal tide, the annual determination shows an amplitude (56 b) slightly lower and a phase (51°) much smaller than the values (58 b, 72°) that would be derived, for the position of Rarotonga, from the spherical harmonic analysis given byHaurwitz andCowley (1969). The seasonal variation of this oscillation, as given by the monthly and J, E, D values, shows most of the characteristic features found in world-wide determinations. In particular, the near equality of the J, D amplitudes at Rarotonga tends to support theHaurwitz andCowley (1969) suggestion of negative J-D values in southern middle latitudes. For the solar tides, the semidiurnal and terdiurnal oscillations at Rarotonga are similar to those found at other stations in the south-west Pacific region. However, for the diurnal oscillation, the annual amplitude (232 b) is only about half the value (465 b) indicated for the position of Rarotonga by the world maps of theS ₁(p) annual harmonic coefficients given byHaurwitz (1965). It thus seems likely that the relatively small area of lowS ₁(p) annual amplitude in the eastern part of the south Pacific, as indicated by these maps, is much more extensive than formerly supposed.     

On recurrence relations for multipole coefficients

Summary General recurrence relations between the coefficients in thenth and (n+1)th order spherical harmonic multipole expansions are derived. The particular application presented here is the derivation of the equations concerned with representing the geomagnetic field by magnetic multipoles. The equations up to the 3rd order multipole are given as an example of the method. The main advantage in using these recurrence relations rather than other methods is that the mathematics is reduced to merely a matter of successive substitutions and this allows a fast step by step generation of the required equations, in a form for which there is a simple numerical program for solution.     

On the Mathematical Analysis of an Elastic-gravitational Layered Earth Model for Magmatic Intrusion: The Stationary Case

In the early eighties Rundle (1980, 1981a,b, 1982) developed the techniques needed for calculations of displacements and gravity changes due to internal sources of strain in layered linear elastic-gravitational media. The approximation of the solution for the half space was obtained by using the propagator matrix technique. The Earth model considered is elastic-gravitational, composed of several homogeneous layers overlying a bottom half space. Two dislocation sources can be considered, representing magma intrusions and faults. In recent decades theoretical and computational extensions of that model have been developed by Rundle and co-workers (e.g., Fernández and Rundle, 1994a,b; Fernández et al., 1997, 2005a; Tiampo et al., 2004; Charco et al., 2006, 2007a,b). The source can be located at any depth in the media. In this work we prove that the perturbed equations representing the elastic-gravitational deformation problem, with the natural boundary and transmission conditions, leads to a well-posed problem even for varied domains and general data. We present constructive proof of the existence and we show the uniqueness and the continuous dependence with respect to the data of weak solutions of the coupled elastic-gravitational field equations.     

A mathematical structure for a theory of electromagnetic induction in the Earth in low latitude

Summary In low latitude the spatial distribution functions of the source field over the surface and the dimensions of the source, are important in any theory of electromagnetic induction developed for studying the conductivity structure of the Earth. The author has built up a mathematical structure for a theory of electromagnetic induction in anyn-layered earth model in low latitude. No simple solution is assumed for the horizontal distribution function of the source field and no assumption is made about the horizontal gradients of the source. The mathematical structure involves the concept of downward continuity of the field equations inside then-layered earth model. The resulting mathematical functions derived for anyn-layered earth model are complex. Hence a new matrix algebra of complex numbers is introduced by the author and this is built into the theory. From the upward continuity of the field equations, an inequality equation is derived in order to determine the heighth ₀ at which the induction field of the earth becomes negligible compared with the source field. The comparison of such heights at two or more stations under the same influence of the source field can be used for the resolution of the lateral distribution of the earch conductivity structure at these stations. The application of the theory will follow in a subsequent paper.     

Pressure wind adjustment relationships during a multilevel primitive equation prediction process using tropical atmospheric data

Summary In numerical weather forecasting process, with primitive equations, the wind and pressure fields mutually adjust to each other until some form of balance is achieved. The type of balance so achieved by the mass and wind fields during the numerical integration of the primitive equations governing atmospheric motions is not knowna priori. This is particularly so in the case of tropical regions where the pressure wind adjustment laws prevailing in a tropical atmosphere are not well understood.In this study we perform a systematic investigation of the pressure wind adjustment relations during a numerical integration of the primitive equations governing atmospheric motions in a tropical atmosphere. Therefore, a two-day prediction experiment is carried out using the Florida State University Tropical Prediction (FSU) Model (Krishnamurti, 1969;Krishnamurti,et al. 1973;Kanamitsu, 1975). The 200 mb predicted motion (u, v) and height (z) fields are then extracted at 0, 12, 24, 36 and 48 hours of forecast time. Using these motion (u, v) fields three other 200 mb height (z) fields were computed from the inverse nonlinear, linear and quasigeostrophic balance equations. Each of these three diagnostic heights for the 200 mb pressure surface were compared with the respective 200 mb heights obtained from the Florida State University Tropical Preciction Model. The comparison is done by computing the root-mean-square differences between the predicted 200 mb height fields and each of the three 200 mb heights obtained from the inverse non-linear, linear and quasigeostrophic balance equations. The results show that the root-meansquare differences between thez fields from the FSU model and those obtained from the non-linear and linear balance equations lie within the ranges 23 to 44 and 25 to 50 metres respectively. The root-mean-square differences between the predicted heights and the heights computed from the quasigeostrophic balance equation lie in the range 54 to 62 metres. These root-mean-square differences are of significant magnitude since large-scale disturbances in the tropical atmosphere are associated with rather small pressure changes.The variations of these root-mean-square differences as one moves from one forecast time to another exhibit no clear increasing or decreasing trend. In fact the variations appear somewhat random. This rather unsystematic time variation of the root-mean-square differences is a manifestation of the constant changes of the physics in the model as different weather systems evolve in the course of the forecasting process. It seems therefore that the pressure-wind adjustments that take place during a numerical integration of the model equations are of complex nature and cannot simply be approximated by simple diagnostic relations like the ones used in this study.Most of this work was done while the author was at the Florida State University, tallahassee, USA.     

Luni-solar 18.6-year signal in tree-rings from Argentina and Chile

Spectrum analysis of 32 tree-ring chronologies from Argentina and Chile yields evidence for two peaks with periods 19.2±1.6 years (30 out of 32 records) and 10.5±0.4 years in 22 instances. Tests by thet-statistic show that the long-period peak is significant at a confidence level of 99%. This signal is identified as the luni-solar 18.6-year M _n term reported earlier byCurrie (1983) in two treering chronologies from the same region, and later in tree-rings from North America, Tasmania, New Zealand, and South Africa (Currie, 1991a-c). Amplitude and phase of the M _n signal are nonstationary with respect to both time and geography. In particular, abrupt 180° phase changes in wave polarity are often observed.     

Changes in geomagnetic multipole parameters 1942.5–1962.5

Summary From a smooth series of spherical harmonic coefficients for the geomagnetic potential, the corresponding multipole parameters have been calculated for five epochs from 1942.5 until 1962.5, at five year intervals. Changes in multipole parameters are discussed in relation to the secular variation field and to theSchmidt eccentric dipole.     

CodaQ as a combination of scattering and intrinsic attenuation: Numerical simulations with the boundary integral method

Numerical modelling ofSH wave seismograms in media whose material properties are prescribed by a random distribution of many perfectly elastic cavities and by intrinsic absorption of seismic energy (anelasticity) demonstrates that the main characteristics of the coda waves, namely amplitude decay and duration, are well described by singly scattered waves in anelastic media rather than by multiply scattered waves in either elastic or anelastic media. We use the Boundary Integral scheme developed byBenites et al. (1992) to compute the complete wave field and measure the values of the direct waveQ and coda wavesQ in a wide range of frequencies, determining the spatial decay of the direct wave log-amplitude relation and the temporal decay of the coda envelope, respectively. The effects of both intrinsic absorption and pure scattering on the overall attenuation can be quantified separately by computing theQ values for corresponding models with (anelastic) and without (elastic) absorption. For the models considered in this study, the values of codaQ ^–1 in anelastic media are in good agreement with the sum of the corresponding scatteringQ ^–1 and intrinsicQ ^–1 values, as established by the single-scattering model ofAki andChouet (1975). Also, for the same random model with intrinsic absorption it appears that the singly scattered waves propagate without significant loss of energy as compared with the multiply scattered waves, which are strongly affected by absorption, suggesting its dominant role in the attenuation of coda waves.     

P in the shadow zone of the earth's core—Part I

Summary Regional variations have been indicated in the slope of theP travel-time curve in the shadow zone of the earth's core. Further study is needed since the uncertainties of the slope are large, especially for the observations from North American stations. There is no significant difference between themean slope of theP travel-time curve in the 95°102.9 range and those obtained byJeffreys, andJeffreys andBullen. However, there is a significant difference between themean slope in the 103° to 135° range as obtained in this study, and those obtained byJeffreys andBullen, and in a later revision byJeffreys. Themean travel-time curve ofP in the shadow zone of the earth's core should be lowered. A trial travel-time table is given with amean slope of 4.41 sec/deg. This table is in close agreement with the times obtained byGutenberg andRichter, and with the trial travel-times ofLehmann. Under the assumption of diffraction the longitudinal wave velocity has been determined to be 13.7 km/sec at the core-mantle boundary.This paper was presented at the Annual Meeting of the Seismological Society of America Reno, Nevada, 1966.     

The optimum Bayesian probability procedure and the prediction of strong earthquakes felt in Mexico city

Bayes' theorem has possible application to earthquake prediction because it can be used to represent the dependence of the inter-arrival time (T) of thenext event on magnitude (M) of thepreceding earthquake (Ferraes, 1975;Bufe et al., 1977;Shimazaki andNakata, 1980;Sykes andQuittmeyer, 1981). First, we derive the basic formulas, assuming that the earthquake process behaves as a Poisson process. Under this assumption the likelihood probabilities are determined by the Poisson distribution (Ferraes, 1985) after which we introduce the conjugate family of Gamma prior distributions. Finally, to maximize the posterior Bayesian probabilityP(/M) we use calculus and introduce the analytical condition .Subsequently we estimate the occurrence of the next future large earthquake to be felt in Mexico City. Given the probabilistic model, the prediction is obtained from the data set that include all events withM7.5 felt in Mexico City from 1900 to 1985. These earthquakes occur in the Middle-America trench, along Mexico, but are felt in Mexico City. To see the full significance of the analysis, we give the result using two models: (1) The Poisson-Gamma, and (2) The Poisson-Exponential (a special case of the Gamma).Using the Poisson-Gamma model, the next expected event will occur in the next time interval =2.564 years from the last event (occurred on September 19, 1985) or equivalently, the expected event will occur approximately in April, 1988.Using the Poisson-Exponential model, the next expected damaging earthquake will occur in the next time interval =2.381 years from the last event, or equivalently in January, 1988.It should be noted that very strong agreement exists between the two predicted occurrence times, using both models.     

Correlation between terrestrial heat flow and thermal conductivity

Summary The significant correlation coefficient between the terrestial heat flow and thermal conductivity computed from the continental heat flow data byHorai andNur [1]²) may be explained as a natural consequence of terrestrial heat flow through a random medium. The theory predicts a value of 0.40 for the correlation coefficient. A simple statistical test shows that the majority of the computed coefficients belong to the statistical population whose mean is equal to the theoretical correlation coefficient. There are, however, a few observations of unsually high correlation coefficient which cannot be explained by the above hypothesis.     

Possibility of ground observations of electron spin-flip radiation from lowerE-region electrons

Summary Landovitz & Marshall (¹) have suggested a maserlike mechanism to explain the decameter emission from the Jovian ionosphere. Although the application of the suggested mechanism for emission outwards into space from our planet is obvious, it is our purpose to show that if this mechanism is indeed operative, emission of electron spin-flip radiation from the electrons in the lower part of theE-region is also possible. An order of magnitude estimate predicts that thisE-region radiation which travels downward can be observed by ground receivers.     

Some minerals as new natural models of ferrites

Summary The electron density distribution in the intermediateE-F layer is determined by developing theN(z) profile into a power series. The unknown coefficients are found by means of the boundary conditions for transition towards theE andF1 layers as well as by the value of the maximum electron density in the intermediate layer. In case that stratiform layers in theE-F layer which can be sounded are not available, the measured value for the nondeviative absorption at short waves reflected by theF layer is made use of. The comparisons show the reliable accuracy of the method when seven terms are used in the power series.     

Statistical analysis of earthquake activity at Etna volcano (March 1981 eruption)

Seismic activity that preceded, accompanied, and followed the 17–23 March 1981 Etnean eruption has been statistically analyzed.On the grounds of both time evolution of seismicity and catalogue completeness, three time intervals have been defined (12 February–2 March, 12–17 March, 19–31 March) and for each of these periods both the b coefficient of theGutenberg-Richter's (1956) relationship and the E parameter of the cluster size (Shlien andToksoz, 1970) have been calculated.No significant variations were observed between the first and third periods, while lower values of bothb andE coefficients were found in the second one. These findings might indicate that changes in the seismicity features occur just before the eruption start.Small but fast variations in the stress field acting on the volcano might originate this type of seismic activity, while the importance of the tectonic control on volcanic phenomena seems to be confirmed.