Approximate expression for the hilbert transform of a certain class of functions and their application to the ray theory of seismic waves

Summary Approximate expressions for the Hilbert transform of the functionf(t)=exp(- ₀ ² t ²/²) cos( ₀ t+v) are determined. This function, given a suitable choice of the three parameters ₀, and v, approximates a wide class of seismic signals very well. The approximate expressions for the Hilbert transform enable very simple formulae to be given for the elementary seismograms of the individual seismic body waves (in the zero approximation of the ray theory). This accelerates the computation of ray theoretical seismograms considerably.     

Vital and mortal staining of algae in the presence of chlorine-produced oxidants

Evans blue and neutral red were tested as mortal and vital stains respectively for eight estuarine algal species which had been exposed to chlorine-produced oxidants in a continuous-flow system. The effect of CPO on staining with Evans blue was negligible. High concentrations of CPO affected staining with neutral red in several instances; this is probably due to CPO-induced mortality of test organisms during the exposure or staining period. Neutral red leached fromSkeletonema costatum andOlisthodiscus luteus before the end of the staining period. Staining ofDunaliella tertiolecta with neutral red proceeded more slowly. Evens blue, which was incorporated quickly and remained in the cells, is recommended for live-dead determinations for all species examined exceptNitzschia closterium, for which neutral red should be used. Neither stain was effective onMychonastes ruminatus (Simpson and Van Valkenburg 1978).     

“Pandora box” — Matrix in the calculus of observations

Summary If the condition R(A)=k(n), whereA is the design matrix of the type n × k and k the number of parameters to be determined, is not satisfied, or if the covariance matrixH is singular, it is possible to determine the adjusted value of the unbiased estimable function of the parameters f(), its dispersion D( (x)) and ² as the unbiased estimate of the value of ² by means of an arbitrary g-inversion of the matrix . The matrix , because of its remarkable properties, is called the Pandora Box matrix. The paper gives the proofs of these properties and the manner in which they can be employed in the calculus of observations.     

“Spectral ω2 model” and variable absorption coefficient

Summary Aki's spectral ² model[1] is used to estimate the amplitude field at epicentral distances up to 1000 km in the case of an absorption coefficient of seismic waves which varies with distance. Velocity spectra, the periods of the maximum of these spectra and the maximum velocity amplitudes are obtained. The results are compared with[2] and it is shown that the divergence of the amplitude field decreases if a variable absorption coefficient is used. The theoretical results, obtained in this case, approach the results seen in practice. The possibility of determining the limits of epicentral distances, at which the amplitude field may be considered as linear, is given.     

Identity of the characteristics of electrodynamic seismographs with non-standard periods of seismometers and galvanometers

Summary The maximum changes of magnification were determined for electrodynamic seismographs with standard characteristics and for some experimental long-period seismographs, the constants of which are given in Tab. 1, when the period of the seismometer or galvanometer has a deviation of not more than 5% from the standard value. Under the assumption of control of the other constants of the seismograph, identical amplitude and phase responses with a small change of the absolute magnification of the seismograph may be achieved with characteristicsAII ( ² >0.2), AIV ( ² 0.4), B ( ² >0.3) Nos28, 32 and33. This deviation can also be compensated by adjusting the optical distance. The procedure of adjusting the identical characteristics is suitable for systems with which an accurate setting of the period is difficult and for systems with an uncontrollable period, provided their values are within the limits of allowed deviations from the standard constants.     

Time variation of earthquake activity in the Balkan region

Summary Three quantities M, E ^1/2 and E ^2/3 are used for studying the Balkan earthquake provinces. Most of them show a regular trend of activity, for some of them the observation period of 70 years is too short. Some graphs give evidence of the coincidence or migration of activity.     

Dynamic loading of the boundaries in the finite-difference study of diffraction

Summary The finite-difference method can be used for obtaining the theoretical seismic response of a block structure to an incident plane wave. Computer time is saved by solving an equivalent problem of dynamic loading of the boundary of the block structure. The loading is performed by means of a set of discrete body forces, replacing the incident wave at the interface.     

Mechanism of solar-terrestrial relations and changes of atmospheric circulation

Summary As a result of investigating the relations between the variations of geomagnetic activity and meteorological factors [1, 2] a mechanism of solar-terrestrial relationships and a model of the changes of atmospheric circulation in the Northern Hemisphere are proposed; this provides an explanation of the causes of the fluctuation of the climate, of dry and cold periods and differing vegetation conditions in various years in dependence on the intensity of geomagnetic activity.     

On one generalization of trochoidal waves

Summary The concept of the generalized trochoidal waves discussed in[1] is revised and modified. A new formula defining the auxiliary function (b, c) was found with the aid of the results derived in[3] and some physical considerations.