Homogeneous magnitude system with unified level for usage in seismological practice

Summary A homogeneous magnitude system (HMS) for determining comparable magnitudes of shallow earthquakes was established and tested on the basis of several thousands of observations of 32 Eurasian seismic stations for seven different wave types. The magnitude level of the HMS was fixed by the level of LH-wave magnitudes, which allows us to maintain the continuity of the HMS magnitudes with the routinely used surface wave magnitudes. The comparable level for magnitudes determined from other wave types was obtained by shifting all the magnitude scales to a common point at magnitude 6·75. The compatible calibrating functions are tabulated and recommended for testing in seismological practice.     

To the problem of earthquake magnitudes determination

Summary Causes of inconsistency in magnitudes determined by broad-band and short-period instruments and by different systems of observations are elucidated. In so doing, both observations of standard stations of USSO of the USSR and those of Soviet frequency selecting seismic stations () are employed. On the basis of large statistic material of the stationare network of USSO, a dependence of spectral constitution ofP waves and frequency-temporal fields constructed for some earthquakes have been revealed as well as a dependence of magnitude values upon an arrival time of maximal particle velocity. It has been shown that the range of measuring (A/T) _max should be enlarged at least to 15 sec. A conclusion is drawn that the most stable magnitude consistent with the Catalogue by Gutenberg is the one determined by medium-period instruments.     

ON CONFIDENCE INTERVALS FOR THE PRODUCT OF THREE MEANS OF THREE NORMALEY DISTRIBUTED POPULATIONS

In many environmental applications,such as exposure assessment and risk modelling,the desiredestimate is a random variable computed as the product of three independently distributed randomvariables.These variables may not necessarily have the same mean and variance.The method for findingthe 100(1-α)% confidence interval for the mean of the product random variable has been proposed bysome practitioners as the product of the 100(1-α)% confidence interval of the three means.In this paperwe show that the distribution of the product of three independent normal random variables is not normal.We find the mean and variance of the product distribution.Further,we show that although the meanof the product is equal to the product of the means,the product of the three confidence intervals is nota good approximation of the confidence intervals for the mean of the product variable.The confidenceinterval of the mean of the product variable may be estimated by computer simulation.An algorithmfor estimating the confidence interval for the mean of the product random variable is given.The programimplementing this algorithm is given as an appendix.