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CHEN YUN-TAI;LIN BANG-HUI;LI XING-CAI;WANG MIAO-YUEInstitute of Geophysics, Academia SinicaXIA DA-DE;WANG XING-HUIThe Seismological Brigade of Chengdu, National Seismological BureauLIU WAN-QIN;LI ZHI-YONGInstitute of Geophysics, Academia Sinica  
Using the observational data of small earthquakes which occurred in Qiaojia andShimian, it is found that the half period of first P arrivals is nearly constant for theshocks of small magnitudes, and increases proportionally with magnitudes for largerearthquakes. It is also pointed out that the logarithm of the amplitudes of theinitial motion of P-waves increases proportionally with the magnitudes. Taking aradially expanding circular shear crack with uniform dislocation as the theoreticalmodel of the moderate and small earthquake sources, the far-field displacement ofseismic body waves radiated from such a model is derived.By using the expression offar-field displacement, the quantitative relations between the source parameters, wavevelocities and the half period, the amplitude of the first arrivals are inferred, andconsequently, the empirical relationships between the half period as well as theamplitude of the first P arrivals and the magnitude of earthquakes are explained.Considering the attenuation and dispersion of waves in the medium, the effect ofthe free surface as well as the response characteristics of the seismograph instru-ments, the theoretical seismograms from this dislocation source are synthesized bythe convolution technique, and a method by which the source parameters as well asQ value of the medium can be directly determined from the half period and theamplitude of the first P arrivals on the observed seismograms, is proposed. By apply-ing the present method, the source parameters of small earthquakes as well as Qvalues of the medium of the two regions metioned above are estimated. The Q valuesof the medium of the Qiaojia region and the Shimian region are 620 and 560, res-pectively. The stress drops of the small earthquakes in the Shimian region areestimated to be about 2 to 30 bars,and that of the small earthquakes in the Qiaojiaregion, are rather low and close to each other, the mean value of which is about 1.4bars. Comparing these results with the stress drops of the foreshocks and the mainshocks of the Xinfengjiang (1962) and Haicheng (1975) earthquakes, we note the fact that the small earthquakes in the Qiaojia region are similar to the fore-shocks of these two large shocks in the character of their stress drops, and so it maynot be neglected that these small shocks in the Qiaojia region are foreshocks priorto a larger earthquake. Taking the mean value (about 1.4 bars) of the stress dropsof the small earthquakes as an estimation of the lower limit of the stress drop ofthis hypothetical earthquake, it may be inferred that, from the empirical relationshipbetween the stress drop and the magnitude of the mainshock, the lower limit of themagnitude of this hypothetical earthquake will be about 5.2.
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