SCALING LAW FROM TWO-DIMENSIONAL FAULTING MODEL

The spectra of the far-field body wave displacement for various magnitude earthquakes are derived,using a two-dimensional faulting model featuring a rectangular fault. There are three corner frequencies fc1,fc2,fc3, in the displacement spectra,fc1 and fc2 relate to faulting times for the length and width directions on the rectangular fault respectively,and fc3 corresponds to the rise time of the source lime function. According to these three corner frequency values,four spectral regions are defined,u()=u(0)f0,fc1 in the first region; u()1/f,fc1c2 in the second region; u() 1/f2,fc2c3 in the third region;u()1/f3,f>fc3 in the fourth region. Since there are different attenuation rates with frequency in the spectra,this case results in different source parameter relations for different magnitude ranges (i.e. different ranges of seismic moment). It is supposed that earthquake faulting is satisfied with the three conditions of geometrical similarity,stress environment and dynamic similarity,then seismic moment,faulting time along the length and width of the fault and rise time can be all scaled with fault length. The constants in scaling relations can be determined from seismic moment data for about 800 earthquakes that occurred during 1981-1983 given by Dziewonski and Woodhouse (1983),and Ms,mb data by ISC Bulletion. Thus the relations between the source parameters can be deduced from the scaling law,rather than pure statistical relations.