Revisiting the Pulse-Width Method to Estimate the Source and Attenuation Parameters from Local Earthquake Seismic Records

The quality factor Q is the medium properties quantifying seismic waves attenuation due to anelastic rock behavior. It can be measured from earthquake seismic signals both in frequency and time domain and separately for P and S waves. Assuming  that Q is frequency-independent over the seismic frequency band, Kjartansson (1979) developed a model suggesting that, if the seismic source generates a symmetric pulse, the pulse width at any station is proportional to t* via a coefficient, named C. Here t* represents the travel time divided by Q. It is noteworthy that C may depend on Q and remains relatively constant for Q>20. To test the validity of the model under more general source and propagation conditions, we applied it to a set of simulated seismograms generated by different earthquake sources and recorded at seismic stations located at the surface of a homogeneous half-space. The source model is a circular rupture propagating at uniform rupture speed, under the action of a constant stress-drop and for different seismic moments (magnitudes). The far-field source radiated pulses for both direct P and S waves are generally represented by a non-symmetric triangles that are convolved with the Kjartansson’s attenuation function to simulate the propagation to the station. We developed an automatic technique to measure both pulse width and half-width on synthetic attenuated signals and validated it against the known theoretical values.  In our simulations we explored a wide range of values for magnitude, stress drop, rupture velocity and Q. Since these parameters affect the shape of the triangular pulse, we investigate their possible influence on C of the Kjartansson’ equation. Preliminary results show that C depends on Q (even for Q>20) and magnitude. Here we present the complete analysis of the results with the aim to obtain the explicit dependence of C on the most waveform-sensitive source and attenuation parameters in terms of a polynomial expansion.   References Kjartansson. Constant Q–Wave propagation and attenuation. J. Geophys. Res., 84, 4737-4748, 1979. Doi 10.1029/JB084iB09p04737