An automatic waveform modeling method to estimate source and attenuation parameters for earthquakes

An automatic waveform modeling method to estimate source and attenuation parameters for earthquakes   

R. Petito Penna¹, A. Zollo^1,2, G. Russo², S. Nazeri², G. De Landro²

¹ Scuola Superiore Meridionale, Napoli, Italia

² Dipartimento di Fisica Ettore Pancini, Università degli Studi di Napoli Federico II, Napoli, Italia

Seismic waves in the Earth's crust experience attenuation, affecting waveform, amplitude, and duration. Anelastic attenuation is quantified by the quality factor Q, the ratio of energy lost per wave cycle to total radiated energy. Kjartansson (1979) developed a model where Q is spatially variable but frequency-independent, predicting a linear relationship between pulse width T_d^c and the attenuation parameter t_c^* :

Here, c refers to P or S phase, T_d^c is the pulse duration at the receiver, T₀  is the apparent source duration, TT_c  is the travel time, and Q_c is the quality factor. C_d^c  is a constant coefficient. This relation also applies to half duration T_hd^c, defined as the time between the pulse peak and its beginning.

We propose a time-domain technique to estimate source parameters and Q by measuring pulse durations (T_d^c and T_hd^c) for P- and S-wave displacement signals in an anelastic medium. These signals are recorded at stations around epicenters with a known velocity model. Based on circular kinematic rupture models (Sato and Hirasawa, 1973; Madariaga, 1976), our method approximates the far-field displacement waveform with a scalene triangular function and finds the theoretical waveform that best fits the recorded P (or S) pulse.

For each seismic station, the procedure reads three ground motion records, calculates the displacement modulus, and detects P and S phase arrivals using a kurtosis-based technique (Ross et al., 2014). It selects a time window around each phase, searching for the best-fit triangular waveform by adjusting total duration T_d^c, half duration T_hd^c, and peak amplitude A^P. A cross-correlation function aligns real and theoretical signals, calculating the cost function:

where N is the window length, n is the time instant, A^Real is the real signal amplitude, and A^Theo is the theoretical amplitude. The [i, j, k] indices correspond to the i-th value of T_d^c, the j-th value of T_hd^c and the k-th value of A^P. The best-fit signal corresponds to the smallest F value, repeated across stations.

The next step is to fit total durations to travel times to estimate T₀ and stress drop Δσ from the slope, providing information about the ratio C_d^c/Q. Applying this to 500 earthquakes (0<M_w<4) in Nagano, Japan (November-December 2014), we found average stress drops of <Δσ_P>=(0.09±0.05)MPa for P-waves and <Δσ_S>=(0.04±0.03)MPa for S-waves, with average Q values <Q_P>=143±14 and <Q_S>=340±133. C_d^c was set to 1.    

Kjartansson's model assumes C_d^c is independent of Q, stress-drop ∆σ, and magnitude M. However, our analysis on synthetic triangular signals suggests these dependencies are present. Validating these dependencies with real signals is crucial. We show it's possible to test C_d^c's dependency on magnitude, stress-drop, and Q by combining waveform fitting results with signal spectrum modeling, extending the proposed methodology's applications.