Earthquake Source Parameter Determination based on Waveform Inversion of Fourier Transformed Seismograms (SWIFT) is based on the inversion method of Nakano et. al., 2008. This section summarized the methodology performed in this software. The Software estimates source centroid locations and focal mechanisms of earthquakes by solving the inverse problem in the frequency domain for efficient computations. The observed velocity seismograms are corrected for instrument response and then integrated in time to obtain the displacement seismograms. The waveforms are then bandpass filtered between 50 seconds and 100 seconds and decimated to a sampling frequency of 0.5 Hz. A total of data length of 512 s (256 data points in each channel) is used.
The formulation of the displacement field excited by a point source in the frequency domain is given as
u ̃_n (ω_k )= ∑_(i=1)^(N_m)▒〖G ̃_ni (ω_k ) m ̃_i (ω_k ) 〗 ,k=1,…,N_f (1)
where ω_k is the angular frequency, u ̃_n (ω_k ), m ̃_i (ω_k ) and G ̃_ni (ω_k ) are the Fourier transforms of the nth trace of a displacement seismogram, the ith base of the moment function tensor, and the spatial derivative of Green’s function, respectively; N_m is the number of independent bases of moment tensor components; and N_f is the number of frequency components used for the waveform inversion. In matrix form, Eq. (1) is given as
d ̃(ω_k )= G ̃(ω_k ) m ̃(ω_k ) ,k=1,…,N_f (2)
where d ̃(ω_k ) is the data vector consisting of u ̃_n (ω_k ), G ̃(ω_k ) and is the data kernel matrix with its elements G ̃_ni (ω_k ), and m ̃(ω_k ) is the model parameter vector consisting of m ̃_i (ω_k ). In this approach, the matrix equations for all frequencies are independent of each other and can be solved separately, and the computation is much more efficient than that for solving the inverse problem in the time domain (Nakano et al. 2008). In the inversion method (Nakano et al. 2008), a double-couple focal mechanism is assumed in order to stabilize the solution obtained using data from a small number of seismic stations. The source centroid location is estimated by a spatial grid search which minimizes the normalized...