D. Malytskyy1, Dr. Sci. (Phys.-Math.), Prof., E-mail: firstname.lastname@example.org,
O. Muyla1, Cand. Sci. (Phys.-Math.), Research Associate, E-mail: email@example.com,
O. Hrytsaj1, Postgraduate Student, E-mail: firstname.lastname@example.org,
O. Kutniv1, Engineer, E-mail: email@example.com,
O. Obidina1, Postgraduate Student, E-mail: firstname.lastname@example.org
MOMENT TENSOR INVERSION OF WAVE FORMS
1Carpathian Branch of Subbotin Institute of Geophysics NAS of Ukraine, 3-b Naukova Str., Lviv, Ukraine 79060
The authors present a moment tensor inversion of waveforms, which is more robust and yields more stable and more accurate results than standard approaches. The inversion is solved in two steps. First, a point source of seismic waves is considered, with defined location and origin time. Matrix method is used to solve the problem of wave propagation in the medium modeled as a horizontally layered heterogeneous elastic structure (isotropic and/or anisotropic). In order to allow the source mechanism to change with time each moment tensor component has its own time history. The source is described by the full moment tensor Mlm A numerical technique developed based on forward modeling is used for the inversion of the observed waveforms for the components of moment tensor and the earthquake source-time function (STF(t)). The method provides a good estimate for the complete mechanism when records are treated, which corresponds to a velocity model contained inside the interpolation range. The method of waveform inversion using only direct P- and S-waves at stations that we have developed allows us to retrieve the moment tensor of a point source as a function of time.
We computed the moment tensor solutions also using the graphic method. The traditional graphical method is based on the P-waves prior arrival using information about fuzzy first motion and the S/P amplitude ratio. The polarities between P-waves first motion were defined from complete records on seismograms taking into account the possible inversion of the sign on the z-component. A logarithm of the S/P amplitude ratio is calculated using seismic data received at each station from the three components. Input data for the azimuth and take-off angle are calculated by software packages for each event. Finally, the proposed moment tensor inversion is tested on real data for the earthquakes of 24.04.2011 (13h02m12s, 35.92°N, 14.95°E (near Malta), Mw4.0) and 29.12.2013 (17h09m0.04s, 41.37°N, 14.45°E (Southern Italy), Mw4.9).
Keywords: matrix method, moment time function, earthquake mechanism, tensor of seismic moment.
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