**D.
Malytskyy**^{1}**,
Dr. Sci. (Phys.-Math.), Prof.****,
****E-mail:
dmytro@cb-igph.lviv.ua,**

**O.
Muyla**^{1}**,
Cand. Sci. (Phys.-Math.), Research Associate****,
****E-mail:
orestaro@gmail.com,**

**O.
Hrytsaj**^{1}**,
Postgraduate Student****,
****E-mail:
grycaj.oksana@gmail.com,**

**O.
Kutniv**^{1}**,
Engineer****,
****E-mail:
okutniv@yahoo.com,**

**O.
Obidina**^{1}**,
Postgraduate Student****,
****E-mail:
jane.det@yandex.ua**

**MOMENT
TENSOR INVERSION OF WAVE FORMS**

^{1}**Carpathian
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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