The moment magnitude of the earthquake would be calculated by following formula
Moment magnitude Mw=2/3 log (Mo-9.1)
Seismic moment (Mo) = μ*S*D
My doubt is how could we get rupture length (S) and Slip of an area (D) immediately. Is there any standard model to calculate these parameters?
Dear colleague,
What type of seisimeter that you are using? This mathematic formula is very accurate and commonly used!!
Regards
Dear friends
The main question is why same magnitude Mw does show differences in PGA values for the same epicentral distance?
As you know well that Mw is related to released energy for specific earthquake, so why their recorded accelerations vary for the same distance and Mw for different seismotectonic regions?
regards
Dear Ramesh,
consider that, as a general property, the value of the amplitude spectrum of displacement at frequency=0 is proportional to the seismic moment Mo (see Aki & Richards “Quantitative Seismology” ed. 2009, chapter 10).
So, if you take the signal of your seismic event, compensate for attenuation and geometrical spreading, convert it to displacement and compute the amplitude spectrum then the value at f=0 (I call it Ao) gives you a measure of Mo. Depending on the type os sensor you are using, probably you don’t get the recording of signals down to f=0, but you can approximate it by considering the behaviour of the spectrum at low frequencies.
To get the final value of the Mo, and so of Mw, you need to link Ao to Mo. This can be done assuming some model of the rupture which allows to link the kinematic parameteres to the geometrical/seismic parameter of the rupture. A model often used is the Brune-Madariaga model that assumes circular rupture and is suited for moderate (let say up to Mw=5) and shallow (into the crust) earthquakes. In this case you get:
Mo=2πρv^3Ao/0.6
Where ρ is density and v velocity at source, and 0.6 accounts for average radiation pattern.
Hope the above can help.
Kind regards,
Lorenzo
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