The Strain Energy, Seismic Moment and Magnitudes of Large Earthquakes

The strain energy E_st, as potential energy, released by an earthquake and the seismic moment M_o are two fundamental physical earthquake parameters. The earthquake rupture process ``represents'' the release of the accumulated E_st. The moment M_o, first obtained in 1966 by Aki, revolutioned the quantification of earthquake size and led to the elimination of the limitations of the conventional magnitudes (originally ML, Richter, 1930) mb, Ms, m, MGR. Both M_o and E_st, not in a 1-to-1 correspondence, are uniform measures of the size, although E_st is presently less accurate than M_o. Est is partitioned in seismic- (E_s), fracture- (E_g) and frictional-energy E_f, and E_f is lost as frictional heat energy. The available E_st = E_s + E_g (Aki and Richards (1980), Kostrov and Das, (1988) for fundamentals on M_o and E_st). Related to M_o, E_st and E_s, several modern magnitudes were defined under various assumptions: the moment magnitude M_w (Kanamori, 1977), strain energy magnitude M_E (Purcaru and Berckhemer, 1978), tsunami magnitude M_t (Abe, 1979), mantle magnitude M_m (Okal and Talandier, 1987), seismic energy magnitude M_e (Choy and Boatright, 1995, Yanovskaya et al, 1996), body-wave magnitude M_pw (Tsuboi et al, 1998). The available E_st = (1/2μ )Δ σ M_o, Δ σ ~=~average stress drop, and M_E is % \[M_E = 2/3(\log M_o + \log(\Delta\sigma/\mu)-12.1) ,\] % and log E_st = 11.8 + 1.5 M_E. The estimation of E_st was modified to include M_o, Δ and μ of predominant high slip zones (asperities) to account for multiple events (Purcaru, 1997): % \[E_{st} = \frac{1}{2} \sum_i {\frac{1}{\mu_i} M_{o,i} \Delta\sigma_i} , \sum_i M_{o,i} = M_o \] % We derived the energy balance of E_st, E_s and E_g as: % \[ E_{st}/M_o = (1+e(g,s)) E_s/M_o , e(g,s) = E_g/E_s \] % We analyzed a set of about 90 large earthquakes and found that, depending on the goal these magnitudes quantify differently the rupture process, thus providing complementary means of earthquake characterization. Results for some classes of large earthquakes are discussed.