Estimation of Radiated Energy of Recent Great Earthquakes Using the Normal-mode Theory

Abstract:

Despite its fundamental importance in seismology, accurate estimation of radiated energy remains challenging. The interaction of the elastic field with the near-source structure, especially the free surface, makes the radiation field very complex. Here we address this problem using the normal-mode theory. Radiated energy estimations require a detailed finite source model for the spatial and temporal slip distribution. We use the slip models for recent great earthquakes provided by various investigators. We place a slip model in a spherically symmetric Earth (PREM), and compute the radiated energy by modal summation. For each mode, the volume integral of the energy density over the Earth’s volume can be obtained analytically. The final expression involves a sum over the source patches nested in the modal summation itself. In practice we perform modal summation up to 80 mHz. We explore the effect of several factors such as the focal mechanism, the source depth, the source duration, the source directivity and the seismic moment. Not surprisingly, the source depth plays a key role. The effect can be very significant for events presenting large slip at shallow depths. Deep earthquakes and strike-slip earthquakes are essentially unaffected by the free surface. Similar to the situation in moment tensor determinations, shallow dipping reverse or normal focal mechanisms can be heavily affected. The preliminary estimates of the radiated energy for the frequency ≤ 80 mHz are; the 2004 Sumatra earthquake, 8.3x10¹⁶ J (average for 2 rupture models), the 2010 Maule, 1.6x10¹⁷ J (2), the 2011 Tohoku-oki, 1.1x10¹⁷ J (5), the 2012 Sumatra, 2.4x10¹⁷ J (2), the 1994 Bolivia, 4.1x10¹⁵ J (1), the 2013 Okhotsk, 2.0x10¹⁶ J (1), and the 2010 Mentawai, 2.9x10¹⁴ J (1). To obtain the total radiated energy, the radiated energy for frequency ≥ 80 mHz estimated with other methods (e.g., integration of velocity records) needs to be added.