## 1 Introduction

[2] The duration of dynamic rupture is an important parameter for describing earthquake source processes, most notably rupture directivity, length, and velocity of large earthquakes. Together with the total radiated seismic energy *E*, the rupture duration *T _{R}* is a powerful tool for rapidly discriminating between normal and slow ruptures, such as those of tsunami earthquakes [e.g.,

*Convers and Newman*, 2011;

*Newman et al*., 2011]. Detailed estimates of earthquake rupture duration can be obtained from inverted source-time functions [e.g.,

*Houston*, 2001], but given its increasing importance in early determinations for tsunami warning or rapid damage assessments, it is important to accurately determine this parameter along with earthquake location, magnitudes, and focal mechanism rapidly after an earthquake occurs.

[3] Different approaches to rapidly estimating *T _{R}* have been attempted. An estimate using the time at which 90% of the radiated energy was recorded was developed by

*Lomax*[2005]. Another estimate was obtained from the 25% drawdown of energy from its maximum in the envelope of a velocity seismogram between 2 and 4 Hz [

*Hara*, 2007]. Both of the above methods are relatively robust, but require an arbitrary cutoff that may fail with noisy data or for complex ruptures.

*Convers and Newman*[2011] use the crossover duration

*T*

_{XO}, marking the transition between near-linear cumulative energy growth and subsequent scattered energy, to estimate the termination of rupture and the point where they calculate the radiated energy. While

*T*

_{XO}works well in most cases, it requires averaging results from numerous stations and usually needs a minute or more of additional energy after the observation of the completed rupture before an accurate estimate can be made. In this study, we propose a new method that can be computed on individual stations following cessation of observed rupture.

[4] An earthquake's dynamic rupture process is also characterized by *E* [*Boatwright and Choy*, 1986; *Venkataraman and Kanamori*, 2004]. While the seismic moment *M*_{0} defines the work performed in an earthquake, *E* describes the strength of the event; information particularly useful in estimating the strong ground shaking and tsunami hazard [*Choy and Boatwright*, 1995]. In the case of earthquakes with high apparent stress drop, shaking can be over 10 times larger than expected given *M*_{0} [*Choy and Kirby*, 2004]. For earthquakes in the shallow subduction megathrust, the rupture velocity *V _{R}* is greatly reduced, and hence little high-frequency shaking is observed [

*Bilek and Lay*, 1999]. In such cases,

*E*decreases considerably relative to

*M*

_{0}and serves as a discriminant for slow rupturing “tsunami earthquakes” (TsE) [

*Newman and Okal*, 1998]. It is this deficiency in high-frequency energy that led

*Kanamori*[1972] to define TsEs as having much larger tsunami than expected given their magnitude.

[5] While both *T _{R}* and

*E*are independently useful for assessing an earthquake's size, the combination of these is a powerful tsunami earthquake discriminant, because while

*M*

_{0}scales with the cube of the

*T*for most earthquakes [

_{R}*Houston*, 2001], slow TsEs are both deficient in

*E*and excessive in

*T*.

_{R}*Newman et al*. [2011] combined

*E*and

*T*

_{R}^{3}for the real-time discrimination of the 2010 Mentawai TsE. This method, while similar to the (

*E*/

*M*), does not require the accurate estimation of

_{0}*M*

_{0}, rendering it more useful for real-time evaluation.