DIRDOP: a directivity approach to determining the seismic rupture velocity vector

Abstract

Directivity effects are a characteristic of seismic source finiteness and are a consequence of the rupture spread in preferential directions. These effects are manifested through seismic spectral deviations as a function of the observation location. The directivity by Doppler effect method permits estimation of the directions and rupture velocities, beginning from the duration of common pulses, which are identified in waveforms or relative source time functions. The general model of directivity that supports the method presented here is a Doppler analysis based on a kinematic source model of rupture (Haskell, Bull Seismol Soc Am 54:1811-1841, 1964) and a structural medium with spherical symmetry. To evaluate its performance, we subjected the method to a series of tests with synthetic data obtained from ten typical seismic ruptures. The experimental conditions studied correspond with scenarios of simple and complex, unilaterally and bilaterally extended ruptures with different mechanisms and datasets with different levels of azimuthal coverage. The obtained results generally agree with the expected values. We also present four real case studies, applying the

Resolution of rupture directivity in weak events: 1‐D versus 2‐D source parameterizations for the 2011, Mw 4.6 and 5.2 Lorca earthquakes, Spain

“…Rupture directivity is more difficult to assess for weak earthquakes. Different methodologies have been proposed to identify directivity [e.g., Boore and Joyner , ; Somerville et al ., ; Warren and Shearer , ; Seekins and Boatwright , ; Caldeira et al ., ; Cesca et al ., ], exploring for example the azimuthal patterns of peak ground velocity, acceleration, or apparent source duration. Apparent duration is predicted to be smaller in the forward direction of rupture propagation and larger in the backward direction [ Benioff , ; Ben‐Menahem , ], analogous to the Doppler shift in apparent frequency for a moving source.…”

Reply to Comment on “The earthquakes of 29 July 2003, 12 February 2007, and 17 December 2009 in the region of Cape Saint Vincent (SW Iberia) and their relation with the 1755 Lisbon earthquake” by C. Pro, E. Buforn, M. Bezzeghoud and A. Udías

“…The comment states that the directivity effects are a problematic explanation because the effects have been observed in the near field only, typically up to 20 km away from the fault. But we do not agree this assessment because the effects depend on several factors, Tectonophysics 628 (2014) 246-247 such as fault dimension and rupture velocity (Caldeira et al, 2009;Udías et al, 2014). In fact, the directivity effects are proportional to the total rupture length, which must have been very large for this destructive earthquake, for example Stich et al (2007) suggests a fault length of 230-315 km.…”

“…In addition, the directivity effects on teleseismic waveforms can be observed when the rupture length is greater than 15-20 km (Pro, 2002). Besides, these effects do not depend on focal mechanisms and it is very important to distinguish between the rupture propagation direction and the fault slip direction, because they are often different (Caldeira et al, 2009). When the rupture front propagates toward the site and the direction of slip on the fault is aligned with the site, forward rupture directivity effects occur.…”

“…Grandin et al (2007b) show that only a few parameters are crucial when simulating ground motion at low frequency range (f b 0.5 Hz). The moment magnitude, focal mechanism and source location influence the distribution of intensities in the near field (Caldeira et al, 2009;Udías et al, 2014). For large and great earthquakes (M N 6.5), other details of the seismic source can alter dramatically this distribution.…”

Ground motion simulations of the SW Iberia margin: rupture directivity and earth structure effects

“…This distinctive characteristic, which is known as directivity (Ben-Menahem 1961), is manifested by an increase in the frequency and amplitude of seismic waves when the rupture occurs in the direction of the seismic station and a decrease if it occurs in the opposite direction (e.g. Caldeira et al 2009). These effects are maxima when the rupture direction is in the axis of the propagation direction and are not present when the rupture direction is perpendicular to the propagation direction.…”