Rupture length and duration of the 2004 Aceh‐Sumatra earthquake from the phases of the Earth's gravest free oscillations

Abstract

[1] The Aceh-Sumatra 2004 earthquake strongly excited the Earth's free oscillations. Well separated split multiplets provide useful information on the earthquake source. Particularly, the phases of split singlets constrain the duration, rupture length and mean rupture velocity. We analyze the initial phases of some of the Earth's gravest free oscillations ( 0 S 2 , 0 S 3 , 0 S 0 and 1 S 0 ) in order to constrain the space-time finiteness of the source. We use recordings of vertical broadband seismometers and superconducting gravimeters from several worldwide geophysical networks. We estimate a rupture length of about 1220 km, a source time duration of about 500 s, and a mean rupture velocity of 2.4 km/s. Citation: Lambotte, S., L. Rivera, and Introduction[2] Soon after the great Chilean 1960 earthquake, Benioff et al. [1961], Ness et al. [1961] and Alsop et al. [1961] reported accurate measurements of spectral peaks that were associated with the Earth's gravest free oscillations. Recordings of this event also provided the first observational evidence for splitting of the lowest frequency modes. This splitting was attributed to the Earth's rotation by Backus and Gilbert [1961] and Pekeris et al. [1961]. Splitting effect due to ellipticity was introduced later on by Usami and Satô [1962] and Dahlen [1968].[3] The 2004 Aceh-Sumatra earthquake is the largest earthquake ever recorded since the 1960 Chilean earthquake and the 1964 Alaskan earthquake. Initial teleseismic bodywave studies suggested a rupture length of about 400-600 km (e.g., J. [Ni et al., 2005;Lomax, 2005] suggest a longer rupture of over 1200 -1300 km. This is consistent with the location of the aftershocks that extend more than 1000 km northward from the epicenter.[4] Free oscillations are widely used to study the Earth's structure [e.g., Ritzwoller et al., 1986;Woodhouse et al., 1986;Smith and Masters, 1989;Widmer et al., 1992]. Free oscillations with periods between 50 and 300 s are also used to study source parameters of moderate and large earthquakes [e.g., . The gravest normal modes can also provide information on the focal mechanism, seismic moment [Abe, 1970;Geller and Stein, 1977;Kedar et al., 1994;Stein and Okal, 2005], duration and length of the earthquake rupture. Phases of free oscillations are seldom explicitly studied, except for the radial modes, [see Park et al., 2005a]. We demonstrate in this study how it is possible to retrieve the spatio-temporal extension of the rupture using the initial phases of some of the gravest modes ( 0 S 2 , 0 S 3 , 0 S 0 and 1 S 0 ) excited by the Aceh-Sumatra 2004 earthquake. Basics[5] Deviations from spherical symmetry such as rotation, ellipticity and lateral heterogeneities remove the degeneracy and hence force free oscillations multiplets to split. In general, each singlet within a multiplet will have a slightly different central frequency. Generally, to model the split spectrum of a multiplet, it is necessary to account for the Earth's rotation, ellipticity and heterogeneity. For the gravest m...

Long-period toroidal earth free oscillations from the great Sumatra-Andaman earthquake observed by paired laser extensometers in Gran Sasso, Italy

“…At longest period, Park et al (2005) reports initial phases of Earth's radial modes that are consistent with a time‐limited rupture. Lambotte et al (2006, 2007) show that amplitude variations between singlets of 0 S 2 are consistent with a time‐limited northward‐propagating rupture model. No corresponding study has been performed with toroidal modes.…”

“…The gravest free oscillations with periods T > 1000 s have been observable only after the largest earthquakes. Spectra from both seismic and gravimeter data from the Sumatra–Andaman earthquake exhibit the gravest modes with unprecedented signal‐to‐noise levels (Park et al 2005; Rosat et al 2005; Lambotte et al 2006, 2007). Horizontal seismic records are often noisy and superconducting gravimeter data is sensitive primarily to vertical motion, so measurements of horizontal strain offer an important data complement, especially for the detection and characterization of toroidal free oscillations n T l .…”

“…For an earthquake source that is a stepfunction in time, the beating envelope of each seismic free oscillation decays exponentially with time according to its intrinsic attenuation parameter, quantified by the quality factor Q. Though the exceptionally long rupture time of the Sumatra–Andaman earthquake affects the initial phase and amplitude of the gravest free oscillations (Park et al 2005; Lambotte et al 2006, 2007), the rupture itself would not distort the oscillation envelope far from simple exponential decay.…”

Geometry of a large‐scale, low‐angle, midcrustal thrust (Woodroffe Thrust, central Australia)

“…If this precursor was a pseudotachylyte‐rich zone, it must have developed on a crustal‐scale seismic fault similar to a present‐day megathrust and capable of rupturing the center of the Australian continent along a strike length of 600 km or more. The size of the Woodroffe Thrust is comparable with the dimensions of major earthquake ruptures along subduction zones such as, for example, the M w 9.0 Sumatra‐Andaman megathrust earthquake of 2004, which had a rupture length of ~1200 km and maximum thrust displacements of 10–20 m [ Ammon et al ., ; Lomax , ; Ni et al ., ; Park et al ., ; Stein and Okal , ; Vigny et al ., ; Lambotte et al ., ]. Similarly, the M w 9.5 great Chilean earthquake of 1960 had a rupture length of ~1000 km and maximum thrust displacements of 20–40 m [ Benioff et al ., ; Press et al ., ; Plafker and Savage , ; Cifuentes , ].…”

Spherical harmonic stacking for the singlets of Earth's normal modes of free oscillation

“…In addition to the amplitude, one can of course attend to the phase of the SHS. Lambotte et al [] solved for the phases of the 0 S 3 singlets (using singlet stripping) to infer for the spatial extent and temporal duration of the Sumatra‐Andaman source. Our estimated phases, assuming a point and step‐function source, range within ~30° of theirs.…”