Computing coset leaders and leader codewords of binary codes

In this paper we use the Gr\"obner representation of a binary linear code $\mathcal C$ to give efficient algorithms for computing the whole set of coset leaders, denoted by $\mathrm{CL}(\mathcal C)$ and the set of leader codewords, denoted by $\mathrm L(\mathcal C)$. The first algorithm could be adapted to provide not only the Newton and the covering radius of $\mathcal C$ but also to determine the coset leader weight distribution. Moreover, providing the set of leader codewords we have a test-set for decoding by a gradient-like decoding algorithm. Another contribution of this article is the relation stablished between zero neighbours and leader codewords

Slip distribution, coseismic deformation and Coulomb stress change for the 12 May 2008Wenchuan (China, Mw7.9) earthquake

The May 12, 2008 Wenchuan earthquake (Mw7.9) took place at the transition between the mountainous chain of Shan and the basin of Sichuan along the Longmen Shan Fault zone (31.1oN, 103.3oE; USGS). With a magnitude of 7.9 and a depth of ∼19 km the earthquake produced a 300-km-long fault rupture. It was the largest earthquake recorded in the region during the last centuries. It claimed more than 69,000 lives, induced widespread destruction over the region and raised concern about seismic hazard and source characterization for the Sichuan province. In the frame of our study, we selected 40 broadband waveforms (IRIS Consortium, USA) with good quality and satisfactory azimuthal coverage. Body waveforms were prepared for inversion using Kikuchi and Kanamori’s method [1] to obtain the spatiotem- poral slip distribution of a finite rupture model (length=300 km, strike=229o, dip=33o, width=60 km). The slip distribution model obtained was used to determine the coseismic deformation and the stress change distribution using the Coulomb 3.0 software [2]. Our coseismic deformation results was compared with data from GPS stations located near the fault rupture. Results show that directions of coseismic deformations are consistent with GPS observations close to the fault. Finally, we compare aftershock hypocenters that occurred during one month after the main shock with the Coulomb stress changes caused by this shock in the region. We observed that most aftershocks are located along the main fault plane without any noticeable clustering in the areas of increased stress. Our results suggest the rupture of the 2008 Wenchuan earthquake was essentially unilateral, from SW to NE (N49E), covering a 260km length and with duration about 105 sec. The strongest moment release occurred about 85km from the hypocenter, ∼30sec after the start of the rupture. Motions are dominated by thrust mechanism, but the superficial section of the second half of the rupture also shows a significant strike-slip component. [1]- Kikuchi, M., and Kanamori, H., 1982, Inversion of complex body waves: Bull. Seismol. Soc. Am., v. 72, p. 491-506. [2] -King, G. C. P., Stein, R. S. y Lin, J, 1994, Static stress changes and the triggering of earthquakes. Bull. Seismol. Soc. Am. 84,935-953

Influence of model parameters on synthesized high-frequency strong-motion waveforms

Waveform modeling is an important and helpful instrument of modern seismology that may provide valuable information. However, synthesizing seismograms requires to define many parameters, which differently affect the final result. Such parameters may be: the design of the grid, the structure model, the source time functions, the source mechanism, the rupture velocity. Variations in parameters may produce significantly different seismograms. We synthesize seismograms from a hypothetical earthquake and numerically estimate the influence of some of the used parameters. Firstly, we present the results for high-frequency near-fault waveforms obtained from defined model by changing tested parameters. Secondly, we present the results of a quantitative comparison of contributions from certain parameters on synthetic waveforms by using misfit criteria. For the synthesis of waveforms we used 2D/3D elastic finite-difference wave propagation code E3D [1] based on the elastodynamic formulation of the wave equation on a staggered grid. This code gave us the opportunity to perform all needed manipulations using a computer cluster. To assess the obtained results, we use misfit criteria [2] where seismograms are compared in time-frequency and phase by applying a continuous wavelet transform to the seismic signal. [1] - Larsen, S. and C.A. Schultz (1995). ELAS3D: 2D/3D elastic finite-difference wave propagation code, Technical Report No. UCRL-MA-121792, 19 pp. [2] - Kristekova, M., Kristek, J., Moczo, P., Day, S.M., 2006. Misfit criteria for quantitative comparison of seismograms. Bul. of Seis. Soc. of Am. 96(5), 1836–1850

Earthquake Source and Seismic Strain Rate: Portugal in the Context of The Western Part of the Eurasia - Africa Plate Boundary

Fault plane solutions, stress-pattern and deformation rate along the Western part of the Eurasia-Africa Plate Boundary, particu- larly between Azores triple junction and Gibraltar are analyzed. A selection of shallow depth seismic events (1.9 = M = 8.0) occurred in the period 1900-2003 have been carefully checked and analysed. The distribution of the focal mechanisms have been analysed by means of different techniques, projections and graphic representations. Seismic moment tensors, moment rate, slip velocity and b values have been estimated. Based on these results, we propose the following: 1) Between the Azores triple junction and Terceira island predominates strike- slip motion with nodal planes trending NNW-SSE and ENW-SSE; between the Terceira island and the beginning of the of Gloria fault the normal mechanisms predominate with nodal plans in the direction of islands. Deformation rate in both regions is 7.4 and 2.4 cm/year respectively. 2) In the continuation of the plate boundary, along the Gloria Fault until the Iberian continental margin we clearly have right-lateral motion in the E-W direction with a deformation rate of 1.8 cm/year. 3) The Eastern part of the Plate boundary, in Portugal continental, is very complex, however we identify some important patterns in the following regions: western Iberian margin (strike-slip), Lisboa and Vale do Tejo (dip-slip), ...vora and vicinity (strike-slip), region of Algarve (strike-slip) and inter-plates boundary zone (inverse). These regions are affected by compression oriented and a deformation rate of 0,55 cm/year

The 2007 Azores earthquakes: A case of triggering?

On 5 April (Mw=6.3) and 7 April 2007 (Mw=6.1 ) two earthquakes occur at the Formigas Islets (Azores Islands), both with same epicenter and felt (I=V/VI MSK) in S. Miguel Island. The rupture process of these earthquakes has been studied from body wave inversion of broad band data at telesesimic distances. Results obtained shown normal faulting for both shocks, with planes oriented in NW–SE direction, with focus at shallow depth (10 km and 6 km respectively). The slip distribution over the fault plane (152/44/-88) shows for the 05-04-07 event, the rupture propagating downward and a duration of 12s for the source time function. For the 07-04-07 event, the slip distribution over the fault plane (125/52/-81) shows de rupture propagating downward and duration of 10s for the STF. From these results we have estimated the static Coulomb stress change. We find that the static stress change caused by the 5 April event is higher, about 2 bar at epicenter the location of the second event (April 7), triggering the second rupture. Locations of aftershocks do not agree well with areas of increased Coulomb failure stress, which can be explained by the complexities of the rupture process oy by uncertainties at the hypocerter locatio

Recent Seismic Activity in the Azores Region

This seismic activity in the Azores Region is characterized by sequences of low-magnitude events, usually with epicenter off-shore. These seismic sequences are sometimes triggered by larger events, felt by the population, that could produce significant material and human losses. This characteristic is confirmed by the historical and instrumental seismicity, in particular by the recent earthquakes occurred on 1980 (Mw=6.8), 1997 (Mw=6.2), 1998 (Mw=6.2) and 2007 (Mw=6.3, Mw=6.1). The mechanism responsible for this spatial and temporal seismic pattern still yet not very well known. In this work we discuss the recent (2007) seismic activity of the Azores region by analyzing the spatial and temporal distribution of seismic events associated with two sequences with different characteristics. The fisrt one is a seismic swarm started on April 21st 2007, centered at about 40 kilometers west of the Faial Island (maximum magnitude mb=4.0). The second one corresponds to an aftershock sequence associated to the events of 2007/04/05 (Mw=6.3) and 2007/04/07 (Mw=6.1), both with epicenter in the Formigas Islets and felt (I=V/VI in Mercali scale) in S. Miguel. We calculate the static Coulomb stress change for both events using focal mechanisms derived from the inversion of body waves. We find that the static stress change caused by the April 5 event is higher, about 2 bar at the location of the second event (April 7), triggering the second rupture. Locations of aftershocks do not agree well with areas of increased Coulomb failure stress