On the determination of the earthquake slip distribution via linear programming techniques

The description that one can have of the seismic source is the mani- festation of an imagined model, obviously outlined from Physic Theories and supported by mathematical methods. In that context, the modelling of earthquake rupture consists in finding values of the parameters of the selected physics-mathematical model, through which it becomes possible to reproduce numerically the records of earthquake effects on the Earths surface. We present and test a Linear Programming (LP) inversion in dual form, for reconstructing the kinematics of the rupture of large earthquakes through space-time seismic slip distribution on finite faults planes

Seismicity and Ground Motion Simulations of the SW Iberia Margin

In this study, we focus on the region between Gorringe Bank and the Horseshoe Fault located in the SW Iberia margin, which is believed to be the site of the great 1755 earthquake. We model ground motions using an extended source located near the Horseshoe scarp to generate synthetic waveforms using a wave propagation code, based on the finite-difference method. We compare the simulated waveforms using a 3-D velocity model down to the Moho discontinuity with a simple 1-D layered mod- el. The radiated wave field is very sensitive to the velocity model and a small number of source parameters; in particular, the rupture directivity. The rupture directivity (controlled by the rupture initiation location), the strike direction and the fault di- mensions are critical to the azimuthal distribution of the maximum amplitude oscilla- tions. We show that the use of a stratified 1-D model is inappropriate in SW Iberia, where sources are located in the oceanic domain and receivers in the continental do- main. The crustal structure varies dramatically along the ray paths, with large-scale heterogeneities of low or high velocities. Moreover, combined with the geometric li- mitations inherent to the region, a strong trade-off between several parameters is of- ten observed; this is particularly critical when studying moderate magnitude earth- quakes (M< 6), which constitute the bulk of the seismic catalogue in SW Iberia

Source rupture process, directivity and and Coulomb stress change of the 12 January 2010 (Port-au-Prince Haiti, Mw7.0) earthquake

The Haiti earthquake occurred on Tuesday, January 12, 2010 at 21:53:10 UTC. Its epi- center was at 18.46 degrees North, 72.53 degrees West, about 25 km WSW of Haiti’s capital, Port-au-Prince, along the tectonic boundary between Caribbean and North America plate dominated by left-lateral stri- ke slip motion and compression with 2 cm/yr of slip velocity eastward with respect to the North America plate. The earthquake was relatively shallow (about 13 km depth) with Mw 7.0 and CMT mechanism solution indica- ting left-lateral strike slip movement with a fault plane oriented toward the WNW-ESE. More than 10 aftershocks ranging from 5.0 to 5.9 in magnitude struck the area in hours following the main shock. Most of these af- tershocks have occurred to the west of the mainshock in the Mirogoane Lakes region and its distribution suggests that the length of the rupture was around 70 km. Rupture velocity and direction was constrained by using the directivity effect determined from broad-band waveforms recorded at regio- nal and teleseismic distances using DIRDOP computational code (DIRectivity DOPpler effect) [1]. The Results show that the rup- ture spread mainly from WNW to ESE with a velocity of 2.5 km/s. In order to obtain the spatiotemporal slip distribution of a fi- nite rupture model we have used teleseismic body wave and the Kikuchi and Kanamori’s method [2]. The inversion show complex source time function with a total scalar seismic moment of 2.2 x 1019Nm (Mw=6.9) a source duration of about 18 sec with a main energy relesea in the first 13 sec. Finally, we compared a map of aftershocks with the Coulomb stress changes caused by the main shock in the region [3]. [1] Kikuchi, M., and Kanamori, H., 1982, Inversion of com- plex body waves: Bull. Seismol. Soc. Am., v. 72, p. 491-506. [2] Caldeira B., Bezzeghoud M, Borges JF, 2009; DIRDOP: a directivity ap- proach to determining the seismic rupture velocity vector. J Seismology, DOI 10.1007/ s10950-009-9183-x [3] 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. More than 10 aftershocks ranging from 5.0 to 5.9 in magnitude struck the area in hours following the main shock. Most of these aftershocks have occurred to the west of the mainshock in the Mirogoane Lakes region and its distribution suggests that the length of the rupture was around 70 km. In order to obtain the spatiotemporal slip distribution of a finite rupture model we have used teleseismic body wave and the Kikuchi and Kanamori's method [1]. Rupture velocity was constrained by using the directivity effect determined from waveforms recorded at regional and teleseismic distances [2]. The spatiotemporal slip estimated points to a unilateral rupture that propagates from WNW to ESE with a rupture velocity of 2.5 km/s. Finally, we compared a map of aftershocks with the Coulomb stress changes caused by the event in the region [3]. [1]- Kikuchi, M., and Kanamori, H., 1982, Inversion of complex body waves: Bull. Seismol. Soc. Am., v. 72, p. 491-506. [2] Caldeira B., Bezzeghoud M, Borges JF, 2009; DIRDOP: a directivity approach to determining the seismic rupture velocity vector. J Seismology, DOI 10.1007/s10950-009-9183-x [3] -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

Seismic Source Directivity from Doppler Effect Analysis, Part I: Theory

The directivity effects, a characteristic of finiteness seismic sources, are generated by the rupture in preferential directions. Those effects are manifested through different cadencies in the seismological measures from azimuthally distributed stations. The apparent durations are expressed as (e.g. Aki and Richards, 1980), (1), where L, v, c and ??are, respectively, the fault length, the rupture velocity, the wave velocity and the angle between rupture direction and ray. This time duration can be measured directly from waveform or indirectly from Relative Source Time Function (RSTF). Equation (1) is deduced from a simple source model (Haskell model) that considers unidirectional uniform rupture propagation and a homogeneous elastic isotropic media. If we consider a more general propagation model, with spherical concentric layers, we obtain (2), where p is the ray parameter and the earth radius. Similar equation can be obtained through physical considerations about a model composed by a sequence of subevents unilater- ally distributed along a line (Doppler Effect). Based on the same considerations we can do a more detailed analysis through (3), where is the time interval between 2 identified pulses in the rupture referential and j indicate the number of station. Based on this theory, we have developed a computational code DIRDOP (DIRectivity DOPpler effect) which determines the rupture direction and velocity from pulse durations observed in waveforms or RSTF. We used this code to analyse recent major seismic events including the unilateral 23 June, 1999 Arequipa (Peru, Mw=8.2) earthquake and the bilateral 21 May 2003 Boumerdes (Algeria, Mw=6.7) earthquake amongst others. The results are similar to those obtained by other methods

Rupture process of the recent large Sumatra earthquakes: 26/12/2004 (Mw=9.3) and 28/03/2005 (Mw=8.6)

The Sumatra mega-earthquake with magnitude 9.3 of 26 December 2004 was the strongest earthquake in the world since the 1964 Alaska earthquake and the fourth since 1900. The earthquake occurred on the interface of the India and Burma plates and triggered a massive tsunami that affected several countries throughout South and Southeast Asia. The rupture, estimated by the aftershock distribution, start from central Sumatra northward for about 1200 kilometres (Borges et al., 2004). Three months latter in 28 March 2005, about 200 km south of this event, but at a greater depth (28 km) occurred a magnitude 8.6 earthquake. This event was probably triggered by stress variations caused by the December Sumatra mega-earthquake (McCloskey et al., 2005). In this work we describe the rupture process of the both earthquakes estimated from teleseismic broad-band waveform data

The 2004 and 2005 Sumatra Earthquakes: Implications for the Lisbon earthquake

The Sumatra mega-earthquake of 26 December 2004 (Mw=9.3) was the strongest earthquake in the world since the 1964 Alaska earthquake and the fifth strongest since 1900. The earthquake occurred at the interface of the India and Burma plates and triggered a massive tsunami that affected several countries throughout South and Southeast Asia. Three months later, on 28 March 2005, about 200 km south of this event but at a greater depth (28 km), occurred a magnitude 8.7 earthquake. This event was probably triggered by stress variations caused by the December mega-earthquake. In this work we describe the rupture process of both earthquakes, estimated from teleseismic broad-band waveform data provided by IRIS-DMC stations. The rupture direction and velocity were determined from common pulse durations observed in P waveforms using DIRDOP computational code (DIRectivity DOPpler effect). The modified Kikuchi and Kanamori method has been used to determine the slip distribution. For the mega- earthquake two segments of 150 km width (along dip) and 990 km total length with different azimuth were estimated, based on the subduction geometry, aftershock distribution and CMT. Results show that the rupture spread mainly to the North with an average velocity of 2.7 km/s. The focal mechanism shows thrust motion on a plane oriented in a NNW-SSE direction and a horizontal pressure axis in the NNE-SSW direction. The fault slip distribution shows the following pattern: 1) the rupture nucleated at the hypocenter as a circular crack breaking a shallow asperity of about 60 km radius during the first 60 sec; 2) after the initial break to the NNW, the rupture propagated during ~180 s and broke a middle large asperity centred at about 360 km from the epicentre; 3) finally, the rupture propagated further to the north and broke a third asperity centred at ~840 km from the epicentre during at least 110 sec. The maximum slip reaches 14 m in the central asperity and the total seismic moment is Mo=3.0x1022 Nm (Mw=8.9), which is less than the value given by the ESMC and USGS (the loss of seismic scalar moment was released in a third segment located to the north). The total source duration and rupture length are estimated to be above 350 sec and 990 km, respectively. For the earthquake of 28 March 2005, a rectangular rupture plane with 400 km length (along the strike direction) and 125 km width (along the dip direction) was obtained from the subduction geometry, aftershock distribution and CMT. Results show that the rupture spread during about 110s in the southwest direction with an average velocity of ~3.3 km/s. Most of the seismic moment was released at the break of two asperities: the largest one located at about 90km from the hypocenter, and the other one at 175 km from the hypocenter. These two asperities correspond on the surface to the areas most affected by the event (Nias Island). The maximum slip reaches 11.5 m in the largest asperity and the total seismic moment is Mo=0.82x1022 Nm (Mw=8.6). The focal mechanism shows thrust motion similar to this shown by the mega-earthquake. Probably, the 1755 Lisbon earthquake (Mw∼9.0) released as much or more energy as any seismic event of recorded history prior to 2004 December. Nevertheless, the location of the source, responsible for the Lisbon tsunami, is not well known; the epicentres suggested by various authors are separated by some hundreds of km. We compare the similarities and differences of these two mega- earthquakes (Sumatra and Lisbon) with the purpose of reducing the uncertainties relative to the location of the seismogenic zone responsible for the 1755 Lisbon earthquake. Lessons learned from the Sumatra earthquake, through scientific studies, should help to reduce the number of victims and damage during future earthquakes in Portugal

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

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

Strong ground motion in southern Portugal due to the 1755 Lisbon earthquake

The strong earthquake (M=8.8) that struck a large part of the Iberian Peninsula and Northern Morocco on November 1, 1755, was caused by the motion along a fault which localisation and spatial extent are still uncertain. According to recent numerical modelling of tsunami wave travel times, it seems that the tsunamigenic fault may be lo- cated off the southwestern coast of Portugal. Multi-channel seismic profiles in the area showed the existence of large submarine hills of tectonic origin, 100 km offshore Cabo de São Vincente, and led to the identification of active faults that may be responsible for the earthquake. E3D, a finite-difference seismic wave propagation code, is used to implement various source rupture scenarios. Based on available geophysical data and geological evidences, we propose a 3D velocity model of the upper mantle, crust, and sedimentary cover, for south Portugal and the adjacent Atlantic area. The model is constrained thanks to data available from recent instrumental earthquakes. We are able to test several possibilities, and to compare synthetic ground motion obtained onshore with historical evaluations of seismic intensity. Directivity of the source, as well as site effects, may explain the particular distribution of strong ground motion observations

The recent 2007 Portugal earthquake (Mw=6.1) in the seismotectonic context of the SW Atlantic area

An event of magnitude Mw 6.1(EMSC) occurred on 12/02/2007 at 10:35 UTC off coast of South-Western Portugal. The earthquake had its epicentre in the eastern Horseshoe Abyssal Plain, at 175 km South-West of San Vicente Cape (Figure 1). This earthquake is the largest earthquake since the great instrumental earthquake, Ms=8.0 (USGS), occurred on February 28th, 1969 in the same epicentral area. This earthquake was followed by four small aftershocks with magnitude less or equal to 3.5. There has been no reported damage associated to the event since habitated regions are too far away from the epicentre. This event has been widely felt in Portugal, particularly in the Algarve Region (I=IV – IM information), Southern Spain and Western Morocco and up to 700 km away of the epicentre (Salamanca, Madrid) (EMSC report in http://www.emsc-csem.org)