Study of the earthquake source process and seismic hazards

Extended Abstract

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We study two problems related to seismic source seismology. Firstly, kinematic and dynamic inversion of the 2004 Parkfield earthquake in California and secondly, the migration of seismicity following the 2010 Darfield earthquake in New Zealand.

We explore a recently developed method for carrying out kinematic inversions. It is based on an elliptical sub-fault approximation, where the slip history is modelled using a small set of elliptical patches. We use it to invert near-field strong ground motion to obtain the rupture history of the 2004 September 28, M_w6.0, Parkfield, California, earthquake. The dataset consists of 10 digital 3-component displacement seismograms. We carry out 12 kinematic inversions using different a-priori conditions in order to assess the variability of plausible models. We then select a preferred model based on external criteria that are independent of the inversion procedure. The preferred rupture model has a final seismic moment of 1.21 × 10¹⁸ Nm, distributed on two distinct ellipses. The average rupture speed is ∼2.7 km/s. This model shows a good agreement with the location of large earthquakes (M_w > 3) that have occurred prior to the 2004 Parkfield earthquake, surrounding the two slip patches. Similar behaviour is also observed for the aftershocks. It therefore suggests the presence of permanent asperities that break during large earthquakes.

We subjected our kinematic inversion method to a series of tests. Using artificially generated data, the capacity of the inversion procedure to retrieve the input rupture history of an artificially created earthquake was tested. In a simple case, the inversion retrieves the input rupture model almost perfectly, the only variation being due to the non-uniqueness of kinematic inversions. For a more complicated rupture process, the inversion only retrieves a low-frequency filtered version of the input slip distribution. The behaviour of the Neighbourhood Algorithm (NA) in its search for the optimal solution was also examined. We observed that the space-time location of the rupture front is the main criterion that drives the convergence, the amplitude of slip being only a secondary criterion important mostly at the end of the inversion. We have also investigated how the data processing affects the results of the kinematic inversion by performing another set of inversions, which differ from the initial kinematic inversions of Twardzik et al. (2012) only in the way the data is processed. We performed one inversion using a different frequency band (0.16-0.50 Hz instead of 0.16-1.00 Hz). It shows that the inversion is not very sensitive to high-frequency signals, since we obtain a similar rupture process in the two frequency band. A similar conclusion is reached when we perform an inversion in which velocity records are inverted instead of displacement records. Finally, we looked at the influence of the length of the seismograms that are used to calculate the misfit. We see that the progressive addition of signals from P, S and Rayleigh waves greatly affects the result because it relates to the quantity of information about the rupture process that is given to the algorithm.

We present a full dynamic inversion for the rupture process of the September 28, 2004, M_w6.0, Parkfield, California, earthquake, using an elliptical sub-fault approximation. By carrying out a full dynamic inversion, we attempt to obtain at the simultaneously the geometry of the rupture area and the stress and frictional properties of the fault. In the elliptical sub-fault approximation, the rupture is restricted to occur within the elliptical patches. Inside of each patch, the background stress (Te) is assumed to be uniform and the upper yield stress (Tu) follows an elliptical distribution, with maximum rupture resistance at the centre of the ellipse. The dataset consists of 10 digital 3-component displacement seismograms. The lowest misfit model reached by the inversion is composed of one ellipse elongated along strike and extending from the hypocenter to almost the north-western end of the fault plane. The final seismic moment is 1.18 × 10¹⁸ Nm and the rupture occurs at an approximately constant rupture speed of 2.80 km/s, compatible with a value for κ (ratio of the available energy to energy release rate) of 1.40. In addition to the inversion, we explore the dynamic parameter-space using a Monte-Carlo optimisation method. For this purpose, the geometry of the rupture area is fixed at that obtained from the dynamic inversion. We show that the models distribution in the parameter-space is essentially controlled by the average rupture speed and the final seismic moment. We show that the structure of the parameter-space relative to the rupture speed and the seismic moment defines a very narrow region within which the data are well fitted. It is inside this region that we find models that have an average rupture speed and final seismic moment that reproduce the strong ground motion observed. We then use the fixed-geometry approach to investigate the transition between kinematic models and dynamic models. The geometry of the rupture area is defined from the rupture model obtained by kinematic inversion and then the stress and friction conditions are obtained from a dynamic inversion. In particular, we focus on one kinematic inversion which led to a slip distribution with 2 distinct asperities, requiring a jump of the rupture process. We show first that we fail to find a set of dynamic parameters that reproduces this kind of rupture model while fitting the data at the same time, unless there is a connection between the two asperities. To build the connection between the two distinct ellipses, we developed a new approach that uses b-spline curves in order to define the rupture area. Once there is the connection, it becomes possible to construct a dynamic rupture model that has a rupture geometry similar to the one obtained by kinematic inversion, while fitting the observed near-field ground motion well.

By using P-wave arrival-time data supplied by the International Seismological Centre (ISC), we attempt a relocation of the earthquakes in the vicinity of the September 3, 2010, M_w7.1, Darfield, New-Zealand earthquake, using the method of Joint Hypocenter Determination (JHD). Even after relocation, we observe no significant seismic activity inside the Canterbury Plains, a region that surrounds the epicentral area of the Darfield earthquake. However, during the 40 years preceding that earthquake, we observe a hint of migration towards that region. The P- and T-axis of the large earthquakes between January 1976 and September 2010 suggests that the whole region could have experienced a long-term stress transfer from the Alpine Fault to the plate interior, although the signal is very weak. After the September 2010 Darfield earthquake, we observe a clear eastward progression of the seismic activity, essentially inside a region of positive static stress changes (i.e. brought closer to failure). This causes the occurrence of the February 21, 2011, M_w6.3, Christchurch earthquake. After that earthquake, the direction of the migration is slightly modified so that, after being trapped nearby the epicentral region of the Christchurch earthquake, the seismic activity moves in the north-east direction, again in agreement with region of positive static stress changes caused by the occurrence of the Christchurch earthquake. The Alpine Fault, as well as some portions of the Canterbury Plains, remain seismically quiet at present, but static stress changes calculations show that this sequence has brought them closer to failure.