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The purpose of this thesis is to develop an automated inversion scheme to derive point and finite source parameters for weak earthquakes, here intended with the unusual meaning of earthquakes with magnitudes at the limit or below the bottom magnitude threshold of standard source inversion routines. The adopted inversion approaches entirely rely on existing inversion software, the methodological work mostly targeting the development and tuning of optimized inversion flows. The resulting inversion scheme is tested for very different datasets, and thus allows the discussion on the source inversion problem at different scales. In the first application, dealing with mining induced seismicity, the source parameters determination is addressed at a local scale, with source-sensor distance of less than 3 km. In this context, weak seismicity corresponds to event below magnitude MW 2.0, which are rarely target of automated source inversion routines. The second application considers a regional dataset, namely the aftershock sequence of the 2010 Maule earthquake (Chile), using broadband stations at regional distances, below 300 km. In this case, the magnitude range of the target aftershocks range down to MW 4.0. This dataset is here considered as a weak seismicity case, since the analysis of such moderate seismicity is generally investigated only by moment tensor inversion routines, with no attempt to resolve source duration or finite source parameters. In this work, automated multi-step inversion schemes are applied to both datasets with the aim of resolving point source parameters, both using double couple (DC) and full moment tensor (MT) models, source duration and finite source parameters. A major result of the analysis of weaker events is the increased size of resulting moment tensor catalogues, which interpretation may become not trivial. For this reason, a novel focal mechanism clustering approach is used to automatically classify focal mechanisms, allowing the investigation of the most relevant and repetitive rupture features. The inversion of the mining induced seismicity dataset reveals the repetitive occurrence of similar rupture processes, where the source geometry is controlled by the shape of the mined panel. Moreover, moment tensor solutions indicate a significant contribution of tensile processes. Also the second application highlights some characteristic geometrical features of the fault planes, which show a general consistency with the orientation of the slab. The additional inversion for source duration allowed to verify the empirical correlation for moment normalized earthquakes in subduction zones among a decreasing rupture duration with increasing source depth, which was so far only observed for larger events.
Dynamic earthquake rupture modeling provides information on the rupture physics as the rupture velocity, frictions or tractions acting during the rupture process. Nevertheless, as often based on spatial gridded preset geometries, dynamic modeling is depending on many free parameters leading to both a high non-uniqueness of the results and large computation times. That decreases the possibilities of full Bayesian error analysis.
To assess the named problems we developed the quasi-dynamic rupture model which is presented in this work. It combines the kinematic Eikonal rupture model with a boundary element method for quasi-static slip calculation.
The orientation of the modeled rupture plane is defined by a previously performed moment tensor inversion. The simultanously inverted scalar seismic moment allows an estimation of the extension of the rupture. The modeled rupture plane is discretized by a set of rectangular boundary elements. For each boundary element an applied traction vector is defined as the boundary value.
For insights in the dynamic rupture behaviour the rupture front propagation is calculated for incremental time steps based on the 2D Eikonal equation. The needed location-dependent rupture velocity field is assumed to scale linearly with a layered shear wave velocity field.
At each time all boundary elements enclosed within the rupture front are used to calculate the quasi-static slip distribution. Neither friction nor stress propagation are considered. Therefore the algorithm is assumed to be “quasi-static”. A series of the resulting quasi-static slip snapshots can be used as a quasi-dynamic model of the rupture process.
As many a priori information is used from the earth model (shear wave velocity and elastic parameters) and the moment tensor inversion (rupture extension and orientation) our model is depending on few free parameters as the traction field, the linear factor between rupture and shear wave velocity and the nucleation point and time. Hence stable and fast modeling results are obtained as proven from the comparison to different infinite and finite static crack solutions.
First dynamic applications show promissing results. The location-dependent rise time is automatically derived by the model. Different simple kinematic models as the slip-pulse or the penny-shaped crack model can be reproduced as well as their corresponding slip rate functions. A source time function (STF) approximation calculated from the cumulative sum of moment rates of each boundary element gives results similar to theoretical and empirical known STFs.
The model was also applied to the 2015 Illapel earthquake. Using a simple rectangular rupture geometry and a 2-layered traction regime yields good estimates of both the rupture front propagation and the slip patterns which are comparable to literature results. The STF approximation shows a good fit with previously published STFs.
The quasi-dynamic rupture model is hence able to fastly calculate reproducable slip results. That allows to test full Bayesian error analysis in the future. Further work on a full seismic source inversion or even a traction field inversion can also extend the scope of our model.