S53C-01 INVITED
Robustness Tests for Reliably Determining the Earthquake Rupture Process
Problems related to the determination of the earthquake rupture process details from analysis of body-wave seismograms was first discussed by Kostrov in 1974. We discuss how to use robustness tests to identify the reliable properties of the rupture process obtained from inversion of broadband body wave data (Das and Kostrov, JGR 1990; PEPI 1994). We then interpret the results for the following submarine subduction zone earthquakes: the Mw 8.0 Andreanof Islands earthquake (Das and Kostrov, ibid.), the Mw 8.2 Biak, Indonesia earthquake (Das et al., JGR, 2000) and the Mw 8.4 2001 Peru earthquake (Robinson et al., Science, 2006), in terms of subducting seafloor features and its influence on the earthquake rupture process. In particular, subducting seamounts appear to be affecting the rupture process of all these great earthquakes. The question of how much of a seamount still remains after it is subducted to be able to affect the earthquake rupture on the subduction plane will be addressed.
S53C-02 INVITED
Improving on Inversions for Kinematic Parameters of the Earthquake Source
Since the first inversion of strong motion data for the slip during the 1966 Parkfield earthquake, there have been numerous attempts to infer the kinematic parameters of earthquakes. It is grossly inadequate to think of the distribution of final slip as being a kinematic model. Besides the geometry of the fault and the location of the hypocenter, a kinematic model includes the functional form of the slip rate time function, the temporal parameters of the slip rate function (rise time), the rupture time (equivalently the rupture velocity) and the final slip. All of the parameters can be spatially varying on the fault. The fault and the recording stations are located in a velocity/attenuation structure. Besides the basic uncertainty in the Green's functions regarding the correct velocity/attenuation structure, the fundamental problem is nonlinear with respect to the temporal parameters. The other critical pieces of the puzzle are the distribution of stations and the type of data being inverted. Thus it is no surprise that while there are numerous kinematic inversions for a faulting model, there have been far fewer attempts to address the basic question of what can inversions resolve about the faulting. This has related questions, such as what are the errors in the presented models, which depend on what the resolution is, and also what the data and Green's function errors are and how these errors propagate to the solution. In this presentation we review some of the basic findings about resolution as well as present some results on resolution with respect to the combined inversion of seismic and GPS data. Among the results that need to be emphasized is the most obvious that the distribution of stations inherently limits the resolution. A second major conclusion is that the rupture velocity is variable and has a profound effect on the solution. The rupture velocity and the spatial distribution of slip are fundamentally linked; any use or description of a kinematic model must emphasize each. Of course, because the rupture velocity is nonlinearly related to the data, it is doubly difficult to estimate error in this parameter without considering the correctness of the velocity structure itself. We find that GPS data (static field) can constrain the final slip, but because of the difference in the Green's functions for the static field and dynamic radiation, the inversion should be a two-step process. In the first step the static field data can be inverted using an irregular grid, the spacing determined by the model resolution. The static slip can then constrain the nonlinear inversion of the seismic data.
S53C-03
Using a Global Search Inversion to Constrain Earthquake Kinematic Rupture History and to Assess Model Uncertainty
We use a two-stage nonlinear technique to invert strong motions records and geodetic data to retrieve the rupture history of an earthquake on a finite fault. The unknown model parameters, spatially variable peak slip velocity, slip direction, rupture time and rise time, are given at the vertices of subfaults, whereas the parameters within a subfault can vary through a bilinear interpolation of the vertex values. The forward modeling is performed with a discrete wavenumber technique, whose Green's functions include the complete response of the vertically varying non-attenuating Earth structure. The GPS coseismic data are compared with the synthetic displacements using a L2 norm, while the recorded and modeled waveforms are compared in the frequency domain, using a cost function that is a hybrid representation between L1 and L2 norms. During the first stage (search), an algorithm based on heat-bath simulated annealing generates an ensemble of models that efficiently sample the good data-fitting regions of the parameter space. During this stage multiple Earth structures can be used to allow for uncertainty in the true structure. In the second stage (appraisal), the algorithm performs a statistical analysis of the model ensemble and computes a weighted mean model and its standard deviation by weighting all models by the inverse of the cost function values. We do not use any smoothing operator. This technique, rather than simply looking at the best model, extracts the most stable features of the earthquake rupture that are consistent with the data and gives an estimate of the variability of each model parameter. We present some applications to recent earthquakes such as the 2000 western Tottori (Mw 6.7) and the 2007 Niigata (Mw 6.6) (Japan) earthquakes in order to test and show the effectiveness of the method. Our methodology allows the use of different slip velocity time functions and we emphasize the relevance of adopting source time functions in kinematic inversions compatible with earthquake dynamics. We have verified that the choice of source time function affects ground motion time histories within the frequency band commonly used in waveform inversions and has a clear impact on the inferred peak slip velocity and rise time and, consequently, on the dynamic traction evolution inferred from kinematic models. Furthermore, the assessment of model uncertainty could be useful to predict ground motion time histories for seismic hazard assessment.
S53C-04
Resolution Analysis of finite fault inversions: A back-projection approach.
The resolution of inverted source models of large earthquakes is controlled by frequency contents of \"coherent\" (or \"useful\") seismic observations and their spatial distribution. But it is difficult to distinguish whether some features consistent during different inversions are really required by data or a consequence of "prior" information, such as velocity structures, fault geometry, model parameterizations. Here, we investigate the model spatial resolution by first back projecting and stacking the data at the source regions and then analyzing the spatial- temporal variations of the focusing regions, which arbitrarily defined as the regions with 90% of the peak focusing amplitude. Our preliminary results indicated 1) The spatial-temporal resolution at a particularly direction is controlled by the region of directivity parameter [pcos(θ)] within the seismic network, where p is the horizontal slowness from the hypocenter and θ is the difference between the station azimuth and this orientation. Therefore, the network aperture is more important than the number of stations. 2) Simple stacking method is a robust method to capture the asperities but the sizes of focusing regions are usually much larger than what data could resolve. By carefully weighting the data before the stacking could enhance the spatial resolution in a particular direction. 3) The results based on the teleseismic P waves of a local network usually surfers the trade-off between the source's spatial location and its rupture time. The resolution of the 2001 Kunlunshan earthquake and 2006 Kuril island earthquake will be investigated.
S53C-05
A New Approach for Combining GPS and Seismic Data in Kinematic Inversions
Both GPS and seismic data are routinely used in kinematic inversions of earthquakes. These two types of data are very different: GPS traditionally records the static field, while seismographs record the dynamically radiated wavefield. The two datasets complement each other as they record different components of the seismic field. Therefore, they should be used together in earthquake source inversions. Most joint inversions of GPS and seismic data simply invert all the data (static and dynamic) at the same time. In this procedure, the different datasets must be weighted, and these weights are generally determined empirically. Commonly, GPS data are given a weight that is orders of magnitude larger than that given to seismic data. Is this approach correct? We have developed a new method to combine GPS and seismic data that avoids empirical weighting, and more importantly, takes into account the resolving power of both datasets. This new approach consists of a two-step process: in the first step we invert the static field, thus obtaining the cumulative slip on the fault. This inversion is performed on an irregular grid specifically designed to take into account the spatially heterogeneous resolution of the static data. In particular, the irregular grid accommodates the strong attenuation of the static field with distance (and consequently with depth). The second step consists of an inversion of the seismic data to find the full space-time evolution of slip on the fault. Here, the spatial distribution of slip is constrained by that inferred from the static inversion. It is highly desirable to constrain the seismic inversion given the intrinsic strong trade- offs between temporal and spatial source parameters. Because this two-step approach takes into account the resolution of each dataset, it naturally eliminates artifacts from the resulting slip models. We applied this two-step inversion to the 2004 M6 Parkfield, California, earthquake. We use 43 3-component accelerograms and 13 3- component GPS displacement measurements. All the data were recorded very close to the fault, constituting an excellent dataset to test our method. We discuss the results of our two-step approach, emphasizing the effect of the irregular grid used to determine the static slip solution. We also discuss the possibility that the earthquake started as a super-shear rupture. We compare our final model with models obtained by inversion of individual datasets and with other joint inversions. Finally, we examine robust features and identify artifacts still present in the final slip model.
S53C-06
Inversion of Geodetic Data Monitoring the 2002 Silent Earthquake in the Guerrero Seismic gap: Resolution and non Uniqueness Analysis
The 2002 Guerrero silent event began in october 2001 and lasted for 6-7 months. The equivalent Mw of the event was 7.5. Permanent GPS stations have monitored this event. The analysis of the full data set using MIT's GAMIT 10.3 software gives clear evidence for the slow slip event by eliminating all major non tectonical signals. Horizontal displacements up to 6 cm over an area of ~500 * 250 km2 have been recorded. Both horizontal and vertical displacements were inverted simultaneously to map the slip distribution on the plate interface during this slow-slip event. Our results show that the slip occurred both in the locked (seismogenic) and the partially coupled transition zones. A time window inversions scheme has been developed to illustrate the slip kinematics. During the first 6 months, the slip propagated from the central part toward the edges. At the end of the event the slip propagated in the opposite direction (from the edges toward the central part). Our results also indicate significant time dependent rake changes. Resolution and non uniqueness analysis have been performed to illustrate the effects of stations locations and inversion smoothing choices.
S53C-07
Frequency Domain Inversion of Strong Motions: Application to the Blind Test for Kinematic Source Inversion (EC-project SPICE)
We have applied a frequency domain inversion method to the Blind Test for Kinematic Source Inversion (Mai et al., EC-project SPICE). The parameters describing the rupture process are the local slip, the rupture time and the rise time. Green's functions are numerically evaluated with the Discrete Wavenumber Method. A Generalized Least Square Inversion is used to retrieve the final source parameters. The inversion procedure is based on an iterative Quasi Newton Algorithm (Tarantola and Valette, 1982). A spatial smoothing constraint is introduced through the covariance matrice of the parameter space vector to prevent from unrealistic slip value bumps between two neighbouring subfaults. The resolution matrice illustrates how well the inverse problem can be solved by the data. The values of the resolution are used in a relative way to compare the resolution of different parts of the fault. Since the problem is intrinsically nonlinear the final results depends on the a priori chosen initial parameterization. In order to analyze the non-uniqueness of the solution, we therefore test a population of starting models.
S53C-08
Earthquake Source Inversion Blindtest: Initial Results and Further Developments
Images of earthquake ruptures, obtained from modelling/inverting seismic and/or geodetic data exhibit a high degree in spatial complexity. This earthquake source heterogeneity controls seismic radiation, and is determined by the details of the dynamic rupture process. In turn, such rupture models are used for studying source dynamics and for ground-motion prediction. But how reliable and trustworthy are these earthquake source inversions? Rupture models for a given earthquake, obtained by different research teams, often display striking disparities (see http://www.seismo.ethz.ch/srcmod) However, well resolved, robust, and hence reliable source-rupture models are an integral part to better understand earthquake source physics and to improve seismic hazard assessment. Therefore it is timely to conduct a large-scale validation exercise for comparing the methods, parameterization and data-handling in earthquake source inversions.We recently started a blind test in which several research groups derive a kinematic rupture model from synthetic seismograms calculated for an input model unknown to the source modelers. The first results, for an input rupture model with heterogeneous slip but constant rise time and rupture velocity, reveal large differences between the input and inverted model in some cases, while a few studies achieve high correlation between the input and inferred model. Here we report on the statistical assessment of the set of inverted rupture models to quantitatively investigate their degree of (dis-)similarity. We briefly discuss the different inversion approaches, their possible strength and weaknesses, and the use of appropriate misfit criteria. Finally we present new blind-test models, with increasing source complexity and ambient noise on the synthetics. The goal is to attract a large group of source modelers to join this source-inversion blindtest in order to conduct a large-scale validation exercise to rigorously asses the performance and reliability of current inversion methods and to discuss future developments. http://www.seismo.ethz.ch/staff/martin/BlindTest.html