# Introduction & Background

Finite-fault earthquake source inversions have grown into a standard analysis tool for studying the kinematics of earthquake ruptures by inverting seismic and/or geodetic data. A number of researchers/institutions even develop “near real-time rapid source inversions” that are published online a few hours after moderate to large earthquakes. These rupture models are then often updated in the following days and weeks as more data become available and a more careful analysis can be carried out. While such earthquake source inversions in principle provide information to better understand details of the earthquake rupture process, their resolution and robustness are often questionable (e.g. Beresnev, 2003), owing to the non-linearity of the inversion problem and the resulting non-uniqueness of the solutions. Adding to the general under-determined nature of the inverse problem particular parameter choices that the researchers have to make regarding fault geometry, Earth structure, forward-modeling approach, data selection and data processing, the resulting earthquake source models are often not comparable.

For instance, the large number of source models for the 2011 Tohoku earthquake shows certain consistent features (large slip in the center of the fault), but also significant differences in the details. Many finite-fault studies of well-recorded earthquakes reveal similar and even greater problems: multiple rupture models, obtained for the same earthquake but by different researchers, are not consistent with each other. This is well illustrated for example in case of the 1999 M 7.6 Izmit earthquake (see http://equake-rc.info/srcmod)

If kinematic rupture models for a single earthquake already exhibit large “intra-event” variability, one may ask about the reliability of corresponding kinematics-constrained dynamic rupture models (e.g. Zhang et al., 2003; Mai et al., 2006). Earthquake source inversions can help to examine the conditions for and occurrence of pulse-like ruptures (Heaton, 1990) and super-shear rupture propagation (e.g. Archuleta, 1984; Dunham et al., 2003), allow to determine the heterogeneity spectrum of earthquake slip (Mai and Beroza, 2002; Lavallee et al., 2006), and aid in Coulomb-stress calculation after large earthquakes (Stein, 2003). However, without a better understanding and proper quantification of the underlying uncertainties in earthquake rupture models, subsequent rupture-model based research suffers from even larger resolution and reliability issues.

Over the years, many source inversion approaches have been proposed, ranging from strongly constrained linearized inversions (e.g. Olsen and Apsel, 1982; Hartzell and Heaton, 1983) to fully non-linear inversions that search the model space without stringent constraints (e.g. Liu et al., 2004; Monelli et al., 2009). These inversions use seismic data (strong motion, teleseismic, e.g. Wald et al., 1991; Yoshida et al., 1996), geodetic measurements (to resolve fault geometry and the final static displacement, e.g. Jonsson et al., 2002) or a combination of both, potentially augmented by additional information on surface-rupture or other constraints (e.g. Asano et al., 2005). Required Green’s functions are computed using a variety of techniques and parameterizations of the Earth’ crust (layered 1D models, fully 3D models, e.g. Graves and Wald, 1991; Wald and Graves, 1991), while some methods use small earthquakes as empirical Green’s functions (Dreger, 1994).

However, uncertainty quantification in earthquake source inversion has received little attention so far. Recently, Hartzell et al. (2007) showed rupture model variability due to varying inversion parameterization, while Monelli and co-workers formalized a fully non-linear estimation including a Bayesian approach that includes data uncertainties (Monelli and Mai, 2008; Monelli et al., 2009). Differences in assumed fault geometry and Earth structure, computation of Green’s function, choices in inversion method and its parameterization, data selection and data processing, application of smoothing and/or damping, and other constraints and assumptions strongly affect the final solution. Because there is no unique solution in earthquake source inversion problems, seismologists face the dilemma how to define, classify, or quantify the “best” model, and how to assess the reliability and robustness of published models.

**The SIV-project targets to provide an online cooperation platform to test and validate earthquake source inversion approaches through a series of benchmark exercises. We generate a suite of realizations of earthquake rupture models (using a variety of techniques) for which synthetic seismogramms (and possible other data, like permanent displacements) are computed and then distributed through the SIV-platform. Researchers can then use these data, and apply their inversion/modeling procedures to these benchmark exercises. The SIV-platform provides the capability to upload the inverted rupture model and its corresponding predicted data, and then to quantitatively compare the various available solutions and predictions with each other. We also aim at providing several quantitative metrics that allow to assess the good-of-fit of both the inversion solution and the corresponding predicted data to help identify and discriminate "good" from "not-so-good" models. The ultimate goal is to identify those inversion approaches that provide the most robust and reliable earthquake source models, including appropriate uncertainty quantification, upon which future source inversion studies can build.**