## 1. Introduction

[2] One of the fundamental quantities in earthquake source physics is the static stress change associated with earthquake faulting. The static stress change on the fault plane itself is linked to the dynamics of earthquake rupture and hence also to the associated energy release and seismic radiation. Its knowledge is therefore required in dynamic rupture modeling of past (and future) earthquakes [*Peyrat et al.*, 2001]. Moreover, stress-drop distributions for simulated slip maps in scenario earthquakes for near-source strong-motion simulations allow to constrain the temporal rupture evolution [*Guatteri et al.*, 2003] and the energy budget of earthquake rupture [*Guatteri et al.*, 2004].

[3] Estimating the distributed stress changes on the fault plane directly from seismological data is cumbersome [*Peyrat and Olsen*, 2004], and usually it is inferred from imaged slip distributions [e.g., *Bouchon*, 1997]. Kinematic source inversions have revealed the complexity of earthquake rupture at all scales [*Heaton*, 1990; *Somerville et al.*, 1999; *Mai and Beroza*, 2002]. Therefore, also static stress changes on the rupture plane are highly heterogeneous, exhibiting locally large stress drop in the region of high slip but also zones of stress increase.

[4] *Okada* [1992] derived analytical expressions to compute static stress changes for given final displacements in an elastic homogeneous half space. In contrast, finite difference methods (FDM) [e.g., *Ide and Takeo*, 1997; *Day et al.*, 1998] and the discrete wave number method by *Bouchon* [1997] require knowledge of the entire slip-time history at each point of the fault, but these approaches return the complete spatio-temporal evolution of stress changes on a fault plane. However, computations are time consuming for all methods mentioned so far, particularly for large grid sizes.

[5] In this study, we propose a shortcut to calculating stress changes on a 2D fault plane, based on the work by *Andrews* [1980]. He presented a wave number representation relating the distribution of static slip to the associated collinear static stress change. We give a brief introduction of Andrews' method and our extensions to it and discuss its range of applicability. We then examine the method under various initial assumptions and evaluate its performance in terms of computational speed and accuracy, when compared to the analytical solutions obtained with Okada's formulations. This comparison is performed for synthetic slip distributions as well as for examples of inverted slip maps of past earthquakes.