## 1 Introduction

[2] The ongoing growth and improvement of Global Positioning System (GPS) networks deployed in tectonically active regions has resulted in a considerable increase in the quantity and quality of GPS-derived observations of seismic deformation fields: data that are of great value in earthquake source studies. Recently, *O'Toole et al*. [2012] showed that high-rate GPS waveforms can be inverted using the centroid–moment tensor (CMT) algorithm of *Dziewonski et al*. [1981], allowing an optimal point source description of an earthquake to be determined from these time series. In principle, this adapted CMT method could also be applied to more widely available GPS-measured static displacement data, as we investigate in the present work.

[3] Such an undertaking is of interest in the context of earthquake early warning, because near-field geodetic measurements allow rapid magnitude determination and the construction of slip models in the minutes following an earthquake [e.g., *Blewitt et al*., 2006, 2009; *Allen and Ziv*, 2011; *Crowell et al*., 2012; *Wright et al*., 2012]. To make such inversions tractable in real-time, the fault's location and orientation are commonly assumed a priori using catalogues of known active faults, thus rendering the inverse problem linear. Because such information may be ambiguous, erroneous, or lacking, and earthquakes can occur on previously unidentified faults, an alternative approach is to construct a fault plane from the best point source recovered from the same geodetic data set. *Crowell et al*. [2012] found that aspects such as the total moment, location of peak slip, and slip extent obtained in source inversions using fault geometries taken from fault catalogues and moment tensor inversions are, broadly speaking, comparable. Consequently, there is great potential value in determining moment tensors from static displacement data for earthquake early warning, as it eliminates the need for a priori knowledge of the style of faulting in a particular area.

[4] Although geodetic source inversions assuming a finite fault are now routinely carried out, we are aware of only one previous study that performed inversions of static displacement data for an earthquake's CMT parameters [*Melgar et al*., 2011]. Using a precomputed library of excitation kernels, they performed a series of inversions on a grid of points distributed in space, choosing the location and moment tensor that yield the lowest data misfit as their CMT solution. The method proposed here is an alternative to that of *Melgar et al*. [2011], the main differences being that we solve directly for the centroid position without restriction to a grid, and our forward modeling method is efficient enough that all necessary computations are performed on-the-fly, allowing a priori assumptions about possible earthquake locations to be minimized. All that we require to perform an inversion is a static displacement data set, a crustal model, and an initial estimate of the source location from which we iterate to find the centroid position and moment tensor that best explain the data. In this paper, we perform source inversions using static displacements observed by GPS receivers of the California Real Time Network (CRTN) for the 2010 *M*_{W} 7.2 El Mayor-Cucapah, Mexico, earthquake. We introduce damping of the centroid location update into our iterative scheme to ensure that the inversion converges stably and demonstrate the potential of this new method by performing a CMT inversion of the El Mayor-Cucapah static displacement data set in simulated real-time.