Stabilizing the empirical Green function analysis:: Development of the projected Landweber method

The empirical Green function approach is a very useful tool to study the seismic source properties when we are not able to model the propagation accurately. One of the problems of implementing the method, however, arises from the usual instability of the deconvolution inherent to the approach. Starting from the projected Landweber method introduced in seismology by Bertero et al. (1997), we propose to stabilize the process by taking into account physical constraints on the result of the deconvolution, which is in this case the relative source time function. Compared with Bertero et al.'s method, we add a new constraint that imposes that the area of the relative source time functions, which represents the seismic moment ratio, has to remain the same for all stations. We show how to take into account this important constraint in the framework of the projected Landweber method. Then, we illustrate with a synthetic example how this constraint is useful to model the earthquake kinematic process. Finally, we apply this technique to the very large 23 June 2001 Peru earthquake (M-w 8.4), for which we infer an along-trench rupture length of about 180 km. We image a high moment release 60-km-long zone 150 km away from the hypocenter.