Fault slip and rupture velocity inversion by isochrone backprojection

A new technique is proposed here for the retrieval of slip images from the backprojection of high-frequency displacement records. When direct S waves are seen to be dominant in the near-source data, Green functions can be approximated by the far-field terms, as described by ray theory. Assuming that the slip rapidly reaches the final value (i.e. short slip duration), the measured displacement can be ascribed to the slip contributions lying on the corresponding isochrone on the fault plane. Here we use the far-field representation theorem to backproject on the fault plane the displacement amplitudes measured along the seismogram. Through the weighted stack of amplitude maps obtained from different stations we recover high slip zones on the fault. The resolution analysis of the backprojected images is realized with spike tests (that we refer to as 'image Green functions'), which revealed to be an useful tool for detecting and locating artificial distortions of high slip patches, due to a poor data coverage. However, when the slip is uniformly spread along the isochrones, energy is scattered everywhere on the fault, leading to defocusing effects on the final images. A partial deconvolution technique is proposed by reiterating the backprojection. An important implication of this study is that slip maps can be obtained as functions of the rupture time on the fault, that is, the method can be used to retrieve variable rupture velocity kinematic models. Since the latter parameter is not known a priori, we suggest that a data set of coupled rupture velocity and slip maps is built up and the optimal model is chosen according to a waveform fitness criterion. This procedure allows the slip inversion to be separated from the rupture velocity inversion, significantly reducing the number of parameters to be estimated. Additionally, the parametrization of the rupture velocity is done on a less dense grid than the slip. By way of example, the technique is applied to estimation of the kinematic rupture model of the 2000 Tottori earthquake (M = 6.8), based on the inversion of near-source strong-motion data.