We address the problem to retrieve the space-time slip function from the inversion of high frequency earthquake records using the kinematic approach. In the part 1, after describing the characteristics of short period data, we introduce the problem of inversion. We talk about a method for simulating synthetic seismograms (forward problem) and then some difficult aspects of inverse problem, like non-linearity and trade-off among parameters. Moreover we point out differences among local and global search techniques and present the genetic algorithm optimization technique. In the part 2 we present a non-linear inversion technique based on a multi-scale approach and its application both to a synthetic case and to the 1989 Loma Prieta, California, earthquake. Finally we present an error estimation procedure and its application to the results obtained for the Loma Prieta earthquake case.