Inverting seismograms of weak events for empirical Green's tensor derivatives

Given a station and a suite of clustered weak event records whose focal mechanisms are known, empirical Green's tensor spatial derivatives (EGTD) can be calculated, almost free of the source effects. The inversion method solves an overdetermined system of linear algebraic equations in the frequency domain, and a FFT provides the time histories. They represent a least-squares averaged representation of the path between the station and the entire focal zone, including multiple P and S phases, coda waves, etc. The method can be used for modelling earthquakes whose focal mechanisms are quite different from the weak events employed. This is proved here using both synthetic seismograms and earthquake swarm records with variable focal mechanisms. It is expected that the EGTD method can improve strong motion syntheses and source inversions.