The question is interesting, but also very broad and consequently difficult to answer with a short simple reply. You ask for a method, which is in my view not the same as a piece of software, but asks for the physics behind it. In order to determine earthquake source parameters, one has to work from a large, regional scale towards increasingly smaller scales. The first think to do is to establish the tectonic regime in which an earthquake takes place, i.e. extension, strike-slip, compression or reactivation of existing structures. The tectonic regime gives us the regional stress orientations and a rough estimate of the stress magnitudes. The next step is to see whether the earthquake has taken place in a structure that is controlled by the regional tectonics, or is it in a local structure that resulted from the regional deformation. For example, a low-angle thrust is the result from regional horizontal compression, but extensional faulting in the outer arc of a large thrusted anticline is a local feature for which the local stress magnitudes and orientations are different from the regional stresses.
An other complicating factor can be the presence of a regional decollement such as salt or over-pressured clay. Such horizons can completely decouple the strata above and below it, causing more complications in finding earthquake source parameters.
As you see, you have asked an interesting question that requires a 'multi-parameter' answer. Success and have fun.
Earthquake source parameters, like, Stress drop, Source Radius, Corner Frequency, Scalar Seismic Moment and Moment magnitude can be obtained by simply, Spectral model of Brune (1970) and Madariaga, (1976). SEISAN is a good freely available software for estimation of source parameters using spectral model.
Except this, source parameters can be obtained by following inversion technique of(Boatwright, (1980)
The answer depends also on the particular situation which type of earthquakes, which extension of your seismological network, which azimuthal gaps, the velocity model, generally you need a suitable program based on a robust algorithm and correctly applied to a situation that fits with the particularities of the algorithm. Most important of all, and concerning automatically generated results, all results must be checked by a seismologist. So do not hesitat to check and recheck .
Worth noting for your region ( the Zagros thrust zone) that some systematic discrepancies concerning the O-C residuales resulting from the use of arrival times from some seismological stations were noticed, the most likely cause may be in an incompatibility of the velocity models used in this complex area which may affect the calculated earthquake source parameters. This is based upon my following paper available on RG Article Abou Karaki N., 1993, Testing the efficiency of seismologica...