We propose an inversion method for retrieving the focal parameters of small to moderate earthquakes by using the near-source S-wave polarizations, which are expected to be less sensitive than amplitude data to source details or propagation effects. We first studied the variability of the polarization vector for complete synthetic records generated in simple media with a shallow low-velocity layer, for various distances (0 to 50 km), source depths (1 to 15 km), and mechanisms. In the frequency band 1 to 2 Hz, a polarization fluctuation of less than 20° is found for sources deeper than 5 km. The mean angular difference between ray theory and complete field polarization is less than 10° when the complete waveform meets the two following criteria: (1) The polarization is nearly stable (less than 30° of variability) and (2) the motion is nearly horizontal (vector dip less than 30°).
The inversion method uses a norm related to the angular difference in polarization between the real and synthetic waveforms generated by a point double couple. As the problem is highly nonlinear, the model space (strike, dip, slip, location) should be finely sampled and systematically explored in the whole domain of interest. We tested the inversion resolution with synthetic data for a strike-slip and a dip-slip source at 10 km in depth (no error in location) recorded at eight stations within 30 km, assuming an error of 25° on the synthetic polarization. The dip-slip inversion gives a good resolution in dip (15° of uncertainty), but a strong correlation between strike and slip, because no recording site was close to the near vertical principal axis of the stress tensor in the test. On the contrary, the near horizontal major axis of the tensor is very well constrained. The strike-slip inversion gives a good resolution in the three parameters, with uncertainties of about 10°. A 25° change in the strike, dip, or slip angle statistically results in a 25° rotation of the polarization. With numerous stations, the overdetermination of the problem reduces the model error to values lower than 25°. The absence of records in specific areas introduces additional solutions for the possible mechanisms. Finally, the sensitivity of polarization to 3 km shift in source location is globally smaller than for 25° of rotation of any fault angle. The application of this method to real data requires the evaluation of the reliability in the polarizations computed for simplified media. An uncertainty of 25° is expected to be a reasonable assumption for distances smaller than 30 km in the 1 to 2 Hz frequency band; more generally, the error is expected to increase with distance and frequency.