A probabilistic approach to the inversion of data from a seismic array andits application to volcanic signals

Array techniques are particularly well-suited for detecting and quantifying the complex seismic wavefields associated with volcanic activity such as v olcanic tremor and long period events. The methods based on the analysis of the signal in the frequency domain, or spectral methods, have the main adv antages of both resolving closely spaced sources and reducing the necessary computer time, but may severely fail in the analysis of monochromatic, non -stationary signals. Conversely, the time-domain methods, based on the maxi mization of a multichannel coherence estimate, can be applied even for shor t-duration pulses. However, for both the time and the frequency domain appr oaches, an exhaustive definition of the errors associated with the slowness vector estimate is not yet available. Such a definition become crucial onc e the slowness vector estimates are used to infer source location and exten t. In this work we develop a method based on a probabilistic formalism, whi ch allows for a complete definition of the uncertainties associated with th e estimate of frequency-slowness power spectra from measurement of the zero -lag cross-correlation. The method is based on the estimate of the theoreti cal frequency-slowness power spectrum, which is expressed as the convolutio n of the true signal slowness with the array response pattern. Using a Baye sian formalism, the a posteriori probability density function for signal sl owness is expressed as the difference, in the least-squares sense, between the model spectrum and that derived from application of the zero-lag cross- correlation technique. The method is tested using synthetic waveforms resem bling the quasi-monochromatic signals often associated with the volcanic ac tivity. Examples of application to data from Stromboli volcano, Italy, allo w for the estimate of source location and extent of the explosive activity.