Modeling Green's Function Errors through a Statistical Approach: Application to the 2009 Mw 6.1 L'Aquila, Italy, Earthquake Sequence

Seismic data can be used to infer the rupture evolution of moderate-to-large earthquakes. Researchers often retrieve significantly different rupture models for a single event, even though their solutions match the data acceptably well. For this reason it is important to estimate the reliability of inferred rupture models. One of the main sources of error in such inversions is the inaccuracy of the theoretical Green's functions (GFs). In this work we propose a quantitative approach to model this source of uncertainty and we analyze the 2009 L'Aquila, Italy, main shock and aftershocks as a case study. In order to measure the errors in theoretical GFs, we assume that the observed ground motions from small aftershocks located on the fault surface of the Mw 6.1 main shock are true point-dislocation GFs. Our erroneous theoretical GFs have been computed using a frequency-wavenumber code in a regionally calibrated velocity structure. The error in a theoretical GF for a particular point source location, observation station, and component of motion is taken to be the complex difference between the Fourier spectra of the aftershock seismogram and the theoretical GF multiplied by the aftershock's moment. The distributions of the real and imaginary parts of the errors are characterized by an "S" curve in normal probability plots, that is, these distributions are not Gaussian but rather `heavy-tailed'. The observed distributions are consistent with a model in which the errors in the theoretical GFs have a normal probability density function (PDF) with σT depending on frequency and component of motion, and the erroneous seismic moments have a log-normal PDF with a standard deviation σM=ln(3). We have developed a semi-analytic expression for the PDF of the complex difference data. The results obtained provide a new quantitative tool when dealing with finite-fault kinematic inversion, seismic moment determination, shake-map generation and ground motion prediction.