Earthquake Moment Magnitudes from Peak Ground Displacements and Synthetic Green's Functions

We suggest an approach employing full waveforms from synthetic seismograms to estimate moment magnitudes and their uncertainties from peak amplitudes. The new method is theoretically derived. It does not change the established routines of traditional procedures for magnitude determination, while overcoming some of the limitations such as saturation, scattering and source complexity. Attenuation functions are derived on-the-fly for each source-station combination from synthetic seismograms using Green's function databases representing various velocity models if required. In a bootstrap approach, source depth, geometry, dynamic and kinematic parameters are randomly selected within a realistic range. After calibration with observations, attenuation functions can be extrapolated to distances, depths, regions and magnitudes for which no observations exist. Additionally, individual frequency filters and sensor types can be mixed independently of any definition of traditional magnitude scales. Uncertainties of attenuation functions are estimated for every source-station geometry including the sensor characteristics and its potential frequency saturation. Therefore, realistic uncertainties of mean magnitudes can be estimated even in case of only few measurements. The method is especially useful to estimate local and moment magnitudes for temporary deployments or for monitoring induced seismicity in regions with only few tectonic events.