Amplitude and phase differentiation of synthetic seismograms: a must for waveform inversion at regional scale

We study systematically, using the differential seismogram technique developed by Du et al. (1998, referred to as Paper I hereafter), the effects of structural model perturbations on both the amplitude and the phase of synthetic seismograms computed using modal summation. The detailed frequency- and time-domain analysis shows that seismogram amplitude differentiation, which has frequently been neglected in conventional structural waveform inversion schemes, plays a critical role in the computation of differential seismograms, i.e. of the structural linear constraint, especially for higher modes. Since waveform inversion with numerical procedures for the differentiation of seismogram amplitudes is computationally very expensive, a fully analytical waveform inversion scheme is developed. As a test, the synthetic seismograms corresponding to the fundamental and first few higher modes of Rayleigh waves are computed for a series of geophysically realistic structural models and then inverted. Examples of waveform inversion for real data—four recordings of the Roermand earthquake (1992 April 13, Ms=5.4)—are presented. The results obtained with amplitude and phase differentiations are compared with those obtained with phase differentiation only, and possible biases resulting from the use of phase differentiation only as a constraint on the structural model are discussed.