The influence of crustal scattering on translational and rotational motions in regional and teleseismic coda waves

Monte Carlo solutions to the radiative transfer equations are used to model translational and rotational motion seismogram envelopes in random elastic media with deterministic background structure assuming multiple anisotropic scattering. Observation and modelling of the three additional components of rotational motions can provide independent information about wave propagation in the Earth's structure. Rotational motions around the vertical axis observed in the P-wave coda are of particular interest as they can only be excited by horizontally polarized shear waves and therefore indicate the conversion from P to SH energy by multiple scattering at 3-D heterogeneities. To investigate crustal scattering and attenuation parameters in south-east Germany beneath the Grafenberg array multicomponent seismogram envelopes of rotational and translational motions are synthesized and compared to seismic data from regional swarm-earthquakes and of deep teleseismic events. In the regional case a nonlinear genetic inversion is used to estimate scattering and attenuation parameters at high frequencies (4-8 Hz). Our preferred model of crustal heterogeneity consists of a medium with random velocity and density fluctuations described by an exponential autocorrelation function with a correlation length of a few hundred metres and fluctuations in the range of 3 per cent. The quality factor for elastic S-waves attenuation Q(i)(S) is around 700. In a second, step simulations of teleseismic P-wave arrivals using this estimated set of scattering and attenuation parameters are compared to observed seismogram envelopes from deep events. Simulations of teleseismic events with the parameters found from the regional inversion show good agreement with the measured seismogram envelopes. This includes ringlaser observations of vertical rotations in the teleseismic P-wave coda that naturally result from the proposed model of wave scattering. The model also predicts, that the elastic energy recorded in the teleseismic P coda is not equipartitioned, unlike the coda of regional events, but contains an excess of shear energy. The results confirm that scattering generating the teleseismic P-wave coda mainly occurs in the crustal part of the lithosphere beneath the receiver. Our observations do not require scattering of high frequency waves in the mantle, but weak scattering in the lithospheric mantle cannot be ruled out.