Love wave amplitude decay from rotational ground motions

SUMMARY The broad-band surface wave magnitude equation assigns magnitudes based on source–receiver distance and peak surface wave amplitude. It is standard practice to use the vertical component of peak ground velocity to determine magnitude, such that only contributions from the vertical motion of Rayleigh waves are present in the surface wave train. With the advent of rotational ground motion observations from instruments such as ring laser gyroscopes, it is possible to measure rotational ground motions about three orthogonal axes. For surface waves, observations of rotations about the vertical axis are theoretically only sensitive to the transverse nature of Love waves, unaffected by either component of Rayleigh waves. We use this concept to separate and study the amplitude information of surface waves independently. With a large database of recorded seismic waveforms for colocated translations and rotations, collected in Wettzell, Germany, we empirically define magnitude scale attenuation constants as a method for quantifying amplitude decay. Through this differential analysis, we determine a necessity for separate surface wave magnitude equations through measurements of translations and rotations. Synthetic seismograms were concurrently produced using an open-source spectral-element wave propagation code, for comparisons against observations. Although synthetically derived amplitude decays agree for translations, they do not accurately predict the decay found for rotations. Synthetics also overpredict amplitudes for both rotations and translations. Results from observations imply that rotation amplitudes decay faster over distance with respect to velocity amplitudes, and that the current surface wave magnitude equation is insufficient for predicting observed translation and rotation amplitudes. We attribute variations in amplitude decay characteristics to the different effects of attenuation on Love and Rayleigh waves, with potential influence from local velocity structure and scattering effects. The lack of agreement in synthetics is attributed to the insufficiency of synthetic attenuation and velocity structure to replicate the effects seen in observations.