Non‐Plane Geometries of Seismic Surface Wavefields and Their Implications For Regional Surface‐Wave Tomography

SUMMARY Seismic surface waves exhibit much more complicated wavefields than is commonly assumed. We are led to this conclusion after analysing 90 teleseismic events recorded at on average eight broad‐band stations in Southern Germany. Large amplitude and phase fluctuations across the network are observed which, as we show, are definitely not due to instrument response or calibration problems. In order to give an impression of how surface wavefields may look in reality, we fit wavefields to the observed network data using basis wavefields derived from Hermite‐Gaussian functions. We show both amplitude and phase distributions of several events. Synthetic wavefields, generated by acoustic finite‐difference computations in a random medium with realistic correlation length and rms velocity fluctuations, support the interpretation that most of the observed wavefield anomalies have accumulated on the path of the wave from the source to the network. Even if no lateral heterogeneities existed in the region of the network, the large‐scale features of the observed wavefields would remain nearly unaltered. We also model the synthetic wavefields using Hermite‐Gaussian wavefields and achieve extremely good fits. In view of the large anomalies of the wavefields, we investigate their implications for the regional surface‐wave tomography. In this method, one infers regional structure from a set of measurements of phase traveltime between pairs of stations. the basic assumption of the method is that the wavefield incident on the network be plane. Thus, all observed phase traveltime anomalies are interpreted in terms of regional heterogeneous structure. the consequence is a seemingly highly inconsistent data set. We perform several tomographic experiments with realistic synthetic data sets. Our experiments indicate that regional surface‐wave tomography may work, if there is an excellent coverage of paths crossing the region and if each path is sampled several times. Under realistic conditions, that is on a sparse network with not much more than one velocity value per path, the imaging power of surface‐wave tomography is very poor. Owing to the seeming inconsistency of the phase traveltimes, variance reduction is generally low. With an increasing number of traveltime data it further decreases, while at the same time the imaging power increases. the opposite behaviour is observed if the number of data is reduced—variance reduction increases, but imaging power decreases. Hence, in connection with regional surface‐wave tomography, high variance reduction indicates a lack of data rather than the goodness of reconstruction.