Wave-theoretical inversion of teleseismic surface waves in a regional network: phase-velocity maps and a three-dimensional upper-mantle shear-wave-velocity model for southern Germany

Abstract

Summary Using teleseimic surface-wave data from 110 selected earthquakes recorded at 10broad-band stations in southern Germany we construct phase-velocity maps of Rayleigh waves for southern Germany. In a further step these maps are inverted for a three-dimensional model of the SV velocity of the upper 200 km of the mantle. We attempt to take into account the effect of heterogeneous structure outside the study region by jointly inverting the data for heterogeneous phase velocity inside the study region and the distortion of the incoming wavefields by the surrounding structure. The total wavefield in the study region is computed with a scattering formalism which includes multiple forward scattering and single backscattering. Since, in principle, the data can be perfectly fit by the incoming wavefields without any heterogeneous structure inside the study area, we impose additional constraints on the incoming wavefields to reduce the non-uniqueness. The most important constraint is an energy criterion which states that the energy of the modelled wavefield in the study area, averaged over many events, should be equal to the energy sampled by the stations. We demonstrate that enforcing this criterion generates phase-velocity maps with heterogeneous structure. Nevertheless, we are able to satisfy the energy criterion without any heterogeneous structure at the price of an only slightly increased data misfit. Hence, it must be concluded that a seismic network of size and station density such as the one used in this study is still insufficient to demonstrate convincingly the existence of heterogeneities in the network area using teleseismic surface waves. Any reasonable structure combined with the appropriate incoming wavefields would allow an acceptable fit of our data. This frustrating conclusion, of course, applies to all other comparable studies which use teleseismic surface waves. Although we cannot convincingly show that any phase-velocity map we find should be preferred over others, we are able to obtain good reconstructions of test structures from realistic synthetic data with the same station and event distribution as the real data. Moreover, we find that the geometric pattern of the phase-velocity maps obtained from real data depends only weakly on the constraints applied in the inversion, while the amplitude of the phase-velocity perturbations is almost completely determined by the constraints. For all periods considered the fit to the data is extremely good. The reduction of the quadratic misfit relative to the case of plane incoming waves and no structure is dramatic for the shorter periods. The 3-D model of vertical shear-wave velocity down to a depth of 200 km exhibits a basic division into four quadrants separated by a vertical plane intersecting the surface along a nearly west–east line and a horizontal plane at about 130 km depth. The northern rants show high velocities in the top 120 km and low velocities below 140 km. The opposite is the case for the southern quadrants. An exception to this general feature is a pronounced low-velocity zone in the northwestern corner of the region.