An alternative parameterisation for surface waves in a transverse isotropic medium

Abstract

The elastic properties of the Earth can only be retrieved by seismic waves when assumptions about the seismic anisotropy are made. One such an assumption is to assume that the Earth is transverse isotropic. In a transverse isotropic Earth Love waves are sensitive to two independent elastic parameters and Rayleigh waves to four parameters. In addition these waves are sensitive to density. However, resolving four elastic parameters together with density as function of depth from Rayleigh waves phase velocity curves is difficult as the large number of parameters can make the inverse problem easily under-determined. We show that the partial derivatives of fundamental and higher mode Rayleigh wave phase velocities with respect to the parameters of transverse isotropy for periods 20< T<200 s are very similar to each other. This means that the inversion of Rayleigh phase velocity data has intrinsic trade-offs. We show that Rayleigh wave data can only resolve three combinations of parameters of the transverse isotropic medium: the S-velocity β V, the sum of the horizontal and vertical P-velocity α +=1/2[ α H+ α V] and their difference α −=1/2[ α H− α V]. The influence of α − is limited to only the upper 100 km Earth. To take full advantage of this parameter set the data-set should consist of both fundamental and higher mode data with periods between 20< T<200 s. For this parameter set the influence of the density is small and we think it cannot be resolved when realistic variations in all parameters are considered. For Love waves the only relevant parameter is β H as β V and ρ cannot be resolved. We support our conclusions by a synthetic experiment where the bias in the inversion of Rayleigh wave phase velocity is investigated when the data is inverted for the reduced alternative parameter set.