An alternative parameterisation for surface waves in a transverse isotropic medium

The elastic properties of the Earth can only be retrieved by seismic waves when assumptions about the seismic anisotropy are made, One such an assumpt ion is to assume that the Earth is transverse isotropic. In a transverse is otropic Earth Love waves are sensitive to two independent elastic parameter s and Rayleigh waves to four parameters. In addition these waves are sensit ive to density. However, resolving four elastic parameters together with de nsity as function of depth from Rayleigh waves phase velocity curves is dif ficult as the large number of parameters can make the inverse problem easil y 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 in trinsic trade-offs. We show that Rayleigh wave data can only resolve three combinations of parameters of the transverse isotropic medium: the S-veloci ty beta(v), the sum of the horizontal and vertical P-velocity alpha(+)= 1/2 [alpha(H) + alpha(V)] and their difference alpha(-)=1/2[alpha(H) - alpha(V) ]. The influence of alpha(-) is limited to only the upper 100 km Earth. To take full advantage of this parameter set the data-set should consist of bo th fundamental and higher mode data with periods between 20 < T < 200 s. Fo r this parameter set the influence of the density is small and we think it cannot be resolved when realistic variations in all parameters are consider ed. For Love waves the only relevant parameter is beta(H) as beta(V) and rh o cannot be resolved. We support our conclusions by a synthetic experiment where the bias in the inversion of Rayleigh wave phase velocity is investig ated when the data is inverted for the reduced alternative parameter set. ( C) 2000 Elsevier Science B.V. All rights reserved.