Estimation of the radial variation of seismic velocities and density in the earth

Abstract

An inversion procedure is developed to estimate the radial variations of compressional velocity, shear velocity, and density in the Earth. The radial distributions are defined as spherically symmetric averages of the actual distributions in the laterally heterogeneous Earth, and the nature of the averaging implied by averaging certain sets of eigenperiod and travel-time data is examined. For travel-time data, the spherical averaging yields the Terrestrial Monopole if the data sample a distribution derived from a uniform distribution of sources and receivers. Since this is difficult to obtain for absolute times, differential travel times are used to constrain the velocities. It is shown that the bias inherent in available sets of differential travel-time data is considerably less than that in equivalent sets of absolute travel-time data, if the phase combination is suitably chosen. Observations are presented for the phase combinations PcP-P, ScS-S, P'(AB)-P'(DF), and P'(BC)-P'(DF). The inversion algorithm developed is based on a linear approximation to the perturbation equations and is shown to provide a stable method for estimating the radial distributions of velocities and density from a finite number of inaccurate data. The linear inversion theory presented is complete; it allows one to estimate the resolving power of the data and the resolvability of specified features in the model. Three estimates of the radial distributions are derived using an extensive set of eigenperiod and travel-time data. One model, designated model B1, fits 127 of the 177 eigenperiods of the Dziewonski-Gilbert set within their formal 95% confidence intervals. This model satisfies extensive sets of auxillary data as well. It is shown from resolving power calculations that little information is lost by using differential travel times in lieu of absolute times. It is demonstrated that the nature of the averaging in the estimation procedure for given sets of gross Earth data can be improved by judicious specification of the norm on the space of models.