Ratio of relative S to P velocity heterogeneity in the lower mantle

The parameter nu = partial derivative lnv(s)/partial derivative lnv(p), the ratio of relative S to P velocity heterogeneity, can be measured seismically and is important in determining the mineral physics of the deep mantle. However, seismic results are inconclusive because they have generally been based on P and S velocity models which are similar, but not proportional, and which are derived from seismic data sets in different frequency ranges and sample the mantle in different ways. Hence current values of nu are subject to inconsistencies which arise from comparing models of differing resolution. Furthermore, heterogeneity within the Earth may be frequency dependent, and this characteristic may also bias v. We overcome these difficulties by computing P and S models from data sets with the same period and similar data coverages and by deriving the ratio in its most rigorous form, whereby we assume proportionality of P and S models and calculate nu as a proportionality factor. We proceed by jointly inverting P and S arrival time data from the International Seismological Centre between the years 1964 and 1993 for ratios and compressional models expanded to at most degree 8 laterally in terms of spherical harmonics and up to degree 6 in depth in terms of Legendre polynomials. We also quantify the sensitivity of our results to data weighting and three-dimensional model parameterization and determine to what depth we are justified in assuming proportionality of P and S heterogeneity. We parameterize nu in terms of Legendre polynomials and find that there is an insignificant improvement in variance reduction beyond degree 1. Hence we find that nu increases linearly from 1.7 to 2.6 between 700 and 2000 km depth, which is the greatest depth to which we believe our results are reliable. We also compare our results with those from theoretical mineral physics and find that seismically derived values are significantly larger and increasing at a greater rate. Reconciliation of these results requires at least modifications to the physical mechanisms currently postulated.