submitted to Geophys. J. Int. Heterogeneity spectrum inversion from a stochastic analysis of global surface-wave delay-time data S. Della Mora 1 , L. Boschi 2 , T. W. Becker 3 , D. Giardini 4 1 E.T.H. Z¨ urich, Institute for Geophysics. E-mail: dellamora@tomo.ig.erdw.ethz.ch 2 E.T.H. Z¨ urich, Institute for Geophysics. E-mail: boschi@tomo.ig.erdw.ethz.ch 3 University of Southern California, Los Angeles. E-mail: twb@usc.edu 4 E.T.H. Z¨ urich, Institute for Geophysics. E-mail: domenico.giardini@sed.ethz.ch SUMMARY The wavelength of mantle heterogeneity reflects the nature of Earth’s dynamics, and constraining it on the basis of seismic data is useful to evaluate the likelihood of different proposed models of mantle convection. We neglect the geographic distribu- tion of mantle heterogeneity, inverting global delay-time data to determine directly the heterogeneity spectrum of the Earth. Inverting for the spectrum is in principle (fewer unknowns) more robust than inverting for three-dimensional (3D) structure: as a result, this approach should ultimately help us to constrain the properties of planetary structure at wavelengths shorter than those of current 3D models. The linearized algorithm that we employ is based on the work of Gudmundsson and co- workers in the early 1990s: seismic rays starting from sources in the same cell and arriving at receivers in the same cell are collected, and the variance of the associ- ated delay times is calculated; this exercise is repeated varying the grid size. The dependence of calculated variance on the inter-source and inter-receiver distance can then be linked to the heterogeneity spectrum via a linearized least-squares inversion. Here, we limit ourselves to a two-dimensional problem, analysing surface-wave dis-