Low-wavenumber signatures of time-dependent mantle convection

Abstract

Spectral analysis is applied to idealized two-dimensional numerical models of mantle convection. Examining the spectral signature of known model temperature fields represents the forward problem corresponding to the inverse problem of inferring the unknown temperature field in the mantle from the spectral components of lateral heterogeneity obtained by seismic tomography. Previous two-dimensional Fourier analyses of steady convection cells indicate that, with current levels of resolution, tomographic techniques have a much better chance of detecting horizontal boundary layers than vertical plumes. From an examination of the shape of the spectral envelopes of the power spectrum of lateral heterogeneity at various depths in steady convection cells, it has been suggested that evidence for thermal boundary layers in the mantle may be contained in the published spectral amplitudes of lateral heterogeneity. This possibility is expanded on in the present study. Here we examine the effects, on the spectral signature of lateral heterogeneity, of averaging the model temperature field over vertical intervals of a few hundred kilometers, of large amounts of internal heating, of time-dependent flow and of aspect ratios greater than unity. The vertical averaging is an attempt to mimic the finite vertical resolution of tomographic inversions. The various complications considered here are found to render the distinction between the spectra of lateral heterogeneity, inside and outside of thermal boundary layers, less clear than in the simpler models considered previously. Nevertheless, the boundary layer spectra continue to contain significant information on the dominant scale of the model flow solutions.