Probing Mantle Heterogeneity Across Spatial Scales

Inferences of mantle heterogeneity in terms of temperature, composition, grain size, melt and crystal structure may vary across local, regional and global scales. Probing these scale-dependent effects require quantitative comparisons and reconciliation of tomographic models that vary in their regional scope, parameterization, regularization and observational constraints. While a range of techniques like radial correlation functions and spherical harmonic analyses have revealed global features like the dominance of long-wavelength variations in mantle heterogeneity, they have limited applicability for specific regions of interest like subduction zones and continental cratons. Moreover, issues like discrepant 1-D reference Earth models and related baseline corrections have impeded the reconciliation of heterogeneity between various regional and global models. We implement a new wavelet-based approach that allows for structure to be filtered simultaneously in both the spectral and spatial domain, allowing us to characterize heterogeneity on a range of scales and in different geographical regions. Our algorithm extends a recent method that expanded lateral variations into the wavelet domain constructed on a cubed sphere. The isolation of reference velocities in the wavelet scaling function facilitates comparisons between models constructed with arbitrary 1-D reference Earth models. The wavelet transformation allows us to quantify the scale-dependent consistency between tomographic models in a region of interest and investigate the fits to data afforded by heterogeneity at various dominant wavelengths. We find substantial and spatially varying differences in the spectrum of heterogeneity between two representative global Vp models constructed using different data and methodologies. Applying the orthonormality of the wavelet expansion, we isolate detailed variations in velocity from models and evaluate additional fits to data afforded by adding such complexities to long-wavelength variations. Our method provides a way to probe and evaluate localized features in a multi-scale description of mantle heterogeneity.