Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity

TL;DR

This paper introduces spherical wavelet bases for analyzing and inverting global seismic data, enabling multiresolution modeling, efficient computation, and sparse solutions for seismic heterogeneity, enhancing global tomographic models.

Contribution

It presents a novel spherical wavelet framework for seismic tomography that improves multiresolution analysis and sparse inversion of global seismic models.

Findings

Wavelet coefficients reveal scale-dependent seismic heterogeneity.

Sparse solutions improve inversion efficiency and interpretability.

Method demonstrates potential for future global seismic tomography applications.

Abstract

We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies with position within the Earth. Our procedure is numerically efficient and can be implemented with parallel computing. We discuss two possible types of discrete wavelet transforms in the angular dimension of the cubed sphere. We discuss benefits and drawbacks of these constructions and apply them to analyze the information present in two published seismic wavespeed models of the mantle, for the statistics and power of wavelet coefficients across scales. The localization and sparsity properties of wavelet bases allow finding a sparse solution to inverse problems by iterative minimization of a combination of the $\ell_2$ norm of data fit and the $\ell_1$ norm on the wavelet coefficients. By validation with realistic synthetic experiments we illustrate the likely gains of our new approach in future inversions of finite-frequency seismic data and show its readiness for global seismic tomography.