Accelerating global tomography inversions with multiple land and offshore datasets

Understanding mantle circulation and its current thermo-chemical state requires integrating information about S and P wave velocities, as well as their anisotropic variations within the mantle. Seismic tomography provides a method for mapping seismic observations—such as surface wave group velocities and body wave travel times—onto mantle properties, including S and P wave velocities and their anisotropic variations.

Projecting seismic datasets onto mantle properties (e.g., S and P velocities and their anisotropic variations) through spherical harmonics and radial spline basis functions typically involves finding the eigenvalues and eigenvectors of a symmetric, dense, positive-definite matrix. The size of this matrix depends on the maximum degree of the spherical harmonics, the number of radial splines, and the parameters included in the tomography. For instance, when considering both P and S wave velocities, along with their anisotropic variations, the eigenvalue-eigenvector problem becomes computationally very demanding. Such computations require efficient parallel processing schemes, especially on high-performance computing (HPC) clusters.

We present a new library designed for inverting Gram matrices, optimized to utilize an arbitrary number of cores on a single machine or an HPC cluster. This library can also be employed to compute the eigenvalues and eigenvectors of any symmetric positive-definite matrix, making it ideal for solving seismic tomography problems with a large number of unknown parameters. We carry out extensive synthetic inversion tests combining land and offshore surface and body wave synthetic data and quantify the resolution improvements due to offshore data. Additionally, we present preliminary results towards a new SPGlobe-rani model, which integrates ~43,000,000 surface wave and ~600,000 body wave travel time global measurements, expanded into spherical harmonic basis functions up to degree 35 and with 21 radial splines, and with crustal corrections applied.