Fast Computation of Global Sensitivity Kernel Database Based on Spectral-Element Simulations

Abstract

Finite-frequency sensitivity kernels, a theoretical improvement from simple infinitely thin ray paths, have been used extensively in recent global and regional tomographic inversions. These sensitivity kernels provide more consistent and accurate interpretation of a growing number of broadband measurements, and are critical in mapping 3D heterogeneous structures of the mantle. Based on Born approximation, the calculation of sensitivity kernels requires the interaction of the forward wavefield and an adjoint wavefield generated by placing adjoint sources at stations. Both fields can be obtained accurately through numerical simulations of seismic wave propagation, particularly important for kernels of phases that cannot be sufficiently described by ray theory (such as core-diffracted waves). However, the total number of forward and adjoint numerical simulations required to build kernels for individual source–receiver pairs and to form the design matrix for classical tomography is computationally unaffordable. In this paper, we take advantage of the symmetry of 1D reference models, perform moment tensor forward and point force adjoint spectral-element simulations, and save six-component strain fields only on the equatorial plane based on the open-source spectral-element simulation package, SPECFEM3D_GLOBE. Sensitivity kernels for seismic phases at any epicentral distance can be efficiently computed by combining forward and adjoint strain wavefields from the saved strain field database, which significantly reduces both the number of simulations and the amount of storage required for global tomographic problems. Based on this technique, we compute traveltime, amplitude and/or boundary kernels of isotropic and radially anisotropic elastic parameters for various ( $$P$$ , $$S$$ , $$P_{\mathrm{diff}}$$ , $$S_{\mathrm{diff}}$$ , depth, surface-reflected, surface wave, S 660 S boundary, etc.) phases for 1D ak135 model, in preparation for future global tomographic inversions.