Error Propagation and Control in 2D and 3D Hybrid Seismic Wave Simulations for Box Tomography

ABSTRACT To enhance the local resolution of global waveform tomography models, particularly in areas of interest within the Earth’s deep structures, a higher resolution localized tomography approach (referred to as “box tomography”) is crucial for a more detailed understanding of the Earth’s internal structure and geodynamics. Because the small-scale features targeted by box tomography are finer than those in global reference models, distinct spatial meshes are necessary for global and local (hybrid) forward simulations. Within the spectral element method (SEM) framework, we employ the intrinsic Lagrangian spatial interpolation to compute and store hybrid inputs (displacement/potential) in the global numerical simulation. These hybrid inputs are subsequently imposed into the localized domain during the iterative box tomography. However, inaccurate spatial Lagrange interpolation can lead to imprecise hybrid inputs, and this error can propagate from the global simulation to the hybrid simulation. It is essential to quantitatively analyze this error propagation and control it to ensure the credibility of box tomography. We introduce a unique spatial window function into the conventional “direct discrete differentiation” hybrid method. When the local mesh and structure align with those in the global simulation, the synthetic hybrid waveforms match the global ones, serving as a reference for quantitatively assessing error propagation stemming from changes in the local spatial mesh during hybrid simulation. Significantly, the relative waveform error arising due to spatial Lagrange interpolation is around 5% when employing the traditional SEM with five Gauss–Lobatto–Legendre points per minimum wavelength in the 3D global simulation through SPECFEM3D_GLOBE. Ultimately, we achieve hybrid waveforms with an accuracy of about 1.5% by increasing the spectral elements by about 1.5 times in the standard global simulation.