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Abstract Applying full-waveform methods to image small-scale structures of geophysical interest buried within the Earth requires the computation of the seismic wavefield over large distances compared to the target wavelengths. This represents a considerable computational cost when using state-of-the-art numerical integration of the equations of motion in three-dimensional earth models. “Box Tomography” is a hybrid method that breaks up the wavefield computation into three parts, only one of which needs to be iterated for each model update, significantly saving computational time. To deploy this method in remote regions containing a fluid-solid boundary, one needs to construct artificial sources that confine the seismic wavefield within a small region that straddles this boundary. The difficulty arises from the need to combine the solid-fluid coupling with a hybrid numerical simulation in this region. Here, we report a reconciliation of different displacement potential expressions used for solving the acoustic wave equation and propose a unified framework for hybrid simulations. This represents a significant step towards applying ’Box Tomography’ in arbitrary regions inside the Earth, achieving a thousand-fold computational cost reduction compared to standard approaches without compromising accuracy. We also present examples of benchmarks of the hybrid simulations in the case of target regions at the ocean floor and the core-mantle boundary. 

SUMMARY We present a time-domain distributional finite-difference scheme based on the Lebedev staggered grid for the numerical simulation of wave propagation in acoustic and elastic media. The central aspect of the proposed method is the representation of the stresses and displacements with different sets of B-splines functions organized according to the staggered grid. The distributional finite-difference approach allows domain-decomposition, heterogeneity of the medium, curvilinear mesh, anisotropy, non-conformal interfaces, discontinuous grid and fluid–solid interfaces. Numerical examples show that the proposed scheme is suitable to model wave propagation through the Earth, where sharp interfaces separate large, relatively homogeneous layers. A few domains or elements are sufficient to represent the Earth’s internal structure without relying on advanced meshing techniques. We compare seismograms obtained with the proposed scheme and the spectral element method, and we show that our approach offers superior accuracy, reduced memory usage, and comparable efficiency. 

Abstract We have extended the distributional finite difference method (DFDM) to simulate the seismic‐wave propagation in 3D regional earth models. DFDM shares similarities to the discontinuous finite element method on a global scale and to the finite difference method locally. Instead of using linear staggered finite‐difference operators, we employ DFDM operators based on B‐splines and a definition of derivatives in the sense of distributions, to obtain accurate spatial derivatives. The weighted residuals method used in DFDM's locally weak formalism of spatial derivatives accurately and naturally accounts for the free surface, curvilinear meshing, and solid‐fluid coupling, for which it only requires setting the shear modulus and the continuity condition to zero. The computational efficiency of DFDM is comparable to the spectral element method (SEM) due to the more accurate mass matrix and a new band‐diagonal mass factorization. Numerical examples show that the superior accuracy of the band‐diagonal mass and stiffness matrices in DFDM enables fewer points per wavelength, approaching the spectral limit, and compensates for the increased computational burden due to four Lebedev staggered grids. Specifically, DFDM needs 2.5 points per wavelength, compared to the five points per wavelength required in SEM for 0.5% waveform error in a homogeneous model. Notably, while maintaining the same accuracy in the solid domain, DFDM demonstrates superior accuracy in the fluid domain compared to SEM. To validate its accuracy and flexibility, we present various 3D benchmarks involving homogeneous and heterogeneous regional elastic models and solid‐fluid coupling in both Cartesian and spherical settings.