## Abstract:

The core-mantle boundary (CMB) in the deep Earth is of great interest for better understanding the Earth’s dynamics and evolution. Numerous studies have mapped out structural anomalies possibly of both thermal and chemical origin in the lower-most mantle, from large low-shear-velocity provinces (LLVPs) to relative small-scale ultralow velocity zones (ULVZs) above the CMB. High-resolution images of these structures provide critical constraints for further dynamical interpretation in combination with mineral physical and geochemical evidences.

Full-waveform Inversion (FWI, sometimes also known as adjoint tomography) is a promising high-resolution imaging technique. But it can be computationally prohibitive when applied to the CMB. For example, using the wave-equation solvers such as the spectral element method (SEM), it is expensive to model seismic waves shorter than 10 seconds at the global scale, and nearly impossible to model waves shorter than 5 seconds. A compromise can be made by restricting SEM simulations in a target region encompassing possible local 3D heterogeneities, while relying on a relatively inexpensive semi-analytical solver to provide wavefields for a simple 1D background model.

To model the response of seismic waves to local heterogeneities near the CMB, we carry out numerical experiments in 2D synthetic proof-of-concept models. These examples show how waves travel through the CMB can be modeled by hybrid methods between a 1D solver and 2D local solver, and then readily reconstructed back to the Earth’s surface by Kirchhoff integral. The ability to accurately model scattered waves generated by heterogeneities of various scales at the CMB will allow us to image fine-scale structures at the CMB, similar to typical FWI techniques.