FWI-EDU: an open-source dual-language framework for understanding full-waveform inversion algorithms and their parallel implementations

ABSTRACT Full-waveform inversion (FWI) is a high-resolution seismic imaging method widely used in geophysical exploration. However, its mathematical formulation, computational cost, and parallel implementation details often make it difficult for students and early-stage researchers to understand the complete workflow from theory to executable code. Many existing FWI-related software packages are powerful and highly optimized, but their broad functionality and complex software architectures are not primarily designed for step-by-step education or rapid algorithmic prototyping. To address this need, we present FWI-EDU, an open-source dual-language framework for two-dimensional acoustic FWI. The framework provides corresponding MATLAB and C implementations that follow a consistent FWI workflow, allowing users to trace the transition from readable algorithmic scripts to a more efficient low-level implementation. The MATLAB version emphasizes readability, visualization, and interactive experimentation, whereas the C version illustrates explicit memory management, OpenMP-based parallelization, and checkpointing-based wavefield reconstruction. FWI-EDU implements key components of time-domain acoustic FWI, including finite-difference forward modeling, adjoint-state gradient calculation, frequency-based multiscale inversion, gradient spatial preconditioning, step-length estimation, and model constraints. It also includes auxiliary MATLAB applications for acquisition-geometry design and seismic-record visualization, which support a reproducible workflow from survey setup to inversion experiments. Numerical tests based on the Marmousi-II model demonstrate that the MATLAB and C implementations produce consistent modeling and inversion results, while also showing their differences in computational efficiency, memory usage, and development convenience. These results indicate that FWI-EDU can serve as a transparent and practical platform for FWI education, code-based algorithm understanding, and rapid prototyping of new inversion ideas.