Abstract: Full waveform inversion has been widely researched in various fields, including oil and gas as well as mineral exploration, due to its performance in high-precision imaging. However, its gradient calculation process often demands huge storage and computational resources. To address this issue, this paper proposes an acoustic full waveform inversion method based on optimized effective boundary storage. By employing the time and space intervals determined by the Nyquist sampling theorem, this method resamples the wavefield at the effective boundaries in both domains to significantly reduce the required storage for the boundary wavefield. Cubic spline interpolation is used to achieve accurate wavefield reconstruction. Synthetic data tests on 2D Overthrust and BP models demonstrate the method's feasibility by improving computational efficiency and significantly reducing memory consumption.