Abstract: Internal multiple interference, affecting both seismic data processing and interpretation, has been observed for long time. Although great progress has been achieved in developing a variety of internal-multiple-elimination (IME) methods, how to increase accuracy and reduce cost of IME still poses a significant challenge. A new method is proposed to effectively and efficiently eliminate internal multiples, along with its application in internal-multiple-eliminated-migration (IMEM), addressing this issue. This method stems from two-way wave equation depth-extrapolation scheme and associated up/down wavefield separation, which can accomplish depth-extrapolation of both up-going and down-going wavefields simultaneously, and complete internal-multiple-elimination processing, adaptively and efficiently. The proposed method has several features: (1) input data is same as that for conventional migration: source signature (used for migration only), macro velocity model, and receiver data, without additional requirements for source/receiver sampling; (2) method is efficient, without need of iterative calculations (which are typically needed for most of IME algorithms); and (3) method is cost effective: IME is completed in the same depth-extrapolation scheme of IMEM, without need of a separate processing and additional cost. Several synthesized data models are used to test the proposed method: one-dimensional model, horizontal layered model, multi-layer model with one curved layer, and SEG/EAGE Salt model. Additionally, we perform a sensitivity analysis of velocity using smoothed models. This analysis reveals that although the accuracy of velocity measurements impacts our proposed method, it significantly reduces internal multiple false imaging compared to traditional RTM techniques. When applied to actual seismic data from a carbonate reservoir zone, our method demonstrates superior clarity in imaging results, even in the presence of high-velocity carbonate formations, outperforming conventional migration methods in deep strata.