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Seismic data collection involves vast amounts of data in the range of multiple hundreds of terabytes. Very high data compression algorithms are thus required to make seismic data analysis more efficient in terms of storage and transmission bandwidth. We present an adaptive filtering algorithm for seismic data compression based on the wavelet packet transform. The main objective is to achieve higher compression rates for seismic data at a quality above 40 dB in the SNR perspective. The wavelet transform is known for its good localization in time and frequency, a feature that has been utilized for data compression. Wavelet packets are introduced to give extra freedom in selecting appropriate position, scale. and frequency decomposition for more data compression. Our algorithm is developed so that the selection of the best tree decomposition of any given signal is adaptively obtained with respect to an entropy-based criterion. Our algorithm is tested on different seismic data sets. Results indicate that the proposed algorithm is more efficient when compared to other algorithms in the same category without showing any visible artifacts in the decompressed signals.