In this paper, we propose a new sparse dictionary learning scheme for lossy compression of seismic signals collected at a single sensor from multiple source shots. The method leverages the entropy constraint and delay compensation for dictionary learning. Using the proposed method for delay compensation in seismic data squeezes more redundancy out of the data which results in a sparser representation for a given dictionary. The objective of entropy constraint term in dictionary learning is to make the sparse coefficients tailored to the compression objective. To solve the above hybrid dictionary learning problem, delay-compensated and entropy-constrained dictionary learning is developed and alternating scheme is proposed for optimization. Furthermore, an offline-training-online-testing way is adopted for the proposed dictionary learning scheme in the seismic data compression. The experimental results demonstrate the effectiveness of the proposed method for maintaining a desirable rate-distortion trade-off for the seismic signal compression.