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As seismic wave propagates through earth materials, wave amplitude attenuates as a result of several factors. From measurement of amplitude of seismic data, attenuation measurement can be computed which can provide a viable tool for lithology discrimination and weak ground motion prediction for the region under study.In this study, we discuss the effect of the medium on seismic wave propagations (particularly seismic wave attenuation) from which we model seismic wave attenuation mathematically and analyze the 2D- graphical model of the region under study. In doing so, we see the interrelationship between the attenuation coefficient and distance, attenuation coefficient and frequency content of the wave, and dissipation factors Q-1 and the frequency. From the model the attenuating behaviors of the region are discussed from the attenuation coefficient curve versus depth and evaluate the effects of the geology of the region on wave propagation for the Main Ethiopian Rift, Western and Eastern Ethiopian plateaus.