In recent years, seismic metamaterials (SMs) have attracted considerable attention for their capacity to manipulate seismic wave propagation. Unlike conventional seismic mitigation methods, SMs offer broader applicability and enhanced seismic energy absorption capabilities. Despite the burgeoning interest in SM research, the focus has predominantly been on the design of SM unit cells. The introduction of SM layout pattern design, a novel strategy to achieve superior wave shielding performance, has proven effective in enhancing the seismic protection of infrastructures. However, existing research on SM pattern design primarily centers on graded SMs with linear layouts, neglecting the exploration of more intricate layout patterns. To bridge this research gap, this study proposes a hierarchical design strategy that integrates a novel embedded SM unit cell design with the exploration of three graded SM layout patterns including one linear and two polynomial patterns. Subsequently, the frequency domain analysis (FDA) method is developed to assess the wave attenuation performances of the proposed SMs. The analysis results demonstrate that compared to the non-graded SM, the proposed graded SMs exhibit elevated seismic wave attenuation capabilities, suggesting potentials for advanced wave reduction.