Despite widespread use for extending absorption bandwidth, the coexistence and coupling mechanism of multiple resonance is not well understood. We propose two models to describe the multi-resonant behavior of a broadband metamaterial absorber with geometrical-array substrate （GAS）. The multi-resonance coupling of GAS is well described by logarithmic law. The interaction between metasurface and GAS can further broaden the absorption bandwidth by generating a new resonance which coexists with original resonances in substrate. The proposed models can thoroughly describe this multiple-resonance behavior, highlighting guidelines for designing broadband absorbers.
