I'll give it my best shot:
If a flexible structure is subject to an earthquake, the movement of the structure will vary depending on the frequencies of the earthquake versus the natural frequencies of the structure. If the structure is perfectly rigid, its natural frequency is infinite, its period is zero, and it simply moves in unison with the ground, and the acceleration should be the "Zero Period Acceleration" in that case. That may be adjusted by various other factors as well, and you would need to check the exact definition in the source you're using. A structure with zero period would be a "rigid structure" in ASCE 7-05, if I remember the terminology right.
In older seismic codes, they had the US divided into 4 or 5 different seismic zones, and depending on which zone, you used a specific coefficient in the seismic design. Generally, the acceleration used in the design would be proportional to these zone factors. Current seismic codes use maps with continuous variation in the different variables, rather than distinct zones. See ASCE 7-05, for example. In referring to ASCE 7, see the section on "non-building structures not similar to buildings".
Hope this helps, if not, perhaps explain more specifically what you're trying to do.