A seismic, water, or acoustic wave damping structure can include a structural arrangement of at least two elements, each with an inner volume and containing a medium resistant to passage of an anticipated wave. Example elements can be earth boreholes or water pylons. The structural arrangement can taper from an upper aperture to a lower aperture, the structural arrangement defining a protection zone at the upper aperture. The structural arrangement can be configured to attenuate power from the anticipated wave within the protection zone relative to power from the anticipated wave external to the protection zone. A grouping may include elements that form acute or obtuse angles with a direction of a wave to attenuate wave power. High-value buildings or other structure in a protection zone on land or in water can be substantially shielded from seismic or water waves.