What are standing wave patterns? 

Waves in nature come in many forms:  on water, in air, in electric fields, and through solid objects such as rock, metal, or the Earth itself.  In any of these cases, the wave is a pulse or oscillation of energy that travels through the material in question even though the material itself is not traveling.  Sound waves can travel many miles through the air, at very high speed, and yet the air itself is not moving, except as a minute vibration passed along from air molecule to air molecule in a chain of collisions.

It is helpful to think of waves on water, as these can be seen with the human eye.  Water waves are seen as series of high points (crests) and low points (troughs) that propagate (travel) along a given direction.  When a pair of water waves encounter each another, they interact or “interfere” with each other to produce a combined wave form.  Where the crests combine, new crests form that are higher than either of the original wave tops.  Where the troughs combine, even deeper troughs appear.  Where a crest combines with a trough, their respective high points and low points tend to nullify each other, creating an intermediate height of water surface.

In waters where many waves traveling in all directions interact, peak-like wave tops and hole-like troughs can form, all appearing to “dance” up and down in place.  In these circumstances, the horizontal motion of the individual waves can be lost to the eye altogether and the combined waves may appear to “stand” in place.  Such waves are called “standing waves.”

In the picture to the left, two individual waves, one blue and one violet, are shown.  These could be two different ripples on a watery surface, two different vibrations on a guitar string, or two different sound waves in the air.

When the two individual waves interact, or "interfere," with each other, the actual appearance of the combined waves is a result of the peaks and troughs of the two individual waves adding to or subtracting from each other.

The result of adding the two above waves together is shown in the second picture.

In Tectonic Basin, the vibrations in the steel plate underneath the sand are acoustic (sound) waves. These vibrations travel back and forth across the plate, moving in all directions. When these traveling waves interact they interfere with each other in a manner similar to water waves.  The interference of acoustic waves creates the troughs and crests of wave patterns in the sand of Tectonic Basin. Under the right conditions, some of these waves may appear to stand still, or nearly so.

Are sand dunes in nature formed by wave interference?

The forces that create sand dunes on Earth and on other planets are not tectonic or acoustic in nature.  Air movement carrying dust and sand particles forms sand dunes.  (For more information, see Aeolian Landscape.)  Nevertheless, tectonic waves do move through the Earth and along its surface, and their effects can be seen when they are exceptionally strong, as during an earthquake.

How do faulted landscapes develop?

In “Tectonic Basin” lines form in the sand where dunes intersect one another. These lines suggest faulted landscapes similar to what can be seen when flying over the San Andreas Fault in Central California. Although traveling and standing waves may be involved in an earthquake, these fault lines form in a different way. They are the result of tectonic plate motions and the crustal forces associated with them.

Earthquakes and the fault zones in California are the outcome of the Pacific Plate sliding north past the North American Plate. Plates are distinct, essentially rigid sections of the Earth’s crust. The sliding process creates discontinuities in the landscape, which are the lines in the fracture zones that we see

What other sculptures share similar features with "Tectonic Basin"? 

Duning is presented most vividly in Aeolian Landscape, although the dunes are wind-formed as opposed to the traveling and standing waves you observe in Tectonic Basin. The sculpture Rift Zone offers a view of geothermal activity that takes place predominantly around crustal tectonic faults. But the formations in Rift Zone look very different from the waves in Tectonic Basin.

Photo Credit:  United States Geologic Survey