normal mode

The term normal­ mode is used in seismology to refer to the set of standing waves of a given frequency that cover the entire surface such that while one portion of the surface rises while another portion falls versa, in a continuing pattern. They are the analog on the surface of an object (e.g., sphere) of the standing waves of a vibrating string. The commencement of a vibration at some location on the surface of a sphere (e.g., an earthquake) instigates waves that travel across the sphere's surface from the location, like ripples from a stone thrown into a pond. They are initially traveling waves, but once they encircle the sphere, meeting each other, they interfere, with each wave-frequency either strengthened or weakened. Normal modes are wave-patterns that result, persisting once the whole surface is covered with waves: they are those in which the waves are maximally strengthened by their interference and they take longest to dissipate.

An analogous type of wave is the ringing of a bell: different portions of its surface are moving oppositely. A first approximation (for a spherical object) fits the normal modes to a multipole expansion of the surface. Actual vibrations, e.g., of planets and stars can include a normal­ mode or the sum of a number of them. On Earth (geoseismology), normal modes are detected and stand out for a while following some large earthquakes. In studies of stars (asteroseismology, including the Sun, i.e., helioseismology) and gas giants (e.g., Jupiter), the normal modes may be constantly detectable and constitute the substantial portion of the available seismic data.

The term normal­ mode is more generally used in the mathematics of oscillations, modeling vibrations of the above type, and any type that produces standing waves of a single frequency. Characteristics of the vibrating object determine the frequencies of the vibrations, which are resonant frequencies, i.e., frequencies which most easily occur.