Normal mode splitting functions

Similarly to when a bell is hit, and the arising standing wave patterns produce a
sound, standing waves arise on the Earth after large magnitude earthquakes (typically
magnitude 7.5 or larger). The vibrations that these standing waves (so-called normal
modes) produce can be measured using seismometers – instruments that measure the
displacement of the Earth’s surface. The resulting frequency measurements that we
obtain can be related to the material inside the Earth: similarly to the sound of a bell
or music instrument being dependent on the material or string thickness.

When a large magnitude earthquake occurs and excites its normal modes, we
do not just get one standing wave, but a multitude of them. To stay with the analogy
of music instruments, the different waves can be seen as the fundamental tone and
overtones in different directions. We name these standing waves using two numbers:
the radial order *n* and angular order *l* to identify different normal modes. Each o