What is the term for the logarithm of the maximum seismic-wave amplitude recorded on a seismograph?

The term that describes the logarithm of the maximum seismic-wave amplitude recorded on a seismograph is Local Magnitude, commonly referred to as M_L. This measurement is specifically designed to quantify the size of an earthquake based on the amplitude of the seismic waves it produces. The Local Magnitude scale provides a logarithmic output, meaning that each whole number increase on the scale corresponds to a tenfold increase in measured amplitude, thus highlighting the strength of seismic events.

Local Magnitude is particularly important for understanding and assessing earthquakes that occur near the seismograph location, as it reflects the local effects of seismic waves. While the term "magnitude" can refer to various scales used to measure earthquakes, in this context, Local Magnitude specifically pertains to the amplitudes recorded on seismographs, distinguishing it from related concepts such as intensity, which measures the earthquake's effects on people, buildings, and the Earth's surface.