Final answer:
The amount of ground displacement in an earthquake is critical for measuring its strength and is represented logarithmically on the Richter scale. Large-amplitude seismic waves cause more displacement, and the energy in earthquake waves is directly proportional to the amplitude squared.
Step-by-step explanation:
The amount of ground displacement in an earthquake is a measure of the size of the waves created by the earthquake, which is directly related to the energy released during the seismic event. This measure is important in quantifying the strength and potential destructiveness of an earthquake.
The size of these seismic waves and the corresponding ground displacement are typically recorded on the Richter scale, using a semi-log plot to represent the amplitude of the waves logarithmically against the assigned intensity of the earthquake. Geologists use this data in conjunction with the differences in the arrival times of P-waves and S-waves to determine the location of the earthquake's epicenter.
Specifically, the energy in earthquake waves is a function of their amplitude; waves with large amplitudes result in large ground displacements and, therefore, more damage. This is because the energy in a wave is directly proportional to the amplitude squared. The concept that larger displacements need greater forces (F = kx) to be created is fundamental to understanding the relationship between a wave's amplitude and the energy it carries.
Thus, when we discuss the severity of an earthquake, we often refer to its magnitude as quantified by scales like the Richter scale, which describes the ground displacement and hence gives an indirect measure of the earthquake's energy.