I began a lecture on earthquake size; we will finish next class. Get the notes and read the appropriate sections in the class texts if you need more background. Some of the material online is very good on these subjects. Detail can be found in wikipedia, for example.
The earliest metrics of earthquake size were based on their impact upon societies. The suffering, social impact, and economic impacts are recorded historically for many earthquakes. Since the 1700’s we have tried to be more systematic about measuring earthquake size using the scale of damage to human-made structures. In the late 1800’s the development of the seismometer led to classic magnitude scales (developed in the 1930’s) and satellite geodesy has led to additional measures based on ground deformation.
Magnitude is based on observations of the size of the ground shaking produced by an earthquake. The simple idea is that larger earthquakes produce larger vibrations. To measure the ground vibrations precisely, we use seismometers. Seismometers are sensors used to measure ground motion; seismographs are instruments used to record the motions as a function of time; and seismograms are plots of the motion versus time.
Magnitude is usually computed using two observations from each seismogram – the largest amplitude and the period of the motion. We will talk about period and frequency later. The magnitude of the earthquake can be measured using a number of different parts of a seismogram, and thus we have a number of different types of magnitudes.
Richter originally used the logarithmic (base 10) difference between the observed largest ground motion and a reference value $$M_L = log_{10} A – log_{10}~A_0~,$$where \(A\) now represents the amplitude of the ground motion. The subscript in \(M_L\) stands for “local”, and we call this measure, local magnitude because originally this measure was local to southern California, where Richter was working. The above formula works fine if the earthquakes are the same distance away. However, we must also account the fact that vibrations observed farther from an earthquake are naturally smaller. Richter recognized that some type of distance-based correction would be necessary if seismometers at all distances were to produce consistent estimates for the same earthquake.
Having even a repeatable, easy-to-measure estimate of earthquake size is very valuable if you want to compare earthquakes. Richter recognized this quickly and in collaboration with a colleague at CalTech, Gutenberg, he developed other magnitude measures that were appropriate for waves recorded at greater distances from the earthquake.
In-class activity: Students started a calculation of the magnitude of the 2011 Virginia Earthquake.