Things You'll Need
Instructions
Calculate the standard body-wave magnitude. The formula for the standard body-wave magnitude is mb = log10(A/T) + Q(D,h). In this formula A is the amplitude of the wave in microns, as measured by a seismograph. T represents time in seconds. Q(D,h) is a correction factor based on the function of distance (D) in degrees between the epicenter of the earthquake and the station and focal depth (h) in kilometers. The first waves to reach the seismic station are P, or primary waves. The second body waves to reach the seismic station are S or secondary waves.
Calculate the magnitude of the surface waves. Surface waves reach the seismic station after body waves. The standard formula for measuring surface waves is MS = log10 (A/T) + 1.66 log10 (D) + 3.30. There are variations of these standard formulas that account for variations in specific geographic regions. While surface waves are of a lower frequency than body waves and arrive after body waves, they are responsible for most of the damage from earthquakes. Deeper earthquakes cause less damage than earthquakes closer to the surface. There are two types of surface waves: Love waves, named a British mathematician (1911), and Rayleigh waves, first identified in 1885. Love waves are fastest and move the ground side to side, whereas Rayleigh waves roll like the waves across the surface of the ocean.
Analyze the waveforms produced by the seismograph. Factors to consider are the direction of the fault movement and the orientation of the fault. Fault geometry is determined from waveforms that are recorded at various distances and azimuths from the earthquake. (The azimuth is the horizontal angle of the observer's bearing in surveying.)
Calculate the seismic moment. The formula for calculating the seismic moment is MO = µS<d>. In this formula µ is the shear strength of the faulted rock, S is the area of the fault, and <d> is the average displacement on the fault. Seismic moment is considered to provide a truer measure of the earthquake size than magnitude, because it is based on fault geometry and observer azimuth. Additionally, seismic moment has the advantage of not having an intrinsic upper boundary in its calculation.
Calculate the magnitude of the earthquake based on the seismic moment, MW. The formula for this is MW = 2/3 log10(MO) - 10.7, where MO equals µS<d>, as discussed in the previous section. Chile, in 1960, and Alaska, in 1964, are two of the largest seismic moments recorded in history.