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How to Calculate Seismic Forces & Moments

To gain a complete picture of the magnitude, size, energy and potential damage of an earthquake, use a variety of methods. The magnitude of seismic waves based on the Richter scale is often reported in the news. However, in addition to traditional methods, calculate the seismic moment, the magnitude based on the seismic moment and the magnitude based on the energy level of the earthquake. The seismic moment takes into account the average amount of slip as well as the geological force necessary to cause the rocks to slip. These calculations provide a more complete and accurate understanding of the true impact of an earthquake.

Things You'll Need

Seismograph
Distance of earthquake to seismic center
Focal depth of earthquake

Instructions

Magnitude of Body and Surface Waves
- 1
  Calculate the amplitude (A) of ground motion (in microns) with a seismograph. Record the number of seconds for which you are recording the ground motion.
- 2
  Divide the amplitude by the time (T). Calculate the log10 of that quotient. The formula for steps 1 and 2 is log10(A/T).
- 3
  Determine the distance (D) of the epicenter of the earthquake and the seismic station in degrees. Determine the distance in kilometers (h) of the focal depth. Multiply D by h and complete the calculation using the formula mb = log10(A/T) + Q(D,h), where mb represents the magnitude of the body waves of the earthquake.
- 4
  Repeat these calculations to determine the surface-wave magnitude using the formula Ms = log10 (A/T) + 1.66 log10 (D) + 3.30, where Ms represents the surface-wave magnitude.
Seismic Moment
- 5
  
  Seismic moment considers the shear strength of the rock, the area and average displacement.
  
  Determine the shear strength of the faulted rock (µ). Calculate the area of the fault (S). Area is equal to the length multiplied by the width. Determine the average displacement of the fault <d>.
- 6
  Multiply the shear strength of the faulted rock (µ) by the area (S).
- 7
  Multiply the resultant quotient by the average displacement <d> of the fault. The formula for calculating seismic moment is Mo = µS<d>, where Mo represents the seismic moment. The U.S. Geological Survey of the U.S. Department of the Interior states that seismic moment provides a "more consistent" measure of the earthquake size than standard magnitude measurements.
- 8
  Calculate the magnitude (Mw) of the earthquake based on the seismic moment (Mo), using the formula Mw = 2/3 log10(Mo) - 10.7. The Mo value is calculated from low-frequency seismic data. Using the seismic moment (Mo) to calculate magnitude provides a more accurate scale in measuring and comparing magnitudes of various earthquakes than conventional methods.
Magnitude Based on Energy
- 9
  Record the high-frequency energy value of the earthquake as computed by a digitally recording seismograph.
- 10
  Multiply this energy reading by 2/3log10 using the formula Me = 2/3 log10E, where Me represents the magnitude based on energy radiated by an earthquake.
- 11
  Subtract 2.9 from the resultant figure. The complete formula for calculating the magnitude based on energy radiated by an earthquake (Me) is Me = 2/3 log10E - 2.9. As the magnitude energy (Me) increases by one unit, the seismic energy increases 32 times. Me indicates the seismic potential for damage.

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