Earthquake magnitudes differ in names and scales with varying observation and calculation methods

The earthquake magnitude referred to in an earthquake report is a value used to describe the earthquake size. In Taiwan, the Richter scale, also known as the local magnitude (ML), is used.

It was a scale developed in 1935 for the purpose of measuring earthquakes occurring in California. The scale is defined as a dimensionless real number (6.5, for example) by taking the natural logarithm of the maximum amplitude of a seismic wave recorded by the Wood-Anderson torsion seismometer located at the seismic observation point.

Saturation is reached for earthquakes measuring over 7.5 on the Richter scale due to limitations of the Wood-Anderson torsion seismometer. This means that earthquakes beyond certain magnitudes tend to register similar values on the scale. Additionally, measurements registered on the Richter scale at observation point for earthquakes 600 kilometers away from the epicenter, usually bear significant errors and turn out to be useless. Therefore, seismologists try to describe the magnitude of distant earthquakes by using the surface wave magnitude (Ms) and the body wave magnitude (Mb). Both wave magnitudes are calculated based on the maximum amplitude of the specific wave mode found in the seismic waves. However, both scales still exhibit saturation phenomenon for large- magnitude earthquakes.

Early in the 21st century, seismologists adopted the moment magnitude scale (Mw) that can directly represent the physical characteristics of the earthquake ruptures (such as the magnitude of fault movement and the seismic energy involved). The formula for estimation is as follows:

The formula for estimation

Here, Mo is the seismic moment used by seismologists for depicting the amount of energy released during an earthquake, defined as:

Mo = u DS

µ is the rigidity or shear modulus of the materials in the fault;
D is the average displacement on the fault; and
S is the area of the rupture along the geologic fault where the earthquake occurred.

The moment magnitude scale has an advantage over the Richter scale in that it does not reach saturation, which means that large-magnitude earthquakes will be more accurately reported. Additionally, the scale is more directly linked to the physical characteristics of the hypocenter. As a result, the moment magnitude scale has replaced the Richter scale to become the most frequently used scale by seismologists for estimating large-magnitude earthquakes. It has been used by the United States Geological Survey (USGS) which is engaged in global seismic monitoring and reporting services for describing earthquakes with magnitudes beyond 3.5.

Both the Richter scale and moment magnitude scale use their own unique theory and application regarding registering data for the same earthquake. Despite the difference in numerical values, they measure the same amount of energy released by the earthquake. A similar analogy can be drawn by measuring a height and coming up with either 1.78 meters or 178 centimeters-both describe the same height despite their being different in numerical values. The following table is a comparison of major earthquakes that have occurred in Taiwan in recent years, with both Taiwan's Richter scale measurement and the USGS's measurement using the moment magnitude scale:

Time Richter magnitude scale Moment magnitude scale (USGS)
1999/09/21 01:47 Jiji(Chi-Chi) Earthquake
7.3 7.7
2002/03/31 14:52 Hualien Earthquake
6.8 7.1
2003/12/10 12:38 Chenggong Earthquake
6.6 6.8
2005/06/06 03:06 Yilan Earthquake
5.9 5.8