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The size of an earthquake

Modern Magnitude Scales

The most known magnitude measurement − ″THE RICHTER SCALE ″ IS NO LONGER USED! As our understanding of earthquakes increased more accurate and more robust measurements of magnitude were developed. These include but are not limited to body wave magnitude (mb), surface wave magnitude (Ms), and Moment magnitude. Magnitudes are measurements of the energy released. Every magnitude measurement has the form:

M = log (A¦T)+ F (h, Δ) + C

Where A is the amplitude of the signal, T is the dominant period of the signal, F is a functional correction of the variation of magnitude due to the variation of depth and distance, and C is a regional scale factor.

Duration Magnitude

This is another empirical magnitude scale developed by each regional network. Because this is an empirical scale the exact equation used by each network will be slightly different. This scale is most effective for smaller events between 0 and ~5 in magnitude. The duration magnitude is computed by searching for the time at which the amplitude of the signal returns to the pre-earthquake level as well as the maximum amplitude of the signal. These two data points are then input into the local empirical equation to determine the magnitude of the event. Given that most events in the Puerto Rico and Virgin Islands region are within the applicable range you will often see PRSN report magnitudes as md.

Body Wave Magnitude (mb) and Surface Wave Magnitud

Early global studies used body wave magnitude and surface wave magnitude. Body wave magnitudes are measured using the body wave train usually using the P-wave.
The equation of body wave magnitude is as follows:

Mb = log (A¦T)+ + Q (h, Δ)

Here A is the ground motion amplitude (in microns after removal of the instrument response), T is the wave period, Q is the empirical term depending on distance and focal depth (global or for a local region). Mb is not used for epicentral distances greater than 100º in order to avoid diffracted waveforms. Diffracted waveforms such as Pdiff are generated when the energy of the wave interacts with Earth's liquid outer core. The outer core is relatively slow compared to the shallower mantle, so some of the energy travels along the core-mantle boundary instead of going into the core before returning to the Earth's surface. As an analogy the energy traveling along the interface is can be thought of a car driving on a highway whereas any energy entering the core would be taking the smaller and slower country roads. Drivers would prefer to take the highway just like the energy from the seismic wave prefers to travel along the interface. The energy that travels along the interface is what generates these diffracted waveforms.
Surface wave magnitude, Ms, is measured using the largest amplitude of the surface waves.
The general equation has the form:

Ms = log (A¦T)+ + 1.66 log (Δ) +3.3

Often the largest amplitude Rayleigh waves are generally at a period of 20s. In this case the general equation becomes:

Ms = logA20 + 1.66log (Δ) +2.0

Both of these amplitudes were designed to match local magnitudes measured in California. These magnitudes while useful for the general public and emergency management, do not have direct connect to the source physics of the earthquake source. To connect the source physics to magnitude, scientists developed the Moment Magnitude scale (Mw).

Moment Magnitude (Mw)

Unlike the other magnitude measurements, moment magnitude links directly to the fault properties. In equation form:

Mw = logM0/1.5-10.73

Mo is the seismic moment in dyne-cm and can be defined by the physical properties of the fault:
  • M0 = μDS = μDfL2
  • μ: rigidity at the source depth
  • D: Average slip on the fault
  • S: The fault Area
  • S = fL2
  • f: ratio of width to length
  • L: length of the fault

In simple terms the Moment magnitude relates directly to the area of the fault that moved during the earthquake, how far the fault moved, and how much the material the of fault resists slipping. Because this magnitude links directly to the fault properties it is considered the most useful for scientists. The advantages of Moment Magnitude are as follows:
Directly tied to earthquake faulting process Does not saturate: For large magnitudes (>6.5) mb and Ms may underestimate the size of the event. When this happens seismologist call this magnitude saturation.

Richter Scale (M)

The Richter scale measures the earthquake by its size, taking into account the energy released. This scale was devised by the Japanese Wodatti in 1931; however, the American Charles F. Richter developed it in the State of California and from there retained his last name. It differs from the Modified Mercalli, in that the latter interprets the intensity with which the earthquake damaged human facilities. For its part, the Richter scale measures the energy released by the telluric movement. The seismologist quantifies the magnitude by the traces left by the earthquakes in the seismograph. This scale considers the relationship between the maximum amplitude of the traces and the epicentral distance. It is claimed that it is the most used scale, but it is the one that is used most incorrectly by the public.

The magnitude of an earthquake is determined by taking the logarithm (in base 10) of the greatest movement of the soil recorded during the arrival of a type of seismic wave and applying the standard distance correction. As the scale is logarithmic, the magnitude increases by one unit with the increase of ten units in the amplitude or duration of the seismic wave record. However, in terms of energy released by an earthquake, an increase in unity in magnitude increases the amount of energy released by a factor of approximately 30. Although there are different scales of magnitude, based on different waves, most of them are reported on the Richter scale in honor of Dr. Charles F. Richter who developed the concept in 1935.

The following image shows how frequent an earthquake occurs according to its magnitude in a year and a comparison of the energy released with different events.

Modified Mercalli Scale (MM)

Intensity is a non-instrumental perceptibility measure of damage to structures, ground surface effects and human reactions to earthquake shaking. It is a descriptive method which has been traditionally used to establish earthquake size, especially for pre-instrumental events. Earthquake intensities are usually obtained from interviews of observers after the event. Since human observers and structures are scattered more widely than any seismological observatory could reasonably hop to scatter instruments, intensity observations provide information that helps characterize the distribution of ground shaking in a region. Discreet scales are used to quantify seismic intensity, the levels are represented by Roman numerals and each degree of intensity provides a qualitative description of earthquake effects. In the Caribbean, the Modified Mercalli scale is used. This scale was prepared by Rossi of Italy and Forel of Switzerland in the 1880s. This scale uses human experiences to determine the level of shaking experienced during an earthquake. The amount of felt shaking depends on the depth, location, magnitude of the event as well as the population density, building construction, and local geology. If you feel shaking that may be related to any earthquake you should report it to the PRSN using our web interface: Did You Feel It Form

Below is a table comparing the values of intensity, magnitude and acceleration.

Intensity Intensity Scale Mercalli Modified Magnitude (Richter Scale) Max. Terrain Acceleration (g)
I Not Felt < 2.3 < 0.002
II Felt only by some people in resting position, especially in high floors. Suspended objects oscillate a little. 2.3 - 2.9 0.002 - 0.003
III Felt indoors. Many people do not recognize it as an earthquake. Standing cars sway. Vibrations like the passage of a small truck. Duration appreciable. 3.0 - 4.1 0.004 - 0.007
IV Felt indoors by many, few on the outside. Windows, dishes, doors vibrate. The walls creaked. Vibrations like the passage of a big truck; Shaking sensation like a heavy ball. Stationary cars shaking noticeable. 3.7 - 4.2 0.015 - 0.02
V Felt by almost everyone. Many wake up. Dishes & windows may break. Some masonry houses crack. Unstable objects overturned. Doors swing in and out. 4.3 - 4.9 0.03 - 0.04
VI Trees and shrubs visibly shaken. Felt by everyone, many are frightened and run outside. It's hard to walk. Windows, dishes and glass objects break. Some heavy furniture moves; Some masonry houses fall. Light damage. 5.0 - 5.6 0.06 - 0.07
VII Everyone runs outside. Small damage to structures specially designed for earthquakes, slight to moderate damage to correctly built buildings and considerable damage to poorly built structures. Difficult to drive. 5.7 - 6.2 0.1 - 0.15
VIII Slight damage to structures specially designed for earthquakes, partial collapse may occur in current buildings and higher in poorly constructed structures. The panels of the walls fall off frames. Monuments, columns and walls fall. Heavy furniture overturn. Small slides of sand and mud. Changes in the flow of sources and wells. Difficult to drive. 6.3 - 6.9 0.25 - 0.3
IX Significant damage to structures of good design and construction, well-designed structures displaced from its foundations; Higher in current buildings with partial and total collapse. Wide cracks in the floor. Ejection of sand and mud in alluvial areas. Broken underground pipes. 7.0 - 7.6 0.5 - 0.55
X Some well-constructed structures in wood and bridges destroyed, most of the building and structures destroyed with their foundations. Large cracks in the floor. Landslides, water goes beyond the banks of channels of rivers, lakes, etc. Sand and mud displaced laterally. 7.7 - 8.2 > 0.6
XI Collapse of most cement and concrete structures. Bridges and other transport routes seriously affected 8.3- 9.0 > 0.6
XII Total loss in infrastructure. Large masses of displaced rocks. Heavy objects vertically thrown into the air with ease. >9.0 > 0.6