Earthquake magnitude is a quantitative, mathematical calculation to measure the energy released at the source of an earthquake. On the other hand, earthquake intensity is the qualitative measurement of the strength of shaking produced by an earthquake.

**Content**

**Earthquake (Seismic) Magnitude Scales****Earthquake (Seismic) Intensity Scales****Earthquake Magnitude/Intensity Comparison****Which is the “correct” magnitude?**

### Earthquake (Seismic) Magnitude Scales

Magnitude scales describe, numerically, the size of the earthquake using mathematical equations and characteristics from the seismic waves recorded on seismographs.

Determination of an earthquake’s magnitude generally involves identifying specific types of seismic waves on a seismogram, and then measuring one or more characteristics of a wave, such as its timing, orientation, amplitude, frequency, or duration. Additional adjustments are usually made for distance, kind of crust, and the characteristics of the seismograph that recorded the seismogram.

The various magnitude scales represent different ways of deriving magnitude from information as is available. All magnitude scales retain the logarithmic scale as devised by Charles Richter, and are adjusted so the mid-range approximately correlates with the original “Richter” scale.

There are several magnitude scales that are used across the world. Comprehensive and technical information can be found on the USGS’ website. In the Eastern Caribbean, there are a some that are frequently used.

#### Richter Magnitude Scale (ml, ML, M_{L})

The Richter Magnitude, or local magnitude scale, was the first scale for measuring earthquakes. It was developed in 1935 by Charles F Richter.

Richter established two features now common to all magnitude scales.

**How is the M _{L} Scale Calculated?
**

The original Richter scale was developed to relate the amplitude of a seismic wave and the distance of the S and P waves on the seismogram. It is based on the maximum amplitude of a seismogram recorded on a Wood-Anderson torsion seismograph. Although these instruments are no longer widely in use, ML values are calculated using modern instrumentation with appropriate adjustments.

The most important, and widely known fact about this scale is that it is logarithmic. Each unit represents a ten-fold increase in the *amplitude* of the seismic waves and each unit of magnitude represents a nearly 32-fold increase in the *energy* (strength) of an earthquake.

**Limitations**

All “Local” (ML) magnitudes are based on the maximum amplitude of the ground shaking, without distinguishing the different seismic waves. They underestimate the strength of:

*d*i*stant earthquakes*(over ~600 km) because of attenuation of the S-waves,- d
*eep earthquakes*because the surface waves are smaller, and - s
*trong earthquakes*(over M ~7) because they do not take into account the duration of shaking.

Because of these shortcomings, other magnitude scales were developed.

In Trinidad and Tobago, this scale is rarely used. In the few times it is utilized by international seismological organizations such as the USGS, it is because no other types of magnitude using available scales were able to be calculated.

This type of scale is used for earthquakes of magnitudes 2.0 to 6.5, at distances of 0 to 600 kilometers away from seismometers.

#### Body Wave Magnitude Scale (mb)

Body-waves consist of P-waves that are the first to arrive (see above seismogram), or S-waves, or reflections of either. Body-waves travel through rock directly. (Havskov & Ottemöller 2009)

While there are several iterations of body magnitude scales, most times in the Trinidad and Tobago region, if this scale is used, the **mb** iteration is reported.

**How is the mb Scale Calculated? **

The **mb** or **m _{b}** scale uses only P-waves measured in the first few seconds on a specific model of short-period seismograph. The short period improves detection of smaller events.

Measurement of mb has changed several times. The modern practice by the USGS is to measure short-period **mb** scale at less than three seconds, while the broadband **mB _{BB} ** scale is measured at periods of up to 30 seconds.

**Limitations**

The mb scale is typically used for earthquakes of magnitude 4.0 to 6.5, at distances of 15 to 100 degrees away from the seismometer.

It is reported for most M4.0-4.5 to 6.5 earthquakes that are observed teleseismically (recorded far distances from the earthquake source). Typically, with a light (M4.0-4.9) or moderate (M5.0-5.9) earthquake occurs near Trinidad and Tobago, this type of magnitude is published by the USGS.

Mb tends to saturate at about M 6.5 or larger.

#### Moment Magnitude (M_{W} or Mw)

The **Moment Magnitude **(M_{W} or Mw) is a measure of an earthquake’s magnitude based on its seismic moment (the energy released). It’s numerical value is similar to the magnitudes on the original Richter Scale.

**How is the M**_{W}** Scale Calculated? **

The M_{W} scale is based on an earthquake’s seismic moment. This is a measure of how much work an earthquake does in sliding one area of rock past another area of rock.

In the simplest case the moment can be calculated knowing only the amount of slip, the area of the surface ruptured or slipped, and a factor for the resistance or friction encountered.

These factors can be estimated for an existing fault to determine the magnitude of past earthquakes, or what might be anticipated for the future.

Our neighbouring seismological organization, FUNVISIS, typically publishes the M_{W} magnitude as their earthquake solutions.

An earthquake’s seismic moment can be estimated in various ways, which are the bases of the **M _{wb}**,

**M**,

_{wr}**M**,

_{wc}**M**,

_{ww}**M**,

_{wp}**M**, and

_{i}**M**scales, all subtypes of the generic M

_{wpd}_{w}scale.

In the Trinidad and Tobago region, these values are typically calculated and published by international seismological centers such as the USGS or GFZ.

Generally, for larger events, the USGS (NEIC) publishes the Mw_{b}, M_{wc} and most commonly the M_{ww} magnitudes. FUNVISIS publishes the M_{wr} for larger events.

The differences amongst these M_{W} magnitude types are fairly complex geophysical and mathematical calculations but are generally seen as the most accurate in determining the magnitude of larger earthquakes, generally above M6.0.

**M**_{ww} is generally calculated by USGS for all M5.0 or larger earthquakes worldwide, but generally robust for all M5.5 worldwide. Provides consistent results to M~4.5 within a regional network of high-quality broadband stations. It is the authoritative USGS magnitude if computed. The August 21st 2018 earthquake magnitude by the USGS was M_{ww} 7.3, versus the UWI SRC’s magnitude of M6.9 (more on this below).

**M**_{w} and **M**_{wr} are usually calculated by FUNVISIS, with M_{wr} for larger events, within their area of responsibility. Generally, source complexity and dimensions at larger magnitudes (~M7.0 or greater) limits M_{wr} applicability.

M_{w} magnitude is usually calculated there is there a large number of high quality broadband stations, where M_{w} values can be calculated for events as small as M4.0. In FUNVISIS’ case, it is calculated for all magnitudes of earthquakes.

**Limitations**

Since the seismic moment is required for the calculation of a moment magnitude, this type of magnitude scale is generally used for quakes with magnitudes larger than M4.0 by the USGS. FUNVISIS, on the other hand, calculates the moment magnitude for all events.

#### Duration Magnitude Scale (Md, md *OR* Mt )

The duration magnitude is the magnitude that is published by the University of the West Indies Seismic Research Centre (Page 6) for all seismic events within their area of responsibility for the Eastern Caribbean.

Across the world, the duration magnitude is denoted by Md or md. At the UWI SRC, it is denoted by Mt. This should not be confused with the Tsunami magnitude of M_{t}.

**How is the Duration Magnitude Scale Calculated? **

**M _{d}** designates various scales that estimate magnitude from the

*duration*or length of some part of the seismic wave-train. The seismic wave interval measured on the time axis of an earthquake record – starting with the first seismic wave onset until the wavetrain amplitude diminishes to at least 10% of its maximum recorded value. This is referred to as “earthquake duration”.

Duration magnitude is especially useful for measuring local or regional earthquakes, both powerful earthquakes that might drive the seismometer off-scale (a problem with the analog instruments formerly used) and preventing measurement of the maximum wave amplitude, and weak earthquakes, whose maximum amplitude is not accurately measured.

Even for distant earthquakes, measuring the duration of the shaking (as well as the amplitude) provides a better measure of the earthquake’s total energy.

### Earthquake (Seismic) Intensity Scales

**Intensity** measures the
strength of shaking produced by the earthquake at a certain location. It is
determined from effects on people, human structures, and the natural
environment. Intensity is typically represented by Roman numerals, to
emphasize the point of it being an integer value historically. However, in the
age of technology, most seismologists use Arabic numerals. (Musson
et al., 2012)

The use of intensity scales is historically important because no instrumentation is necessary, and useful measurements of an earthquake can be made by an unequipped observer. This is how we can estimate a magnitude for historical earthquakes in the Caribbean, and beyond, before seismometers were present.

The first scale to be used internationally was the ten-degree Rossi-Forel Scale of 1883. The scale of Sieberg became the foundation of all modern twelve-degree scales.

Across the modern world, there are three intensity scales that are predominantly used to characterize earthquake shaking and earthquake damage:

- The Japan Meteorological Agency
*shindo*or Seismic Intensity Scale - The European Macroseismic Scale
- The Modified Mercalli Intensity Scale (below)

#### Modified Mercalli Intensity Scale

The **Modified Mercalli intensity scale **(**MM** or **MMI**),
descended from Giuseppe Mercalli‘s **Mercalli intensity
scale** of 1902, is a seismic intensity scale used for
measuring the *intensity of shaking* produced by an earthquake.

This scale is generally used by most countries and seismological agencies across the world, including Trinidad and Tobago.

Most versions of the MMI that are typically found on the internet are abridged versions or some arrangement and/or amalgamation of different published definitions of the MMI. A comprehensive (i.e. another amalgamation) MMI is presented below, taking into account the works of Stover & Coffman (1993), Wood & Neumann (1931) and edits from Musson.

Generally, the lower degrees of the Modified Mercalli Intensity scale generally deal with the manner in which the earthquake is felt by people. The higher numbers of the scale are based on observed structural damage and are assigned by structural engineers.

The UWI Seismic Research Centre also has an abridged version, which can be found on their website.

In Trinidad and Tobago, we generally experience events that cause
shaking resulting MMI values less than IV. The strong M6.9 earthquake on 21^{st}
August 2018, the average MMI value was IV, with the maximum values of VIII.

Peak ground acceleration (PGA) is the effective Peak Ground Acceleration during the earthquake. That is the maximum horizontal ground acceleration excluding high frequency spikes. PGA of the M6.9 quake in stations across Port of Spain ranged from 0.16g to 0.27g. More information can be found on the preliminary report complied by the UWI Seismic Research Center.

#### Earthquake Magnitude/Intensity Comparison

Hence, the above magnitudes may sometimes generate stronger or weaker shaking than expected. In turn, there may be higher or lower MMI values reported depending on the characteristics of the earthquake.

Shaking is driven by the seismic energy released by an earthquake. Earthquakes differ in how much of their energy is radiated as seismic waves. Deeper earthquakes also have less interaction with the surface, and their energy is spread out across a larger area. Shaking intensity is localized, generally diminishing with distance from the earthquake’s epicenter, but can be amplified in sedimentary basins and certain kinds of unconsolidated soils.

### Which is the “correct” magnitude?

Across the globe, different seismic monitoring agencies use different methods, or several methods, for processing earthquake parameters. Each method has its limitations and will likely produce different results within the ranges of uncertainty of that data. This is generally accepted within the scientific community.

Additionally, to meet the public’s need for information, seismological agencies have now began publishing and updating information as an earthquake occurs. The data is usually automatically processed with limited data by computers and published either directly online for the public (USGS, EMSC etc.), or sent to stakeholders, then to the public (U.W.I. SRC).

Because limited amounts of data are used for these preliminary outputs, it is common to see minor changes in latitude, longitude, depths and magnitude.

Furthermore, because of the difference in magnitude types, you will likely see even more variation amongst seismic reports from different organizations (UWI SRC, FUNVISIS, USGS, BSCF (France) etc.).

#### In Trinidad, Tobago & The Eastern Caribbean

In the case of Trinidad and Tobago, automated posts from the U.W.I. Seismic Research Centre are posted onto their social media platforms within minutes of the event. These events are always then reviewed by a seismologist or seismic analyst at the SRC. In most instances, the reviewed solution is then posted to their website.

There is usually a 10 km margin of error in latitude and longitude, but often tens of km in depth, between preliminary results and reviewed results (which is standard for monitoring agencies*)*, magnitude tends to change as more data come to hand, even with manual processing.

Ultimately, there is no *correct* method to calculate magnitude as each method has its strengths and weaknesses. It is important to note that for Trinidad, Tobago and the remainder of the English-speaking Eastern Caribbean, the University of the West Indies Seismic Research Center is the authoritative agency for seismic hazards in the English-speaking Eastern Caribbean. It operates the widest and densest network of seismic stations in the region. Thus, it is likely to consistently yield the most accurate results for the islands under its area of responsibility, which includes Trinidad & Tobago.