**Earthquake Magnitude**

Anywhere in the world, magnitude is a numerical representation of the size or strength of an earthquake.

The magnitude of an earthquake is directly proportional to the amount of elastic energy that is released during the event.

The data recorded by a seismometer can be used to determine the time, location, and magnitude of an earthquake.

The earthquake’s amplitude is measured based on its epicentral distance on the seismogram.

Seismometers are devices that detect and measure the vibrations caused by earthquakes as they travel through the Earth.

“Every seismometer measures the vibrations of the earth directly beneath its location.”

Sensitive instruments can detect strong earthquakes from anywhere in the world due to the amplification of ground motions.

Ground motion can now be accurately amplified and recorded in modern systems at periods between 0.1 and 100 seconds.

The earthquake magnitude scales were created in response to a need to measure the severity of earthquakes.

The desire for an objective measure of earthquake size

Technological advances > seismometers.

**Richter’s Local Magnitude (ML)**

In 1935, seismologist Charles F. Richter introduced earthquake magnitude at the California Institute of Technology.

Initially, the definition was limited to California earthquakes which occur within 600 km of a certain type of seismograph known as the Woods-Anderson torsion instrument.

The fundamental concept behind his idea was straightforward. He proposed that by measuring the distance between a seismograph and an earthquake, and carefully observing the maximum signal amplitude recorded on the seismograph, it would be possible to create a reliable quantitative ranking system that accurately reflects the earthquake’s inherent size or strength.

The magnitude of an earthquake is determined by the logarithm of waves’ amplitudes recorded by seismographs using the Richter scale.

**Richter’s Local Magnitude (ML)**

Wadati in Japan and Richter in California observed in the 1930s that while seismograms from various occurrences showed varying peak amplitudes, the peak amplitudes for each earthquake declined with distance in a comparable way.

**Richter’s Local Magnitude**

**Richter’s Observations**

**Richter’s Local Magnitude (ML)**

Richter created the first magnitude scale, known as Richter’s Local Magnitude for Southern California, using these measurements.

He used the logarithmic astronomical brightness scale as the basis for his formula to determine the magnitude.

At a reference distance, he assumed a reference motion. He calibrated the attenuation function in order to calculate the magnitude at various distances.

Note: A change of one magnitude unit corresponds to a change in the amplitude of ground shaking of a factor of ten on a logarithmic scale-like magnitude.

**Richter’s Local Magnitude (ML)**

Richter (1935) determined that an earthquake’s local magnitude (ML) as recorded at a station could be

ML = log A – log Ao ( ∆)

where Ao (∆) is the highest amplitude at ∆ km for a typical earthquake, and A is the greatest amplitude in millimeters recorded on the Wood-Anderson seismograph for an earthquake at an epicentral distance of ∆ km.

As a result, the local magnitude is a figure that is specific to the earthquake and is unrelated to the recording station’s location.

Three arbitrary choices are made in the above definition:

- Making use of the conventional Wood-Anderson seismograph
- the application of standard logarithms to the base 10 and
- choosing a conventional earthquake, whose amplitudes are represented by Ao (∆) as a function of distance.

Selecting the value of Ao (∆) at a specific distance will establish the zero level. Richter determined that the zero level of Ao (∆) was located 100 kilometers from the epicenter of the earthquake at 1 µm, or 0.001 mm. Therefore, magnitude 3 is attributed to an earthquake with a trace amplitude of A= 1 mm that is observed at a distance of 100 km on a typical Wood-Anderson seismograph.

Richter arbitrarily selected -log Ao = 3 at ∆ = 100 km in order to prevent negative magnitudes in the earthquakes. Put another way, a table of -log Ao as a function of epicentral distance in kilometers is required to compute ML.

Richter’s table of -log Ao as a function of epicentral distance is based on the observed amplitudes of a number of well-located earthquakes (1958, p. 342).

An earthquake’s approximate epicentral distance, which can be calculated using S-P time, is necessary to know in practical situations. Next, on a typical Wood-Anderson seismogram, the highest trace amplitude is recorded in millimeters, and its logarithm to base 10 is calculated. The quantity recorded as -log Ao for the relevant station distance from the epicenter is then increased by this value.

For the seismogram, the total represents a local magnitude value. The Wood Anderson seismograph consists of two components, the EW and NS, and the station magnitude can be determined by taking the average of the two magnitude measurements.

An estimate of the local magnitude (ML) of the earthquake is then calculated as the average of all the station magnitudes.

It is defined under particular attenuation circumstances that apply to southern California.

Valid only with a single kind of seismometer.

If a local attenuation correction is applied and the simulated Wood-Anderson response is calculated, it can be used elsewhere.

Note: It is often used now, although it is a measure of ground shaking at frequencies of engineering interest.