magnitude and magnitude scales: Richter, Modified Mercalli and Moment Magnitude

What is Magnitude?

Magnitude measures the energy released at the source of an earthquake. Think of it like the volume of a song: the louder the song, the more energy it carries. In earthquakes, the louder (higher magnitude) the quake, the more damage it can cause.

Developed in 1935 by Charles Richter. It uses the amplitude of seismic waves recorded by a seismograph.

Formula: $M_L = \log_{10} A - \log_{10} A_0(\delta)$, where $A$ is the maximum amplitude and $A_0(\delta)$ corrects for distance.

• Each whole number increase ≈ 32× more energy.
• Example: A 5.0 quake releases ~32× more energy than a 4.0 quake.

⚠️ Exam tip: Remember the 32× rule and that Richter is best for local, small to moderate quakes.

Unlike magnitude, MMI measures observed effects on people, buildings, and nature.

⚠️ Exam tip: Use the MMI scale to describe damage in case studies; it’s all about what people actually experience.

Modern standard for large quakes. It uses the seismic moment:

$M_w = \frac{2}{3}\log_{10} M_0 - 10.7$

where $M_0$ = shear‑fault area × average slip × rigidity.

Analogy: Shear‑fault area × slip is like the size of a giant pizza slice that’s been pulled apart.

1. Measure the fault area (in square metres).
2. Estimate average slip (how far the ground moved).
3. Multiply by rock rigidity (~30 GPa).
4. Plug into the formula.

⚠️ Exam tip: Remember Mw is preferred for large, deep quakes and gives a more accurate energy estimate than Richter.

⚠️ Exam tip: When asked to compare, highlight the scale’s purpose, data source, and typical use case.

• Mw = 9.0 (largest recorded)

• MMI: X–XI (devastating)

• Richter: 8.5 (local measurement)

Analogy: Think of the quake as a giant earthquake “boom” that shook the entire Pacific rim, causing a tsunami that was like a giant wave of water crashing onto the coast.

⚠️ Exam tip: Use this example to illustrate how different scales can coexist and why Mw is preferred for global comparisons.