Earthquake Magnitude & Intensity Converter

The core relationship is between the Moment Magnitude ($M_w$) and the Seismic Moment ($M_0$). The seismic moment is calculated from the fault's physical properties: area, average slip, and the rigidity of the rock. $M_w$ is then derived from it, creating a scale that doesn't saturate for very large earthquakes.

Where $M_0$ is the seismic moment in Newton-meters (N·m). The constant 9.1 is a scaling factor to make the magnitude values roughly consistent with older scales.

To estimate how shaking weakens with distance, the calculator uses the Fukushima–Tanaka (1990) attenuation relation for peak horizontal acceleration.

PGA is in gal (cm/s²) and $M$ is treated as $M_w$. In the original relation $R$ is the shortest distance to the fault rupture; this tool uses the hypocentral distance $\sqrt{R^2+h^2}$ from the epicentral distance and depth. The $0.032\cdot10^{0.41M}$ term keeps near-source values finite, and $-0.0034R$ represents anelastic attenuation.

Earthquake-Resistant Building Design: Engineers use PGA values from attenuation models to define the design basis earthquake for a region. The seismic intensity scales (like JMA or MMI) help create building codes that specify different construction requirements for zones expecting moderate vs. severe shaking.

Emergency Response & Rapid Assessment: Immediately after a quake, rapid estimates of magnitude and predicted intensity distribution (ShakeMaps) are generated. This allows emergency services to prioritize areas likely to have suffered the worst damage and direct rescue resources effectively.

Public Communication & Education: Translating magnitude into TNT equivalent or comparing it to historical quakes (e.g., with log₁₀E = 1.5M + 4.8 an M6.5 quake releases about 85 kt of TNT, roughly six Hiroshima bombs) helps the public grasp the immense power involved, fostering better preparedness.

Insurance & Risk Modeling: Insurance companies use probabilistic seismic hazard analysis, which relies on magnitude-frequency relationships and attenuation laws, to model financial risk and set premiums for properties in earthquake-prone areas.

There are several key points you should be aware of when using this tool, especially if you're considering practical applications. First, "the calculation results are only a guideline for average ground conditions". The Fukushima–Tanaka relation is a regression for average site conditions and does not reflect the ground at a particular site. Shaking is stronger on soft sediments and weaker on hard rock. For example, even at the same 20km distance from the epicenter, while a hard mountainous area might calculate as a seismic intensity of 5 Lower, a reclaimed land or valley plain could potentially experience an intensity of 5 Upper or higher. Next, note that the relationship between magnitude and seismic intensity is not a simple proportion. Just because an M7 earthquake has about 32 times the energy of an M6 (log₁₀E = 1.5M + 4.8), it doesn't mean the seismic intensity increases by one full grade. At locations sufficiently far from the hypocenter, the intensity may hardly change even if the magnitude increases by 1. Finally, the difference between "epicentral distance" and "hypocentral distance". The tool's input is "Epicentral Distance R", but the actual shaking is determined by the straight-line "Hypocentral Distance" from the earthquake's focus. If you input 1 km (the minimum) for the epicentral distance for an earthquake with a depth of 50 km, it will be calculated using a hypocentral distance of 50 km. This difference can be ignored for calculations at points far from the epicenter, but you need to be mindful of it when dealing with shallow earthquakes near the epicenter.