Adjust magnitude, focal depth, and epicentral distance to instantly compute PGA, JMA seismic intensity, and MMI scale. Visualize seismic wave propagation from hypocenter to surface.
What exactly is the difference between an earthquake's "magnitude" and its "intensity"? They sound similar.
🎓
Great question! Basically, magnitude is a single number that measures the total energy released at the earthquake's source. Intensity describes the shaking strength and damage experienced at a specific location. For instance, a magnitude 7 quake might cause violent shaking (high intensity) near the epicenter but only weak shaking far away. Try moving the Magnitude slider above to M7, then increase the Epicentral Distance R to see how the predicted intensity drops.
🙋
Wait, really? So the magnitude is fixed, but the intensity changes with distance. What's the "PGA" that the simulator calculates?
🎓
Exactly! PGA stands for Peak Ground Acceleration. It's the strongest "jolt" or acceleration of the ground during shaking, measured in %g (percentage of gravity). It's a key engineering parameter for designing buildings. The simulator uses an attenuation formula to estimate PGA based on magnitude and distance. For example, set M to 6.5 and R to 50 km. You'll see a PGA value—that's the estimated maximum ground acceleration a structure at that distance would experience.
🙋
Okay, that makes sense. But I see the simulator also outputs "Seismic Moment" and "TNT Equivalent." What do those tell us about the earthquake?
🎓
Those are powerful physical interpretations. The Seismic Moment ($M_0$) quantifies the total force and slip on the fault—it's the most fundamental measure of an earthquake's size. The TNT equivalent translates the released seismic energy into an amount of explosives, which is much more tangible. A common case: a magnitude 8.0 quake releases energy equivalent to about 1 gigaton of TNT. Try sliding the magnitude up to 9.0 and watch the TNT equivalent jump to over 30 gigatons—that's over 600 times the most powerful nuclear weapon ever tested.
Physical Model & Key Equations
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.
$$M_w = \frac{2}{3}(\log_{10}M_0 - 9.1)$$
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, we use an attenuation relationship. A simplified form predicts the Peak Ground Acceleration (PGA) based on the earthquake's magnitude and your distance from it.
Here, PGA is in %g, $M_w$ is the moment magnitude, and $R$ is the epicentral distance in kilometers. The term $-1.68\log_{10} R$ models the geometric spreading and damping of seismic waves as they travel through the Earth.
Frequently Asked Questions
When the epicentral distance is very large, the effect of changes in magnitude or depth on PGA may fall within the error range of the attenuation formula. Additionally, since seismic intensity is displayed as an integer, small changes in PGA may not result in a change in the intensity class. Please move the slider finely to check the numerical changes in PGA.
The MMI (Modified Mercalli Intensity) is a 12-level intensity scale mainly used overseas, based on building damage and human perception. The JMA seismic intensity is a unique Japanese 10-level scale (0 to 7), calculated from waveforms measured by seismic intensity meters. This tool estimates both from PGA, but since local ground characteristics are not considered, please use the values as references only.
This tool provides a simple estimation using a single attenuation formula (empirical equation). In actual earthquakes, factors such as ground amplification, fault rupture direction, and topographic effects can cause errors of about ±50% compared to observed values. Discrepancies tend to be larger, especially when the epicentral distance is short or on soft ground, so please use this tool only for understanding general trends.
It schematically displays wave fronts spreading concentrically from the hypocenter. The color shading corresponds to the magnitude of PGA, with colors closer to red indicating stronger shaking. Actual seismic waves have different velocities for P-waves and S-waves and are refracted by the ground, but this visualization uses a simplified model assuming homogeneous ground.
Real-World Applications
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., "This M6.5 quake released energy similar to 20 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.
Common Misunderstandings and Points to Note
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 tool's formulas assume generic bedrock (basement rock). In reality, the shaking can often be amplified 2 to 3 times on softer soil layers (alluvium) deposited on top of this bedrock. 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 10 times the energy of an M6, 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 0 km 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.
Enter earthquake magnitude (3–9.5 Mw) in the magVal field and depth in kilometers (5–700 km typical range).
Input epicentral distance in kilometers; the converter calculates PGA attenuation using empirical models (Boore et al. 2014).
Read seismic moment M₀ in newton-meters, energy release in joules, TNT equivalent in kilotons, JMA intensity (0–7), and MMI scale (I–XII) from output panels.
Worked Example
A 7.2 Mw earthquake at 20 km depth, 50 km epicentral distance: seismic moment M₀ = 1.51 × 10¹⁹ N·m, energy release E = 4.37 × 10¹⁶ J (equivalent to 10.4 megatons TNT), estimated PGA at 50 km ≈ 280 gal (2.8 m/s²), JMA intensity grade 6-Strong, MMI VII–VIII (Damaging). At 10 km distance, PGA rises to 850 gal; at 100 km, attenuates to 85 gal.
Practical Notes
Shallow earthquakes (depth <30 km) produce higher PGA than deep events of equal magnitude; subduction zone ruptures (70–150 km) generate extended duration strong motion.
Magnitude 8.5+ events (e.g., 2004 Sumatra) release energy equivalent to thousands of megatons; MMI XII implies total destruction, tsunami generation likely for offshore M>7.5.
PGA attenuation depends on local geology; soft alluvial basins (Tokyo, Mexico City) amplify motion 2–5×; bedrock sites reduce PGA by 30–50% versus equivalent distance.