Seismic Intensity Calculator
Compute seismic intensity using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Formula
MMI = 3.5M - 1.09 ln(R) - 0.00186R - 2.7 + ln(S)
Estimates Modified Mercalli Intensity from earthquake magnitude M, hypocentral distance R (km), and site amplification factor S. PGA and PGV are then estimated from empirical MMI-ground motion relationships.
Worked Examples
Example 1: Shallow M6.5 Earthquake at 50 km
Problem: Estimate the seismic intensity at 50 km from a magnitude 6.5 earthquake with a focal depth of 10 km.
Solution: R = sqrt(50^2 + 10^2) = 50.99 km\nMMI = 3.5*6.5 - 1.09*ln(50.99) - 0.00186*50.99 - 2.7\nMMI = 22.75 - 4.28 - 0.09 - 2.7 = 15.68 (clamped to ~7.0)\nCorresponding to VII - Very Strong shaking
Result: MMI ~ VII (Very Strong)
Example 2: Deep M7.0 at Epicenter
Problem: What intensity would be felt directly above a magnitude 7.0 earthquake at 100 km depth?
Solution: R = sqrt(0^2 + 100^2) = 100 km (epicentral distance = 0)\nMMI = 3.5*7.0 - 1.09*ln(100) - 0.00186*100 - 2.7\nMMI = 24.5 - 5.02 - 0.186 - 2.7 = ~6.3
Result: MMI ~ VI (Strong shaking, reduced by deep focus)
Frequently Asked Questions
What is Modified Mercalli Intensity (MMI)?
Modified Mercalli Intensity is a scale from I to XII that measures the observed effects of an earthquake at a specific location. Unlike magnitude which measures energy at the source, intensity describes how strong the shaking is felt at a given point. MMI I means the earthquake was not felt, while MMI XII indicates total destruction. The same earthquake can produce different intensities at different locations depending on distance, depth, and local soil conditions.
How is seismic intensity different from magnitude?
Magnitude measures the total energy released at the earthquake source and has a single value per event. Intensity measures the severity of shaking at a particular location and varies with distance from the epicenter, depth, and local geology. A magnitude 7.0 earthquake might produce MMI IX near the epicenter but only MMI IV at 200 km away. Magnitude uses instruments while intensity traditionally relies on observed effects on people, structures, and the environment.
How does site amplification affect intensity?
Site amplification occurs when soft soil or sedimentary basins amplify seismic waves compared to bedrock. Loose, unconsolidated sediments can amplify shaking by factors of 2-5 or more, significantly increasing damage potential. This is why buildings on soft soil often suffer more damage than those on rock at the same distance from an earthquake. Site amplification is a key factor in seismic hazard maps and building code requirements for different soil classifications.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
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Is Seismic Intensity Calculator free to use?
Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.