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Modified Mercalli Intensity from Peak Ground Acceleration (Worden and Others)

Also known as MMI from PGA · intensity from peak ground acceleration · instrumental intensity · ground motion to intensity conversion · GMICE · Worden 2012 PGA MMI · shaking intensity from an accelerograph · PGA to Mercalli · peak acceleration to felt intensity · ShakeMap intensity from PGA · Modified Mercalli intensity from accelerometer · instrumental Mercalli intensity

MMI={1.78+1.55log⁡10Ylog⁡10Y≤1.57−1.60+3.70log⁡10Ylog⁡10Y>1.57,Y=PGA (cm/s2)\mathrm{MMI} = \begin{cases} 1.78 + 1.55\log_{10} Y & \log_{10} Y \le 1.57\\ -1.60 + 3.70\log_{10} Y & \log_{10} Y > 1.57\end{cases},\quad Y = \mathrm{PGA}\ (\mathrm{cm/s^2})
sig figs

Worked example: USGS code: 10 gal → MMI 3.33. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

See also
Moment Magnitude (Mw): The size of the earthquake whose shaking this intensity describes.Gutenberg–Richter Frequency–Magnitude Relation: How often earthquakes of a given size occur, to set the shaking against how likely it is.Radiated Energy from Surface-Wave Magnitude: The energy radiated by the earthquake whose shaking is measured, from its magnitude.

Where Modified Mercalli Intensity from Peak Ground Acceleration (Worden and Others) fits

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Modified Mercalli Intensity from Peak Ground Acceleration (Worden and Others) explained

breakgentlesteeperMMIlog PGA

Peak ground acceleration is a reading from an instrument; Modified Mercalli intensity describes how the shaking was felt. This relation connects them: it gives the instrumental intensity that goes with a measured acceleration. Worden, Gerstenberger, Rhoades and Wald (2012) fitted it to about 200 000 felt reports from California. The acceleration YY is in cm/s² (1 cm/s² is a gal, and 981 gal is 1 g), and the intensity is a straight line in log⁡10Y\log_{10} Y, so each tenfold increase in acceleration adds a fixed number of intensity units, 1.55 below the break and 3.70 above it.

There are two lines. Up to log⁡10Y=1.57\log_{10} Y = 1.57, which is 37 cm/s² or about 0.04 g, MMI=1.78+1.55log⁡10Y\mathrm{MMI} = 1.78 + 1.55\log_{10} Y; above it, MMI=−1.60+3.70log⁡10Y\mathrm{MMI} = -1.60 + 3.70\log_{10} Y. The slope is steeper in strong shaking, so the intensity climbs faster there. The two lines do not quite meet at the break: they give 4.2135 and 4.2090, a step of 0.0045. Going back from an intensity to an acceleration, the page switches branch at an MMI of 4.22, as the USGS library does.

The page's checks are easy to follow by hand. At 1 gal the logarithm is zero and the intensity is the constant 1.78. At 10 cm/s² the intensity is 3.33, at 100 cm/s² it is 5.80, and at 1 g (981 gal) it is 9.47. The case of 10 gal giving 3.33 is the page's example. The coefficients are the ones the USGS ShakeMap library (shakelib) prints for the relation; the paper's own table was behind a paywall and was not opened.

The relation is for California earthquakes and for intensities from 2 up; the paper discusses a steeper segment from 1 to 2, but the library does not give coefficients for it. For a given acceleration the intensity scatters by 0.66 of an intensity unit, so treat the answer as a typical value, not a certainty. It is the other direction from the library's felt-intensity page, which starts from the magnitude and the distance and has no accelerograph in it, and it is no substitute for a damage survey.

Modified Mercalli Intensity from Peak Ground Acceleration (Worden and Others) formula

MMI={1.78+1.55log⁡10Ylog⁡10Y≤1.57−1.60+3.70log⁡10Ylog⁡10Y>1.57,Y=PGA (cm/s2)\mathrm{MMI} = \begin{cases} 1.78 + 1.55\log_{10} Y & \log_{10} Y \le 1.57\\ -1.60 + 3.70\log_{10} Y & \log_{10} Y > 1.57\end{cases},\quad Y = \mathrm{PGA}\ (\mathrm{cm/s^2})
Where
  • MMI\mathrm{MMI}= Modified Mercalli intensity
  • YY= Peak ground acceleration (Gal)
Where this comes from
  • Worden, C. B., Gerstenberger, M. C., Rhoades, D. A., & Wald, D. J. (2012). Probabilistic relationships between ground-motion parameters and Modified Mercalli Intensity in California. Bulletin of the Seismological Society of America, 102(1), 204-221 (the DOI record was checked in Crossref; the paper is behind the SSA paywall, Semantic Scholar lists it as closed, and it was not opened). Read it
  • U.S. Geological Survey, ShakeMap library shakelib (US federal work; public domain), module shakelib.gmice.wgrw12, 'Implements the ground motion intensity conversion equations (GMICE) of Worden et al. (2012)', source read 23 Oct 2026 in the project's documentation: for the peak ground acceleration c1 = 1.78, c2 = 1.55, c3 = -1.60, c4 = 3.70, t1 = 1.57, t2 = 4.22, with 'MMI = C1 + C2 log(Y) for log(Y) <= T1' and 'MMI = C3 + C4 log(Y) for log(Y) > T1', the acceleration Y in cm/s2 (the code converts from g with 981), the inverse switching branches at an intensity of T2 = 4.22, a standard deviation of the intensity of 0.66, and a steeper segment for intensities from 1 to 2 ('discussed in the paper but not specifically implemented there'). Read it
Revised 30 October 2026
Cite this page

formula.expert. (2026, October 30). Modified Mercalli Intensity from Peak Ground Acceleration (Worden and Others) Calculator. https://formula.expert/solvers/mmi-from-peak-ground-acceleration

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