The moment magnitude scale is the standard measure seismologists use worldwide to quantify earthquake size, and it replaced the older Richter scale because it does not max out on large earthquakes. Developed in 1979 by Hiroo Kanamori and Thomas Hanks, it is rooted in a physical property of the earthquake itself called seismic moment, which accounts for how much rock moved, over how large an area, and how far it slipped. That physical grounding is what makes it reliable across the full range of earthquake sizes, from tiny fractures deep underground to the largest events ever recorded.
Why the Richter Scale Stopped Working
The Richter scale, introduced in the 1930s by Charles Richter, measures earthquake size by reading the amplitude of seismic waves on a specific type of seismograph. It worked well for moderate, local earthquakes in Southern California, which is what it was designed for. But it has a ceiling. Once earthquakes get large enough, the seismic waves the Richter scale relies on stop growing in proportion to the actual energy being released. The readings flatten out, or “saturate,” around magnitude 7. A truly enormous earthquake and a merely very large one can produce similar Richter readings, which is a serious problem if you need to tell the difference between a damaging regional quake and a civilization-shaking catastrophe.
A related scale, the surface-wave magnitude (Ms), extends the range somewhat by using longer-period waves that travel along Earth’s surface. But it too saturates, around magnitude 8. For the most powerful earthquakes on record, neither scale can give an honest number. Kanamori recognized this in the late 1970s and looked for a measurement tied to the physics of what actually happens at the fault, rather than to the behavior of a particular type of seismic wave recorded at a particular distance.
What Seismic Moment Actually Captures
Every earthquake involves a patch of a fault surface slipping. Three things determine how big that slip event is: the area of the fault that broke, the average distance the two sides moved past each other, and the rigidity of the surrounding rock. Multiply those three together and you get the seismic moment, a single number with units of force times distance. A tiny crack a few meters across that slips a fraction of a millimeter has a small seismic moment. A rupture stretching hundreds of kilometers that displaces the ground by several meters has an enormous one.
The moment magnitude formula converts that physical quantity into a number on a familiar scale. In the original 1979 paper, Hanks and Kanamori wrote it as M = ⅔ log M₀ − 10.7, where M₀ is the seismic moment measured in dyne-centimeters (the unit convention of the era).1Journal of Geophysical Research: Solid Earth. A moment magnitude scale In modern metric units the same relationship is written as Mw = (log M₀ − 9.1) / 1.5, which was derived by plugging a known ratio between radiated energy and seismic moment into an older empirical formula connecting energy to surface-wave magnitude.2Earth, Planets and Space. A theoretical basis of the moment magnitude scale The two forms say the same thing. What matters for a non-specialist is that the scale is logarithmic: each whole number step up represents roughly 32 times more energy released, and the jump from, say, magnitude 7 to magnitude 9 represents about a thousandfold increase in energy.
The constants in the formula were chosen deliberately so that moment magnitude lines up with the older Richter and surface-wave magnitudes in the range where those scales work well, roughly magnitude 3 to 7. That is why you rarely hear anyone distinguish between magnitude types for moderate earthquakes: the numbers are nearly the same. The scales only diverge noticeably at the high end, precisely where the older scales saturate and moment magnitude keeps going.
How Seismologists Actually Measure It
You cannot read seismic moment directly off a seismogram the way Richter read wave amplitude. Instead, seismologists work backward from recordings of seismic waves at stations around the world. The standard approach is called moment tensor inversion: computers compare observed waveforms to synthetic waveforms generated by mathematical models of the Earth and search for the earthquake source parameters that best reproduce what the instruments recorded. The output is a set of numbers describing the orientation of the fault, the direction of slip, and the seismic moment.
The most widely used catalog of these solutions is maintained by the Global Centroid Moment Tensor (GCMT) project, which has been systematically determining moment tensors for earthquakes worldwide since 1976. The project continuously refines its methods. Recent updates account for the fact that Earth’s interior is not a uniform ball of rock but a highly heterogeneous structure with varying wave speeds, and the inversions now use three-dimensional models of the planet’s interior to generate more accurate synthetic seismograms.3Geophysical Journal International. Global centroid moment tensor solutions in a heterogeneous earth: the CMT3D catalogue These refinements matter because even small errors in the assumed Earth structure can shift the estimated seismic moment and, with it, the magnitude.
For the biggest earthquakes, this analysis can take hours or even days to finalize. The initial magnitude number you see on a news ticker minutes after an earthquake is a preliminary estimate, often based on simpler wave-amplitude methods. The authoritative moment magnitude may be revised upward or downward once the full waveform inversion is complete. That is why you sometimes see magnitude numbers change in the days following a major earthquake.
Getting Faster for Tsunami Warnings
Hours of analysis is fine for a catalog entry, but it is useless when a coastal population needs to know whether a tsunami is coming. Tsunamis generated by undersea earthquakes can cross an ocean in a matter of hours, and local tsunamis can arrive in minutes. Knowing the moment magnitude quickly is critical because it is one of the primary inputs for estimating whether an earthquake has displaced enough water to generate a dangerous wave.
One solution involves a type of very-long-period seismic wave called the W phase, which arrives at distant stations well before the more familiar surface waves. Researchers have shown that inverting W phase recordings can yield a reliable moment magnitude and fault mechanism within minutes of a large earthquake’s origin. The method was tested on several major events, including the 2004 Sumatra-Andaman earthquake, the 2005 Nias earthquake, the 2006 Kuril Islands earthquake, and the 2007 Sumatra earthquake, and it produced solutions consistent with the detailed analyses that came later.4Geophysical Journal International. Source inversion of W phase: speeding up seismic tsunami warning Pacific and Indian Ocean tsunami warning centers now routinely use W phase analysis.
Another approach combines seismic data with real-time GPS measurements of ground displacement. Seismometers are excellent at recording rapid shaking, but their readings can clip or become difficult to interpret during the very largest earthquakes when the ground moves slowly over long periods. GPS stations, meanwhile, directly track how far the ground has shifted. A recent study examining 17 earthquakes of magnitude 7 and above found that combining these two data streams produced rapid magnitude estimates, arriving roughly two to three minutes after the earthquake began, with an accuracy of about 0.2 magnitude units.5Journal of Geophysical Research: Solid Earth. Rapid Earthquake Magnitude Estimation for Local Early Warning Systems Using Seismogeodesy That level of precision, that quickly, is a meaningful improvement for early warning systems.
Magnitude Versus Intensity
One of the most persistent sources of confusion in earthquake communication is the difference between magnitude and intensity. Magnitude is a single number describing the total size of the earthquake at its source. Intensity describes how strongly the shaking is felt at a particular location, and it varies from place to place. A magnitude 7 earthquake has one magnitude, but the shaking intensity will be violent near the fault and barely perceptible hundreds of kilometers away. Intensity is measured on a separate scale entirely, the Modified Mercalli Intensity scale, which runs from I (not felt) to XII (total destruction) and is based on observed effects on people, buildings, and the landscape.
The distinction matters for historical earthquakes that occurred before modern instruments existed. The great New Madrid earthquakes of 1811 and 1812, which shook the central United States so violently that they rang church bells in Boston, were never recorded by seismographs. To estimate their moment magnitudes, researchers mapped the geographic distribution of reported shaking intensities from historical accounts and used calibrated relationships between felt area and magnitude. This analysis produced estimated moment magnitudes of about 7.2 to 7.3 for the first mainshock in December 1811, about 7.0 for the January 1812 event, and about 7.4 to 7.5 for the February 1812 event.6Journal of Geophysical Research: Solid Earth. On the Modified Mercalli intensities and magnitudes of the 1811–1812 New Madrid earthquakes Those are large earthquakes by any standard, but considerably smaller than the magnitude 8+ estimates that circulated in earlier, less rigorous assessments. The moment magnitude scale gave a more physically grounded answer even for events that predated instruments by over a century.
The Scale at Its Extremes
At the top end, the largest earthquake ever recorded by instruments is the 1960 Valdivia earthquake in southern Chile, assigned a moment magnitude of 9.5.7Geophysical Journal International. The Chiloé Mw 7.6 earthquake of 2016 December 25 in Southern Chile and its relation to the Mw 9.5 1960 Valdivia earthquake That event ruptured roughly a thousand kilometers of fault, generated a Pacific-wide tsunami, and released energy equivalent to about a quarter of all seismic energy released globally in the entire twentieth century. On the old surface-wave magnitude scale, it would have been capped somewhere around 8.3 to 8.5, a drastic underestimate that would have obscured just how exceptional the event was.
There is a practical upper limit to how large an earthquake can get, set by the geometry of Earth’s tectonic plates. The longest subduction zones on Earth are roughly a few thousand kilometers, and the fault cannot rupture farther than it extends. Geophysicists estimate the theoretical maximum somewhere around magnitude 9.5 to 10, depending on assumptions about fault length and how deep the rupture extends. A magnitude 10 would require a fault rupture stretching thousands of kilometers, essentially the entire length of a major subduction zone slipping simultaneously, and nothing in the geological record clearly points to such an event.
At the bottom end, the moment magnitude scale extends far below what anyone would feel. Microseismic events recorded during underground mining and tunnel excavation have been assigned moment magnitudes as small as negative 4, meaning the total energy released was comparable to the impact of a dropped book.8Geophysical Research Letters. Moment tensor inversion of induced microseisnmic events: Evidence of non‐shear failures in the −4 < M < −2 moment magnitude range The scale handles these tiny events and the largest ones with the same formula, which is one of its major practical advantages.
Induced Earthquakes and the Small-Magnitude Problem
The rapid growth of wastewater injection and hydraulic fracturing in the oil and gas industry has produced swarms of small earthquakes in regions that were previously seismically quiet. Monitoring these events requires reliable magnitude measurements, and that is where a subtle problem emerges. For small earthquakes below about magnitude 3, moment magnitude and local magnitude (the modernized descendant of the Richter scale that most regional networks report) can disagree substantially.
A study of over 31,000 earthquakes caused by wastewater injection in the Raton Basin along the Colorado-New Mexico border found significant differences between moment magnitude and local magnitude for events below magnitude 3. The researchers derived conversion formulas to translate between the two scales and demonstrated that moment magnitudes could be reliably estimated down to about magnitude 1 using recordings of scattered seismic wave energy, a technique that works even with a small, local monitoring network.9Seismica. Small earthquake moment magnitude and implications for frequency–magnitude scaling of injection induced earthquakes of the Raton Basin
This matters because many regulatory frameworks use magnitude thresholds as triggers. A “traffic light” system might require operators to pause injection when earthquakes exceed a certain magnitude, and whether that threshold is in local magnitude or moment magnitude can change which events trip the alarm. If the two scales give different numbers for the same earthquake, a quake that reads 2.8 on one scale might read 3.2 on the other, and that difference can determine whether operations continue or shut down. Getting the magnitude scale right is not just an academic exercise in these contexts.10International Meeting for Applied Geoscience & Energy. Moment Magnitude Computation and Instrumentation Selection for Induced-Seismicity Traffic Light Systems
Events That Do Not Fit Neatly on the Scale
The moment magnitude scale was built around a model of an earthquake as two blocks of rock sliding past each other along a flat surface. This “double-couple” source model works well for the vast majority of tectonic earthquakes. But not every seismic event fits that template. Volcanic eruptions, underground collapses, and explosions produce seismic waves with patterns that cannot be explained by simple fault slip. These are called non-double-couple events, and determining their moment magnitude requires more complex analysis.
The 2014-2015 Bárðarbunga volcanic sequence in Iceland is a good example. That event included a caldera collapse and associated seismicity that generated wave patterns inconsistent with simple faulting. Researchers developed specialized inversion methods that combine waveform data with first-motion polarity information to tease apart the different components of these unusual sources.11Journal of Geophysical Research: Solid Earth. Non‐Double‐Couple Components of Seismic Source: Method and Application to the 2014–2015 Bárðarbunga Volcanic Event Sequence, Iceland You can still assign a moment magnitude to such events, but interpreting what that number means physically requires extra care. A magnitude 5 volcanic collapse is not the same hazard as a magnitude 5 tectonic earthquake, even though the number is the same.
Slow earthquakes present a different kind of challenge. Some fault zones release energy not in a sudden, violent snap but over hours, days, or even weeks, in events called slow slip events. These are accompanied by low-frequency earthquakes, tiny seismic signals that repeat in patterns linked to the creeping fault. Researchers studying slow slip in subduction zones have found that the relationship between the geodetically measured slip and the seismically radiated energy is not constant. It changes as the slow slip event evolves, suggesting that the fault patches generating the low-frequency earthquakes become saturated as the broader slip grows in area and moment.12AGU Advances. Subdaily Slow Fault Slip Dynamics Captured by Low‐Frequency Earthquakes The moment magnitude of an individual low-frequency earthquake can be calculated, but summing them up to represent the whole slow slip event is not straightforward, because so much of the energy release is aseismic, meaning it happens without producing the kind of waves seismographs are designed to record.
Why Reporters Still Say “Richter Scale”
Despite the fact that virtually every national and international seismological agency has used moment magnitude as its primary scale for decades, news reports still routinely refer to “the Richter scale.” Part of this is simple inertia: the Richter name has been embedded in public consciousness since the mid-twentieth century, and it sounds more specific and authoritative than the technically correct “moment magnitude.” Part of it is that, for moderate earthquakes, the numbers are nearly identical, so calling a magnitude 5.4 earthquake “5.4 on the Richter scale” versus “moment magnitude 5.4” makes no practical difference to the audience.
Where the mislabeling becomes genuinely misleading is at the extremes. Describing the 2011 Tohoku earthquake as “9.0 on the Richter scale” implies a measurement system that would have been physically incapable of producing that number. The Richter scale would have saturated somewhere around 7 for that event. The moment magnitude of 9.0 reflects a fundamentally different calculation based on the physical size of the rupture, and calling it by the wrong name obscures the scientific achievement of being able to measure earthquakes that large in the first place.
Seismologists have largely given up correcting the public on this point, treating “Richter” as a colloquial synonym for “earthquake magnitude” rather than a specific technical term. But if you want to speak precisely, the number you see in earthquake reports from the U.S. Geological Survey, the European-Mediterranean Seismological Centre, or Japan’s Meteorological Agency is moment magnitude unless otherwise noted. It is the scale that works everywhere the earth breaks.