Magnitude and Intensity

After an earthquake, you can expect to see a number of measurements describing it. Most common among these are the magnitude, intensity, location, and focal mechanisms. These are related but distinct, and knowing the differences is key to understanding the earthquake.

Magnitude describes the relative size or energy release of an earthquake. A familiar analogy to help understand earthquake metrics is to think about a light bulb. One measure of the strength of a light bulb is how much energy it uses. A 100-watt bulb is brighter than a 50-watt bulb. The wattage of a bulb tells you about the strength of the light source. In the same way, an earthquake's magnitude is an objective measurement of the ground motion produced by an earthquake. There are different magnitude types using different measurements and describing different technical aspects of the event, but they are all calibrated to give roughly the same number.

Earthquake magnitude has no physical units, nor a meaningful 0. This is because we can't easily measure the energy the way we can with an electric circuit, so seismologists commonly use a relative measure, the magnitude. As a thought experiment, it is simple to choose a particular earthquake recorded at a particular distance as a standard reference earthquake and call it a magnitude 1. An earthquake that causes ground motion at a seismic station (when corrected for distance) 10 times larger than the reference earthquake is M2. An earthquake causing motion at that distance 10 times larger than an M2 is an M3, and so on. To achieve a tenfold increase in ground motion requires about 32 times the energy. When referring to the energy released in an earthquake this 32 multiplier is used. An earthquake that releases about 32 times less energy and causes motion 10 times smaller than an M1 is an M0, and magnitudes can even be negative (although it requires extremely sensitive instruments to measure earthquakes that small).

There are different approaches to using seismograph recordings to quantify earthquake sizes, with numerous versions of each. This is why sometimes different agencies may list slightly different magnitudes for the same earthquake. One approach is to use some measure of peak amplitudes recorded on seismograms. A second is to use the duration of shaking recorded. A third is to try to match the actual waveform wiggle-for-wiggle with a mathematical model (a "synthetic seismogram"), and report the size of the modeled earthquake.

All amplitude-based magnitudes rely on a base-10 logarithm of the peak amplitude measured by a seismograph. This is because there are many factors of 10 difference, up to billions, between the smallest and largest measurable amplitudes of observed ground motions.

The oldest and best known amplitude-based magnitude is the Local Magnitude (M_L), formerly referred to as the Richter Magnitude. This method was developed by Dr. Charles Richter and Beno Gutenberg of CalTech in 1935 to measure the ratio of small- to medium-sized earthquakes. It was never intended to measure large or distant earthquakes. Written as M_L, it remains the go-to method for measuring small- to medium-sized earthquakes within 600 km of the recording seismograph. Richter used seismograms recorded on a particular instrument, the Wood-Anderson torsion seismograph. Today, we use more modern instruments and account for differences in instrument sensitivity to mimic what the historical Wood-Anderson seismograph would have produced.  Most of the modern PNSN earthquake catalog uses M_L.

Body wave magnitude (M_b), is also an amplitude-based measurement, but it is best applied to earthquakes more than 3000 km from the recording station (called teleseisms). It is useful for measuring the size of both deep and shallow earthquakes. Body waves are seismic waves that travel through the Earth.

Surface wave magnitude (M_s), is based on the amplitude of surface waves that propagate along Earth's surface that are generated by large to teleseismic earthquakes. Surface waves are long period (low frequency) waves, with the largest events exciting the longest periods. Earthquakes larger than M7 often generate surface waves with periods over 5 minutes long that circumnavigate the Earth multiple times.

See also: Earthquake Waves.

In general, local magnitudes "saturate" (lose resolution) for earthquakes exceeding ~M5.5 or so, body wave magnitudes stay on scale to somewhat larger magnitudes, and surface wave magnitudes saturate at about M8. This is in general because of the frequencies of the seismic waves that each uses. The higher-frequency methods (e.g., local) cannot distinguish between larger earthquakes, while the low frequency measures (e.g., surface waves) characterize the long-wavelength energy that radiates from a large rupture surface.

The duration magnitude (M_d), or coda magnitude, is derived from the observation that the ratio of peak amplitude to the duration of shaking from an earthquake are related. The PNSN often calculates the size of smaller earthquakes in the Pacific Northwest using the durations averaged from a number of seismograms to obtain M_d estimates. This estimate of magnitude is particularly useful when recordings saturate or "clip" and scientists cannot measure the peak amplitude. In the past, a seismic analyst picked the duration on each seismogram by eye independently, which was somewhat subjective and variable, as the background noise varies greatly. The modern method, made possible by faster computers, is to model the decaying amplitude of the seismogram in order to automatically and objectively define a duration.  Modern seismographs do not saturate as easily as those from decades ago, so the PNSN catalog before the 2010s has, relatively speaking, more earthquake magnitudes based on M_d magnitudes.

Modern digital seismic instrumentation along with modern computers have permitted us to model seismograms wiggle-for-wiggle. To do this, we use a standard model of the Earth and of the earthquake source to generate synthetic seismograms. Many combinations of the location, size, and orientation of the rupture are calculated to find the best match the observed waveforms. The magnitude that is derived from this waveform modeling is called the moment magnitude (M_w), and it is the preferred estimate of earthquake size by seismologists and the only one applicable to great earthquakes with M>8. Seismic moment is equal to the rigidity (strength) of the rock around the fault times the area times the amount of slip (how much the fault moved). Since we can measure the deformation of the Earth itself from such massive earthquake ruptures, we are able to make an independent estimate of the energy they release. So with moment magnitude, we can directly relate the magnitude to the energy released during rupture. Moment magnitude often is not possible to calculate for events smaller than about M5.

It is worthwhile to note that all of these approaches have been calibrated and defined with respect to each other such that they all agree, on average, in the ranges in which they overlap. So for general purposes an M6 is an M6 is an M6, regardless of the method that generated it. But also it is interesting that Richter's original local magnitude, since it came first, was the one that all the other techniques needed to align with. So, in a sense, the "Richter Scale" that news reporters often cite (to the chagrin of modern seismologists who use local magnitude or moment magnitude) is really a pretty apt homage.

Earthquake intensity measures how strongly an earthquake shakes a specific location. Returning to the light bulb analogy, it is the brightness with which you perceive the light at a given place in a room. Can you read a fine-print book by the lamp? Pick up a needle? Perform delicate surgery? That depends on the wattage of the bulb, but also how far you are from it. Similarly, the intensity of an earthquake at your location depends on both the magnitude and your distance from the hypocenter. It is also sensitive to how soft the ground is, with loose saturated sands and soils amplifying shaking more than stiff rigid rock. The distribution of intensity around an earthquake is complicated by the fact that the inside of the Earth is not perfectly homogeneous and the energy distribution from an earthquake can have complex directionality.

One common way to measure earthquake intensity is through the Modified Mercalli Intensity Scale (MMI). This scale is derived from an earlier ten-degree Rossi-Forel scale, which was later revised by Italian volcanologist Giuseppe Mercalli in 1884 and 1906 to measure the earthquake's effects. Measurements of intensity using the Modified Mercalli scale are composed of 10 increasing levels that range from imperceptible shaking to catastrophic destruction, usually designated by Roman numerals to emphasize their semi-quantitative nature. An earthquake can be described with a single value of magnitude (perhaps with slight variation due to calculation method), but a range of intensities spreading out from the epicenter in a bullseye pattern. 

Intensities are often displayed on a map to better represent how shaking is felt over a region. In the early days of seismology, intensity values were sometimes derived from postmaster reports from each post office in the area of shaking. Postcards describing earthquake impact levels were distributed by seismic networks and responses were mapped by seismologists. These days, seismic intensity maps draw upon data from seismic stations and public reports, most commonly through the USGS “Did You Feel It?” system. The example below shows the estimated shaking footprint from the 2001 Nisqually Earthquake.