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One earthquake may have one reported moment magnitude, but a neighbourhood near the fault and another much farther away can experience very different shaking. Neither statement is contradictory.
Magnitude describes the source; intensity describes observed effects at a location. We build the source calculation, separate site conditions from event size, test a fictional two-town comparison and explain why no universal magnitude-to-intensity conversion is valid.
Define the question
Start at chapter 1 · Define source magnitude and local intensity without mixing units.
Build the scientific model
Start at chapter 3 · Use seismic moment and the logarithmic magnitude formula.
Compare what changes
Start at chapter 6 · Construct two-site interpretations of the same event.
Audit evidence and limits
Start at chapter 8 · Separate measurement, observation and risk.
Practise and continue
Start at chapter 11 · Check changed moments and continue into related Earth science.
Full chapter index · Practice and worked checks · Seismology subject root
Chapter index
Define the question · Chapters 1–2
Build the scientific model · Chapters 3–5
Compare what changes · Chapters 6–7
Audit evidence and limits · Chapters 8–10
Practise and continue · Chapters 11–12
An earthquake starts when part of a fault slips and releases stored strain energy. Seismic waves spread outward through the Earth. The event has source properties, while shaking varies from place to place as the waves travel through different paths and interact with local geology and built environments.
Magnitude is an estimate of the size of the seismic event on a defined magnitude scale. Intensity is a measure of how strongly the earthquake was felt or what effects were observed at a particular place, using a stated intensity scale. Saying ‘the earthquake was intensity VI everywhere’ confuses an event descriptor with a spatial field of local effects.
CHAPTER 2 OF 12 · Define the question
2. Do not call every magnitude the Richter scale
Different methods estimate magnitude from different wave measurements and frequency ranges. Local magnitude, ML, was developed for particular instrument and distance conditions; surface-wave and body-wave magnitudes have their own operating ranges and limitations. Modern large-event reporting often favours moment magnitude, Mw, because it relates to the physical seismic moment of rupture.
Even when agencies publish an event as Mw 6.0, a later revised value may differ after additional station data and source modelling are considered. This is a refinement of a measurement, not evidence that the quake changed size after it occurred. Always include the scale and, for time-sensitive news, distinguish preliminary from reviewed estimates.
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CHAPTER 3 OF 12 · Build the scientific model
3. Build seismic moment from rupture geometry
In a simplified uniform-slip model, the seismic moment is M0 = μAD. Here μ is the shear modulus of the rock in pascals, A is ruptured fault area in square metres, and D is average slip in metres. Multiplying units gives Pa × m² × m = N·m, the SI unit of seismic moment.
Take a fictional fault segment with μ = 3 × 1010 Pa, A = 1 × 108 m² and D = 0.50 m. The moment is M0 = 3 × 1010 × 1 × 108 × 0.50 = 1.5 × 1018 N·m. This is an illustrative arithmetic model, not a measurement of a named earthquake.
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CHAPTER 4 OF 12 · Build the scientific model
4. Convert the seismic moment to Mw correctly
A common SI expression is Mw ≈ (2/3)[log10(M0 in N·m) − 9.1]. The numerical constant includes the chosen units and convention; using a formula calibrated for dyne-centimetres with an N·m input gives a wrong answer. Magnitude itself is dimensionless, although the logarithm uses a specified reference-unit convention.
For M0 = 1.5 × 1018 N·m, log10(M0) ≈ 18.1761. Thus Mw ≈ (2/3)(18.1761 − 9.1) = 6.05. This value characterises the assumed source model; it does not say how violently every building will shake.
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CHAPTER 5 OF 12 · Build the scientific model
5. Understand the logarithm, not just the headline number
A tenfold increase in seismic moment changes moment magnitude by (2/3)log10(10) ≈ 0.667. A one-unit increase in Mw corresponds to a seismic-moment factor of about 101.5 ≈ 31.6. These are relations between seismic moment and magnitude under the stated convention.
Do not automatically translate a moment ratio into the exact same ratio of radiated seismic energy, damage or local shaking. Rupture geometry, stress drop, depth and energy partition influence those quantities. For example, doubling the illustrative slip from 0.50 to 1.00 m while keeping μ and A fixed doubles M0 and raises Mw by only about 0.201.
| Illustrative slip | Moment M0 | Moment magnitude Mw |
|---|---|---|
| 0.50 m | 1.5 × 1018 N·m | ≈ 6.05 |
| 1.00 m | 3.0 × 1018 N·m | ≈ 6.25 |
| 5.00 m | 1.5 × 1019 N·m | ≈ 6.72 |
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CHAPTER 6 OF 12 · Compare what changes
6. Define Modified Mercalli intensity as a local description
The Modified Mercalli Intensity (MMI) scale uses Roman numerals I through XII and describes the effects and felt experience of shaking at a location. It involves observations such as whether shaking was noticed, objects moved and structures were affected. It is not another way of writing Mw with Roman numerals.
Intensity assignments depend on evidence, including reports, damage patterns and where available instrumental estimates correlated with effects. Different regions also use other intensity scales and procedures. State the scale explicitly. MMI VI, for example, is a local intensity category, not a substitute for calling the whole earthquake ‘magnitude six’.
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CHAPTER 7 OF 12 · Compare what changes
7. Why the same earthquake produces a patchwork of effects
Shaking generally changes with distance from the rupture, but a map is not simply concentric rings centred on one epicentre. Source directivity, rupture depth, wave propagation, sedimentary basins, local soil response, topography and building characteristics can create a complicated spatial pattern.
Imagine two fictional observation sites during the same Mw 6.05 event. Site A is near the rupture over a basin that can amplify relevant frequencies, while Site B is farther away on different ground. Their intensity descriptions may differ materially. This is a qualitative example only: assigning exact Roman-numeral intensities to those sites would require appropriate site measurements and effect reports.
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CHAPTER 8 OF 12 · Audit evidence and limits
8. Distinguish intensity from damage and hazard
Intensity is based on shaking effects and observations, but damage is also a function of exposure and vulnerability. Two buildings on the same street may respond differently because of construction, design, condition, height and dynamic characteristics. A strong shaking measure alone does not fix the loss experienced by every person or structure.
Seismic hazard concerns potential earthquake effects under defined scenarios or probabilities; risk also considers assets, people and vulnerability. A map of observed intensity after one event is not the same as a long-term hazard map. The words refer to related but distinct questions, and mixing them weakens preparedness and engineering decisions.
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CHAPTER 9 OF 12 · Audit evidence and limits
9. Why there is no universal Mw-to-MMI lookup table
Magnitude can help explain the scale of a source and potential shaking, but it cannot uniquely determine local intensity. A deep, distant event and a shallow, nearby event can have different felt effects even if their Mw values are similar. Conversely, two earthquakes with unlike magnitudes may produce comparable local intensity at selected sites.
Empirical prediction models can estimate expected ground motion given magnitude, distance and site parameters. Intensity may then be estimated or assigned from appropriate observations and relationships. Every such step contains model and measurement uncertainty. A single magnitude number cannot replace location, geology and measured or reported effects.
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CHAPTER 10 OF 12 · Audit evidence and limits
10. Read competing media numbers without confusion
A breaking news report may mention a preliminary magnitude of 6.1, later revised to 6.0. Another article may say some district experienced MMI VII. These figures can coexist because they come from different processes and describe different aspects of the same event. Check dates, agencies, scale labels and whether the information refers to a measurement, modelled shaking or observed damage.
Numbers taken from distinct catalogues should not be treated as directly interchangeable without checking the magnitude scales, source data and review status. For lessons and articles, identify the source of each claim and avoid using intensity observations to reverse-engineer an exact magnitude without a defensible model.
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CHAPTER 11 OF 12 · Practise and continue
11. Practise two changes to the source model
Exercise A: keep the illustrative shear modulus and rupture area unchanged but double average slip. The moment becomes 3.0 × 1018 N·m and Mw rises from approximately 6.05 to 6.25. Exercise B: if M0 increases by a factor of 31.6, the magnitude rises by about one unit, not thirty-one units.
Exercise C is conceptual: an agency reports Mw 6.0 and two towns report different MMI categories. Can both be correct? Yes. Moment magnitude is source-related, while intensity depends on the local effects and evidence. A complete scientific explanation says why the measurements differ before asking which town is ‘right’.
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CHAPTER 12 OF 12 · Practise and continue
12. A field-ready checklist for seismological claims
When reading earthquake data, record (1) the stated magnitude scale; (2) whether its value is preliminary; (3) location and depth; (4) how the affected site relates to the rupture; (5) whether ‘intensity’ denotes a named macroseismic scale or modelled ground shaking; and (6) the limits of the observations.
For more on why event locations themselves have uncertainties, read station geometry and directional location uncertainty. For how paired arrivals help constrain an origin, follow the Wadati-plot guide. These pieces connect source characterisation to the measurement process without merging all seismology into one headline.
Sources and connected reading
This is an original educational explanation. Numerical cases labelled illustrative are teaching models, not reported site observations, device measurements or experimental results. Apply a formula only within the conditions stated in the relevant chapter.