magnitude and magnitude scales: Richter, Modified Mercalli and Moment Magnitude

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Earthquake and Volcanic Hazards – Magnitude, Impacts and Management (Cambridge A‑Level Geography 9696)

Learning Objectives

  • Explain why magnitude is measured and how it differs from intensity.
  • Describe the three principal magnitude/ intensity scales – Richter (local magnitude $M_L$), Modified Mercalli Intensity (MMI) and Moment Magnitude ($M_w$) – including formulas, ranges of applicability and limitations.
  • Identify the global distribution of earthquakes and volcanoes and link this to plate‑boundary settings.
  • Outline the main earthquake and volcanic hazards, the factors that modify vulnerability and the typical impacts on people and the environment.
  • Evaluate the main monitoring and management strategies used to reduce risk.
  • Apply knowledge to a recent case study and assess the success of the response.

1. Global Distribution of Earthquakes and Volcanoes

Both phenomena are concentrated along plate‑boundary zones where the lithosphere is actively deforming.

1.1 Plate‑boundary context

  • Convergent (subduction) boundaries – deep‑focus earthquakes (0–700 km) and the world’s most explosive volcanoes (e.g., “Ring of Fire”).
  • Divergent boundaries – shallow, low‑magnitude quakes and basaltic fissure eruptions (e.g., Iceland, East African Rift).
  • Transform boundaries – shallow, moderate‑magnitude earthquakes (e.g., San Andreas fault).
  • Intraplate settings – occasional large earthquakes and volcanic fields caused by re‑activation of old faults or mantle plumes (e.g., New Madrid, USA; Hawaiian volcanoes).

Suggested diagram: World map showing earthquake epicentres (1970‑2020) and volcano locations overlaid on plate‑boundary lines, colour‑coded by depth (earthquakes) and volcano type.

2. Earthquake Hazards and Their Impacts

Hazard Cause / Process Typical Quantitative Indicator Typical Impacts Illustrative Example
Ground‑shaking Release of seismic energy; amplitude controlled by magnitude, depth and local geology. Peak Ground Acceleration (PGA) ≈ 0.3 g for moderate shaking (MMI VI). Structural damage, collapse of poorly built houses, injuries. 2010 Chile (Mw 8.8) – widespread building failure in coastal towns.
Liquefaction Saturation of loose, water‑logged sediments during strong shaking. Factor of Safety < 1.0 on the Standard Penetration Test (SPT) < 15 m. Loss of bearing capacity, tilting or sinking of structures, sand boils. 2011 Tohoku, Japan – extensive liquefaction on the Sendai plain.
Surface rupture Visible displacement along the fault plane that reaches the surface. Offset up to several metres (e.g., 5 m on the North Anatolian fault). Direct damage to infrastructure crossing the fault, creation of scarps. 1999 Kocaeli, Turkey – 5 m offset along the North Anatolian fault.
Secondary landslides Slope instability triggered by shaking. Number of landslides > 20 000 in the 2008 Wenchuan event. Road blockage, burial of settlements, damming of rivers. 2008 Wenchuan, China – > 20 000 landslides over 100 000 km².
Tsunamis Sudden vertical displacement of the sea floor during a large shallow quake. Run‑up heights > 30 m for Mw > 9 events. Coastal flooding, loss of life, destruction of ports and low‑lying areas. 2004 Indian Ocean (Mw 9.1) – > 230 000 deaths across 14 countries.
Aftershocks Smaller earthquakes in the same fault zone as stress readjusts. Typical frequency decay follows Omori’s law (n ∝ 1/t). Further damage to weakened structures, prolonged anxiety. 2015 Gorkha, Nepal – aftershocks > M 5 for several weeks.

3. Volcanic Hazards and Their Impacts

Hazard Typical Process Typical Quantitative Indicator Impacts Case Example
Lava flows Effusive eruption of low‑viscosity basaltic magma. Flow rate 10–100 m³ s⁻¹ (typical for Hawaiian eruptions). Destruction of infrastructure in the flow path; creation of new land. 2021 Kīlauea, Hawaii – > 1 km² of new basaltic surface.
Pyroclastic flows / density currents Fast‑moving avalanches of hot gas, ash and rock fragments. Velocity 100–700 m s⁻¹; temperature 200–700 °C. Extreme thermal damage, burial of settlements, high mortality. 1991 Mount Pinatubo – > 10 km s⁻¹ flows, > 800 deaths.
Volcanic ash fall Fine particles ejected high into the plume and carried by wind. Mass loading > 10 kg m⁻² can cause roof collapse. Roof collapse, respiratory problems, disruption of air traffic. 2010 Eyjafjallajökull, Iceland – 6‑week European airspace shutdown.
Lahars (volcanic mudflows) Mixture of volcanic debris and water (rain or melted snow). Peak discharge 10³–10⁵ m³ s⁻¹. Destruction of river valleys, burial of villages, long‑term sedimentation. 1991 Mount Pinatubo – lahars continued for > 10 years.
Volcanic gases (SO₂, CO₂, H₂S) Release of magmatic gases during eruption or degassing. SO₂ flux > 10⁵ t day⁻¹ can generate acid rain. Acid rain, crop damage, asphyxiation in low‑lying areas. 1994 Rabaul, PNG – lethal CO₂ concentrations in crater lakes.

Note on explosivity: The Volcanic Explosivity Index (VEI) is a logarithmic scale (0–8) that quantifies eruption magnitude based on erupted volume, plume height and eruption style. Higher VEI values (≥ 4) are associated with widespread ash fall, pyroclastic flows and greater societal impact.

4. Human and Physical Factors that Modify Vulnerability

  • Building standards & construction materials – reinforced‑concrete frames, base isolation, and strict codes reduce damage.
  • Population density & land‑use patterns – dense urban centres on alluvial plains experience higher casualties.
  • Local geology – soft sediments amplify shaking; bedrock attenuates it.
  • Topography – steep slopes increase landslide risk; coastal lowlands increase tsunami exposure.
  • Socio‑economic status – poorer communities have fewer resources for retrofitting and emergency response.

5. Magnitude and Intensity Scales

5.1 Richter (Local) Magnitude – $M_L$

Developed by Charles Richter (1935) for Southern California. Based on the maximum amplitude of the first‑arriving P‑wave recorded on a Wood‑Anderson seismograph.

Formula (simplified):

$M_L = \log_{10}\!\left(\dfrac{A}{A_0(\delta)}\right)$
  • $A$ = peak amplitude of the seismic wave (µm) on the Wood‑Anderson trace.
  • $A_0(\delta)$ = empirically derived distance‑correction factor (µm) for epicentral distance $\delta$ (degrees).
  • Effective for shallow crustal events (depth < 70 km) with magnitudes ≈ 3 – 7.
  • Logarithmic: each whole‑number increase = ten‑fold increase in amplitude and ≈ 31.6‑fold increase in released energy.
  • Limitation – saturation: for $M_L \gtrsim 7$ the scale under‑estimates the size of very large earthquakes.

5.2 Modified Mercalli Intensity (MMI) Scale

Qualitative, observational scale that describes the effects of shaking on people, structures and the natural environment. Ranges from I (not felt) to XII (total destruction).

IntensityTypical Observations
I – Not feltOnly a few people notice a faint tremor.
III – WeakNoticeable shaking indoors; hanging objects swing.
VI – StrongAll feel shaking; plaster cracks; slight damage to poorly built structures.
IX – ViolentGeneral panic; considerable damage to well‑built structures; ground fissures.
XII – CatastrophicNear‑total destruction; ground may be visibly displaced.
  • Intensity varies with distance from the epicentre, local geology and building quality.
  • Useful for rapid damage assessment and for historical earthquakes where instrumental data are absent.

5.3 Moment Magnitude – $M_w$

Introduced in the 1970s to provide a scale that does not saturate for the largest events. It is derived from the seismic moment ($M_0$), a physical measure of faulting.

Seismic moment:

$M_0 = \mu \, A \, D$
  • $\mu$ = shear modulus of the rocks (≈ $3 \times 10^{10}$ Pa).
  • $A$ = area of the fault that slipped (m²).
  • $D$ = average slip on the fault (m).

Moment magnitude formula:

$M_w = \dfrac{2}{3}\log_{10} M_0 - 6.07\quad\text{(where $M_0$ is in N·m)}$
  • Applicable to all earthquake sizes, from micro‑quakes to the greatest megathrust events (Mw ≈ 10).
  • Directly proportional to the total energy released, providing a uniform global catalogue.
  • Does not saturate; therefore it is the preferred scale for scientific research and for comparing the largest earthquakes.
  • Limitation: requires detailed source parameters; not instantly available for every quake.

5.4 Comparative Overview

Scale Type Magnitude / Intensity Range Basis of Measurement Primary Use Key Limitation
Richter ($M_L$) Quantitative ≈ 3 – 7 (effective) Maximum amplitude on a Wood‑Anderson seismograph, distance‑corrected Historical records, medium‑size shallow quakes Saturation for $M \gtrsim 7$; only for shallow crustal events
Modified Mercalli (MMI) Qualitative (Intensity) I – XII (descriptive) Observed effects on people, structures and the environment Damage assessment, public communication, engineering design Subjective; varies with distance, geology and building standards
Moment Magnitude ($M_w$) Quantitative 0 – 10+ (theoretical) Seismic moment ($M_0 = \mu A D$) derived from fault geometry and slip Modern global monitoring, scientific research, large‑event comparison Requires detailed source parameters; not instantly available for every quake

6. Linking Magnitude / Intensity to Impacts

Magnitude quantifies the energy released at the source, whereas intensity (MMI) describes the shaking experienced at a specific location. The actual impact depends on a combination of factors:

  • Depth of focus – shallower quakes produce stronger surface shaking.
  • Distance from epicentre – intensity attenuates with distance; attenuation rates differ with crustal structure.
  • Local geology – soft sediments amplify shaking; hard rock dampens it.
  • Topography – basins can trap seismic waves, increasing shaking duration.
  • Building standards & land‑use – modern, seismic‑resistant construction reduces casualties.
  • Population density – higher density increases the number of potential victims.

7. Monitoring and Management Strategies

  • Seismic networks – dense arrays of broadband seismographs provide real‑time magnitude, depth and location.
  • Geodetic techniques – GPS, InSAR and strainmeters detect fault deformation and slow slip.
  • Early‑warning systems – detect the first P‑waves and broadcast alerts before damaging S‑waves arrive (e.g., Japan’s J‑Alert, Mexico’s SASMEX).
  • Building codes & retrofitting – mandatory design standards, base isolation, and reinforcement of existing structures.
  • Land‑use planning – avoidance of construction on active faults, liquefaction‑prone sediments and tsunami inundation zones.
  • Public education & drills – regular “Drop, Cover, Hold‑on” exercises and community awareness programmes.
  • Emergency response – pre‑positioned supplies, rapid damage‑assessment teams, and coordinated rescue operations.

8. Case Study – 2023 Turkey‑Syria Earthquake (Mw 7.8)

Cause and magnitude – Shallow thrust faulting on the East Anatolian fault system; $M_w = 7.8$, $M_L \approx 7.9$.
Impacts – Over 50 000 deaths; massive collapse of non‑engineered masonry buildings; landslides in mountainous terrain; aftershocks > M 5 for weeks.
Vulnerability factors – High population density, prevalence of unreinforced masonry, soft alluvial deposits in the coastal plain.
Management response – Immediate activation of national disaster agencies, international search‑and‑rescue teams, emergency shelters, and a US$1 billion reconstruction fund.
Evaluation – Early‑warning coverage was limited, contributing to high casualties. Rapid mobilisation saved lives, but long‑term rebuilding hinges on effective enforcement of stricter seismic codes and large‑scale retrofitting programmes.

9. Suggested Diagram

Cross‑section of a fault rupture illustrating the fault plane, slip ($D$), rupture area ($A$), and resulting seismic moment ($M_0$). Include annotations for P‑wave and S‑wave propagation, surface rupture and typical depth ranges for different plate‑boundary settings.

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