Measuring Earthquakes: Magnitude and Intensity

Magnitude measures the absolute "size" of the earthquake, irrespective of viewpoint.

Intensity measures the severity of an earthquake at a location.

Like a lightbulb: For a lightbulb, magnitude corresponds to the wattage, which indicates the absolute size in terms of the power it consumes. Intensity corresponds to the apparent brightness of the bulb to a viewer, which varies with location.

Magnitude

Earthquake magnitude is typically measured by the Richter Scale, which is based on the maximum ground amplitude at a location 100 km from the epicenter.

The Richter scale is logarithmic. An increase of 1 point means a 10-fold increase in the characteristic amplitude, and an approximately 31-fold increase in the energy released.

Intensity

Intensity is typically measured by the effects of ground motion at a particular site. In the U.S., it is common to use the modified Mercalli Scale.

       Summary Damage
MMI    Description
Value  Used on Maps          Full Description                                                                                                                       

I.               Not felt.  Marginal and long period effects of large              
                 earthquakes.                                                      

II.              Felt by persons at rest, on upper floors, or favorably placed.    

III.             Felt indoors.  Hanging objects swing.  Vibration like passing of  
                 light trucks.  Duration estimated.  May not be recognized as an   
                 earthquake.                                                       

IV.              Hanging objects swing.  Vibration like passing of heavy trucks;   
                 or sensation of a jolt like a heavy ball striking the walls.      
                 Standing motor cars rock.  Windows, dishes, doors rattle.         
                 Glasses clink.  Crockery clashes.  In the upper range of IV,      
                 wooden walls and frame creak.                                     

V.     Pictures  Felt outdoors; direction estimated.  Sleepers wakened.  Liquids   
       Move      disturbed, some spilled.  Small unstable objects displaced or     
                 upset.  Doors swing, close, open.  Shutters, pictures move.       
                 Pendulum clocks stop, start, change rate.                         

VI.    Objects   Felt by all.  Many frightened and run outdoors.  Persons walk     
       Fall      unsteadily.  Windows, dishes, glassware broken.  Knickknacks,     
                 books, etc., off shelves.  Pictures off walls.  Furniture moved   
                 or overturned.  Weak plaster and masonry D cracked.  Small bells  
                 ring (church, school).  Trees, bushes shaken (visibly, or heard   
                 to rustle).                                                       

VII.   Nonstruct Difficult to stand.  Noticed by drivers of motor cars.  Hanging   
       ural      objects quiver.  Furniture broken.  Damage to masonry D,          
       Damage    including cracks.  Weak chimneys broken at roof line.  Fall of    
                 plaster, loose bricks, stones, tiles, cornices (also unbraced     
                 parapets and architectural ornaments).  Some cracks in masonry    
                 C.  Waves on ponds; water turbid with mud.  Small slides and      
                 caving in along sand or gravel banks.  Large bells ring.          
                 Concrete irrigation ditches damaged.                              

VIII.  Moderate  Steering of motor cars affected.  Damage to masonry C; partial    
       Damage    collapse.  Some damage to masonry B; none to masonry A.  Fall of  
                 stucco and some masonry walls.  Twisting, fall of chimneys,       
                 factory stacks, monuments, towers, elevated tanks.  Frame houses  
                 moved on foundations if not bolted down; loose panel walls        
                 thrown out.  Decayed piling broken off.  Branches broken from     
                 trees.  Changes in flow or temperature of springs and wells.      
                 Cracks in wet ground and on steep slopes.                         

IX.    Heavy     General panic.  Masonry D destroyed; masonry C heavily damaged,   
       Damage    sometimes with complete collapse; masonry B seriously damaged.    
                 (General damage to foundations.)  Frame structures, if not        
                 bolted, shifted off foundations.  Frames racked.  Serious damage  
                 to reservoirs.  Underground pipes broken.  Conspicuous cracks in  
                 ground.  In alluvial areas sand and mud ejected, earthquake       
                 fountains, sand craters.                                          

X.     Extreme   Most masonry and frame structures destroyed with their            
       Damage    foundations.  Some well-built wooden structures and bridges       
                 destroyed.  Serious damage to dams, dikes, embankments.  Large    
                 landslides.  Water thrown on banks of canals, rivers, lakes,      
                 etc.  Sand and mud shifted horizontally on beaches and flat       
                 land.  Rails bent slightly.                                       

XI.              Rails bent greatly.  Underground pipelines completely out of      
                 service.                                                          

XII.             Damage nearly total.  Large rock masses displaced.  Lines of      
                 sight and level distorted.  Objects thrown into the air.          

Isoseismal Maps

1811 New Madrid Earthquake [Bolt 1978, p. 101]

1906 San Francisco Earthquake [Bolt 1989, p. 20]

Central Virginia, December 9, 2003.
[USGS: http://pasadena.wr.usgs.gov/shake/STORE/Xcdbf_03/ciim_display.html ]

Assessing Hazards at a Particular Site

Risk and Return Period

Annual Exceedance Probability: P

The probability that an event level will be met or exceeded during a one-year interval.

General Exceedance Probability: P₀

The probability that an event will be met or exceeded during a interval of n years.

Return Period (mean recurrence): T

The return period is defined as 1/P, e.g. an annual exceedance probability P of 0.1 (10%) implies a return period T of ten years.

The probability that an event will be exceeded during the return period is 1.0 minus the probability that it won't be exceeded during the return period.

The probability that it won't be exceeded during the T-year return period is:

(1 - P)^T

Example: for a 100-year earthquake, T = 100 and P = 0.01.
Probability of non-exceedance during the return period = (1 - 0.01)¹⁰⁰ = 0.37
e.g., there is a 37% chance that the 100-year earthquake will not occur during a 100-year period.

The probability that it will be exceeded during the T-year return period is 1 minus the probability of non-exceedance.

1- (1 - P)^T ~= 0.63

i.e. there is a 63% probability that an event with a 100-year return period will be exceeded during a 100-year interval, and a 0.37% chance that it won't.

The probability that an event with return period T will be exceeded during a period of n years (P₀) is 1.0 minus the probability that it won't be exceeded during that interval.

The probability that the event won't be exceeded during the n-year interval is:

(1 - P)ⁿ

The probability that the event will be exceeded during the n-year interval is:

P₀ = 1 - (1 - P)ⁿ

Example: For a 10-percent probability of exceedance (P₀) over a 50-year (n) interval,

0.1 = 1 - (1 - P)⁵⁰  ->   P = 0.0021   ->   T = 475 years

the annual probability (P) equals 0.0021, corresponding to a return period of 475 years [Gupta 1993, p. 15].

Seismic Risk Maps

NEHRP 1994 Map 5: Contours show 0.3 second spectral response acceleration (expressed as %g) with a 90 percent probability of nonexceedance in 50 years.

Detail of the Mid-Atlantic states.

Detail of Central Virginia.

Compare with 1996 USGS maps for the same quantity: 0.3 second spectral response acceleration (expressed as %g) with a 90 percent probability of nonexceedance in 50 years.

Eastern and Central United States. (http://wwwneic.cr.usgs.gov/eq/hazmaps/0503hz.gif)

Detail of Mid-Atlantic States.

1994 NEHRP

1996 USGS

Questions and explanations:

• Message inquiring about differences.
• Explanation from Edgar V. Leyendecker of USGS (reproduced with permission)
• Explanation from Art Frankel of USGS (reproduced with permission)

Current National Map from USGS

Summary

Hazards

• One cause of earthquakes is the release of energy when built up in moving continental plates at fault lines where the plates interlock.
• The mechanisms of earthquakes in the eastern and central U.S. are not well understood.
• There are several potential natural hazards:
  • Fault rupture.
  • Ground shaking.
  • Ground failure.
    • Liquefaction
    • Landsliding
  • Tsunami
• Some hazards can be mitigated or accounted for in design:
  • Ground compaction through pile driving can sometimes mitigate liquefaction.
  • Buildings can be designed to withstand ground shaking.
• Other hazards, such a landslides, tsunamis, and fault rupture are extremely difficult to mitigate or resist.
  • Important considerations for land use planning.
  • There are some places that you should not build.

Magnitude and intensity

• Earthquakes and their effects can be measured in terms of magnitude and intensity.
  • Magnitude measures the absolute size of an earthquake, and is related to the total energy released. It is commonly measured with the Richter scale.
  • Intensity measures the severity of shaking at a particular site. In the US and Europe, it is commonly measured with the Modified Mercalli Scale.

Seismic Risk

• The concepts of probability of exceedance and return period are commonly used to express the level of risk of an event such as an earthquake or flood.
• The probability that an event will be exceeded during the return period is 1 minus the probability that it won't be exceeded.
• As a result, the probability is 63% that an event will be exceeded during it's return period (e.g. there is a 63% chance that a 100-year flood will be exceeded during a 100-year period.)
• NEHRP provisions and American building codes were long based on levels of shaking with a 10% probability of exceedance during a 50-year period.
  • This corresponds to a 475-year return period.
• More recently, codes have moved to a 2% probability of exceedance during a 50-year return period.
  • This corresponds roughly corresponds to a 2,500 year return period.
  • This increases loads in the midwest and eastern regions relative to the west.
• Knowledge and theories concerning seismic risk in the central and eastern U.S. are incomplete and uncertain.