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Shaking Ground

Linking Earthquake Magnitude and Intensity

How does the magnitude of an earthquake impact shaking?

How does shaking impact intensity and destruction?

Prepared for SSAC byEric Baer - Highline Community College, Seattle WA

© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. 2007

Core Quantitative concept and skillForward modeling

SSAC2007:QE531.EB1.1

Supportive Quantitative concepts and skillsNumber Sense: Logarithmic scalesNumber Sense: Converting units Number Sense: Roman numeralsFunction: Exponential function, power functionCircle: AreaGraph: XY (scatter)Visualization: reading graphsVisualization: map scale

Peer-Reviewed

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Earthquake magnitude is commonly used to represent the size of an earthquake. However, most people want

to understand how much impact or damage earthquakes do. These two concepts are linked by

shaking. Earthquake magnitude can be measured in a variety of ways, most commonly moment magnitude or Richter magnitude. Shaking is measured in units of

acceleration (often a percentage of g). Damage or intensity can be measured by the modified Mercalli

intensity (MMI) scale.

Problem

How does the magnitude of an earthquake impact the amount of shaking one feels and the extent of damage?

Amount of shaking (g’s)

Magnitude and Location

Intensity (MMI)

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Slides 4-9 relate magnitude and shaking (acceleration).

Slides 10-12 relate shaking to intensity.

Slides 13-14 analyze and present results.

Slide 15 give you questions at the end.

Overview of Module

Earthquakes cause damage. The damage is affected not only by the magnitude of the earthquake, but how far away a given location is

from the epicenter of the earthquake. In this lab study you will explore how magnitude and distance impact shaking and damage.

The calculation of intensity from magnitude by way of acceleration is an example of mathematical modeling. We use magnitude to calculate

(model) acceleration by means of one relationship (function), and acceleration to determine (model) intensity by means of another relation.

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Relating Acceleration to Magnitude and Distance

Predictions of damage from an earthquake are not easy to make, and require several critical assumptions. Two assumptions we will make are:

•That there are no local soil effects (such as liquefaction)•That ground shaking will cause the damage (i.e., no tsunami, large fires, etc.)

The amount of shaking (acceleration) at a specific location in an earthquake depends on three factors:

•Distance to the focus,•Magnitude of the quake,•Local geologic effects, such as increased amplitude in water-saturated ground (which we will ignore).

The relationship between magnitude and acceleration is

a =1300*(e0.67*M)*(D+25)−1.6

Where a is acceleration (in units of cm/sec2), M is magnitude, and D is distance (in km) (From Donovan, 1973)

Create a spreadsheet to calculate shaking for a given magnitude and

distance

This is a multivariable function, a = f(M,D). The e0.68M part is an exponential function. The (D+25)−1.6 part is a power function.

B C D2 Magnitude Distance (km) Acceleration (cm/sec2)

3 6 2 371.21368

= Cell with an equation in it.

= Cell with a number in it.

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Change the acceleration units

The amount of shaking in an earthquake is measured in terms of acceleration. The units are typically in “g’s” where 1g is the acceleration (force per unit mass) you feel due to gravity. If earthquake shaking is 1g,

that means that it is equivalent to the acceleration due to gravity. Therefore, if you were standing on a scale and experienced an additional vertical g, the scale would range from 0, when you are thrown upwards and briefly become

weightless, to twice your weight, when you land. Typical accelerations in earthquakes are between 0.05 and 1g. 0.005g would be barely felt (and not felt by many), shaking over 0.05g is unpleasant, and few buildings would

survive an acceleration of more than 0.5g.

Convert the acceleration to g’s (divide by 980

cm/sec2) - create a new column.

= Cell with an equation in it.

= Cell with a number in it.

Acceleration is a critical factor measurement in an earthquake

because it determines how much force is applied to a structure.

F=ma

Since the mass of a structure is constant, the acceleration is the

determinant of the force. If the force applied exceeds the strength of the

building, it will fail.

B C D E2 Magnitude Distance (km) Acceleration (cm/sec2) a (g 's)3 6 2 371.21368 0.37879

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Create a large table

Create a table of distance vs. acceleration for M6, M6.5, M7, M7.5, M8, and M9 earthquakes. Use distances of 2, 5, 10, 20, 40, 100, 200, 500, and 1000 km.

The fill down and right commands are helpful

here. = Cell with an equation in it.

= Cell with a number in it. To make this table you will need to make use of absolute references in excel. This is done by putting a $ in front of the cell reference. Normally, excel references are relative. As an

illustration, put the formula =A1 into cell B2. What this really says to excel is “look up and left one cell and put that into the cell.” you can see this if you

copy the formula down to B3; the formula becomes =A2. However, if you put $ into the original formula, {=$A$1}

then the formula copies exactly the same to any cell. You can even do

mixed fixed and absolute cell references by using the $ on either the

column or row reference.

A B1 32 2 33 2

This cell has formula =A1

This cell has formula =A1

This cell has formula =A2 because it was copied

This cell has formula =A2 because it was copiedNeed more help

with this?

Try this tutorial

Need more help with this?

Try this tutorial

B C D E F G

2 a =1300/980*(e^ 0.67*M )*(D +25)^(?1.6)34 Mag ---> 6 6.5 7 7.5 8 95 D (km)6 2 0.3784 0.5290 0.7395 1.0338 1.4451 2.82427 5 0.3197 0.4469 0.6248 0.8734 1.2210 2.38608 10 0.2498 0.3492 0.4882 0.6825 0.9541 1.86459 20 0.1671 0.2336 0.3266 0.4565 0.6382 1.247210 40 0.0928 0.1297 0.1813 0.2535 0.3543 0.692511 100 0.0326 0.0456 0.0637 0.0890 0.1245 0.243212 200 0.0127 0.0178 0.0249 0.0348 0.0486 0.095013 500 0.0033 0.0046 0.0064 0.0090 0.0125 0.024514 1000 0.0011 0.0016 0.0022 0.0031 0.0043 0.0084

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Create a Graph

Create a XY-scatter plot of acceleration versus distance for M6, M6.5, M7, M7.5, M8, and M9 earthquakes.

Make the x-axis logarithmic.

Acceleration Vs. Distance

0

0.5

1

1.5

2

2.5

3

1 10 100 1000

Distance from epicenter (km)

Ac

ce

lera

tio

n (

gu

nit

s) Magnitude 6

M 6.5

M 7

M 7.5

M 8

M 9

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Acceleration vs. distance at different scales

Change the scale(s) on your graph so you can zoom in and read the graph easily at large and small accelerations.

Acceleration Vs. Distance

0

0.5

1

1 10 100 1000

Distance from epicenter (km)

Ac

ce

lera

tio

n (

g u

nit

s)

Magnitude 6

M 6.5

M 7

M 7.5

M 8

M 9 Acceleration Vs. Distance

0

0.05

0.1

0.15

0.2

0.25

0.3

10 100 1000

Distance from epicenter (km)

Ac

ce

lera

tio

n (

g u

nit

s) Magnitude 6

M 6.5

M 7

M 7.5

M 8

M 9

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Read a Graph

For each magnitude earthquake, how far from the earthquake will the shaking be

unpleasant (= 0.05 g)?

Over what area will the earthquake be unpleasant?

The formula for area of a circle is A = πr2

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For each earthquake, determine the area in which the shaking will be unpleasant but not catastrophic (i.e., between 0.05g

and 0.5g)?

General Information

You will need to find the area of each circle and

then subtract the area of catastrophic damage

from the area of unpleasant damage

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Once we know how much shaking an area will receive, we can convert this to intensity. The modified Mercalli intensity scale (MMI) is the most commonly used intensity scale. One can correlate acceleration with

intensity, as was done by Trifunac and Brady (1975) and Wald et al. (1999 a, b) (see http://pasadena.wr.usgs.gov/shake/pubs/regress/node3.html#SECTION00030000000000000000 ) for details.

If you do not know about the modified Mercalli intensity scale (MMI), skip to the last slide which explains it.

On your graph, by hand, color in horizontal bands that show

the modified Mercalli scale.

You may need to change the scale (horizontal and vertical) to complete this successfully. If needed, make

multiple graphs with different scales.

Converting Shaking to Intensity

Modified Mercalli Intensity Acceleration (g)

I .0017-.0005

II .0017-.005

III 0.005-0.014

IV 0.014-0.039

V 0.039.-0.092

VI 0.092-0.18

VII 0.18-0.34

VIII 0.34-0.65

IX 0.65-1.24

X+ Above 1.24

Mercalli intensity is represented by Roman

Numerals in order to

differentiate them from

Magnitudes and to show that they are

only integers.

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Take a map and draw a circle with a radius of the MMI-4 limit for the M8 earthquake. Use a compass. Place the center of the circle at New Madrid, the center of 3 great

earthquakes in the early 19th century. You can read more on this quake at http://earthquake.usgs.gov/regional/states/events/1811-1812_iso.php

In order to make your calculations more visual, draw an isoseismic map on a base map of the United States. Use the results of your calculations for the M8 and M6 earthquakes.

You will need to scale the circle using the bar scale that is marked on the map!

Drawing the circles

Draw in the boundaries of each of the other Mercalli intensities and color in each of the concentric circles. In the end, you will have a series of concentric circles

representing the Mercalli intensities for an M8 earthquake.

Map from the National Atlas http://nationalatlas.gov

Need a bigger copy of this

map? Download it!

New Madrid

600 kilometers

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End of Module Assignments

1. Print out your three graphs of shaking (acceleration) vs. distance, with appropriate labels for each of the earthquake magnitudes. (Refer to Slides 7-8)

2. On each graph, color and label the shaking (acceleration) that is equivalent to each MMI level. These will be horizontal regions across your graph. (See Slide 11)

3. What are the areas (in km2) that receive catastrophic (MMI X or above), severe (MMI IX and MMI VIII), moderate (MMI VI – MMI VII), and light (MMI IV-VI) damage for a M6, M7, M8, and a M9 quake. Turn in your answers as a table.

4. In a M8 earthquake, compare the probability of your being in a MMI VI region vs. a MMI IX region. Which should you be more worried about?

5. How many times “worse” is a M8 than a M6 earthquake? What did you use to determine what was “worse”? Note that there is no single correct answer.

6. Look at the Mercalli Intensity maps made from reports of damage from these quakes at http://earthquake.usgs.gov/regional/states/events/1811-1812_iso.php . What differences do you note between your model events and the actual data? What might cause the differences?

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Cited References

• Donovan, N.C., (1973). A statistical evaluation of strong motion data including the Feb. 9,1971, San Fernando earthquake. Proc., 5WCEE, Rome, Italy, 1: 1252-1261. Go back

• Trifunac, M. D., and A. G. Brady (1975). On the correlation of seismic intensity scales with the peaks of recorded ground motion, Bull. Seism. Soc. Am. 65, 139-162. Go back

• Wald, D. J., T. Heaton, H. Kanamori, P. Maechling, and V. Quitoriano (1999a). Research and Development of TriNet "Shake" Maps, Earthquake Spectra, 15. Go back

• Wald, D.J., V. Quitoriano, T.H. Heaton, and H. Kanamori (1999b). Relationships between peak ground acceleration, peak ground velocity, and modified Mercalli intensity in California, Earthq. Spectra 15, 557-564. Go back

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The Modified Mercalli Intensity Scale

The modified Mercalli intensity scale rates the damage on a scale of I-XII as follows:

MMI ValueShaking Severity 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.

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

VIModerate Felt by all. Many frightened and run outdoors. Persons walk 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).

VIIStrong Difficult to stand. Noticed by drivers of motor cars. Hanging objects quiver. Furniture broken. Damage to masonry D, 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.

VIIIVery Strong

Steering of motor cars affected. Damage to masonry C; partial 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.

IXViolent General panic. Masonry D destroyed; masonry C heavily damaged, 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.

XVery Violent

Most masonry and frame structures destroyed with their 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.

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