arth

9

Winter

2016

Homework

#3.

(Due

at

4

pm

Friday,

Jan

29th,

2016)

Read

Chapter

6

and

Chapter

8

in

Earthquakes

(Bolt)

and

the

online

presentations.

You

also

need

a

ruler

to

do

some

measurements

1. On the figure below, the 10 km scale bar (assume the same scale both horizontally

and vertically) is given. What is the approximate moment magnitude of this

earthquake if the average fault slip (D) is 5 meters during the event? Using the

information below to solve the problem.

Seismic moment Mo, defined as Mo= µ x A x D, where A= L x W. L the length of

the fault, W the width of the fault, D is the average slip on the fault, and µ is shear

modulus. Mo measured in Nm, is related to magnitude by the following relation:

Log(Mo) = 1.5Mw+ 9.0

or solving for Mw we find Mw=2/3log M0 − 6

Solving for Mo we find Mo = 101.5Mw +9 (Nm)

In the equations above, Mw is the moment magnitude, and Mo is the seismic

moment. Use µ = 3.0X1010 N/m2 for the value of shear modulus.

2. If the moment magnitude increases by 2, how many times will seismic moment

increase?

3. What

is

the

energy

in

Joules

of

this

earthquake?

4. The

1964

Alaska

earthquake

was

rated

by

measuring

seismograms

as

body

wave

magnitude

mb=6.5,

surface

wave

magnitude

Ms=8.6,

and

the

moment

magnitude

of

9.2

Explain

the

difference

and

why

Mw

is

the

best

description

for

the

size

of

this

earthquake.

5. Using

the

formula

in

problem

1

to

estimate

the

seismic

moment

of

the

above

1964

Alaska

earthquake.

6. According

to

Bath

law

(we

will

learn

later),

on

average

the

largest

aftershock

has

a

magnitude

about

1.0

smaller

than

the

mainshock.

What

is

the

ratio

of

mainshock

and

the

aftershock

in

seismic

moment?

What

is

the

ratio

in

peak

ground

motion

at

the

same

station?

Here

we

assume

the

mainshock

and

aftershock

at

roughly

same

location.

7. In

2004,

a

movie

named

“10.5”

aired

as

a

television

miniseries

in

the

United

States

on

May

2,

2004

and

May

3,

2004.

It

is

a

disaster

movie.

The

plot

focuses

on

a

series

of

catastrophic

earthquakes

along

the

United

States’

west

coast.

The

last

one

has

a

magnitude

of

10.5

in

Richter

scale.

It

is

actually

a

fun

movie,

you

can

see

a

trailer

in

youtube

(https://www.youtube.com/watch?v=KJmCFfNWAE4).

The

largest

one

occurred

on

the

San

Andreas

fault.

As

we

discussed

in

class,

it

has

a

length

of

1300

km.

The

width

of

this

fault

is

about

15

km.

Let’s

suppose

that

the

moment

magnitude

of

this

event

is

10.5

as

well.

Please

estimate

its

average

slip?

(using

the

rigidity

value

given

in

problem

1).