It is now known that the energy radiated by an earthquake is concentrated over a
ID: 287823 • Letter: I
Question
It is now known that the energy radiated by an earthquake is concentrated over a different bandwidth and at higher frequencies. With the worldwide deployment of modern digitally recording seismograph with broad bandwidth response, computerized methods are now able to make accurate and explicit estimates of energy on a routine basis for all major earthquakes. A magnitude based on energy radiated by an earthquake, , can now be defined as
Where E is the radiated seismic energy measured in Joules, and is the magnitudes computed from high frequency seismic data, it is a measure of seismic potential for damage, and has no units.”*
Answer the following questions by showing all of your work:
Solve the above formula for E.
Using the formula you derived in (1) to calculate how much more radiated seismic energy is released for each 1 magnitude on the earthquake scale.
Compare the 1989 San Francisco, US earthquake that had 7.1 magnitude to that of the 2003 Bam, Iran earthquake, which had 6.3 magnitude.
Use the internet to find the death tolls for the two earthquakes mentioned in question (3).
Discuss the factors that determine the devastation caused by an earthquake.
https://earthquake.usgs.gov/learn/topics/measure.php“
Explanation / Answer
M = (2/3) log(E / 10^4.4)
For each unit increase in magnitude M, the amplitude increases by a factor of 10.
From above formula: Energy is proportional to 10(1.5M).
Consider the energy (E1) from a magnitude M and from (E2) from magnitude M+1
E2/E1 = (10(1.5M + 1.5))/( 101.5M)
E2/E1 = 101.5 = 32
Thus, for each unit increase in magnitude, the energy increases by a factor of 32.
In 1989, magnitude = 7.1
-------------------------
7.1 = (2/3) log(E / 10^4.4)
10.59 = log(E / 10^4.4)
10^10.59 = 10^log(E / 10^4.4)
10^10.59 = (E / 10^4.4)
10^10.59* 10^4.4 = E
In 2003, magnitude = 6.3
-------------------------
6.3= (2/3) log(E / 10^4.4)
9.4= log(E / 10^4.4)
10^9.4 = 10^log(E / 10^4.4)
10^9.4 = (E / 10^4.4)
10^9.4 * 10^4.4 = E
Therefore, the ratio of the energies of the two
quakes is:
ratio =
= (10^10.59 * 10^4.4) / (10^9.4 * 10^4.4)
= 10^10.59 / 10^9.4
= 10^1.19
= 15.488
Therefore, the 1989 earthquake was 15.488 times
more powerful than the 2003 quake.
On 17 October 1989, San Francisco was rocked by a powerful earthquake at just after 5pm local time. It lasted just 15 seconds, but left 63 people dead - most of them killed when a two-tier freeway collapsed - and there was massive damage to buildings all over the city.
The 2003 Bam earthquake struck the Kerman province of southeastern Iran at 01:56 UTC (5:26 AM Iran Standard Time) on December 26. The shock had a moment magnitude of 6.6 and a maximum Mercalli intensity of IX (Violent). The earthquake was particularly destructive in Bam, with the death toll amounting to at least 26,271 people and injuring up to 30,000.
There are several factors that determine just how destructive an earthquake can be:
Location: This one is kind of obvious—an earthquake that hits in a populated area is more likely to do damage than one that hits an unpopulated area or the middle of the ocean.
Magnitude: Scientists assign a number to represent the amount of seismic energy released by an earthquake. The Richter magnitude scale, as it is known, is logarithmic, so each step up represents an increase in energy of a factor of 10. The more energy in an earthquake, the more destructive it can be.
Depth: Earthquakes can happen anywhere from at the surface to 700 kilometers below. In general, deeper earthquakes are less damaging because their energy dissipates before it reaches the surface. The recent New Zealand earthquake is thought to have occurred at a more shallow depth than the one last year.
Distance from the epicenter: The epicenter is the point at the surface right above where the earthquake originates and is usually the place where the earthquake’s intensity is the greatest.
Local geologic conditions: The nature of the ground at the surface of an earthquake can have a profound influence on the level of damage. Loose, sandy, soggy soil, like in Mexico City, can liquefy if the shaking is strong and long enough, for example. That doesn’t bode well for any structures on the surface.
Secondary effects: Earthquakes can trigger landslides, fires, floods or tsunamis. It was not the 2004 Sumatran-Andaman earthquake that caused so much damage in 2004 but the Indian Ocean tsunami it triggered. Nearly a quarter of a million people in 14 countries were killed when coastal communities were inundated by the water.
Architecture: Even the strongest buildings may not survive a bad earthquake, but architecture plays a huge role in what and who survives a quake. The January 2010 Haiti earthquake, for example, was made far worse by poor construction, weak cement and unenforced building codes.
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