Logarithms

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Team Pick - Logarithms

Have you ever experienced an earthquake? Although I have done many earthquake drills during my time in school, I never experienced a real one. However, my parents and grandparents have told me stories about the 2001 Nisqually earthquake, which left a lasting impact on me. First, my dad was working at a cake decorating factory when it happened. He explained to me how he was startled when he saw the walls shake and quickly ran outside with the boss’s orders. Next, my mom was also working and was even pregnant with my sister at the time when it happened. She quickly got under the table and held onto the table leg for dear life. Finally, my grandma was at home with my cousin, who was only a toddler at the time, when the earthquake started shaking the house. My grandma tightly held my cousin in her arms and went under a table as picture frames and items on the shelves were falling down. Even though that earthquake was a very powerful one and deeply influenced those affected, earthquakes of all sizes are very common; in the Tacoma area, there have been around 750 earthquakes in the last year¹. My mom also told me a story about a time when she experienced a smaller earthquake that shook her house but wasn’t large enough to make startle my mom. This made me wonder: How do earthquakes compare? Although we know the magnitudes of earthquakes, how can we tell the difference in intensities between them?

After doing some research, I soon found out that earthquake magnitudes are calculated exponentially instead of linearly. Because of this, the amount of energy released greatly increases as the magnitude number increases to 10.0, which is the maximum as there has never been an earthquake that has ever reached that high and will never reach that high². However, there have been a few earthquakes that have been close and resulted in detrimental consequences, including the 1960 Valdivia earthquake in Chile that had a 9.5 magnitude. I am curious to see how much the intensity differs from the 2001 Nisqually earthquake that had a 6.8 magnitude which affected my family.

The following formula³ uses the concept of log in base 10 to determine the difference in intensities between earthquakes.

Where:

M_B = the magnitude of Earthquake 2

M_A = the magnitude of Earthquake 1

I_B = the intensity of Earthquake 2

I_A = the intensity of Earthquake 1

The magnitude is simply the size of the earthquake. The number to represent the magnitude is displayed on a logarithmic basis that is measured with a seismogram. Intensity, on the other hand, is more subjective and is not a unit that is measured, but instead, is calculated based on data such as the magnitude, energy released, damage caused, human reports, etc.⁴ In this case, we will use magnitudes as our main data points to determine the difference in intensities.

Using this formula, we can now compare the 1960 Valdivia earthquake and the 2001 Nisqually earthquake.

According to the results, the 1960 Valdivia earthquake in Chile is approximately 501 times more intense than the 2001 Nisqually earthquake. These results surprised me as I did not expect the intensity of the Valdivia earthquake to be as substantial compared to the Nisqually earthquake. However, these results are not exactly out of the ballpark either, since logarithms grow exponentially. As the formula is logarithmic, the magnitude number does not grow in a linear manner and instead grows at a large rate, leading to the difference in intensities between both earthquakes being substantial compared to the difference in their magnitude numbers. Either way, earthquakes are not things to be messed with, and although it may be difficult to understand how catastrophic they can be, we can use our experiences of being in an earthquake to use as a comparison to another earthquake, based on the difference in their intensities.

References

¹Past earthquakes in Tacoma, Washington, USA: 2021 - list, stats and map. (n.d.). Vocano Discovery. Retrieved February 22, 2022, from https://www.volcanodiscovery.com/place/162394/earthquakes/tacoma/archive/2021.html

²Can “MegaQuakes” really happen? Like a magnitude 10 or larger? | U.S. Geological Survey. (n.d.). USGS.Gov | Science for a Changing World. Retrieved February 22, 2022, from https://www.usgs.gov/faqs/can-megaquakes-really-happen-magnitude-10-or-larger#:~:text=MegaQuakes%22%20really%20happen%3F-,Like%20a%20magnitude%2010%20or%20larger%3F,fault%2C%20the%20larger%20the%20earthquake

³Richter Scale Is Logarithmic - Expii. (n.d.). Expii. Retrieved February 22, 2022, from https://www.expii.com/t/richter-scale-4433?type=explanation&id=7325

⁴Hayes, G., & Wald, D. (n.d.). Earthquake Magnitude, Energy Release, and Shaking Intensity | U.S. Geological Survey. USGS.Gov | Science for a Changing World. Retrieved April 5, 2022, from https://www.usgs.gov/programs/earthquake-hazards/earthquake-magnitude-energy-release-and-shaking-intensity#:~:text=The%20Richter%20magnitude%20of%20an,the%20epicenter%20of%20the%20earthquakes.