## Leonhard Euler

## Earthquakes

| Understanding the Events Depicted in This Graph |

###### Ceyda Toprak

What observations can you make from the graph? What questions arise for you? Please note that the number of casualties resulting from the recent earthquake in Syria and Turkey has exceeded 40,000 as of February 15th.

This graph, originally presented by The New York Times, displays an approximate count of fatalities caused by a powerful 7.8-magnitude earthquake and subsequent 7.5-magnitude aftershock that impacted southern Turkey and northern Syria in the beginning of February. Initially, the estimated death toll surpassed 20,000 (as of February 9th). However, by February 15th, the number of casualties had escalated beyond 40,000.

Upon closely examining the graph provided above, you can address the following four questions:

What observations can you make?

What questions arise for you?

How does this relate to you and your community?

What is happening in this graph?

Reveal

The depicted map illustrates the earthquakes that occurred on February 6 and 7, as well as previous seismic events since 1900. Notably, it does not include the 5.2-magnitude earthquake that struck the same region on February 27. The Anatolian Plate, primarily encompassing Turkey, is responsible for frequent and perilous geological disturbances as it moves along fault lines. This particular region ranks among the most seismically active areas globally, witnessing over 70 earthquakes of magnitude 6.5 or higher since 1900.

By February 24th, the number of casualties resulting from the three earthquakes in Turkey and Syria has surpassed 50,000 individuals.

Here, we provide explanations of mathematical and statistical terms and their relevance to this graph:

BUBBLE TIME SERIES GRAPH

A bubble time series graph is a modified version of a time series graph where a "bubble" is utilized to represent values of multiple variables for each data point. The positioning of the bubble is determined by the values of two variables, one on the horizontal x-axis and the other on the vertical y-axis. Additional variables can be represented through properties such as the diameter and color of the bubble.

In the earthquake graph, the bubble's placement signifies the year of the earthquake and its magnitude. It is worth noting that the magnitude is measured on the Richter scale, which follows a logarithmic scale. The diameter of the bubble corresponds to the estimated number of deaths. It should be mentioned that the graph does not include the 7.5-magnitude earthquake on February 7th and the 5.2-magnitude earthquake on February 27th as they occurred after the graph was created.

LOG (LOGARITHMIC) SCALE

A logarithmic scale, also known as a log scale, is a method of representing numerical data with a wide range of values in a more compact manner compared to a linear scale. In a log scale, all values are converted to their logarithmic equivalents and then plotted on the graph. The logarithm of a number is the exponent to which a base (typically 10 or another specified number) must be raised to obtain the original value. For instance, the logarithm of 100 is 2 because 10 raised to the power of 2 equals 100. On a linear scale, the intervals between the values on the axes are equal, such as 10, 20, 30, and so on. However, on a log scale, the intervals increase exponentially by a factor of 10, such as 10, 100, 1000, and so forth. The log scale can also be expressed as powers of ten, like 1, 2, 3, and so on.

One example of employing a log scale is for representing wave amplitudes of earthquakes. The wave amplitudes are transformed into logarithmic values (known as the Richter scale) and then plotted on a log scale. In the Richter scale, each whole number increment in magnitude corresponds to a tenfold increase in the seismic disturbance's magnitude, with the released energy escalating by approximately 32 times.

In the earthquake graph, the vertical y-axis scale utilizes a log scale to represent wave amplitudes of earthquakes as powers of 10, commencing at 10,000. Alternatively, earthquakes can also be expressed in seismic energy equivalents, such as kilotons of dynamite. For instance, the interval on the graph from log 4 to log 5 (representing 1 kiloton to 32 kilotons) is equal in size to the interval from log 5 to log 6 (representing 32 kilotons to 1 megaton). The log scale compresses the scale to enhance the visibility of variations in earthquake intensity as measured by the Richter scale. Earthquakes positioned higher on the graph are significantly stronger than those located towards the bottom. As of February 2023, there have been three earthquakes in Turkey with magnitudes of 7.8, 7.5, and 5.2.

References

Hessney, Sharon, et al. “What’s Going On in This Graph? | Earthquakes.” The New York Times, 16 Feb. 2023, www.nytimes.com/2023/02/16/learning/whats-going-on-in-this-graph-march-1-2023.html.