A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of
4.9 * 10^2 µm. Find this earthquake's magnitude.
To find the earthquake's magnitude, we can use the formula:
Magnitude = log10(A) + 3 * log10(D) - 2.92
Where:
- A is the maximum amplitude recorded by the seismograph (in micrometers)
- D is the distance between the seismograph and the epicenter (in kilometers)
In this case, the maximum amplitude (A) is given as 4.9 * 10^2 µm and the distance (D) is 300 km.
Now, let's substitute the given values into the formula:
Magnitude = log10(4.9 * 10^2) + 3 * log10(300) - 2.92
To calculate this, we'll first evaluate the logarithmic terms and then substitute the results into the formula:
Magnitude = log10(490) + 3 * log10(300) - 2.92
Magnitude = 2.6902 + 3 * 2.4771 - 2.92
Magnitude = 2.6902 + 7.4313 - 2.92
Magnitude = 7.2015
Therefore, the earthquake's magnitude is approximately 7.2.