A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 4.3 102µm. Find this earthquake's magnitude.
To find the magnitude of an earthquake, we can use the Richter scale formula. The formula is:
M = log10(A) + 3 * log10(D) - 2.92
Where:
M is the magnitude of the earthquake.
A is the maximum amplitude of the earthquake in µm.
D is the distance from the seismograph to the epicenter of the earthquake in kilometers.
In this case, the maximum amplitude recorded is 4.3 * 10^2 µm, and the distance from the seismograph to the epicenter is 300 km.
Plugging these values into the formula:
M = log10(4.3 * 10^2) + 3 * log10(300) - 2.92
Now let's solve the equation step by step:
1. First, calculate log10(4.3 * 10^2):
log10(4.3 * 10^2) = log10(4.3) + log10(10^2) = log10(4.3) + 2
We can use a calculator or a logarithm table to find log10(4.3).
Assuming log10(4.3) = 0.63, we have:
log10(4.3 * 10^2) = 0.63 + 2 = 2.63
2. Next, calculate log10(300):
Use a calculator or a logarithm table to find log10(300).
Assuming log10(300) = 2.48, we have:
log10(300) = 2.48
3. Now substitute these values back into the original formula:
M = 2.63 + 3 * 2.48 - 2.92
4. Simplify the right side of the equation:
M = 2.63 + 7.44 - 2.92
M = 7.15
Therefore, the magnitude of the earthquake is 7.15.