A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 5.8 x10^2 µm. Find this earthquake's magnitude on the Richter scale.
To find the magnitude of an earthquake on the Richter scale, we can use the formula:
Magnitude = log10(A/A₀) + log10(D) + 3
Where:
- A is the maximum amplitude recorded by the seismograph (in micrometers)
- A₀ is a reference amplitude of 1 micrometer
- D is the distance from the earthquake epicenter to the seismograph (in kilometers)
Let's plug in the given values and calculate the magnitude:
A = 5.8 x 10^2 µm
A₀ = 1 µm
D = 300 km
Magnitude = log10(A/A₀) + log10(D) + 3
Magnitude = log10(5.8 x 10^2 µm / 1 µm) + log10(300 km) + 3
Now, let's simplify each term:
Magnitude = log10(5.8 x 10^2) + log10(300) + 3
Using a calculator or logarithm tables, we find:
log10(5.8 x 10^2) = 2.763
log10(300) = 2.477
Magnitude = 2.763 + 2.477 + 3
Magnitude = 8.24
Therefore, this earthquake's magnitude on the Richter scale is approximately 8.24.