A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 5.2 102 µm. Find this earthquake's magnitude on the Richter scale.
To determine the earthquake's magnitude on the Richter scale, we need to use the formula:
M = log10(A/T) + 1.66(D) - 2.0
Where:
M is the magnitude on the Richter scale,
A is the maximum amplitude of ground motion in µm (in this case 5.2 x 10^2 µm),
T is the period of vibrations in seconds (typically 0.8 seconds for earthquakes),
D is the distance from the epicenter in km (in this case 300 km).
Let's calculate the magnitude using this formula:
M = log10(5.2 x 10^2 / 0.8) + 1.66(300) - 2.0
First, divide 5.2 x 10^2 by 0.8:
M = log10(650) + 1.66(300) - 2.0
Next, calculate log10(650) using a calculator or logarithm table:
M ≈ 2.8129 + 1.66(300) - 2.0
Multiply 1.66 by 300:
M ≈ 2.8129 + 498 - 2.0
Add the two numbers:
M ≈ 501.8129 - 2.0
Finally, subtract 2.0 from 501.8129 to find the magnitude:
M ≈ 499.8129
Therefore, the earthquake's magnitude on the Richter scale is approximately 499.8129.