A semiograph 300km from the epicenter of an earthquake recorded a maxximum amplitude of 5.3x10^2 um. Find this earthquake's magnitude on the Richter scale. (Round your answer to the nearest tenth)
To find the earthquake's magnitude on the Richter scale, we need to use the following formula:
M = log10(A) + 3log10(R) - 2.92
Where:
M is the magnitude on the Richter scale,
A is the maximum amplitude recorded in micrometers (μm),
R is the distance from the epicenter in kilometers.
In this case, we are given:
A = 5.3 x 10^2 μm = 530 μm,
R = 300 km.
Plugging these values into the formula, we get:
M = log10(530) + 3log10(300) - 2.92
Now let's calculate it step by step:
1. Calculate log10(530):
- Use a calculator to find that log10(530) = 2.7243 (rounded to 4 decimal places).
2. Calculate log10(300):
- Use a calculator to find that log10(300) = 2.4771 (rounded to 4 decimal places).
3. Substitute the values into the formula:
M = 2.7243 + 3 * 2.4771 - 2.92
M = 2.7243 + 7.4313 - 2.92
M = 7.2356 (rounded to 4 decimal places).
Therefore, the earthquake's magnitude on the Richter scale is approximately 7.2.