A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 5.9 102 µm. Find this earthquake's magnitude on the Richter scale.
To find the earthquake's magnitude on the Richter scale, you can make use of the formula:
M = log(A/T)
where:
M = magnitude on the Richter scale
A = maximum amplitude of the earthquake in µm
T = period of the seismograph in seconds
In this case, the maximum amplitude of the earthquake is given as 5.9 x 10^2 µm. However, the period of the seismograph is not provided in the question. The period of a typical seismograph is 1 second, so we can assume T to be 1.
Substituting the given values into the formula, we get:
M = log(5.9 x 10^2 / 1)
M = log(5.9 x 10^2)
Using a calculator, log(5.9 x 10^2) ≈ 2.77
Therefore, the earthquake's magnitude on the Richter scale is approximately 2.77.
To find the earthquake's magnitude on the Richter scale, you can use the formula:
M = log10(A) + 3log10(D) - 2.92
Where:
M is the magnitude on the Richter scale,
A is the maximum amplitude recorded by the seismograph in micrometers (µm),
D is the distance from the epicenter to the seismograph in kilometers.
In this case, the maximum amplitude (A) is given as 5.9 x 10^2 µm and the distance (D) from the epicenter to the seismograph is 300 km.
Substituting these values into the formula, we get:
M = log10(5.9 x 10^2) + 3log10(300) - 2.92
Now, let's calculate it step by step:
First, calculate log10(5.9 x 10^2):
log10(5.9 x 10^2) = log10(5.9) + log10(10^2)
= log10(5.9) + 2 (since log10(10^2) = 2)
= 0.770 + 2
= 2.770
Next, calculate 3log10(300):
3log10(300) = 3(log10(3) + log10(10^2))
= 3(log10(3) + 2)
= 3(0.477 + 2)
= 3(2.477)
= 7.431
Now, substitute the values back into the formula:
M = 2.770 + 7.431 - 2.92
M ≈ 7.281
Therefore, the magnitude of this earthquake on the Richter scale is approximately 7.281.