a seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 5.5 *10^2,find the earthquakes magnitude. round one decimal
To find the earthquake's magnitude, we can use the formula for calculating magnitude based on the amplitude recorded by a seismograph:
Magnitude = log10(Amplitude) + D
Where:
- Amplitude is the maximum amplitude recorded by the seismograph.
- D is the distance correction factor, which depends on the distance between the seismograph and the epicenter of the earthquake.
In this case, the amplitude is given as 5.5 * 10^2, and the seismograph is located 300 km from the epicenter.
First, we need to calculate the distance correction factor (D). The formula for calculating D is:
D = log10(Distance) - 2
Where distance is the distance from the seismograph to the epicenter, measured in kilometers.
Now, let's calculate the distance correction factor (D):
D = log10(300) - 2
D ≈ 2.48 - 2
D ≈ 0.48
Next, we can substitute the values into the magnitude formula:
Magnitude = log10(5.5 * 10^2) + 0.48
To calculate the magnitude, we need to evaluate log10(5.5 * 10^2):
log10(5.5 * 10^2) = log10(5.5) + log10(10^2)
= log10(5.5) + 2 [Using the property log(ax) = x * log(a)]
We can use a scientific calculator or an online calculator to find the value of log10(5.5) ≈ 0.7404.
Now, we can substitute these values into the magnitude formula:
Magnitude = 0.7404 + 0.48
Magnitude ≈ 1.2204
Rounded to one decimal place, the earthquake's magnitude is approximately 1.2.