A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 4.9 * 10^2 µm. Find this earthquake's magnitude.
is the answer 6.7 which rounded to nearest on would be 7? Please confirm this answer for me make sure i have it right.
Yes
To find the earthquake's magnitude, we need to use the relationship between the maximum amplitude of seismic waves recorded by a seismograph and the earthquake magnitude. The formula for calculating magnitude using the maximum amplitude is:
Magnitude = log10(A) + 3 * log10(D) - 2.92
Where:
A is the maximum amplitude in micrometers (µm) = 4.9 * 10^2 µm
D is the distance to the epicenter in kilometers (km) = 300 km
Now, let's substitute these values into the formula:
Magnitude = log10(4.9 * 10^2) + 3 * log10(300) - 2.92
To calculate this using a calculator, follow these steps:
1. Calculate log10(4.9 * 10^2)
- For this, enter 4.9, hit the multiplication sign (*), then enter 10, hit the raised to (power) sign (^), and finally enter 2.
- This should give you 2.69019608 as the result.
2. Calculate log10(300)
- Enter 300 and then hit the log10 button.
- This should give you 2.47712125 as the result.
3. Multiply 3 * log10(300)
- Enter 3, hit the multiplication sign (*), and then enter 2.47712125.
- This should give you 7.43136375 as the result.
4. Add the results of steps 1 and 3
- Add 2.69019608 and 7.43136375 together.
- This should give you 10.12155983 as the result.
5. Finally, subtract 2.92 from the result of step 4
- Enter 10.12155983 and then subtract 2.92 from it.
- This should give you 7.20155983 as the final result.
Therefore, the magnitude of the earthquake is approximately 7.2.