a seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude 5.3x10^2 um. Find this earthquake's magnitude. Round this answer to one decimal place.
so, what's the formula relating distance to amplitude?
To find the earthquake's magnitude, you can use the formula:
Magnitude = log(A) + 3log(R) - 2.92
Where:
A is the maximum amplitude of the seismograph (in micrometers),
R is the distance from the seismograph to the epicenter (in kilometers), and
log represents the base-10 logarithm.
Let's substitute the given values into the formula:
A = 5.3x10^2 um
R = 300 km
Magnitude = log(5.3x10^2) + 3log(300) - 2.92
To calculate the logarithms, you can use a scientific calculator or an online calculator. Calculating the log(5.3x10^2) and log(300) gives:
Magnitude = 2.72 + 3(2.48) - 2.92
Magnitude = 2.72 + 7.44 - 2.92
Magnitude = 7.24
Rounding this answer to one decimal place, the magnitude of this earthquake is approximately 7.2.
To find the magnitude of an earthquake based on the amplitude recorded by a seismograph, you can use the Richter scale formula. The formula is:
M = log(A/T)
Where:
M = Magnitude of the earthquake
A = Amplitude of the earthquake
T = Period of oscillation (time in seconds)
In this case, you have the amplitude of the earthquake recorded by the seismograph (A = 5.3x10^2 um). But you don't have the period of oscillation (T). To calculate the magnitude, we need to determine the period of oscillation.
The period of oscillation can be calculated using the distance between the epicenter of the earthquake and the seismograph station. The formula to calculate the period is:
T = 10^(0.67 + 0.025R)
Where:
T = Period of oscillation (in seconds)
R = Distance between the epicenter and the seismograph (in kilometers)
In this case, the distance between the epicenter and the seismograph is given as 300 km. Plug this value into the formula to calculate the period of oscillation:
T = 10^(0.67 + 0.025 * 300)
Calculate the value of T using a calculator:
T ≈ 10^(0.67 + 7.5)
T ≈ 10^(8.17)
T ≈ 19754 seconds
Now that we have the period of oscillation (T) and the amplitude (A), we can use the Richter scale formula to calculate the magnitude (M):
M = log(A/T)
M = log(5.3x10^2 um / 19754 s)
To simplify this calculation, convert the amplitude to meters by dividing it by 10^6:
M = log(5.3x10^2 * 10^-6 m / 19754 s)
Simplify further by canceling out the seconds in the denominator:
M = log(5.3x10^-4 m)
Now, use a calculator to find the logarithm:
M ≈ log(5.3x10^-4)
M ≈ -3.276
Round this answer to one decimal place:
M ≈ -3.3
Therefore, the magnitude of the earthquake is approximately -3.3.