Using the Gutenberg-Richter recurrence relationship, the mean annual rate of exceedance of earthquake occurrence in a seismic belt is 0.3 per year for an earthquake of magnitude 6.0. The return period for an earthquake of magnitude 6.0 in this belt is ______ years.Correct answer is '3.0 to 3.5'. Can you explain this answer?

Question

Answer

Explanation:

The Gutenberg-Richter recurrence relationship is given by:

log N = a - bM

Where,
N = the number of earthquakes of magnitude M or greater that occur each year
a, b = constants
M = magnitude of earthquake

Step 1: Finding the value of b

The given information states that the mean annual rate of exceedance of earthquake occurrence in a seismic belt is 0.3 per year for an earthquake of magnitude 6.0. We can use this information to find the value of b.

log N = a - bM
log 0.3 = a - b(6)
a = log 0.3 + b(6)

Step 2: Finding the return period

The return period is the average time between earthquakes of a certain magnitude. It is given by:

T = 1 / (c * P)

Where,
T = return period
c = constant
P = probability of earthquake occurrence in one year

We can use the information given in Step 1 to find the value of c.

log N = a - bM
log N = log c - bM
c = 10^(a)

Now, we can find the probability of earthquake occurrence in one year for an earthquake of magnitude 6.0.

log N = a - bM
log N = log c - b(6)
N = c * 10^(-b(6))
P = N / 365

Using the above formula, we get:

P = 0.3 / 365 = 0.00082

Now, we can find the return period for an earthquake of magnitude 6.0.

T = 1 / (c * P)
T = 1 / (10^(log 0.3 + b(6)) * 0.00082)

Solving this equation, we get:

T = 3.0 to 3.5 years (approximately)

Conclusion:

The return period for an earthquake of magnitude 6.0 in this seismic belt is approximately 3.0 to 3.5 years.

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