Q.4 In any given year, the probability of an earthquake greater than Magnitude 6 occurring in the
Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes
is ____ years.
The probability of a magnitude 6+ earthquake in the Garhwal Himalayas stands at 0.04 per year, making the average recurrence interval 25 years. This calculation relies on seismic hazard modeling using a Poisson process, where events occur independently.
Recurrence Interval Calculation
Seismic events like earthquakes in tectonically active regions such as the Garhwal Himalayas follow a Poisson distribution for rare occurrences. The annual probability p=0.04 equals the rate parameter λ, so the mean inter-event time is T=1λ=10.04=25 years. This return period indicates the expected average gap, though actual intervals vary due to randomness.
Why 25 Years is Correct
A probability of 0.04 means a 4% chance yearly, inverting to 25 years on average aligns with standard seismology formulas for exponential waiting times in Poisson models. Historical data from Himalayan faults supports such estimates for M6+ events, confirming the math without needing complex simulations.
Analysis of Common Options
Multiple-choice questions on this often include distractors; no exact options appear in sources, but typical GATE-style alternatives include:
| Option | Value (Years) | Explanation |
|---|---|---|
| A | 20 | Incorrect; arises from rough 1/0.05=20 approximation, ignoring precise 0.04. |
| B | 25 | Correct; direct inverse 1/0.04=25. |
| C | 50 | Wrong; might confuse with 50-year cumulative probability (~64%) or double the rate. |
| D | 100 | Incorrect; errors from halving probability (0.02) or long-term fault models. |
Seismic Context in Garhwal
The Garhwal region, part of the Himalayan thrust zone, experiences stress buildup leading to periodic M6+ quakes. Understanding this 25-year average aids disaster preparedness, though time-dependent models may adjust forecasts post-event.
