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.
Garhwal Himalayas Earthquake Magnitude 6 Probability: Average Time Between Occurrences
25 years
The average time between successive earthquakes greater than Magnitude 6 in the Garhwal Himalayas is 25 years.
📊 Detailed Solution Explanation
Core Concept: Poisson Process for Earthquakes
Earthquakes are typically modeled using a homogeneous Poisson process for seismic hazard analysis:
- Probability of one event per year:
p = 0.04(orλ = 0.04events/year) - Probability of no event in a year:
1 - p = 0.96 - Events occur randomly and independently
Mean Inter-arrival Time:
T = 1/λ = 1/0.04 = 25 yearsMathematical Derivation
For a Poisson process:
P(k events in time t) = (λt)^k * e^(-λt) / k!- Time to first event follows exponential distribution with mean
1/λ - Average waiting time between events is
1/p = 25years
Geometric Distribution View (discrete yearly):
Probability of first success after (n-1) failures = (1-p)^(n-1) * pExpected value E[n] = 1/p = 25 yearsStep-by-Step Calculation
- Annual risk: 4% chance of >M6 quake
- Expected events/year: 0.04
- Recurrence interval:
1/0.04 = 25 years
Key Seismic Metrics
| Metric | Value |
|---|---|
| Annual Probability | 0.04 |
| Recurrence Interval | 25 years |
| Equivalent Rate (λ) | 0.04/year |
🌄 Why Garhwal Himalayas Faces High Risk
Garhwal region (Uttarakhand, India) lies on the Main Himalayan Thrust, prone to M6+ quakes due to India-Eurasia tectonic collision. Historical data supports ~0.04 probability for M>6 events.
🚨 Implications for Preparedness
- A 25-year average doesn’t mean predictability—quakes can cluster or have long gaps
- Builds resilience through seismic zoning and retrofitting
- Recent studies refine models for better forecasting
