Infer the hidden earthquake location from P- and S-wave arrival times at several stations,
then verify the result by recomputing travel distances and timing consistency.
Core idea:
S−P time grows with distance because P waves travel faster than S waves.
distance = (S−P) / (1/vS − 1/vP)
with three or more stations, distance circles can localize the epicenter.
1
Answer
The inferred earthquake for the current station data
The answer is based on four stations, each contributing a distance estimate from its S−P gap.
2
Reason
How the page turns arrival times into an epicenter
Timing → distance
If the earthquake is at distance d, then the P and S arrivals occur at
tP = t0 + d/vP and
tS = t0 + d/vS.
Subtracting removes the unknown origin time.
d = (tS − tP) / (1/vS − 1/vP)
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Several stations → one location
Each station defines a circle of possible epicenters. The earthquake should lie near the intersection
of those circles. With noise, the circles usually do not meet perfectly, so the page finds the best fit.
distance circles and best-fit pointhidden event used to synthesize the data
Seismogram-style station traces
These traces are synthetic. They mark the observed P and S arrivals that the solver uses.
P arrivalS arrival
Origin time from P arrivals
Once the epicenter is estimated, each station gives an origin-time estimate
t0 ≈ tP − d/vP.
A consistent solution should make those agree closely.
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3
Check
Independent consistency tests on the inferred event
Distance formula
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Origin-time agreement
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Travel-time replay
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Recovery against hidden truth
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Audit table
Station
Observed P
Observed S
Distance from S−P
Distance from inferred epicenter
Origin time from station
The check layer uses the observed arrivals, recomputed radii, and independently recovered origin times.
It also compares the inferred epicenter with the hidden event that generated the synthetic station data.