Epicenter finding seismology | PDF - Free Printable

It looks like you've uploaded a seismology problem involving the interpretation of seismographs from three different cities—Balboa, Boulder, and Mexico City—to determine the distance to an earthquake epicenter. The data provided includes:

- P-wave arrival times
- S-wave arrival times
- Difference between S and P wave arrivals (S-P time)
- Distance to the epicenter (from a graph or chart not shown here)

You're asked to solve this step-by-step using the given information.

Let’s go through the stepwise procedure as outlined in your image and solve it carefully.

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🌍 Step 1: Understand What We’re Doing

We are analyzing seismograms from three seismic stations (Balboa, Boulder, Mexico City). From these, we can determine:
- When the P-waves (primary waves) arrived
- When the S-waves (secondary waves) arrived
- The time difference between them (S-P interval)
- Use that to find the distance from each station to the earthquake epicenter

This is based on the fact that P-waves travel faster than S-waves, so the longer the delay between their arrivals, the farther away the earthquake was.

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🔍 Step 2: Analyze the Data Table

| City | P-wave arrival (min) | S-wave arrival (min) | Difference (S-P) (min) | Distance to Epicenter (km) |
|--------------|------------------------|------------------------|--------------------------|-------------------------------|
| Balboa | 19 | 23.8 | 4.8 | 3200 |
| Boulder | 16 | 18.4 | 2.4 | 1700 |
| Mexico City | 17.4 | 20.9 | 3.5 | 2400 |

> ✔ The table already gives us the S-P differences and the corresponding distances to the epicenter.

But wait — there's a note at the bottom:

> "Now Distance to epicenter is find from the graph on page 3."
> "As in step 3 they said 4 min 50 seconds for Balboa but you result it 4 min 48 seconds."

So there may be a slight discrepancy in timing. Let's check what's going on.

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🔎 Step 3: Verify the S-P Time Differences

Let’s calculate the S-P time difference for each city:

#### 1. Balboa:
- P-wave: 19.0 min
- S-wave: 23.8 min
- S-P = 23.8 - 19.0 = 4.8 minutes → ✔️ Matches table

But the note says: *"they said 4 min 50 seconds"*, which is 4 + 50/60 = 4.833 minutes, while we have 4.8 min (i.e., 4 min 48 sec).

So:
- 4 min 48 sec = 4.8 min
- 4 min 50 sec = 4.833 min

That’s a small difference — likely due to reading the graph slightly differently. But our calculation is correct based on the table values.

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🧭 Step 4: Use S-P Time to Find Distance

The S-P time difference is used with a travel-time curve graph (which we don’t have here, but it's standard in seismology) to determine distance.

For example:
- An S-P time of 4.8 minutes corresponds to about 3200 km — which matches the table.
- 2.4 min → ~1700 km
- 3.5 min → ~2400 km

These distances are consistent with typical travel-time curves.

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📍 Step 5: Triangulate the Epicenter

To find the exact location of the earthquake, we use triangulation:
- Draw circles around each city with radius equal to the distance to the epicenter.
- The point where all three circles intersect is the epicenter.

Since we have:
- Balboa: 3200 km
- Boulder: 1700 km
- Mexico City: 2400 km

We would plot these on a map and find the intersection point.

However, since no map is provided, we can only conclude:

> The earthquake occurred approximately 3200 km from Balboa, 1700 km from Boulder, and 2400 km from Mexico City.

Based on real geography:
- Boulder is in Colorado (USA)
- Mexico City is in Mexico
- Balboa is near Panama (Central America)

So the epicenter is likely somewhere in the Pacific Ocean, possibly near the coast of Central America or southern Mexico, depending on exact coordinates.

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✔ Final Answer & Explanation

Solution Summary:

1. Calculate S-P time for each station:
- Balboa: 23.8 – 19.0 = 4.8 min
- Boulder: 18.4 – 16.0 = 2.4 min
- Mexico City: 20.9 – 17.4 = 3.5 min

2. Use S-P time to find distance using a travel-time graph:
- 4.8 min → ~3200 km
- 2.4 min → ~1700 km
- 3.5 min → ~2400 km

3. Triangulate using these distances from three known locations.

4. Note: There's a minor discrepancy in the Balboa timing — the text mentions 4 min 50 sec (≈4.83 min), but calculated value is 4 min 48 sec (4.8 min). This could be due to rounding or reading error on the graph.

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📌 Conclusion

The earthquake’s epicenter is located:
- 3200 km from Balboa (Panama)
- 1700 km from Boulder (Colorado)
- 2400 km from Mexico City

Using triangulation, the actual location can be pinpointed on a map.

If you have access to the travel-time graph (page 3), you can verify the distances more precisely.

Let me know if you'd like help drawing the triangulation or interpreting the graph!