VIPSolutionsQuestion 2: ‘During a microearthquake survey in central Turkey, an carthquake was recorded by three seismometers (see below and sce D2L for a PDF version). Using a Wada diagram and the least-squares regression approach from lab 1, calculate the origin time for this event. Using a graphical approach, locate the epicentre relative to the scismometers based on the information in the table that follows. Assume the focus was at the surface and use P- and S-wave velocities of 5.6 and 3.4 kms, respectively. o1 e2 3 [J 50 km [Er —— Tew [we] Sew] EE I EN EE EE ER [Semis | Bw ww] [Sowomeery | | Note: This is problem 5 on page 179 of Fowler (2003).
Question:
Question 2:
‘During a microearthquake survey in central Turkey, an carthquake was recorded by three
seismometers (see below and sce D2L for a PDF version). Using a Wada diagram and
the least-squares regression approach from lab 1, calculate the origin time for this event.
Using a graphical approach, locate the epicentre relative to the scismometers based on the
information in the table that follows. Assume the focus was at the surface and use P- and
S-wave velocities of 5.6 and 3.4 kms, respectively.
o1 e2
3
[J
50 km
[Er ——
Tew [we] Sew]
EE I EN
EE EE ER
[Semis | Bw ww]
[Sowomeery | |
Note: This is problem 5 on page 179 of Fowler (2003).
This is AI generated Response.
Asked by: Harshit
Created at: 2025-09-26 19:38:40
Asked by: Harshit
Created at: 2025-09-26 19:38:40
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# Earthquake Epicenter and Origin Time Calculation
Let's break down the steps to answer the question:
---
## **Step 1: Calculate S-P Times for Each Seismometer**
| Seismometer | S arrival (s) | P arrival (s) | S-P Difference (s) |
|-------------|--------------|--------------|--------------------|
| 1 | 13:20:04.7 | 13:19:58.9 | 5.8 |
| 2 | 13:20:10.8 | 13:20:02.6 | 8.2 |
| 3 | 13:19:57.4 | 13:19:54.5 | 2.9 |
---
## **Step 2: Calculate Epicentral Distances Using S-P Time**
The formula is:
\[
\Delta t = t_S - t_P = d\left(\frac{1}{V_S} - \frac{1}{V_P}\right)
\]
Where:
- \(\Delta t\) = S-P time difference (s)
- \(V_P = 5.6\, \text{km/s}\)
- \(V_S = 3.4\, \text{km/s}\)
- \(d\) = distance from epicenter (km)
Calculate the denominator:
\[
\frac{1}{V_S} - \frac{1}{V_P} = \frac{1}{3.4} - \frac{1}{5.6} \approx .2941 - .1786 = .1155
\]
Now solve for \(d\):
\[
d = \frac{\Delta t}{.1155}
\]
Calculate for each seismometer:
- **Seismometer 1:**
\(d_1 = \frac{5.8}{.1155} \approx 50.2\, \text{km}\)
- **Seismometer 2:**
\(d_2 = \frac{8.2}{.1155} \approx 71.\, \text{km}\)
- **Seismometer 3:**
\(d_3 = \frac{2.9}{.1155} \approx 25.1\, \text{km}\)
---
## **Step 3: Graphically Locate the Epicenter**
1. **Draw circles** around each seismometer on the map, with radii corresponding to the distances above (using the scale bar for reference):
- Seismometer 1: 50.2 km
- Seismometer 2: 71. km
- Seismometer 3: 25.1 km
2. **Epicenter location** is where the three circles intersect.
---
## **Step 4: Calculate Earthquake Origin Time (Using Wadati/Regression)**
P-wave travel time:
\[
t_P = t_ + \frac{d}{V_P}
\]
where \(t_\) is the origin time.
Rearrange for \(t_\):
\[
t_ = t_P - \frac{d}{V_P}
\]
Calculate for each seismometer:
### **Convert P-wave Arrival Times to Seconds Past 13:00:00**
| Seismometer | P arrival (min) | P arrival (s) | Total seconds |
|-------------|-----------------|---------------|--------------|
| 1 | 19 | 58.9 | \(19 \times 60 + 58.9 = 1198.9\) s |
| 2 | 20 | 2.6 | \(20 \times 60 + 2.6 = 1202.6\) s |
| 3 | 19 | 54.5 | \(19 \times 60 + 54.5 = 1194.5\) s |
### **Calculate Origin Time for Each**
\[
t_ = t_P - \frac{d}{V_P}
\]
- **Seismometer 1:**
\(t_ = 1198.9 - \frac{50.2}{5.6} = 1198.9 - 8.96 = 1189.94\) s
- **Seismometer 2:**
\(t_ = 1202.6 - \frac{71.}{5.6} = 1202.6 - 12.68 = 1189.92\) s
- **Seismometer 3:**
\(t_ = 1194.5 - \frac{25.1}{5.6} = 1194.5 - 4.48 = 119.02\) s
**Average Origin Time:**
\[
t_ \approx \frac{1189.94 + 1189.92 + 119.02}{3} = 1189.96\ \text{seconds past 13:00:00}
\]
Which is:
\[
1189.96\ \text{seconds} = 19\ \text{minutes}\ 49.96\ \text{seconds}
\]
So, **Origin Time ≈ 13:19:50**
---
## **Summary Table**
| Seismometer | S-P (s) | Distance (km) | P Arrival (s) | Origin Time (s) |
|-------------|---------|---------------|---------------|-----------------|
| 1 | 5.8 | 50.2 | 1198.9 | 1189.94 |
| 2 | 8.2 | 71. | 1202.6 | 1189.92 |
| 3 | 2.9 | 25.1 | 1194.5 | 119.02 |
---
## **Final Answers**
- **Epicenter Location:** Use a compass to draw circles with radii 50.2 km, 71. km, and 25.1 km around seismometers 1, 2, and 3, respectively. The intersection is the epicenter.
- **Origin Time:** **13:19:50**
---
**If you want a Wadati diagram or further regression analysis, let me know!**
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