FUNDAMENTALS OF SEISMOLOGY
Exercise – Epicenter Localization, Magnitude an Energy of an Earthquake
Localize the epicenter and calculated the local magnitude (ML) and the energy
release for the earthquake recorded in the three stations showed in Figure 1.
Consider the example presented in Figure 2.
Figure 1. Record of an earthquake taken by different stations
Figure 2. Example to analyze a seismogram
To calculate the distance to the epicenter use the three different methods
presented during the class. For that, taking account the next equation and the
information of Figure 3 and Figure 4.
𝑉𝑝 𝑉𝑠
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (𝑘𝑚) = 𝑉
𝑝 −𝑉𝑠
∗ 𝑇𝑠𝑝 = 𝐶 ∗ 𝑇𝑠𝑝
where:
C: the Omori Shear of the earthquake is 8Km/s.
𝑉𝑝 , 𝑉𝑠 :: velocity of P and S waves
𝑇𝑠𝑝 : difference of time between the arrive of P and S waves (s)
Figure 3. Scale to calculate distance to epicenter
Figure 4. Graphic to calculate distance to epicenter
In order to calculate the local magnitude of the earthquake use the next
equation and the Figure 5.
ML = Log10 A + 2,76Log10 D – 2,48
where:
A: maximum amplitude of the earthquake (mm)
D: distance to the epicenter (km)
Figure 5. Figure to calculate the local magnitude
Using the results, complete the Table 1. and localize the epicenter in the Figure
8.
Table 1. Earthquake information
Station
Time
Time
arrive P arrive S
waves (s) waves (s)
(s)
Distan.
Op. 1
(km)
Distan.
Op. 2
(km)
Distan.
Op. 3
(km)
ML
ML
E
Op. 1
Op. 1
Op. 1
78CF
23VN
36JL
Note: for each case, use the distance most critical to calculate the magnitude
and localize the epicenter
Finally, determine the approximate energy released (in ergs) during the
earthquake using the equivalences presented in the Figure 6 and Figure 7.
Figure 6. Energy released in ergs during an earthquake
Figure 7. Examples of equivalences of the energy released during an
earthquake
Figure 8. Localization of the epicenter