*6.1.2 Geiger*

connection to NTP servers is interrupted. We assume that P- and S-waves are generated simultaneously and the focal time difference Tps(r = 0) is zero. We

*(a) Tsp and Tsp - SDsp over hypocenter distance); (b) histograms of Tsp and Tsp - SDsp.*

*(a) Tp and Tp - SD reduced to T0 = 0 over log10(r); (b) histograms of T and Tp - SD reduced to T0 = 0 and*

The assumption Tps(r = 0) makes the calculation of the station delays SDps very

SDpsi ¼ MEAN Tpse,i � re,i*=*Vps

In the following we consider amplitude and travel time data (PGV, Tp, Tsp) of

one particular seismic event (earthquake) after the application of station

As before with Tp, we apply the station delays SDps to Tps and find the minimum standard deviation of (Tpsobserved - Tpscalculated) with Vps = 7300 m/s. **Figure 9** shows a) Tps and (Tps -SDps) versus log10(r) and b) the histograms of Tps and (Tps - SDps) reduced to r = 10 km. The STDs derived from the histogram data are σ0 = 0.212 s for Tps and σ1 = 0.183 s for (Tps – SDps). Consequently the error of hypocenter distances r derived from Tps observations is about Vps\*σ1 � 1.3 km.

Vps = (1/Vs – 1/Vp)-1 … ..difference velocity

SDpsi .....P- wave to S-wave station delay at station "i"

Tpse,i ¼ re,i*=*Vps þ SDpsi (8)

(9)

model Tps as follows:

**6. Locating seismic events**

simple:

**46**

**Figure 9.**

**Figure 8.**

*Earthquakes - From Tectonics to Buildings*

*r = 10 km.*

Ludwig Geiger [13] was the first to present a method to locate an earthquake through minimization of the differences between observed and calculated arrival times. The corresponding cost function for P-wave arrival times according our notation Eq. 5 is:

$$\text{cost function} = \text{STD}(\mathbf{T0}\_i) = \text{STD}\left(\mathbf{T p}\_i - \mathbf{S} \mathbf{D} \mathbf{p}\_i - \mathbf{r}\_i / \mathbf{V} \mathbf{p}\right) \tag{11}$$
