# Seismogram

A seismogram is the graphical output of a seismograph. Figure 1 shows a typical example of a seismogram:

Figure 1: Seismogram

In the graph the x-axis is time, while the y-axis measures the amplitude of the seismic wave. The first small disturbance is due to the fast P-waves. The S-waves travel at a different (lower) velocity and therefore arrive later at the seismic station. The arrival of the S-wave is marked by the first big disturbance in the seismogram (big compared to the signal noise).

### Distance from the epicenter

Knowing the propagation velocity (v) of the S-wave, the time delay between P- and S-waves (t) can be used to calculate the distance from the earthquake epicenter to the location of the seismograph (x). This is simply given by

Since the seismograph is sensitive to movements in all directions, the seismogram only gives information on the absolute value of the distance. This means that the earthquake epicenter can be located anywhere in a radius x from the seismic station. At least two more seismographs are required to determine the exact location of the earthquake.

### Magnitude of the earthquake

The magnitude of the earthquake in the Richter scale can be calculated using the graph in Figure 2. Here, the scale on the left represents the distance from the epicenter in km (calculated as explained above), the middle scale is the magnitude of the earthquake in the Richter scale (the quantity that we want to calculate) and the one on the right represents the highest amplitude of the first S-wave, in mm. The latter can be measured directly on the seismogram.

If you link the values extracted from the seismogram for the left and the right scale with a straight line, the intersect with the middle scale is the magnitude of the earthquake according to the Richter scale.

Figure 2: Richter Scale graph for determining the magnitude of an earthquake