The Point Source parameters

The simplest description of the seismic source is the concept of a point source (see Fig. 1). Even though in contrast with common physical and geological concepts the point source is still used for certain purposes, such as earthquake geographics or earthquake statistics. The parameters for the point source essentially are:

Further parameters concern the description of the energy released from the seismic source. A common measure is the magnitude which is obtained from the seismogram applying suitable corrections for the effects of attenuation due to geometrical spreading and absorption. The local magnitude Ml or MWA is obtained from a record on a WOOD ANDERSON seismometer with an eigenperiod of 0.8 s and a damping coefficient of 65% of critical. Ground motion and MWA are related to each other after:

where Umax is the maximum horizontal amplitude of ground motion, Vmax = 2800 is maximum amplification of the WOOD ANDERSON seismometer, s the hypocentral distance expressed in km and k(s) a factor which increases with distance. The values of k(s) or the product k(s) log(s) are given in most seismological textbooks (e. g, Richter, 1958). For small distances (0 < s < 30 km) relation (4.1) can be approximated with

MWA = log (Umax [mm] * Vmax) + 1.4 log10 s[km] + 0.1 (4.2)

The original definition of MWA by Richter was carried out using earthquakes from California (Richter, 1935, 1958). Even though the relations for calculating the local magnitude are applied world wide, one should be aware that they reflect in principle the characteristics of the California earthquake zones[1]. In general the application of the magnitude MWA is limited to hypocentral distances less than 1000 km and focal depths should not exceed values of ca. 20 km. Note that MWA tends to saturate for large earthquakes at a value of approx. MWA = 7.
In the 1940s Gutenberg and Richter extended the local magnitude scale to include more distant and larger earthquakes. They defined the surface wave magnitude MS as

MS = log A + k(s) log (s) + const. (4.3),

where A is the maximum combined horizontal ground motion amplitude for surface waves with a period of 20 sec. Tables with the values of the product k(s) log(s) can again be found, for example, in Richter (1958, pp. 345-347). Depending on the properties of earthquake scaling laws, the surface magnitude saturates at values of approx. MS = 8.2.

For the sake of completeness we mention also the macroseismic scales or intensities as a measure for the quantification of earthquake radiation. The most common macroseimsic scales (Mercalli-Cancani-Sieberg MCS or Medvedev-Karnik-Sponheuer MKS) consist of 12 degrees corresponding to the effects caused by the earthquake at the surface. It is clear that intensities cannot be used directly for the quantification of earthquake energy since a weak event close to the surface may have the same effect as a strong one with the source situated at greater depth.

[1] For instance, the amplitude decay laws used in Richter’s formulae, in some zones produced distance-dependent local magnitudes, which is certainly undesired.