principles and applications of microearthquake networks

6.4. Estimation of Earthquake Magnitude 153
the simultaneous inversion without having to solve a very large set of
equations. Furthermore, explosion data also can be included in the inversion.
Since the velocity can be different from block to block in the simultaneous
inversion problem, three-dimensional ray tracing must be used in
computing travel times and derivatives in step 2. The problem of ray
tracing in a heterogeneous medium has been discussed in Chapter 4. For
an application of simultaneous inversion using data from a microearthquake
network, readers may refer, for example, to Lee et a/. (1982a).
6.4. Estimation of Earthquake Magnitude
Intensity of effects and amplitudes of ground motion recorded by seismographs
show that there are large variations in the size of earthquakes.
Earthquake intensity is a measure of effects (e.g., broken windows, collapsed
houses, etc.) produced by an earthquake at a particular point of
observation. Thus, the effects of an earthquake may be collapsed houses
at city A, broken windows at city B, and almost nothing damaged at city
C. Unfortunately, intensity observations are subject to uncertainties of
personal estimates and are limited by circumstances of reported effects.
Therefore, it is desirable to have a scale for rating earthquakes in terms of
their energy, independent of the effects produced in populated areas.
In response to this practical need, C. F. Richter proposed a magnitude
scale in 1935 based solely on amplitudes of ground motion recorded by
seismographs. Richter’s procedure to estimate earthquake magnitude followed
a practice by Wadati (193 1) in which the calculated ground amplitudes
in microns for various Japanese stations were plotted against their
epicentral distances. Wadati employed the resulting amplitude-vsdistance
curves to distinguish between deep and shallow earthquakes, to
calculate the absorption coefficient for surface waves, and to make a
rough comparison between the sizes of several strong earthquakes. Realizing
that no great precision is needed, Richter (1935) took several bold
steps to make the estimation of earthquake magnitude simple and easy to
carry out. Consequently, Richter’s magnitude scale has been widely accepted,
and quantification of earthquakes has become an active research
topic in seismology.
6.4.1. Local Magnitude for Southern California Earthquakes
The Richter magnitude scale was originally devised for local earthquakes
in southern California. Richter recognized that these earth-