principles and applications of microearthquake networks

140 6. Methods of Data Analysis
purely horizontal motion on a vertical fault FF’, and the arrows represent
the relative movement of the two sides of the fault. Intuition suggests that
material ahead of the arrows is compressed or pushed away from the
source, whereas material behind the arrows is dilated or pulled toward the
source. Consequently, the area surrounding the earthquake focus is divided
into quadrants in which the first motion of P-waves is alternately a
compression or a dilatation as shown in Fig 26. These quadrants are
separated by two orthogonal planes AA’ and FF’, one of which (FF’) is
the fault plane. The other plane (AA’) is perpendicular to the direction of
fault movement and is called the auxiliary plane.
As cited by Honda (1962), T. Shida in 1919 found that the distribution of
compressions and dilatations of the initial motions of P-waves of two
earthquakes in Japan showed very systematic patterns. This led H.
Nakano in 1923 to investigate theoretically the propagation of seismic
waves that are generated by various force systems acting at a point in an
infinite homogeneous elastic medium. Nakano found that a source consisting
of a single couple (i.e., two forces oppositely directed and separated by
a small distance) would send alternate compressions and dilatations into
quadrants separated by two orthogonal planes, just as our intuition suggests
in Fig. 26. Since the P-wave motion along these planes is null, they
are called nodal planes and correspond to the fault plane and the auxiliary
plane described previously. Encouraged by Nakano’s result, P. Byerly in
1926 recognized that if the directions of first motion of P-waves in regions
around the source are known, it is possible to infer the orientation of the
fault and the direction of motion on it. However, the earth is not homogeneous,
and faulting may take place in any direction along a dipping fault
plane. Therefore, it is necessary to trace the observed first motions of
P-waves back to a hypothetical focal sphere (i.e., a small sphere enclosing
the earthquake focus), and to develop techniques to find the two orthogonal
nodal planes which separate quadrants of compressions and dilatations
on the focal sphere.
From the 1920s to the 1950s, many methods for determining fault planes
were developed by seismologists in the United States, Canada, Japan,
Netherlands, and USSR. Notable among them are P. Byerly, J. H.
Hodgson, H. Honda, V. Keilis-Borok, and L. P. G. Koning. Not only are
first motions of P-waves used, but also data from S-waves and surface
waves. Readers are referred to review articles by Stauder (1962) and by
Honda (1962) for details.
6.2.1. P-Wave First Motion Data
For most microearthquake networks, fault-plane solutions of earthquakes
are based on first motions of P-waves. The reason is identical to