principles and applications of microearthquake networks

138 6. Methotls of Data Analysis
tee reaching a global minimum by an iterative procedure, and readers are
referred to Section 5.4 and the references cited therein. Iterations usually
are terminated if the adjustments or the root-mean-square value of the
residuals falls below some prescribed value, or if the allowed maximum
number of iterations is exceeded.
There are errors and sometimes blunders in reading arrival times and
station coordinates. The least squares method is appropriate if the errors
are independent and random. Otherwise, it will give disproportional
weight to data with large errors and distort the solution so that errors are
spread among the stations. Consequently, low residuals do not necessarily
imply that the earthquake location is good. It must be emphasized that the
quality of an earthquake location depends on the quality of the input data.
No mathematical manipulation can substitute for careful preparation of
the input data. It is quite easy to write an earthquake location program for
a digital computer using Geiger’s method. However, it is difficult to validate
the correctness of the program code. Furthermore, it is not easy to
write an earthquake location program that will handle errors in the input
data properly and let the users know if they are in trouble. The mechanics
of locating earthquakes have been discussed, for example, by Buland
(1976), and problems of implementing a general-purpose earthquake location
program for microearthquake networks are discussed, for example,
by Lee e? al. (1981).
In this section, we have not treated the method for joint hypocenter
determination and related techniques. These techniques are generalizations
of Geiger’s method to include station corrections for travel time
as additional parameters to be determined from a group of earthquakes.
Readers may refer to works, for example, by Douglas (1967), Dewey
(1971), and Bolt e? a/. (1978). Also, we have not dealt with the problem of
using more complicated velocity models for microearthquake location. In
principle, seismic ray tracing in a heterogeneous medium (see Chapter 4)
can be applied in a straightforward manner (e.g., Engdahl and Lee, 1976),
but at present the computation is too expensive for routine work. Recently,
Thurber and Ellsworth (1980) introduced a method to compute
rapidly the minimum time ray path in a heterogeneous medium. They first
constructed a one-dimensional, laterally average velocity model from a
given three-dimensional velocity structure, and then determined the minimum
time ray path by the standard technique for a horizontally layered
velocity model (see Section 4.4.4.). In addition, many advances in seismic
ray tracing and in inversion for velocity structure have been made in
explosion seismology. Numerous publications have appeared, and readers
may refer to works, for example, by McMechan (1976), Mooney and
Prodehl (1978), Cerveny and Hron (1980), and McMechan and Mooney