principles and applications of microearthquake networks

148 6. Methods of Data Analysis
should ease the burden of routine manipulations and allow the human
analysts to concentrate on verifications.
6.3. Simultaneous Inversion for Hypocenter Parameters
and Velocity Structure
The principal data measured from seismograms collected by a microearthquake
network are first P-arrival times and directions of first
P-motion from local earthquakes. These data contain information on the
tectonics and structure of the earth underneath the network. In this section,
we show how to extract information about the velocity structure
from the arrival times. In addition to the hypocenter parameters (origin
time, epicenter coordinates, and focal depth), each earthquake contributes
independent observations to the potential data set for determining the
earth’s velocity structure, provided that the total number of observations
exceeds four.
Crosson (1976a,b) developed a nonlinear least squares modeling procedure
to estimate simultaneously the hypocenter parameters, station corrections,
and parameters for a layered velocity model by using arrival
times from local earthquakes. This approach has been applied to several
seismic networks. Readers may refer to works, for example, by Steppe
and Crosson (1978), Crosson and Koyanagi (1979), Hileman (1979), Horie
and Shibuya (1979), and Sat0 (1979).
Independently, Aki and Lee (1976) developed a similar method for a
general three-dimensional velocity model. Because lateral velocity variations
are known to exist in the earth’s crust (e.g., across the San Andreas
fault as discussed by Engdahl and Lee, 1976), the method developed by
Aki and Lee and extended by Lee et af. (1982a) is more general than
Crosson’s and will be treated here.
6.3.1.
Formulation of the Simultaneous Inversion Problem
The problem of simultaneous inversion for hypocenter parameters and
velocity structure may be formulated by generalizing Geiger’s method of
determining hypocenter parameters. As with the earthquake location
problem, arrival times of any seismic phases can be used in the simultaneous
inversion. However, the following discussion will be restricted to
first P-arrival times, although generalization to include other seismic arrivals
is straightforward.
We are given a set of first P-arrival times observed at rn stations from a
set of n earthquakes, and we wish to determine the hypocenter parameters