Geography Reference
In-Depth Information
The
b
-Value Method: Example Application of the Built-In
Software for Data Analysis
Besides being a way to determine statistically significant magnitude range
(the arrows in Figure 12 A, b), the magnitude-recurrence relationship
lg N = lg
A
m
- b (M
s
-М
o
)
characterizes the seismic process, in terms of the seismic
activity (
A
) normalized to a certain magnitude
M
s
(converted from the energy
scale
K
) and the slope of the recurrence curve (
b
). Application of the algorithm
for visualization of zonal maps can be illustrated with
b
-value cartograms.
Mapping
b
values may be problematic because the seismic process is
irregular within elementary cells and, if there are few earthquakes in a cell,
they may fail to represent the whole range of the magnitude-recurrence
relationships used for estimating the
b
value. Furthermore, the estimation
accuracy depends on the number of events in a sliding window, as well as on
the statistical uniformity of the data sample, i.e. the window should cover a
spatial area of the same geodynamic type and correspond to a time interval
free from critical changes in seismic parameters [38]. That is why the method
should be applied with great care, investigating whenever possible the
distribution of seismicity in each cell and, checking whether the data sample is
representative.
The
b
cartograms for the BRZ (Figure 12 A) have been generated on a
dense grid (0.40.6º), at every 8 years. Such high resolution is possible due to
the use of the complete BAIK catalog (which includes all
M
≥ 1.5 events) for
the 1987-2003 interval and has an acceptable uncertainty:
σ
= 0.08 (see legend
on the right in Figure 12 A, a).
The maps of isolines in Figure 12 A,
a
show a minor difference in average
b
values between the first and second time intervals, within one accuracy
grade according to the color scale (0.90-1.05 and 1.05-1.20). The cartograms
show the boundary of a considerably lower data density passing along 109ºE
between the southwestern and northeastern BRZ.
Reliable definition of each value requires about 100 or more
representative earthquakes of different energies [39]. We apply the concept of
a confidence interval to obtain a statistically exact definition of a required data
sample size and to allow for its influence on the accuracy of the estimated
parameter.
In practical applications, rather exact confidence intervals for selective
estimation (of
b
in this case) can be obtained based on the Moivre-Laplace
theorem [40] used in the probability theory, according to which the 3%
accuracy can be provided if the data sample has the size (
n
) given by:
