APPLICATION OF ONE-WAY VARIANCE ANALYSIS FOR DETECTING SEISMIC
WAVES REFLECTED FROM FREE SURFACE
A.V. Konovalov, A.I. Ivashchenko
Institute of Marine Geology and Geophysics FEB RAS, Yuzhno-Sakhalinsk, Russia
Due to a rare regional network of seismic stations in Sakhalin and Kuril Islands, the
distribution of earthquake source depth is not well investigated. Here we present the method of
independent source depth determination based on detecting seismic waves reflected from the free
surface near the epicenter, using data from the local network of digital seismic stations DAT,
having a maximum of frequency characteristic near 1 Hz.
We consider the point source approximation. In this case the P and pP waves are
theoretically coherent. It means that their amplitude spectra differ by a scalar factor only and
their phase spectra by a linear function of the frequency [1]. Let's consider an initial part of the
P-wave displacement records obtained at several closely spaced seismic stations. We assume that
the crust structure under all stations differs sufficiently, but they are still located so close to each
other that a style of interference between P and pP waves is very similar. These model properties
of radiated signals, in terms of the general linear model, allow applying analysis of variance in a
one-way classification for detecting arrivals of seismic pP- waves reflected from the free surface.
The log spectrum of displacement observed at i-th record (station) adjusted for the source
time function and the instrumental response function can be presented as
y i   f     f    i   f  , where f – frequency,
and the corresponding discrete FFT of log spectrum in time domain has a form
y i  t k    t k    i  t k  ,
(1)
where y i  t k  – complex time series,  t k  – signal produced by interferention of direct P and
reflected pP waves,  i  t k  – noise, caused by reverberation in the crust beneath the station.
Errors in model (1) are assumed to be identically and independently distributed normal with
mean zero and covariance cov  i  t k   j  t k    2 t k  ij .
Let's test a simple hypothesis
H 1 :  t k   0 ,
imposing M (odd) restrictions, where ( M  1) / 2  t / dt , t – error bandwidth, dt – sampling
interval. Designating

S1 t k  
( M 1) / 2

  y t 
N
j   ( M 1) / 2 i 1
i 
k j
2
; S 2 t k   N
( M 1) / 2
  y t 
N
j   ( M 1) / 2 i 1
i 
k j
2
,
(2)
where N – total number of records (stations). Then, the equation
S 2 t k 
(3)
F t k   N  1
S1 t k   S 2 t k 
can be used for testing our hypothesis with F-statistic [2]. The hypothesis H1 is rejected with a
confidence level , if
F t k   F1 2M , 2M N  1 ,
where F1-(2M, 2M(N-1)) – central F-distribution with (2M, 2M(N-1)) degrees of freedom.
The method gives a reliable quantitative criterion for estimation of the time delay
between P and pP wave arrivals.
As an example of application of the given method the Kuril earthquake of magnitude
MLH=5.6 occurred on 25.07.2002 was taken. According to the operative catalogue by SEMSD
GS RAS, the time delay between P and pP wave arrivals is 12.2 sec, measured manually from
records of SKM and SKD instruments at YSS (Yuzhno-Sakhalinsk) seismic station. The
epicentral distance is 517 km.
Fig. 1 illustrates original records of vertical component of velocity measured at several
portable digital seismic stations DAT, located over the southern part of Sakhalin Island. The time
window for processing is 30 sec. The frequency interval used for investigation of log spectrum is
(0.1, 1) Hz. For applying F-statistic, M was taken equal to 7, which corresponds to the bandwidth
equal to 0.3 sec.
In Fig. 2 one can clearly recognize a large peak above the 99.9 % confidence level and
corresponding to the time delay between P and pP arrivals equal to 12.4  0.3 sec.
Similar results were also obtained for a number of other Kuril earthquakes with source
depth within the interval of 30-50 km. This suggests encouraging prospects in further applying
the presented approach for more reliable detecting arrivals of seismic waves reflected from the
free surface near the epicenter and therefore for more reliable source depth determination from
seismic records.
KRS
LSN
pP
pP
P
P
t, sec
0
5
10
15
20
25
30
35
40
45
50
55
t, sec
60
0
5
10
15
20
25
OJD
30
35
40
45
50
55
60
ZGR
pP
pP
P
P
t, sec
0
5
10
15
20
25
30
35
40
45
50
55
t, sec
60
0
5
10
15
20
25
30
35
40
45
50
55
60
Fig.1. (expected time arrivals of P and pP waves here are specified; the names of stations in
abbreviated form are in right top corner
S1 (t)
S2 (t)
F99.9 (14, 42)
F(t)
12.44 sec
80
60
40
20
t, sec
0
5
10
15
20
25
30
0
t, sec
0
5
10
15
20
25
30
Fig.2. On the left - function (2), on the right - F-statistic (3)
References
1. Kemerait R.C., Sutton A.F. Multidimensional approach to seismic depth estimation //
Seismic signal analysis and discrimination. Moscow, Peace, 1986. P.137-157.
2. Shumway R.H., Baumgardt D.R., Der Z.A. A cepstral F statistic for detecting delay-fired
seismic signals // Technometrics. 1998. 40. P.100-110.