al,1998).
The Fanshi-Huai′an-Taibus Qi profilestrikes NNE, in southwest it starts from Fanshicounty of Shanxi Province, through Yangyuan,
Huai′an and Zhangbei of Hebei Province, andnortheastward ends to Taibus Qi of Inner Mongolia,
totaling 302 km long. Figure 1 displays
the map of profile position and seismic distribution
of the studied area. From south to north the
profile crosses through the NE-striking Shanxi
fault zone (Hunyuan, Datong), the WNW striking
Zhangjiakou-Bohai fault zone (Yangyuan,
Huai′an), Inner Mongolia axis, and EW striking
Zhangbei-Chongli fault zone which is near
Zhangbei seismic region (ZHU et al, 1999).
2 Method and data processing
Along the profile five explosions were conducted at different positions. The observation interval
is about 3 km. Figure 2 shows each shot point location and the distribution of each corresponding
reflecting segment of PmP wave. It shows PmP wave reflecting points pass through 3
tectonic units. And in the middle of the profile, Zhangjiakou-Bohai seismic zone, reflecting segments
are the densest and there are records from different shots passing through.
2.1 The complexity coefficients calculation and its tectonic implication
The method of complexity coefficient is based on the general realization on plenty of PmP
data of deep seismic sounding profile in different structural regions. In general, in the stable tec-
Figure 1 Profile position and earthquake
distribution
No3 LAI Xiao-ling: COMPLEXITY FEATURE OF CRUST-MANTLE BOUNDARY IN ZHANGBEI 245
tonic units, the delay time of PmP is short with a
set of distinct phase, whereas in active tectonic
units, the delay time is long with multiple sets of
phase or unclear phase. So it is revealed that both
delay time and the number of wave set are closely
related to the complexity of deep structure.
In calculation of complexity coefficients,
the instantaneous characteristics of wave are employed
(LAI et al, 2001). We firstly process data
by Hilbert transformation, and calculate instantaneous
amplitude, instantaneous phase and instantaneous frequency, then calculate corresponding
complexity coefficients.
A(t) = f 2 (t) + fˆ 2 (t) (1)
( )
ˆ( )
( ) arctan
f t
φ t = f t (2)
( ) ˆ ( )
d
ˆ( ) d ( )
d
( ) dˆ( )
2
( ) 1 f 2 t f 2 t
t
f t f t
t
f t f t
F t
+
−
π
= (3)
Cx=NT (4)
Equations (1), (2) and (3) are respectively the expression of instantaneous amplitude A(t), instantaneous
phase φ (t) and instantaneous frequency F(t). Given by the formulas, f (t) is seismic records
and fˆ(t) is the corresponding Hilbert transformation of seismic records. Equation (4) is
the expression of complexity coefficients that N is the number of the wave sets envelopes and T is
delay time of the wave sets.
In calculation of N, we firstly process wave sets by Hilbert transformation, then calculate instantaneous
characteristics by use of equations (1)~(3), of which instantaneous amplitude A(t)
curves are also called envelope lines, so the number of the wave envelopes can be displayed in
visual graphic.
The picking of wave trains is similar to the picking of travel time and waveform. Its steps are
that, for clear PmP phase, the single record can be picked up directly; for unclear one, we firstly
find reference points on record section, then draw the time windows of PmP sets for the whole
section, and pick the simpler records for analysis.
The complexity coefficients can be used to describe compositive complexity of structure and
property in crust-mantle boundary (LAI et al, 2004). In practice, in the old and stable structur
