11 paths & 21 events registered. 11 paths & 15 events registered
TRANSCRIPT
-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 834
36
38
40
42
44
S14
S13
S12
S11
S9
S8S7
S6S5
S1 S2
LP-WWSSN
11 paths & 21 events registered
-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 834
36
38
40
42
44
S11
S10
LP-WWSSN
S3
S9S1S6
S7
S4
S2S5
11 paths & 15 events registered
-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 834
36
38
40
42
44
S27S46
S45
S43 S42
S39S35
S34S33
S32S30
S28
S26S25S22
S21
S20 S18
S16S15S14S10
S9
S8
S7S6 S3
LP-WWSSN
26 paths & 45 events registered
Instrumental Response
The problem arisen in the recording of a physical phenomena is well illustrated below. The instrument used to perform this record distorts the original true-signal x(t) given the output signal y(t).
For this reason, a further process called deconvolution must be performed to recover the input signal x(t). Unfortunately, the input signal x(t) is never recovered completely. Thus, the signal recovered by the decondition filter is not exactly equal to x(t). Nevertheless, if the deconvolution process is well done, the recovered signal can be used instead of the original signal x(t), with a small error.
Convolution Formula
d)-t(h)(f)t(g
g t f t t( ) = ( ) h( ) G( ) = F( ) H( )
)( )(=)(
)H()F(=)G(
HFG
+
F() = Ground spectrum ,, H() = Instrumental response
)()(= )(
)H(/)G(=)F(
HGF
-
Instrumental Response
0.001 0.01 0.1 1 10 1000.001
0.01
0.1
1
10
0.001 0.01 0.1 1 10 100-360
-270
-180
-90
0
90
180
T = 45 s
Nor
mal
ized
Am
plit
ude
Frequency (Hz)
T = 5 s
T = 45 s T = 5 sP
hase
(de
gree
s)
Frequency (Hz)
Instrumental correction(only amplitude considered)
5 10 15 20 25 30 35 40 451.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
1 min
Gro
up
Vel
ocit
y (k
m/s
)
Period (s)
Observed Corrected
Short periodmagnificationAmplitude
corrected
Observed
Instrumental correction(only phase considered)
5 10 15 20 25 30 35 40 451.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
1 min
Time delay appearsin the observed
Time lag recoveredin the corrected
Gro
up
Vel
ocit
y (k
m/s
)
Period (s)
Observed Corrected
Time lagrecovered
Phasecorrected
Observed
Instrumental correction(amplitude and phase considered)
5 10 15 20 25 30 35 40 451.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Short periodmagnification
1 min
Time delay appearsin the observed
Time lag recoveredin the corrected
Gro
up
Vel
ocit
y (k
m/s
)
Period (s)
Observed Corrected
Time lagrecovered
Amplitudeand phasecorrected
Observed
Filtering process(MFT and TVF combined)
Preprocessed signal(observed seismogram with instrumental correction)
MFT
Group velocity
TVF
Filtered signal MFT Group velocity
(final dispersion curve)
MFT(Multiple Filter Technique)
5 10 15 20 25 30 35 402.0
2.5
3.0
3.5
4.0
4.55 10 15 20 25 30 35 40
120
180
240
300
360
0 60 120 180 240 300 360 420 480 540 600 660 720
5 10 15 20 25 30 35 40
120
180
240
300
360
420
480
540
600
660
Period (s)
Gro
up
Tim
e (s
)
89
90
91
92
93
94
95
96
97
98
99db
Gro
up
Vel
ocit
y (k
m/s
)
Period (s)
Gro
up
Tim
e (s
)
Period (s)
Time (s)
(instrumental response corrected: amplitude and phase)
Seismic eventnº 34
(registered at EBR station)
TVF(Time-Variable Filtering)
5 10 15 20 25 30 35 402.0
2.5
3.0
3.5
4.0
4.5
0 60 120 180 240 300 360 420 480 540 600 660 720
0 60 120 180 240 300 360 420 480 540 600 660 720
Gro
up
Vel
ocit
y (k
m/s
)
Period (s)
Time (s)
Time (s)
TVF
Observed signal (preprocessed)
Filtered signal (time-variable filtered)
Obtained by MFT
MFT application to the time-variable filtered signal
5 10 15 20 25 30 35 40 452.0
2.5
3.0
3.5
4.0
4.55 10 15 20 25 30 35 40 45
120
180
240
300
360
0 60 120 180 240 300 360 420 480 540 600 660 720
5 10 15 20 25 30 35 40 45
120
180
240
300
360
420
480
540
600
660
Period (s)
Gro
up
Tim
e (s
)
89
90
91
92
93
94
95
96
97
98
99db
< 89
Gro
up
Vel
ocit
y (k
m/s
)
Period (s)
Gro
up
Tim
e (s
)
Period (s)
Time (s)
(time-variable filtered)
Filtering process(comparison)
5 10 15 20 25 30 35 40 452.0
2.5
3.0
3.5
4.0
4.5
0 60 120 180 240 300 360 420 480 540 600 660 720
Observed Filtered
Gro
up
Vel
ocit
y (k
m/s
)
Period (s)
Observed Filtered
Time (s)
Period range increased
Wave traincontamination is removed
Group velocity measurement for a path(average group velocity and standard deviation)
0 5 10 15 20 25 30 35 40 45 502.0
2.5
3.0
3.5
4.0
4.5
0 5 10 15 20 25 30 35 40 45 502.0
2.5
3.0
3.5
4.0
4.5
Gro
up
Vel
ocit
y (k
m/s
)
Period (s)
S5-EBR
Event 33 Event 34 Event 35
Gro
up
Vel
ocit
y (k
m/s
)
Period (s)
Dispersion curves obtained after filtering process (MFT and TVF combined) applied to 3 events registered at EBR station.
Average group velocity and standard deviation (vertical bars) obtained from the group velocity measurements showed above.
Forward Modeling(theoretical dispersion curve from a starting model)
80
70
60
50
40
30
20
10
02.0 2.5 3.0 3.5 4.0 4.5 5.0
0 5 10 15 20 25 30 35 40 45 502.0
2.5
3.0
3.5
4.0
4.5
Shear Velocity (km/s)
Dep
th (
km
)
Gro
up V
eloc
ity
(km
/s)
Period (s)
Thickness(km)
(km/s)
(km/s)
(g/cm3)
3 3.30 2.50 2.28
8 6.10 3.48 2.79
6.5 6.85 3.90 3.05
23.5 7.60 4.50 3.20
40 8.10 4.70 3.35
8.10 4.70 3.35
Inversion process for a path(shear velocity structure from a dispersion curve)
80
70
60
50
40
30
20
10
02.0 2.5 3.0 3.5 4.0 4.5 5.0
0 5 10 15 20 25 30 35 40 45 502.0
2.5
3.0
3.5
4.0
4.5
0 10 20 30 40 50 60 70
Shear Velocity (km/s)
Dep
th (
km)
Theoretical Observed G
roup
Vel
ocit
y (k
m/s
)
Period (s)
Depth (km)
Resolving Kernels
S5-EBR
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LP-WWSSN
-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 834
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MAL
-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 834
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TOL
Paths with shear wave velocity structure determined
References
Cara M. (1973). Filtering dispersed wavetrains. Geophys. J. R. astr. Soc., 33, 65-80.
Corchete V., Chourak M. and Hussein H. M., 2007. Shear wave velocity structure of the Sinai Peninsula from Rayleigh wave analysis. Surveys in Geophysics, 28, 299-324.
Dziewonski A., Bloch S. and Landisman M. (1969). A technique for the analysis of transient seismic signals. Bulletin of the Seismological Society of America, 59, No. 1, 427-444.
CONTACT
Prof. Dr. Víctor CorcheteDepartment of Applied Physics
Higher Polytechnic School - CITE II(A)UNIVERSITY OF ALMERIA
04120-ALMERIA. SPAINFAX: + 34 950 015477
e-mail: [email protected]