-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

-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 834

36

38

40

42

44

LP-WWSSN

-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 834

36

38

40

42

44

MAL

-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 834

36

38

40

42

44

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: corchete@ual.es