Shear wave velocity structure estimation using surface waves of different wavelengths
Petr KolínskýDepartment of Seismology
Institute of Rock Structure and MechanicsAcademy of Sciences of the Czech Republic
andDepartment of Geophysics
Faculty of Mathematics and PhysicsCharles University in Prague
New Knowledge and Measurements in Seismology, Engineering Geophysics andGeotechnics – OVA ’06Ostrava, 17. a 18. dubna 2007
surface waves
frequency-time analysis – basics
• multi-channel filtering• Gaussian filters• constant relative resolution filtering• optimal filtration• instantaneous period estimation• compilation of the dispersion curve using
primary, secondary, ... local maxima
frequency-time analysisfrequency - time representation using the Fourier Transform
multi-channel filtering = the inverse FT for different central
frequencies
is a spectrum of the original signal
is the Gaussian filter (weighting function)
we obtain a set of filtered spectra
deeGdeGtS titi 2)(
2 2
2
)()(),(
)(G
2
2)(
e
)(tg
)(G
frequency-time analysis
example of Gaussian filters
0.0 0.1 0.2 0.3 0.4 0.5 0.6frequency (H z)
ampl
itude
pow er spectrumG aussian filte rsfilte red pow er spectra
frequency-time analysis classical depiction of spectrogram
amplitude frequency time group velocity -
scale diagram period diagram
0.75 1.00 1.25 1.50 1.75
log period (s)
2.5
3.0
3.5
4.0
gro
up
ve
loci
ty (
km/s
)
300 400 500
tim e (s)
1.25
1.50
1.75
2.00
2.25lo
g f
req
ue
ncy
*10
00
(H
z)
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
frequency-time analysis
group velocity
epicentral distance
arrival time of energy maximum
ktU
kt
kinst tTU kinst tT
frequency-time analysis
example of several
nearly monochromatic
filtered signals
example of truncating
the filtered signals
how to provide
a proper truncating?
400 450 500 550 600 650tim e from orig in (s)
-1E+6
0E +0
1E +6
-5E +6
0E +0
5E+6
-1E +7
0E +0
1E +7
ampl
itude
s
-1E+7
0E +0
1E +7
-1E +6
0E +0
1E +6
-2E +7
0E +0
2E+7
3.0 s
5.0 s
11.2 s
18.1 s
25.2 s
43.2 s
-1E +5
0E +0
1E +5
75.6 s
400 450 500 550 600 650
nearly m onochrom atic s ignal and its envelopetruncated nearly m onochrom atic s ignalenvelope of truncated nearly m onochrom atic s ignal
-1E +7
0E +0
1E +78.3 s
S body w aves
L1
L0
L0
L0
L0
L0
L0
L0
L0
R 0
R0
3.12 km /s
4.15 km /s
3.39 km /s
3.11 km /s
3.15 km /s
3.35 km /s
3.85 km /s
4.14 km /s
frequency-time analysis
how the
filtered
seismogram is
summed
using the
truncated
filtered signals
400 450 500 550 600 650tim e from orig in (s)
-3E+4
0E+0
3E+4
-1E+7
0E+0
1E+7
-1E+7
0E+0
1E+7-1E+7
0E+0
1E+7
-2E+7
-1E+7
0E+0
1E+7
2E+7
ampl
itude
s
-3E+4
0E+0
3E+4
400 450 500 550 600 650
filte red se ism ogram
raw seism ogram
+
+
+
=
filte ring
nearly m onochrom atic s ignal o f period 43.2 s
nearly m onochrom atic s ignal o f period 25.2 s
nearly m onochrom atic s ignal o f period 18.1 s
nearly m onochrom atic s ignal o f period 11.2 s
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+... o ther filte red s ignals ...
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... o ther filte red s ignals ...
... o ther filtered s ignals ...
... o ther filte red s ignals ...
frequency-time analysis
filtered seismogram
inversion problem
• Isometric Method (IM) was recently developed at Institute of Rock Structure and Mechanics, Academy of Sciences of the Czech Republic, by Jiri Malek
• isometric algorithm connects the advantages of several commonly used methods, see: “Tarantola, A.: Inverse Problem Theory, Elsevier Science B.V, Amsterdam, 1987”
• IM is a fast algorithm, which was developed for solving weakly non-linear inverse problems with many parameters
forward problem
• forward problem is solved during almost all iterations of the inversion
• the dispersion curves are computed by matrix method presented in: “Proskuryakova, T. A., Novotny, O. and Voronina, E. V.: Studies of the Earth Structure by the Surface Wave Method (Central Europe), Nauka, Moscow, 1981 (in Russian)”
• It uses modified Thomson – Haskell matrices for Love waves
• program for computing the forward problem was developed at the Department of Geophysics, Faculty of Mathematics and Physics, Charles University, Prague, by Oldřich Novotný
SVAL - program
• The source code is written in PASCAL using Delphi environment (Borland, version 7.0).
• The code emerges as a result of translation of other codes from FORTRAN language (Kolínský, Novotný). Then it was compiled together with code written in Delphi (Málek).
• It is possible to distribute and execute the SVAL program using one *.exe file (3 MB).
results
velocity models and inversion scattering
measured and inverted dispersion curves
2.0 2.5 3.0 3.5 4.0 4.5S ve locity (km /s)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
2.0 2.5 3.0 3.5 4.0 4.50.0
0.5
1.0
1.5
2.0
2.5
3.0
2.0 2.5 3.0 3.5 4.0 4.5
2.0 2.5 3.0 3.5 4.0 4.5S ve locity (km /s)
0.0
0.5
1.0
1.5
2.0
2.5
3.01.5 2.0 2.5 3.0 3.5 4.0
S ve locity (km /s)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
1.5 2.0 2.5 3.0 3.5 4.0
area of inverted S -ve locities resultant S -ve locity
a b cde
pth
(km
)
2 3 4 5 6 7 8 9 2 31.0
period (s)
grou
p ve
loci
ty (
km/s
)
2 3 4 5 6 7 8 9 2 31.0
2.4
2.8
3.2
3.6
4.0 2 3 4 5 6 789 2 3 4 5 60.1 1.0
grou
p ve
loci
ty (
km/s
)
2 3 4 5 6 789 2 3 4 5 60.1 1.0
period (s)
2.4
2.8
3.2
3.6
4.0
2 3 4 5 6 7 89 2 3 40.1 1.0
period (s)
2 3 4 5 6 7 89 2 3 40.1 1.0
dispersion points estim ated by the frequency-tim e analysisd ispersion curves corresponding to inverted S -ve locity profiles
H R O ZKYN Z
VYSOTR O J
LIBATR O J
depth (km)
shallow seismic measurement
• Date 2004 June• Magnitude very small :-)• event location 14.15 E 49.91 N (Karlštejn)• Depth surface• origin time 13:15:12 UTC• Source hammer beating a metal plate• epicentral distance 50 m• Station Karlštejn• station location 14.15 E 49.91 N• Seismometer SM 6 – 4 Hz
quarry blast
• Date 2003 June 05• Magnitude not estimated• event location 12.668 E 50.261 N (Horní Rozmyšl)• Depth surface• origin time 17:49:59.546 UTC• Source quarry blast• epicentral distance 28.954 km• Station Kynžvart KYNZ• station location 12.604 E 50.004 N• Seismometer Lenartz 3-D 5\,s \\
Aegean Sea Earthquake
• Date 2005 October 20• Magnitude 5.9• event location 26.75 E 38.15 N (Aegean Sea)• Depth 10 km• origin time 21:40:04.09 UTC• Source natural tectonic earthquake• epicentral distance 1632.54 km• Station Háje HAJ• station location 14.04897 E 49.67474 N• Seismometer Guralp 30
South Iran
• Date 2005 November 17• Magnitude 6.0• event location 55.847 E 26.784 N (South Iran)• Depth 10 km• origin time 10:22:19 UTC• Source natural tectonic earthquake• epicentral distance 4441.38 km• Station Nečtiny NEC• station location 13.16864 E 49.97740 N• Seismometer Guralp 30 s
Kuril Islands
• Date 2007 January 13• Magnitude 8.2• event location 154.80 E 46.18 N (Kuril Islands)• Depth 12 km• origin time 04:23:20.2 UTC• Source natural tectonic earthquake• epicentral distance 8607.75 km• Station Panská Ves PVCC• station location 14.5689 E 50.5282 N• Seismometer STS-2 120 s
0.01 0.1 1 10 100 10000.02 0.030.040.050.060.070.080.09 0.2 0.3 0.4 0.50.60.70.80.9 2 3 4 5 6 7 8 9 20 30 40 50 60708090 200 300 400500600700800900
p e rio d (s)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
gro
up
ve
loci
ty (
km/s
)
0
0 .5
1
1.5
2
2.5
3
3.5
4
4.5
1 10 1002 3 4 5 6 7 8 9 20 30 40 50 60 70 80 90 200 300
H orní R ozm yšl - Kynžvart
Lubin - JE R
Egejské m ore - H A J
Kurilské ostrovy - P VC C
K arlš te jn
0.01 0.1 1 10 100 1000
0.02 0.030.040.050.060.070.080.09 0.2 0.3 0.4 0.50.60.70.80.9 2 3 4 5 6 7 8 9 20 30 40 50 60708090 200 300 400500600700800900
p e rio d (s)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
gro
up
ve
loci
ty (
km/s
)
0
0 .5
1
1.5
2
2.5
3
3.5
4
4.5
1 10 1002 3 4 5 6 7 8 9 20 30 40 50 60 70 80 90 200 300
H orní R ozm yšl - Kynžvart
Lubin - JE R
Egejské m ore - H A J
Kurilské ostrovy - P VC C
0.01 0.1 1 10 100 10000.02 0.030.040.050.060.070.080.09 0.2 0.3 0.4 0.50.60.70.80.9 2 3 4 5 6 7 8 9 20 30 40 50 60708090 200 300 400500600700800900
p e rio d (s)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
gro
up
ve
loci
ty (
km/s
)
0
0 .5
1
1.5
2
2.5
3
3.5
4
4.5
1 10 1002 3 4 5 6 7 8 9 20 30 40 50 60 70 80 90 200 300
H orní R ozm yšl - Kynžvart
Lubin - JE R
Ege jské m ore - H AJ
Kurilské ostrovy - PVC C
K arlš te jn
0 1 2 3 4 5S -w a ve ve lo city (km /s)
200
160
120
80
40
0
de
pth
(km
)
200
160
120
80
40
0
0 5 10 15 20 25
0 1 2 3 4 5S-w a ve ve lo city (km /s)
100
10
1
0.1
0.01
0.001
de
pth
(km
)
100
10
1
0.1
0.01
0.001
0 5 10 15 20 25
Resultant shear velocity profiles
Normal view log view
conclusion