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 centralfrequencies

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

grou

p ve

loci

ty (

km/s

)

300 400 500

tim e (s)

1.25

1.50

1.75

2.00

2.25lo

g fr

eque

ncy*

1000

(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 analysisexample of severalnearly monochromaticfiltered signals

example of truncatingthe filtered signals

how to providea 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 signa l 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 waves

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 thefilteredseismogram issummedusing the truncatedfiltered 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 seism ogram

raw seism ogram

+

+

+

=

filte ring

nearly m onochrom atic s ignal of period 43.2 s

nearly m onochrom atic s igna l o f period 25.2 s

nearly m onochrom atic s ignal of period 18 .1 s

nearly m onochrom atic signa l of period 11.2 s

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+... o ther filte red s igna ls ...

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... o ther filtered s igna ls ...

... other filte red s ignals ...

... o ther filtered 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 velocity (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 velocity (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 veloc ity (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-velocities resultant S -ve locitya b c

dept

h (k

m)

2 3 4 5 6 7 8 9 2 31.0

period (s)

grou

p ve

loci

ty (k

m/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 (k

m/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 po in ts estim ated by the frequency-tim e ana lys isdispersion curves corresponding to inverted S-veloc ity profiles

H R O ZKYNZ

VYS OTRO 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 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

grou

p ve

loci

ty (k

m/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 orn í R ozm yšl - Kynžvart

Lubin - JER

Egejské m ore - H A J

K urilské 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

grou

p ve

loci

ty (k

m/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 orn í R ozm yšl - Kynžvart

Lubin - JER

Egejské m ore - H A J

K urilské 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

grou

p ve

loci

ty (k

m/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 - JER

Egejské 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

dept

h (k

m)

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

dept

h (k

m)

1 00

10

1

0 .1

0 .01

0 .001

0 5 10 15 20 25

Resultant shear velocity profiles

Normal view log view

conclusion