Corso di costruzioni in zona simica Modulo di determinazione … · 2020. 9. 24. · Corso di...

FACOLTA’ DI INGEGNERIA DELL’UNIVERSITA’ DEGLI STUDI ROMA III

Laurea magistrale in Ingegneria Civile per la Protezione dai

Rischi Naturali (Dm 270)

Corso di costruzioni in zona simica

Modulo di determinazione della pericolosità sismica

F.Sabetta

5. Accelerometria. Processamento dati.

Trasformata di Fourier. Modello di Brune

Reti e banche dati.

Anno accademico 2020/21

Corso di Sismologia 5 Accelerometria

F. Sabetta 5.2

SUMMARY STRONG-MOTION INSTRUMENTS ....................................................................................... 3 Characteristics of seismographs and accelerographs ............................................................. 3 Recording ranges of seismographs and accelerographs ......................................................... 4 Analogue accelerographs ............................................................................................................. 4 Digital accelerographs .................................................................................................................. 5 DATA PROCESSING .......................................................................................................... 6 Strong motion data processing (analog instruments) .............................................................. 6 FOURIER TRANSFORMS .................................................................................................... 7 Sampling theorem, aliasing and Nyquist Frequency ................................................................. 9 Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) ................................... 10 THEORETICAL SPECTRUM- BRUNE MODEL .......................................................................11 Theoretical acceleration spectrum (omega-squared Brune source model) .......................... 11 DIGITIZATION AND PROCESSING .......................................................................................13 Accelerogram digitization ........................................................................................................... 13 Data processing ........................................................................................................................... 14 Band pass filtering ...................................................................................................................... 15 Instrument response correction ................................................................................................ 17 ANALOG AND DIGITAL INSTRUMENTS ................................................................................18 STRONG-MOTION DATABASES ON THE WEB .....................................................................20 Europe Mediterranean and Middle East data ............................................................................ 21 ITALIAN STRONG MOTION NETWORK .................................................................................22 I TALIAN STRONG MOTION DATA BASE ................................................................................23


F. Sabetta 5.3

Strong-motion instruments

Instrumental recordings of the strong, and potentially destructive, ground movements during earthquakes provide the foundation stone for earthquake engineering since they are the clearest and most comprehensive definition of the actions against which structures and lifelines must be designed.

The instruments that record strong ground-motion are called accelerographs or strong-motion instruments because they record the acceleration of the ground as a function of time, unlike seismographs which record the displacement or velocity of the ground.

The first accelerographs were developed and installed in California in 1932, more than three decades after the first seismographs came into operation. The first recordings were made during the 1933 Long Beach, California earthquake.

Whereas seismographs amplify the movement of the ground hundreds or thousands of times, and hence can record waves from earthquakes almost anywhere on the globe, accelerographs only record strong shaking and hence they must be installed in those areas where strong earthquakes are expected.

Even then, an accelerograph may be installed for months or even years before experiencing ground shaking strong enough to be recorded, so the instruments do not operate continuously. Instead they remain on stand-by until triggered by a certain threshold level of acceleration.

Ground accelerations are generally expressed in g (where g is the acceleration due to gravity, 9.81 m/s2 ) or in gals (1 gal = 1 cm/s2 ~ 1mg).

The accelerographs generally record three mutually perpendicular components of motion in the vertical and two horizontal directions. (from Bommer, 2001a)

Characteristics of seismographs and accelerographs

The classical distinction between seismograph and accelerograph tends to be overtaken by the use of digital instruments with broad band (0-100 Hz) and high dynamic range (~ 140 dB)

1 dB = 20*log(S/N) 1 bit ~ 6dB 24 bit ~ 144 dB ~ 107 (from 0.1 μg to 1 g)

However more than 50% of the instruments operating worldwide are still of analogue type and the cost of a broad band digital instrument may be up to 4 times the cost of an analogue one.

Nat.Freq.

Damping

Response Range of magn.

Recording Applications

SEISMOGRAPH

~ 0.01 - 1 Hz

gen. low damping

~ 10%

flat in ground velocity

~ 0 - 4

(saturation)

continous

Geophysics and Seismology

- Earth interior studies

- Velocity models

- Earthquake location

- Source mechanisms

- Character. of faults

ACCELEROGRAPH

(analogue instrument)

~ 25 Hz

gen. high damping

~ 60%

flat in ground acceleration

~ 4 - 8

~ (0.01-2 g)

threshold

(trigger on vertical

comp. at 0.01 g)

Earthquake Engineering

Geotechnics

- Accel., vel., displ.

- Fourier spectra

- Response spectra

- Site amplification effects

- Antiseismic design


F. Sabetta 5.4

Recording ranges of seismographs and accelerographs

Analogue accelerographs

The first generation of accelerographs is represented by analogue instruments recording on film or paper, the most popular and worldwide used of these instruments being the Kinemetrics SMA-1

0,0

0,5

1,0

1,5

2,0

2,5

3,0

0 5 10 15 20 25 30 35 40 45 50

ground motion frequency (Hz)

ac

ce

lera

tio

n r

es

po

ns

e

====

natural undamped frequency = 25 Hz

from Lay and Wallace (1995)

Response curves of a SDOF oscillator with a natural frequency of 25 Hz for several values of damping

SMA-1 optical-mechanical accelerograph The oscillator, trigger, and timing circuits are at left; the recording drum at right


F. Sabetta 5.5

Digital accelerographs

The second generation of accelerographs operate with a force-balance transducer and record digitally on to solid state or magnetic media. These instruments have a much wider dynamic range than the optical-mechanical instruments of the first generation and there is no need to digitise the record. Furthermore, due to the so called pre-event memory,

they can recover also the first motions of the earthquake shaking.

The motion of the mass is controlled by the sum of two forces: the inertial force due to ground acceleration, and the negative feedback force. The electronic circuit adjusts the feedback force so that the forces

very nearly cancel. We have thus converted the acceleration into an electric signal without depending on the precision of a mechanical suspension.

from Wielandt 2000, http://www.geophys.uni-stuttgart.de/seismometry/man_html/index.html

Kinemetrics ETNA strong motion accelerograph

Kinemetrics

K2 and EVEREST digital recorder

EPISENSOR

Sensor Dynamic range Banwidth Damping

FBA-23 135 dB from 0.01 to 50 Hz

DC - 50 Hz 70% critical

EPISENSO

R

145 dB

from 0.01 to 20 Hz

DC - 200Hz 70% critical

Feedback circuit of a force-balance accelerometer (FBA).

Instrument Dynamic

range

Frequency

response

Sampling

rates

Recording

capacity

Timing

accuracy

Firmware

ETNA

18 bit

108 dB DC - 80 Hz

(200 sps)

100-250

sps

15-40 min. 0.5 msec.

of GPS

multitasking

operating

system

K2

18 bit

>110 dB DC - 80 Hz

(200 sps)

1-500 sps 200 min. 0.5 msec.

of GPS

multitasking

operating

system

EVEREST

24 bit

>130 dB DC - 80 Hz

(200 sps)

1-500 sps 200 min. 0.5 msec.

of GPS

multitasking

operating

system

http://www.geophys.uni-stuttgart.de/seismometry/man_html/index.html


F. Sabetta 5.6

Data processing

Strong motion data processing (analog instruments)

The processing procedure has mainly to do with:

• instrument response correction

• baseline correction and band-pass filtering

Low pass filtering is necessary to remove the high frequency noise introduced by the digitization, strongly amplified by the instrument correction.

High pass filtering is necessary to remove the low frequency noise introduced by: unrolling and enlargement of the film, digitization, and trigger effect (if the instrument doesn’t start recording until some triggering level of motion is reached, the entire accelerogram is in error by the level of motion at the time of triggering). Correction of such errors, termed baseline correction, was originally accomplished by subtracting a best-fit parabola form the accelerogram but is now performed using high-pass filters and modern data processing techniques (USGS-Converse 1992).

The filtering techniques are more reliable and efficient if applied in frequency-domain rather than in time-domain.

This requires some recall to Fourier series and transforms.

About 60% of the accelerometers operating in the world are still of the analogue type.

This makes particularly important the accelerogram correction to remove the noise introduced, especially at low frequencies and in the velocity and displacement time histories, by the recording and the digitization procedure.

Integration of an uncorrected accelerogram will produce a linear error in velocity and a quadratic error in displacement. An acceleration error as small as 0.001g at the beginning of a 30-sec long accelerogram would erroneously predict a displacement of 441 cm at the end of the motion.


F. Sabetta 5.7

Fourier transforms1

At the beginning of the nineteenth century the French mathematician J. Fourier showed that any function f(t) satisfying certain conditions (Dirichlet: periodic, finite N° of discont., finite N° of maxima) can be expressed as a sum of monochromatic periodic functions. Since the Dirichlet conditions are nearly always met in physical processes, Fourier transform is an extraordinarily useful tool in many branches of science.

The functions f(t) and F(w) are said to form a Fourier pair f(t)F(w) corresponding to a mapping from time-domain to frequency-domain. The Fourier transform doesn’t express a point-by-point correspondence in the two domains but only a curve-by-curve correspondence.

1 from Kramer 1996, Lay and Wallace 1995, Bath 1974

dt)tsin()t(f)(b +

−

= dt)tsin()t(f)(b +

−

=

=−= ie)(A)(ib)(a)(F

Fourier Amplitude Spectrum (FAS) Phase Spectrum

+

−

=

deFtf ti)()(21

dtetfF ti+

−

−= )()(


F. Sabetta 5.8

ωn = 2πn/Tf ; note that the frequencies ωn are evenly spaced at a constant frequency increment Δωn = 2πn/Tf representing also the lowest frequency in the spectral analysis.

If x(t) is not periodic but defined over a finite range, the sum of the sinusoidal terms will still converge to x(t) over the defined range. Outside the range the sum will represent a repetition of f(t).

The Fourier series represent the original

function exactly only for n=. For many functions the approximation can be quite good even when n is relatively small.

A plot of cn versus ωn is known as Fourier Amplitude Spectrum (FAS). A plot of Φn versus ωn gives the phase spectrum.

General trigonometric form of the Fourier series for a function x(t) of period T


F. Sabetta 5.9

Fourier transforms of selected analytic time functions (from Bath 1974)

Sampling theorem, aliasing and Nyquist Frequency

Ground motion time histories are not continuous nor analytical functions. They are rather sampled time series with N points spaced at discrete time intervals Δt.

As the record length Tf =NΔt defines the lowest frequency in the spectral analysis, at the other end the digitization sampling interval Δt defines the highest resolvable frequency.

Intuitively we understand that at least 3 points (i.e. two time intervals =2Δt) are the minimum of information needed to define one period.

If F(ω) is not zero for ω>π/Δt, the spectra of adjacent frequency points overlap giving rise to a phenomenon called aliasing.

The only way to avoid aliasing is to limit the highest frequency in F(ω) at a frequency, called Nyquist frequency, fn=1/2Δt

F.A.S. of

a signal

sampled

at 100

pts/s

F.A.S. of

a signal

sampled

at 100

pts/s


F. Sabetta 5.10

Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT)

In case of digitised time series spaced at equal time intervals Dt, for a variable x(tk), k=1,N,

where tk =k t and Tf=Nt, the Discrete Fourier Transform (DFT) is given by

The DFT can also be inverted; a set of data spaced at equal frequency intervals Dw, can be expressed as a function of time using the Inverse Discrete Fourier Transform (IDFT).

Either of these expressions can be easily programmed on a personal computer; the

summation operation is performed N times for each value of n and the computation time is therefore proportional to N2.

As digital computers were developed in the 1960s, Cooley and Tukey (1965) developed a computational algorithm, for the case where N is a power of 2, that has become known as

the Fast Fourier Transform (FFT). The computation time is proportional to Nlog2(N) and FFT is much more efficient than DFT: for example, at N=4096 (212), the FFT is more than 340 times faster than the DFT.

In case of strong motion records normally 50 t 200 pts/s and 2000 N 20000

Where n= n = 2n / Nt

ktniN

1nnk e)(X)t(x

=

=

ktniN

1kkn e)t(xt)(X

−

=

=


F. Sabetta 5.11

Theoretical Spectrum- Brune Model

Theoretical acceleration spectrum (omega-squared Brune source model)2

2 from Boore 1983

seismic moment Distance attenuation (anelastic + geom. spreading)

Where:

Fs (=2) free surface correction,

R, (=0.63) average radiation pattern,

P (=1/2) partition between horizontal components and

(~ 2.7 g/cm3) and v (~3.2 km/s) density and s-wave velocity in the crust.

omega-squared Brune (1970) source spectrum 2c

2

c)/(1

),(S+

=


F. Sabetta 5.12

CORNER FREQUENCY

2/),( kmi eS−=

beyond a given frequency fm depending on local site geology (3-30 Hz) the spectrum decays exponentially.

Normally 0.006 ≤ k ≤ 0.07

from Rovelli, 1988

Where:

is the S-wave velocity (~ 3.2 km/s)

is the dynamic stress drop (~100 bars)

M0 is the seismic moment (dyne•cm)

fc 1/Mw

fc ~ 1 Hz Mw = 5

fc ~ 0.1 Hz Mw = 7

fc ~ 10-(Mw-5)/2

where Q=Qofn

R

ee

ff

fCMfA

QRffk

c

−−

+=

/

2

2

0)/(1

)2()(

from Rovelli, 1988


F. Sabetta 5.13

Spectral shapes are strongly dependent on magnitude and on local site geology (k factor).

Spectral shapes are nearly independent on distance (if R < 100 km).

This because the frequency dependent distance attenuation is given by

e-fr/Q where Q=Q0fn

and it depends from the value of the exponent n of the anelastic attenuation factor Q (in the above figures n=1 giving no frequency dependence)

Digitization and processing

Accelerogram digitization

The film retrieved from the analogue instrument is generally enlarged (4x) before digitization.

Semiautomatic digitizers, with which a user moved a lens with crosshairs across an accelerogram mounted on a digitizing table, were commonly used in the late 1970s.

By pressing a foot-operated switch the coordinates of the crosshairs were recorded.

Acceleration Spectra, R=15 km

0,01

0,10

1,00

10,00

100,00

0,01 0,1 1 10 100

Frequency (Hz)

cm

/s

Mw=4

Mw=5

Mw=6

Mw=7

Acceleration Spectra, R=60 km

0,01

0,10

1,00

10,00

100,00

0,01 0,1 1 10 100

Frequency (Hz)

cm

/s

Mw=4

Mw=5

Mw=6

Mw=7

Displacement Spectra, R=15 km

0,1

1,0

10,0

100,0

1000,0

0,01 0,1 1 10 100

Frequency (Hz)

cm

*s

Mw=5

Mw=6

Mw=7

fc


F. Sabetta 5.14

Fully automatic computer-based digitization, typically at sampling rates of 200 pts/s, is now commonplace.

Data processing

Data processing is more easy and efficient in frequency domain because integration

becomes simply a division by , and filtering, that in time domain is represented by a convolution between filter and record, becomes a multiplication between the respective Fourier transforms.

Automatic digitizer used for the Italian records.

Camera with 1024 photodiodes; up to 400 pts/s and 0.02 mm resolution

Data processing normally includes, besides Fourier and response spectra, integration to get velocity and displacement time histories.

dtfftftf )()()()( 2121 −=

−

)()()()( 2121 FFtftf Convolution

theorem

Acceleration

Velocity

Displacement

from Kramer - 1996


F. Sabetta 5.15

Band pass filtering

The most critical step in the strong motion data processing is the selection of the cut-off and roll-off frequencies for the band-pass filtering of the accelerograms.

The best way to do it is an “expert based” choice on the basis of the visual examination of the F.A.S. and of the filtered integrated displacement time histories.

It follows that a high degree of subjective judgement is implicit in data processing. What kind of data is better to release to the users ?

uncorrected data corrected data

?

• Everyone can choose its own filtering

• Know-how is very rare

• Several different values

The user may not agree on the choices made in the data processing

Band–pass

filtering


F. Sabetta 5.16

Effect of a wrong high-pass filtering on the displacement and response spectrum of a record obtained at Tolmezzo during the 1976 Friuli earthquake


F. Sabetta 5.17

Time [sec]

20191817161514131211109876543210

Dis

pla

cem

ent [c

m]

0.4

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

-0.4

Nocera Umbra analog – Band pass 0.3 - 25 Hz

Time [sec]

20191817161514131211109876543210

Dis

pla

cem

ent [c

m]

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

Nocera Umbra analog– Band pass 0.1 - 25 Hz

Time [sec]

20191817161514131211109876543210

Dis

pla

cem

ent [c

m]

0.5

0

-0.5

-1

-1.5

-2

Nocera Umbra analog– only cubic baseline

High-pass filtering

Instrument response correction

If the instrument response correction is performed in time-domain the results, achieved through the so called finite difference approximation, are satisfactory only if a high sampling frequency is adopted

Instrument response correction is most conveniently performed in frequency-domain where it can be coupled in a single step with the band-pass filtering

The exact instrument correction for a frequency of 25 Hz and damping 0.6 of critical, compared with the finite different approximation for 50 and 200 pts./s

from Joyner & Boore , 1988


F. Sabetta 5.18

Time [sec]

21201918171615141312111098765

Accele

ratio

n [cm

/sec2]

200

150

100

50

0

-50

-100

-150

-200

Time [sec]

21201918171615141312111098765

Accele

ratio

n [cm

/sec2] 150

100

50

0

-50

-100

-150

Time [sec]

21201918171615141312111098765

Accele

ratio

n [cm

/sec2]

100

50

0

-50

-100

-150

Nocera Umbra digital - Band pass 0.1 - 25 Hz


Maximum Acceleration: 157 cm/sec2




Low-pass filtering

Analog and digital instruments

Fourier amplitude spectra of recordings obtained in the same station (Procisa Nuova) by an analog (SMA-1) and a digital (DSA-1) instrument installed side by side


F. Sabetta 5.19

Provided that the record doesn’t comprise very low frequencies (in this case M=4.4), an adequate band-pass filtering can retrieve the same kind of information from an analogue and a digital instrument

from Sabetta , 1986

ML= 4.4

Repic = 21 km

PGA = 0.05 g


F. Sabetta 5.20

Nocera analogico – inversione segno_ correz strum

Band pass 0.3 - 25 Hz

Maximum Acceleration: 192 cm/sec2Time [sec]

20191817161514131211109876543210

Accele

ratio

n [cm

/sec2]

200

150

100

50

0

-50

-100

-150

-200

Nocera Umbra analog



Time [sec]

222120191817161514131211109876

Accele

ratio

n [cm

/sec2]

200

150

100

50

0

-50

-100

-150

-200

Nocera Umbra digital



Accelerograms obtained in the same station (Nocera Umbra) by an analogue (SMA-1)

and a digital (ETNA) instrument installed side by side

Strong-motion databases on the WEB

Strong-motion records are now available in digital format from many parts of the world very easily, particularly through the following Internet sites:

NORTH AND SOUTH AMERICA AND JAPAN

NOAA

http://www.ngdc.noaa.gov/seg/hazard/earthqk.shtml

COSMOS

http://db.cosmos-eq.org

PEER

http://peer.berkeley.edu/smcat/

K-NET JAPAN

http://www.k-net.bosai.go.jp/k-net/index_en.shtml

http://www.ngdc.noaa.gov/seg/hazard/earthqk.shtmlhttp://db.cosmos-eq.org/http://peer.berkeley.edu/smcat/http://www.k-net.bosai.go.jp/k-net/index_en.shtml


F. Sabetta 5.21

Europe Mediterranean and Middle East data

EUROPE AND MIDDLE EAST

ESM European strong motion database

20790 three comp. waveforms with M>=4

http://esm.mi.ingv.it

ITALY

ITACA Italian s.m. database

25222 three comp. waveforms with M>=3

http://itaca.mi.ingv.it/ItacaNet

http://esm.mi.ingv.it/


F. Sabetta 5.22

Italian strong motion network

Italian strong motion stations (old generation)

• Installation began in 1972 under the management of ENEL (Italian Electricity Board).

• Acquired in 1998 by DPC (237 analog stations).

• 528 digital instruments (April 2014) installed in free field with an average spacing of 15 km.

• Digital instruments (Kinemetrics Etna or Everest 18-24 bits) are equipped with GPRS modem for data transmission to the central (Rome) acquisition centre.

• More than 20000 records obtained in 44 years of activity.

• annual cost of management and maintenance 600.000 Euro.

http://www.protezionecivile.gov.it/jcms/it/ran.wp

parametri e forme d’onda possono essere scaricati dal sito:

www.mot1.it/randownload.

Concrete post used to fix the instrument. The post is

directly anchored to the foundation soil (80 cm) and

disengaged from the cabin floor and surface sediments Electrical transformation cabin

used for lodging the instruments


F. Sabetta 5.23

Italian strong motion stations (new generation)

Italian strong motion data base

Power supply

GPS antenna

Digital accelerograph

Solar panel

September 26 1997, 09:40Umbria-Marche earthquake : main shock

Ml = 5.9

Strong Motion Stations

Epicenter

yellow lines :statistic distribution

blue lines : deterministicdistribution related tothe peak accelerationvalues

0.550.31

0.190.17

0.120.090.09

0.08

0.07

0.07

0.05

0.03

0.03

0.030.02

0.02

0.02

0.02

SHAKE MAP based on peak acceleration values derived from triggered RAN stations

Quick transmission of recorded events (PGA) is used for drawing ground shaking maps few minutes after the event.

Digital stations are equipped with GPS absolute timing and high sensitivity sensors.

Rapidly available high quality strong motion data useful for seismic engineering, microzonation, and

seismological research.


F. Sabetta 5.24

http://itaca.mi.ingv.it/ItacaNet/

1. Data base planning and control

2. Records collection and processing

3. Event, station and instrument checking

4. Data base implementation and data dissemination

Analog data

1972-1993: 458 accelerograms by ENEL and ENEA

1993-2004: 214 accelerograms by DPC-USSN

Digital data

1993-2011: 4084 accelerograms by DPC-USSN

TOTAL 4756 time-histories (3 comp).

• Unify in the same format data acquired by different institutions (Enel, ENEA, DPC-USSN)

• Process and correct the accelerograms in order to make them available for different applications

• Distribute data on-line


F. Sabetta 5.25

Italian Strong motion database new release 2019 http://itaca.mi.ingv.it/ItacaNet_30/#/home

ITACA 3.0 contiene più di 40,000 forme d'onda accelerometriche rappresentative delle tre componenti spaziali del moto sismico generate da 1,883 terremoti di magnitudo superiore a


F. Sabetta 5.26

3.0 relativi al periodo 1972-2018. ITACA3.0 include circa 30,000 forme d'onda processate da specialisti.

European Strong motion database http://esm.mi.ingv.it

The database includes 71408 three comp. waveforms with M>=4

The accelerograms are mainly from Italy, Greece, Turkey and Iran

The format of data is the same as in ITACA

ESM includes: European Strong-Motion Database (FP5 1998-2002), ITalian ACcelerometric Archive (ITACA), Strong Ground Motion Database of Turkiye, HEllenic Accelerogram Database (HEAD).

Corso di costruzioni in zona simica Modulo di determinazione … · 2020. 9. 24. · Corso di...

Documents

Transcript of Corso di costruzioni in zona simica Modulo di determinazione … · 2020. 9. 24. · Corso di...