Magnitude & Intensity

Transcription

1 Magnitude & Intensity Lecture 7 Seismometer, Magnitude & Intensity

2 Vibrations: Simple Harmonic Motion Simplest vibrating system: 2 u( x) 2 + ω u( x) = 0 2 t x Displacement u ω is the angular frequency, f = ω / π There are two solutions: u(x)= A sin (ωt) and u(x) = B cos (ωt) A and B are amplitude, or in exponential form: u( t) = U ( ω)exp[ iωt]

3 The Seismometer Basic principle mass attached to a moveable frame when frame is shaken by seismic waves the inertia of the mass causes it s motion to lag behind relative motion recorded on rotating drum, on magnetic tape or digitally Mass is damped to prevent continued oscillation This limits the frequency response of the seismometer Relative motion amplified up to 100s of thousands of times Schematic of a horizontal motion mechanical seismometer

4 Modern seismometers Güralp Systems Ltd Earthscope array - 250

5 Review: Earthquake magnitude Richter magnitude scale M = log A( ) - log A 0 ( ) where A is max trace amplitude at distance and A 0 is at 100 km Surface wave magnitude M S M S = log A + α log + β where A is max amp of 20s period surface waves Magnitude and energy log E s = M s (ergs)

6 z(t) Displacement of m relative to Earth The Inertial Seismometer Mass m Spring stiffness k Damping η F s = - k z Equating the resistive forces on the mass to the inertial forces: 2 dz( t) d k z( t) η = m + 2 dt dt Damping parameter ζ=η/m [ u( t) z( t) ] Resonant undamped angular frequency ω 02 = k/m F d = - η dz/dt u(t) Displacement of Earth

7 Earth noise Individual acceleration spectra at over 100 stations showing Earth noise. Note the microseism peak at 5 to 8s period and the relatively low noise levels at 20 to 200s period.

8 Response of 4 different seismometers Velocity response functions for four different verticalcomponent instruments

9 Strong motion seismometers Designed to pickup strong, high-amplitude shaking close to quake source Insensitive to weak shaking Most common type is the accelerometer Directly records ground acceleration Not continuously recording - triggered by first waves Difficult to differentiate different earthquake waves Standard seismographs go off scale (clipped) by strong ground motions Most useful for understanding response of buildings to earthquakes

10 Strong motion record Acceleration Velocity Displacement Remember the acceleration of the Earth is determined by measuring the acceleration, velocity and displacement

11 Response Spectrum 15 5% damping Spectral acceleration (m/sec 2 ) ,000 year 1,000 year 100,000 year return period Fundamental period (seconds) Arup

12 World seismic hazard maps Accelerations

13 Attenuation of seismic waves: reduction in amplitude / loss of energy a) Elastic attenuation: geometric spreading Spherical body waves spread in 3D Surface waves spread in 2D f(t,r) But even after correcting for geometric spreading there is still attenuation: R.f(t) Elastic Elastic attenuation R Anelastic R b) Anelastic attenuation Permanent rock deformation: close to earthquake source Heat loss due to internal friction e.g. between pore fluids and rock motion

14 Elastic attenuation: geometric spreading Body waves (P, S etc.): As a spherical wave front grows the energy of the source is spread out over a wider and wider area leading to a reduction of amplitude with distance Amplitude Energy: area under the curve Amp 2 solid angle A 1 -area A 2 -area r Energy is proportional to: r 2 1 (i) square of amplitude R 1 R 2 (ii) area of wavefront Find A 2 / A 1 = r 2 2 / r 12 = R 22 / R 1 2 So the wave energy of body waves diminishes as 1/R 2 and the body wave amplitude diminishes as 1/R

15 Elastic attenuation: geometric spreading Surface waves (LR, LQ etc.): Surface wave are consigned to the surface Energy of surface waves falls off as 1/R Energy of body waves falls of as 1/R 2 The spreading of surface wave energy does not translate directly into wave amplitudes, because surface waves are strongly dispersive, and the waveform changes shape Earthquake source R But we can see the dominance of surface waves on teleseismic records is due to the geometric spreading of the wavefront has different dependence on R

16 Anelastic attenuation Anelastic attenuation E f ( t) dt E energy per cycle δe energy lost per cycle t δ E 2 = ( f f dt 1 2) Definition: Quality factor Q = 2 π E / δe Q is dimensionless Q 2π ~ 6 High quality Good transmission Low attenuation Low quality Poor transmission High attenuation

17 Anelastic attenuation There is an exponential decay of amplitude with distance due to anelastic attenuation Amp/Amp 0 long wavelength, low frequency short wavelength high frequency Distance R Short wavelength, high frequency waves are attenuated more than long wavelength, low frequency waves This is why if your upstairs neighbour is playing music, it is the bass which comes through the ceiling

18 In the frequency domain F F Anelastic attenuation ( 0 ω) = F ( ω) exp ( bω ) exp -bω low freq, low energy loss, few cycles ω high freq, high loss, many cycles wave distortion as well as amplitude reduction i.e. change in shape of the wavelet loss of resolution down seismogram c.f. someone playing a stereo in the next room get distortion

19 Attenuation of ground acceleration The range of published average attenuation relationships for acceleration with distance from an earthquake magnitude 6.5 in western North American (after Atkinson and Boore, 1990)

20 Intensity attenuation Average EMS intensity attenuation relationships from analysis of isoseismals of 53 earthquakes, southern Italy (after Coburn et al., 1988).