8. Modified Mercalli Intensity Scale. 8. Modified Mercalli Intensity Scale
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1 8. Modified Mercalli Intensity Scale In 1902, Italian seismologist, G. Mercalli, introduced intensity scale before recording instruments were invented Later, two Californian seismologists (H.O. Wood and F. Neumann, 1931) adapted Mercalli scale to modern construction methods known as modified Mercalli intensity scale, IMM IMM based on subjective human feelings and observations of local damage IMM not a scientific measurement of the ground motion IMM scale is a function of epicentral distance and quality of construction ti at site IMM varies from I to XII Data necessary to determine IMM intensity of an earthquake obtained by interviews and surveys Modified Mercalli Intensity Scale Intensity IMM Description Approximative Peak Ground Horizontal Acceleration (g) I Detected with sensitive instrumentation. Felt by a few persons on upper levels. Suspended objects < 0,003 II may swing. Felt noticeably indoors, but not always recognized as an III earthquake. Parked cars rock slightly. 0,003-0,007 IV Felt indoors by many, some people awaken. Parked cars rock noticeably. 0,007-0,015 V Felt by most people; some breakage of dishes windows and plaster. 0,015-0,030 VI Felt by all; many are frightened; falling plaster and chimneys; minor damage. 0,030-0,070 VII Everybody runs outdoors; damage to buildings varies, depending of the quality of construction. 0,070-0,150 VIII Panel walls thrown out of frames; fall of walls, monuments, chimneys; drivers disturbed. 0,150-0,300 IX Buildings shifted off foundations, cracked, thrown out of plumb; ground cracked; underground pipes broken. 0,300-0,700 X Landslides; rails bent; most masonry and framed structures destroyed; ground cracked. 0,700-1,50 XI Bridges destroyed; new structures remain standing but are greatly damaged. 1,50-3,00 XII Total destruction. 3,00-7,
2 8. Modified Mercalli Intensity Scale IMM results usually expressed in terms of contours of intensities called isoseismal lines Isoseismal contours for New Madrid earthquakes Intensity IMM Description Approximative Peak Ground Horizontal Acceleration (g) I Detected with sensitive instrumentation. Felt by a few persons on upper levels. Suspended objects < 0,003 II may swing. III Felt noticeably indoors, but not always recognized as an earthquake. Parked cars rock slightly. 0,003-0,007 IV Felt indoors by many, some people awaken. Parked cars rock noticeably. 0,007-0,015 V Felt by most people; some breakage of dishes windows and plaster. 0,015-0,030 VI Felt by all; many are frightened; falling plaster and chimneys; minor damage. 0,030-0,070 VII Everybody runs outdoors; damage to buildings varies, depending of the quality of construction. 0,070-0,150 Panel walls thrown out of frames; fall of walls, VIII monuments, chimneys; drivers disturbed. 0,150-0,300 Buildings shifted off foundations, cracked, thrown out of IX plumb; ground cracked; underground pipes broken. 0,300-0,700 Landslides; rails bent; most masonry and framed X structures destroyed; ground cracked. 0,700-1,50 Bridges destroyed; new structures remain standing but are XI greatly damaged. 1,50-3,00 XII Total destruction. 3,00-7, Modified Mercalli Intensity Scale Intensity IMM Description Approximative Peak Ground Horizontal Acceleration (g) I Detected with sensitive instrumentation. Felt by a few persons on upper levels. Suspended objects < 0,003 II may swing. III Felt noticeably indoors, but not always recognized as an earthquake. Parked cars rock slightly. 0,003-0,007 IV Felt indoors by many, some people awaken. Parked cars rock noticeably. 0,007-0,015 V Felt by most people; some breakage of dishes windows and plaster. 0,015-0,030 VI Felt by all; many are frightened; falling plaster and chimneys; minor damage. 0,030-0,070 VII Everybody runs outdoors; damage to buildings varies, depending of the quality of construction. 0,070-0,150 VIII Panel walls thrown out of frames; fall of walls, monuments, chimneys; drivers disturbed. 0,150-0,300 IX Buildings shifted off foundations, cracked, thrown out of plumb; ground cracked; underground pipes broken. 0,300-0,700 X Landslides; rails bent; most masonry and framed structures destroyed; ground cracked. 0,700-1,50 XI Bridges destroyed; new structures remain standing but are greatly damaged. 1,50-3,00 XII Total destruction. 3,00-7,
3 8. Modified Mercalli Intensity Scale Isoseismal contours for 1971 San Fernando earthquakes, Magnitude 6.5 Intensity IMM Description Approximative Peak Ground Horizontal Acceleration (g) I Detected with sensitive instrumentation. Felt by a few persons on upper levels. Suspended objects < 0,003 II may swing. III Felt noticeably indoors, but not always recognized as an earthquake. Parked cars rock slightly. 0,003-0,007 IV Felt indoors by many, some people awaken. Parked cars rock noticeably. 0,007-0,015 V Felt by most people; some breakage of dishes windows and plaster. 0,015-0,030 VI Felt by all; many are frightened; falling plaster and chimneys; minor damage. 0,030-0,070 VII Everybody runs outdoors; damage to buildings varies, depending of the quality of construction. 0,070-0,150 VIII Panel walls thrown out of frames; fall of walls, monuments, chimneys; drivers disturbed. 0,150-0,300 IX Buildings shifted off foundations, cracked, thrown out of plumb; ground cracked; underground pipes broken. 0,300-0,700 X Landslides; rails bent; most masonry and framed structures destroyed; ground cracked. 0,700-1,50 XI Bridges destroyed; new structures remain standing but are greatly damaged. 1,50-3,00 XII Total destruction. 3,00-7, Modified Mercalli Intensity Scale Other intensity scales are used around the world MSK scale ( Medvedev, Sponheuer and Karnik, 1964), used in Europe, has 12 levels and similar to the IMM scale JMA scale (Japan Meteorological Agency) is also used Scale only has eight levels 47 3
4 8. Modified Mercalli Intensity Scale Richter Magnitude Scale In early 1930's, C.F. Richter,,geophysics professor at California Institute of Technology, sought a rational way to describe size of a seismic event (earthquake) Up to that time, only intensity scales were used Richter adopted torsion seismograph, developed by H.O. Wood and J. Anderson, to examine his concept Wood-Anderson seismograph: natural period of 0.8 s 80% of critical viscous damping static magnification of 2800 (ratio of the amplitude read on the seismograph - i.e. the trace amplitude- to the actual amplitude of the ground motion) 49 4
5 9. Richter Magnitude Scale Seismograph Basic Concept h Trace Normalized Amplitude Seismograph 80% Damping 5% Damping 1.25 Frequency (Hz) Richter Magnitude Scale Richter (1935) considered relationship between maximum trace amplitude A and distance R from the epicentre e (epicentral distance) Observed that curves of log 10 A vs R were essentially parallel for different earthquakes Richter chose a particular curve as standard event 51 5
6 9. Richter Magnitude Scale Richter Magnitude Scale Richter defined magnitude of a given earthquake, M L, by calculating difference between its amplitude and amplitude of standard event. (Richter, 1958) M L = log 10 A - log A = Wood-Anderson seismograph amplitude of event in mm A o = Amplitude of standard event for same epicentral distance 10 A o 53 6
7 9. Richter Magnitude Scale Amplitude of Richter scale s standard event (1958). R (km) -log10 Ao R (km) -log10 Ao R (km) -log Ao 0 1, , ,4 5 1, , ,5 10 1, , ,5 15 1, , ,5 20 1, , ,6 25 1, , ,6 30 2, , ,6 35 2, , ,6 40 2, , ,7 45 2, , ,7 50 2, , ,7 55 2, , ,7 60 2, , ,8 65 2, , ,8 70 2, , ,8 80 2, , ,8 85 2, , ,8 90 3, , ,9 95 3, , , , , , , , , , , , , , , ,4 M L= log 10 A - log A o 9. Richter Magnitude Scale Epicentral distance, R, obtained by difference of arrival times between primary and secondary waves (see section 7) For R = 100 km, amplitude on the seismograph of the standard event is equal to A o = mm (-log 10 A o = 3) Richter s logarithmic scale means that an earthquake of M L = 7 produces waves 10 times the amplitude of an earthquake with M L = 6 and 100 times amplitude of M L = 5 Richter used term «magnitude» by analogy to same term used in astronomy to define brightness of a star (magnitude- brightness relationship is reversed in astronomy) 55 7
8 9. Richter Magnitude Scale L.K. Hutton and D.M. Boore (1987) analysed close to records from 972 earthquakes recorded in Southern California Proposed new expression for Richter scale s standard event: d log Ao = 1, log ,00189 (d - 100)+ 3,0 where d the distance to the hypocentre (hypocentral distance) in km (~ R) Valid for distances between 10 and 700 km of the epicentre Richter Magnitude Scale 5 4 -log 10 A o 3 2 Richter (1958) Hutton and Boore (1987) R = d (km) 57 8
9 M L 9. Richter Magnitude Scale Richter Scale Nomogram = log 10 A - log 10 A o Richter Magnitude Scale Assumptions and limitations of local magnitude scale: scale developed for Southern California for other regions, correction factor must tbe introduced dto reflect different structures of earth s crust scale does not take the focal depth into account California earthquakes generally shallow to compensate, hypocentral distance can be used scale restricted to Wood-Anderson seismograph correction to amplification must be introduced when using other instruments scale does not take into account characteristics of recording sites station correction usually introduced based on systematic deviations from the mean obtained from a large number of records 59 9
10 9. Richter Magnitude Scale Every year, around the world: thousands of earthquakes of M L < 4 recorded about a dozen of magnitude M L = 7 recorded only a very few of magnitude M L >8 Richter scale has no upper or lower limits Possible that earthquake exhibits an amplitude lower than amplitude of standard event, creating negative magnitude Physically, maximum value for M L is about 9 maximum value depends on: fault rupture length fault depth local site conditions Richter Magnitude Scale Local magnitude and length of rupture for recent earthquakes. San Francisco (1906) El Centro (1940) Chili (1960) Alaska (1964) San Fernando (1971) Loma Prieta (1989) M ML 8,3 7,1 8,6 8,4 6,6 7,0 L (km)
11 9. Richter Magnitude Scale Evolution of Magnitude Scales Local magnitude, M L, measures spectral amplitude of ground motion in a frequency band varying from 1 to 5 Hz Following Richter s original work, many modifications were introduced leading to variety of magnitude scales depending on different types of waves and different frequency bands Value of an earthquake s magnitude is not absolute but depends on type of waves considered Nowadays, in addition to the local magnitude, which is mostly used in California, three other magnitude scales are commonly used: surface wave magnitude, M s body wave magnitude, m b moment magnitude, M w 63 11
12 10. Evolution of Magnitude Scales Surface Wave Magnitude, M s Gutenberg and Richter (1936) proposed surface wave magnitude, M s, for earthquakes recorded d at great distances (teleseismic distances) from epicentre magnitude M s measures spectral amplitude of ground motion at a frequency of 0.05 Hz empirical relationship between energy released by an earthquake, E, and surface wave magnitude log E = where E = energy released in ergs (1 erg = 99.9 x 10-9 N m = 73.7 x 10-9 ft-pound) M s Evolution of Magnitude Scales Body Wave Magnitude, m b body wave amplitudes relatively insensitive to depth Gutenberg (1945) proposed body wave magnitude scale, m b, for deep focus earthquakes m b scale based on amplitude of primary waves, for a frequency of 1 Hz, recorded at hypocentral distances greater than km in certain regions of the world, like the west coast of North America, primary waves are significantly attenuated at depth ranging from 75 to 200 km value of m b is greatly diminished to overcome this problem, Rayleigh s surface waves are used to determine the body wave magnitude. In this case, the body wave magnitude is written m b L g R.B. Herrmann and O.W. Nuttli (1981) demonstrated that m b L g and M s values practically identical for earthquakes in California 65 12
13 10. Evolution of Magnitude Scales Moment Magnitude, M W measure of size (dissipated energy) of an earthquake M W scale much more recent seismic moment M o defined as rigidity of rock, times fault area, times length of slip M o = G s A G = shear modulus of rock; s = average slip; A = fault area seismic moment has units of work or energy Evolution of Magnitude Scales Moment Magnitude, M W Many researchers believe that seismic moment is most fundamental parameter that can be used to measure strength of an earthquake caused by fault slip Values of seismic moments. Earthquake Mo (dyn-cm) Chili, Micro earthquakes Micro-fractures (laboratory) 10 5 Note : 1 dyn = 1 g-cm/s
14 10. Evolution of Magnitude Scales Moment Magnitude, M W Kanamori (1977) defined moment magnitude, M w, from seismic moment, M o, expressed in dyn-cm M 2 = w log10 M o Evolution of Magnitude Scales Magnitude Summary 69 14
15 10. Evolution of Magnitude Scales Earthquake Energy Sumatra-Andaman (2004) Source: Earthquakes by Bruce A. Bolt 11. Relationships Between Magnitude Scales Use of different scales to define magnitude of an earthquake may cause confusion Usually, news medias will refer to Richter s magnitude scale without specifying type of scale used When Richter and Gutenberg proposed their magnitude scales, M L, M s and m b, their hope was that three scales would produce same numerical values for any earthquake Hypothesis proved to be wrong as each scale measures the amplitude of waves in a specific frequency band Amplitude not constant throughout the frequency spectrum of any typical earthquake Interpretation of magnitude of an earthquake depends of the scale used In California, Richter s magnitude associated with M L when magnitude is smaller than 6.5 and with M s for greater earthquakes 71 15
16 11. Relationships Between Magnitude Scales O.W. Nuttli (1981) demonstrated that relationships between magnitude scales are function of seismic environment He proposed two types of relationships: one for earthquakes along boundaries of tectonic plates (interplate zones) one for earthquakes within continental regions (intraplate zones) Relationships Between Magnitude Scales Relationships between magnitude scales for interplate earthquakes ML or mblg or mn mb Ms Mw 5,0 4,6 4,15 4,6 5,2 4,8 4,35 4,8 5,4 5,0 4,6 5,0 5,6 5,2 5,0 5,2 5,8 5,4 5,8 5,8 6,0 5,6 6,55 6,3 6,2 5,8 7,0 6,9 6,4 6,0 7,45 7,4 6,6 6,2 7,9 7,9 6,8 6,4 8,15 8,2 7,0 6,6 8,4 8,6 7,2 6,8 8,7 9,
17 11. Relationships Between Magnitude Scales Relationships between magnitude scales for intraplate earthquakes. ML or mblg or mn mb Ms Mw 4,0 4,0 2,85 3,8 4,2 4,2 3,1 3,9 4,4 4,4 3,3 4,1 4,6 4,6 3,6 4,3 4,8 4,8 4,0 4,6 5,0 5,0 4,4 4,8 5,2 5,2 4,8 5,1 5,4 5,4 5,2 5,4 5,6 5,6 5,6 5,6 5,8 5,8 6,0 5,9 6,0 6,0 6,4 6,2 6,2 6,2 6,8 6,4 6,4 6,4 7,2 6,7 6,6 6,6 7,6 7,0 6,8 6,8 8,0 7,2 Chapter 7,0 2 Seismology 7,0 and 8,4 Seismicity 7,5 7,2 7,2 8,7 7, Seismic Parameters Influencing Structural Response To determine response of a structure subjected to a particular earthquake, complete acceleration time-history (accelerogram) is required Unlikely that any one record will be adequate Usually necessary to examine an ensemble of records 75 17
18 12. Seismic Parameters Influencing Structural Response Seismic Parameters Influencing Structural Response Structural damage is mainly caused by four important seismic parameters : the amplitude of the ground motion the frequency contents of earthquake accelerograms the duration of earthquakes the site effects 77 18
19 12. Seismic Parameters Influencing Structural Response Amplitude of the Ground Motion can be expressed in various ways: the peak ground acceleration, a max does not take into account complete ground acceleration timehistory not necessarily a good indicator of the earthquake s damage potential the root mean square (RMS) acceleration, a RMS : arms = to 1 2 a (t ) dt to 0 where t o is the total duration of the record RMS acceleration is a factored mean amplitude for the entire accelerogram Seismic Parameters Influencing Structural Response Frequency Contents of Earthquake Accelerograms evaluated in various ways: by counting total number of cycles (or zero crossings) and dividing by total duration of record Zero crossing f = 23 crossings/30 seconds = 0.77 Hz T = 1/0.7Hz = 1.30 sec 79 19
20 12. Seismic Parameters Influencing Structural Response Frequency Contents of Earthquake Accelerograms evaluated in various ways: plotting response spectrum of accelerogram representing the maximum responses of a series of single-degree-of-freedom oscillators with different natural periods and damping ratios Northridge-Rinaldi Seismic Parameters Influencing Structural Response Frequency Contents of Earthquake Accelerograms evaluated in various ways: by plotting a Fourier spectrum representing the frequency distribution, ω, of energy contained in accelerogram 81 20
21 12. Seismic Parameters Influencing Structural Response Frequency Contents of Earthquake Accelerograms Fourier Spectrum Seismic Parameters Influencing Structural Response Frequency Contents of Earthquake Accelerograms Power Spectrum 83 21
22 12. Seismic Parameters Influencing Structural Response Duration of Earthquakes duration of an earthquake is usually described by the strong motion duration of the record definition implies duration of central segment of the record which causes structural damage various methods for calculation of strong motion duration: direct approach takes the time interval between first and last peak, greater to a given value on the accelerogram (usually 0.05 g) Seismic Parameters Influencing Structural Response Duration of Earthquakes method proposed by R. Dobry, I. Idriss and E. Ng (1978), which defines duration as time interval required to accumulate between 5 to 95 % of accelerogram s total energy energy represented by a measure of intensity, I A, (Arias, 1969). I A = g t 0 a 2 (t) dt 85 22
23 12. Seismic Parameters Influencing Structural Response Site Effects local ground-response effects influence of relatively shallow geologic materials on vertically propagating seismic waves soil column beneath a structure responds as a dynamic (nonlinear) oscillator basin effects influence of two- or threedimensional sedimentary basin structures on ground motions, body wave reflections and surface wave generation at basin edges Surface topography ground motion shaking can be amplified along ridges or near the tops of slopes. intensity of ground-motion shaking can be reduced due to topographical effects in canyons or at the base of slopes Attenuation Relationships Mathematical expression describing variation (attenuation) of ground motion as a function of distance from focal point and of earthquake s magnitude Simplification of attenuation phenomenon related to complex physical and tectonic characteristics Initially, attenuation relations for peak ground horizontal acceleration and/or for peak ground horizontal velocity used to construct seismic zoning maps in building codes Current seismic maps based on attenuations for spectral acceleration at various periods K.W. Campbell (1985) presented excellent paper on development of attenuation relations 87 23
24 13. Attenuation Relationships M w = 6.5 M w = Attenuation Relationships General equation for attenuation relation log y x0 + f 1 (M) + f 2 (d) + f 3 (s) log = log 10 or ln y = seismic parameter (a max, v max, S a, etc.) x 0 = constant f 1 = mathematical function of magnitude (M) depends on source type f 2 = mathematical function of the hypocentral distance (d) depends on geometric spread of seismic wave front as it propagates from the source depends seismic wave type (body wave, surface wave, etc) f 3 = mathematical function of the soil conditions at the site (s) Depends on anelastic attenuation of seismic waves caused by material damping (treating soil as viscoelastic materials) and scattering ε = random variable with zero mean and non-zero standard d deviation i Typical attenuation relationships more complicated than basic equation given above. Additional terms needed to account for other effects near-source directivity, faulting mechanism (strike slip, reverse and normal), site conditions (different relationships), and hanging wall/footwall 89 24
25 13. Attenuation Relationships Attenuation relationships use various definitions of site-to-source distance Seismogenic depth: depth of surface materials Attenuation Relationships 91 25
26 13. Attenuation Relationships Attenuation Relationship of Abrahamson and Silva S a (g) = spectral acceleration in g M = moment magnitude r rup = closest distance to the rupture plane in km F = fault type (1 for reverse, 0.5 for reverse/oblique, and 0 otherwise) HW = dummy variable for hanging wall sites (1 for sites over hanging wall and 0 otherwise) S = dummy variable for site class (0 for rock or shallow soil and 1 for deep soil) Attenuation Relationships Attenuation Relationship of Abrahamson and Silva 93 26
27 13. Attenuation Relationships Uncertainties in Attenuation Relationships Obtained empirically from least-square regression of highly scattered data Often attenuation relationships assumed to follow a log-normal distribution (normal distribution of the logarithmic of the ground motion parameter of interest) Generally expressed by an estimate of the standard deviation of the logarithmic of the ground motion parameter of interest, lny, at a given magnitude and distance lny historically assumed constant for all magnitudes and distances Probability that the ground motion parameter exceeds a value Y * from an earthquake of a given magnitude and distance, P[Y>Y*/M = m, d] given by: * * lny lny Y / M m, d 1 F P Y lny Attenuation Relationship of the mean valueof the groud motion parameter Y F Z Z lny Standard Normal Cumulative Distribution Function F Z Z Attenuation Relationships Uncertainties of Attenuation Relationships d d d 95 27
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