Course Outline (1) 2. Engineering Seismology. #2 Engineering Seismology

Transcription

1 CE3.98N Soil Dynamics and Earthquake Engineering # Engineering Seismology January 15, 3 Fumio Yamazaki yamazaki@ait.ac.th SEC/SCE, AIT Introduction 1.1 Earthquakes 1. Consequences of Earthquakes Course Outline (1. Engineering Seismology.1 Mechanism of Earthquakes. Seismic Waves.3 Earthquake Magnitude and Seismic Intensity.4 Seismometers and Seismic Observation.5 Tsunamis Jan Seismic Ground Motion 3.1 Characteristics of Seismic Ground Motion 3. Fourier Spectrum 3.3 Response Spectrum 3.4 Attenuation Relations and Effects of Soil Conditions 3.5 Microtremor Observation Jan. 15. Engineering Seismology Earthquake Motion Japan Meteorological Agency (JMA Kobe Record Note: 1. G = 98 cm/s.1 Mechanism of Earthquakes. Seismic Waves.3 Earthquake Magnitude and Seismic Intensity.4 Seismometers and Seismic Observation.5 Tsunamis 3 Acc (cm/s Vel (cm/s Dis (cm JMA Kobe-NS 5-5 Max=818.5 cm/s Max=91.51 cm/s Max=18.79 cm Acceleration (cm/s Velocity (cm/s Displacement (cm Time (s Kobe NHK TV Station on January 17, 1995 Maximum values are called the peak ground acceleration (PGA, PGV, PGD 4

2 Seismic Waves Body Wave Cross section of the Earth showing the paths of seismic waves generated by earthquakes. Seismic waves may travel either along or near the earth's surface (Rayleigh and Love waves or through the earth's interior (P and S waves. 5 Seismic Waves Surface Wave 6 Body Wave A body wave is a seismic wave that moves through the interior of the earth, as opposed to surface waves that travel near the earth's surface. Almost vertically incident to the ground surface due to the ray theory P wave: P (Primary wave, or compressional wave, is a seismic body wave that shakes the ground back and forth in the same direction and the opposite direction as the direction the wave is moving. S wave: S (Secondary wave, or shear wave, is a seismic body wave that shakes the ground back and forth perpendicular to the direction the wave is moving. SH (H only, transverse and SV (H and V, radial. 7 SH P SV Snell s Law sinθ Incident SH i = const. V i Refracted SH ρ 1,µ 1,G 1 ρ,µ,g Reflected SH θ i V i V j θ k θ j Vk Refracted Reflected Reflection/Refraction of SH-wave Refraction process that produces nearly vertical 8 wave propagation near the ground surface.

3 Basic Terms of Waves π T = u ( x,t ω u( x,t π λ = k Rayleigh wave Surface wave A surface wave is a seismic wave that is trapped near the surface of the earth. T: Period of the wave =1/f λ : wavelength t time the wave propagation velocity V V =λ/τ x space ω = circular frequency = π/t = πf f = frequency (Hz k = wave number = π/λ Love wave Rayleigh wave: A Rayleigh wave is a seismic surface wave causing the ground to shake in an elliptical motion, with no transverse motion. Love wave: A Love wave is a surface wave having a horizontal motion that is transverse (or perpendicular to the direction the wave is traveling. 9 1 Seismic Wave Propagation Propagation of Seismic Wave in the 1995 Kobe EQ Horizontal (North-South Acceleration (cm/s Hypocenter P-wave S-wave SH P SV P-wave: Primary wave, Compressive wave Vp 6 km/s in crust S-wave: Secondary wave, Shear wave Vs 3 km/s in crust P-S time: measure of sitesource distance Distance and arrival time Seismic waves take more time to arrive at stations that are farther away. The average velocity of the wave is just the slope of the line connecting arrivals, or the change in distance divided by the change in time. Variations in such slopes reveal variations in the seismic velocities of rocks. X X tps = = X ( 1/ Vs 1/ Vp Vs Vp tps X = 1/ V 1/ V ( s p

4 Locating Earthquakes Although it is possible to infer a general location for an event from the records of a single station, it is most accurate to use three or more stations. A measurement of the P-S time at single station gives the distance between the station and the event. Drawing a circle on a map around the station's location, with a radius equal to the distance, shows all possible locations for the event. With the P-S time from a second station, the circle around that station will narrow the possible locations down to two points. It is only with a third station's P-S time that should identify which of the two previous possible points is the real one Earthquake Magnitude and Seismic Intensity Magnitude: a number that characterizes the relative size of an earthquake. Magnitude is based on measurement of the maximum motion recorded by a seismograph. Several scales have been defined, but the most commonly used are (1 local magnitude (ML, commonly referred to as "Richter magnitude," ( surface-wave magnitude (Ms, (3 body-wave magnitude (m B, (4 energy magnitude (Me and (5 moment magnitude (Mw. Scales 1-3 have limited range and applicability and do not satisfactorily measure the size of the largest earthquakes. The moment magnitude (Mw scale, based on the concept of seismic moment, is uniformly applicable to all sizes of earthquakes but is more difficult to compute than the other types. All magnitude scales should yield approximately the same value for any given earthquake Local ("Richter" Magnitude (1 Defined by Richter (1935 ML = log 1 A - log 1 B where A is the maximum trace amplitude in µm recorded on a standard short-period seismometer (the Woods-Anderson torsion seismograph and log B is a standard value as a function of distance (within 6 km. Maximum Displacement Epicentral Distance km Local ("Richter" Magnitude ( The basic idea was by knowing the distance from a seismograph to an earthquake and observing the maximum signal amplitude, an empirical quantitative ranking of the earthquake's inherent size could be made. Since the original definition held only for California earthquakes, mostly occurring within the top 16 km of the crust, corrections for variations in earthquake focal depth were unnecessary. Richter's original magnitude scale was then extended to observations of earthquakes of any distance and of focal depths ranging between and 7 km. Woods-Anderson seismograph

5 Body Wave Magnitude Because earthquakes excite both body waves and surface waves, two magnitude scales evolved - the m b and M S scales. The standard body-wave magnitude formula defined by Gutenberg and Richter (1956 is m b = log 1 (A/T + Q(D,h A: the amplitude of ground motion (in microns; T : the corresponding period (in sec.; and Q(D,h: a correction factor that is a function of distance, D (degrees: the angle between epicenter and station h: the focal depth (km of the earthquake. Surface Wave Magnitude IASPEI formula: M s = log (A/T log D where A is the maximum ground amplitude in µm (microns of the vertical component of the surface wave within the period range 18 <= T <=. T is the period in seconds. D is the distance in geocentric degrees (station to epicenter and <= D <= 16. M s magnitudes are not generally computed for depths greater than 5 km. All these magnitudes are considered to be reasonably consistent with Richter's original definition of M L Energy and Magnitude Magnitude vs. Ground Motion and Energy Gutenberg and Richter (1956 relationship: log 1 E= M s A magnitude based on energy radiated by an earthquake, M e, can now be defined, M e = /3 log 1 E -.9 For every increase in magnitude by 1 unit, the associated seismic energy increases by about 3 times. M=7 = M=6 = M=5 x 3 x 1, Table shows, for example, that a magnitude 7. earthquake produces 1 times more ground motion that a magnitude 6. earthquake, but it releases about 3 times more energy. The energy release best indicates the destructive power of an earthquake. 19

6 Problems of Magnitude Size of Faults for Earthquakes with M equal to about 8 1. Variation of magnitude depending on recording sites. Variation of magnitude by various definitions (Measuring different period ranges of seismic motion EQs in Japan 196 Chile EQ M L, M s, m B are not suitable for great earthquakes. 3. Saturation of magnitude at about 8. Hence existing magnitudes were not suitable for great earthquakes. (The periods to measure are too short for the earthquake larger than M=8 196 Chile EQ M w =9.5, Ms=8.3 A=8km km 1 Moment Magnitude Hanks and Kanamori formula (1979 M W = /3 log 1 M O where Mo is the seismic moment of the best double couple in dyne-cm. Although M w and M e are both magnitudes, they describe different physical properties of the earthquake. M w, computed from low-frequency seismic data, is a measure of the area ruptured by an earthquake. M e, computed from high frequency seismic data, is a measure of seismic potential for damage. Consequently, M w and M e often do not have the same numerical value. Seismic Moment The seismic moment is a measure of the size of an earthquake based on the area of fault rupture, the average amount of slip, and the force that was required to overcome the friction sticking the rocks together that were offset by faulting. Moment: Mo= µa D µ = shear modulus = 3 GPa in crust, 75 GPa in mantle A = LW = Fault area D = average displacement during rupture Double couple

7 Frequency of Occurrence of Earthquakes Based on Observations since 19 Descriptor Magnitude Average Annually Great 8 and higher 1 Major Strong Moderate Light , (estimated Minor , (estimated Very Minor < 3. Magnitude - 3: about 1, per day Magnitude 1 - : about 8, per day Empirical Formulas Related to Magnitude Comparison of Size of Faults Length of fault : L (km log 1 L.5M Fault slip in one event : D (m log 1 D.5M 3.3 Using these formulas, Magnitude M Length L (km Slip D (m Magnitude Mw Fault area (km Typical rupture dimensions (km x km x x x x 3 8 1, 5 x Landars, Mw= Kobe, Japan, Mw= Northridge Mw= Siera Madre Mw= Loma Prieta Mw=6.9 Compare the fault area of the magnitude 7.3 (top with that of the magnitude 5.6 (smallest one near the bottom. 8

8 Intensity The intensity is a number (written as a Roman numeral describing the severity of an earthquake in terms of its effects on the earth's surface and on humans and their structures. Several scales exist, but the ones most commonly used are the Modified Mercalli scale (MMI and the Rossi-Forel (RF scale. There are many intensities for an earthquake, depending on where you are, unlike the magnitude, which is one number for each earthquake. 9 Modified Mercalli Intensity (1 I. Not felt except by a very few under especially favorable conditions. II. Felt only by a few persons at rest, especially on upper floors of buildings. III. Felt quite noticeably by persons indoors, especially on upper floors of buildings. Many people do not recognize it as an earthquake. Standing motor cars may rock slightly. Vibrations similar to the passing of a truck. Duration estimated. IV. Felt indoors by many, outdoors by few during the day. At night, some awakened. Dishes, windows, doors disturbed; walls make cracking sound. Sensation like heavy truck striking building. Standing motor cars rocked noticeably. V. Felt by nearly everyone; many awakened. Some dishes, windows broken. Unstable objects overturned. Pendulum clocks may stop. VI. Felt by all, many frightened. Some heavy furniture moved; a few instances of fallen plaster. Damage slight. 3 Modified Mercalli Intensity ( VII. Damage negligible in buildings of good design and construction; slight to moderate in well-built ordinary structures; considerable damage in poorly built or badly designed structures; some chimneys broken. VIII. Damage slight in specially designed structures; considerable damage in ordinary substantial buildings with partial collapse. Damage great in poorly built structures. Fall of chimneys, factory stacks, columns, monuments, walls. Heavy furniture overturned. IX. Damage considerable in specially designed structures; well-designed frame structures thrown out of plumb. Damage great in substantial buildings, with partial collapse. Buildings shifted off foundations. X. Some well-built wooden structures destroyed; most masonry and frame structures destroyed with foundations. Rails bent. XI. Few, if any (masonry structures remain standing. Bridges destroyed. Rails bent greatly. XII. Damage total. Lines of sight and level are distorted. Objects thrown into the air. 31 Isoseismal An isoseismal (line is a contour or line on a map bounding points of equal intensity for a particular earthquake. Map showing intensity for the New Madrid earthquake. 3

9 Problems of intensities 1. The definitions include subjectivity and ambiguity.. Sometimes, confused with magnitude. 3. Depending on the regions and era, the resultant damages are different. Development of Instrumental intensity using acceleration or velocity records for quick ShakeMap. Why intensity is still used? 1. Familiar to general public than acceleration or velocity.. It can be defined without instruments. (historical earthquakes, regions without instruments 3. Conveniently used in field surveys 4. Development of empirical formulas using acceleration and velocity 33 MMI map of the Northridge EQ based on damage surveys 34 Empirical formula of MM Intensity The MMI will be calculated by the formula: log(pga*98=.3*mmi+.14 or MMI=1/.3*(log1(PGA* by Trifunac & Brady (1975. PGA unit is G. Trifunac & Brady (1975 Risk Assessment Tool for Diagnosis of Urban Areas against Seismic Disasters, CD-ROM, 35 MM Intensity descriptions with the corresponding peak acceleration and velocity values used in the ShakeMaps. Instrumental Intensity Acceleration (%g Velocity (cm/s Perceived Shaking Potential Damage <.17 <.1 Not Felt None Weak None Light None Moderate Very light Strong Light Very Strong Moderate Severe Moderate to Heavy Violent Heavy > 14 > 116 Extreme Very Heavy 36

10 Rapid development of ShakeMap using strong motion rcords Mainshock, Foreshocks, Aftershocks The mainshock is the largest earthquake in a sequence, sometimes preceded by one or more foreshocks, and almost always followed by many aftershocks. Foreshocks are relatively smaller earthquakes that precede the largest earthquake in a series, which is termed the mainshock. Not all mainshocks have foreshocks Aftershocks are earthquakes that follow the largest shock of an earthquake sequence. They are smaller than the mainshock and within 1- fault lengths distance from the mainshock fault. Aftershocks can continue over a period of weeks, months, or years. In general, the larger the mainshock, the larger and more numerous the aftershocks, and the longer they will continue. 38 Distribution and number of aftershocks following the M7.8 main shock of 1993 Hokkaido-Nansei-Oki EQ Focal region Daily number of after shocks Omori Formula Number of aftershocks K n( t = t + c n( t = Modified Omori Formula ( p t + c n(t: number of aftershocks per unit time K, c, p: constants to be determined for each earthquake K The 1995 Kobe EQ Number of aftershocks per day Osaka Bay Number per day The area of aftershocks corresponds the focal region of the main shock. Number of aftershocks reduces with 39time. Days after Mainshock4

11 Aftershocks of the 1994 Northridge EQ (by May M3. - M M4. - M M5. - M Seismometers and Seismic Observation Seismographs 41 A seismograph, or seismometer, is an instrument used to detect and record earthquakes. Generally, it consists of a mass attached to a fixed base. During an earthquake, the base moves and the mass does not. The motion of the base with respect to the mass is commonly transformed into an electrical voltage. The electrical voltage is recorded on paper, magnetic tape, or another recording medium. 4 Mechanism of Seismograph An earthquake does not make the pendulum swing. Instead, the pendulum remains fixed as the ground moves beneath it. A pendulum with a short period (left moves along with the support and registers no motion. A pendulum with a long period (right tends to remain in place while the support moves. The boundary between the two types of behavior is the natural period of the pendulum. Only motions faster than the natural period will be detected; any motion slower will not. Seismograph usually refers a displacement-type seismometer Equation of motion of a seismometer Natural period of a pendulum Horizontal motion Vertical motion Equation of motion of a mass m y ( t + cy ( t + ky( t = mu ( t y(t = the displacement of mass with respect to Earth u(t = the displacement of Earth c = the damping constant, k = the spring constant. The natural circular frequency of the system is defined as ω = k / m and the damping ratio is defined as h = c then, km y ( t + hω y ( t + ω y( t = u ( t 44 (1 (

12 Response of a seismometer (1 y ( t + hω y ( t + ω y( t = u ( t ( Eq. ( shows that the Earth acceleration can be recovered by measuring the displacement of the mass and its time derivatives. Considering harmonic Earth displacement of the form: u iωt ( t = U ( ω e (3 where ω=πf is the circular frequency of the Earth displacement. The displacement response of the seismometer mass can be expressed as Then we have y Ground acceleration Response velocity Response acceleration iωt ( t = Y ( ω e (4 iωt (5 u( t = ω U ( ω e iωt y ( t = iωy ( ω e (6 iωt y( t = ω Y ( ω e (7 45 Response of a seismometer ( Substituting Eqs. (3-(7 to Eq. (, and dividing by the common factor of, we obtain ω Y ( ω hiωωy ( ω + ωy ( ω = ω U ( ω (8 or ω Y ( ω = U ( ω ω hiωω + ω ( ω ω = 1 ( ω ω + h( ω ω i U ( ω = H ( ω U ( ω where H(ω is the frequency response function of the sensor. The response function is complex; in polar form it can be expressed as iθ ( ω H ( ω = A( ω e (1 ( ω ω where the amplitude A(ω A( ω = (11 [ 1 ( ω ω ] + 4h ( ω ω and the phase lag θ θ = tan 1 h( ω ω 1 ( ω ω (1 (9 46 i t e ω Response of a seismometer (3 For a long period pendulum ω >> 1 ω with small h A( ω 1 θ 18 The motion of mass is simply opposite to the ground motion. Displacement Measurement For a short period pendulum ω >> ω, the response of the sensor to ground acceleration is given by substituting U ( ω = U ( ω / ω into Eq. (9: 1 Y ( ω = U ( ω hiωω ω (13 + ω In the low frequency limit, we have 1 Y ( ω = U ( ω for ω >> ω (14 ω For small h, θ Accelerometer ω /ω ω /ω Response of a seismometer (4 For a pendulum ω ω, the response of the sensor to ground velocity is given by substituting U ( ω = iu ( ω / ω into Eq. (9: iω Y ω = U ( ω hiωω + ω ω ( (15 1 For ω ω Y ( ω = U ( ω (16 hω For large h, θ 9 Velocity Measurement Modern seismometers have a wide range of linear response both in amplitude and phase. ω /ω ω /ω

13 Example of Recent Strong Motion Accelerometer The IRIS Global Seismographic Network (GSN The goal of the GSN is to deploy 18 permanent seismic recording stations uniformly over the earth's surface. IRIS: Incorporated Research Institutions for Seismology 49 GSN stations designated for the International Monitoring System (IMS of the Comprehensive Test Ban Treaty Seismic Monitor through Internet The Seismic Monitor allows you to monitor global earthquakes in near real-time, visit seismic stations around the world, and search the web for earthquake or region-related links

14 JMA Instrumental Intensity in the Tottori EQ Measured by National Seismic Networks N Strong Motion Stations in Taiwan and Distribution of the JMA seismic intensity for the 1999 Chi-Chi EQ Instrumental Intensity Intensity Note: JMA seismic intensity is calculated from a three-component acceleration record. 54