# Sound Waves and Seismic Waves

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1 Sound Waves and Seismic Waves Seismologists record and analyze waves to determine where an earthquake occurred and how large it was Waves are fundamental to music and seismology Similarities: More high frequency waves if short path is traveled Trombone is retracted, short fault-rupture length (small earthquake) More low frequency waves if long path is traveled Trombone is extended, long fault-rupture length (large earthquake)

2 ISNS 4359 Earthquakes and Volcanoes (aka shake and bake) Lecture 6: Locating EQ s, EQ Magnitude and Intensity Fall 2005

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5 Seismic Velocity Seismic velocity is a material property (like density). There are two kinds of waves Body and Surface waves. There are two kinds of body wave velocity P and S wave velocities. P waves always travel faster than S waves. Seismic velocities depend on quantities like chemical composition, pressure, temperature, etc. Faster Velocities Slower Velocities Lower temperatures Higher temperatures Higher pressures Lower pressures Solid phases Liquid phases

6 Locating the Source of an Earthquake P waves travel about 1.7 times faster than S waves Farther from hypocenter, greater time lag of S wave behind P wave (S-P) (S-P) time indicates how far away earthquake was from station but in what direction?

7 Locating the Source of an Earthquake Need distance of earthquake from three stations to pinpoint location of earthquake: Computer calculation Visualize circles drawn around each station for appropriate distance from station, and intersection of circles at earthquake s location Method is most reliable when earthquake is near surface

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22 Solution to epicenter and hyopcenter Mathematically, the problem is solved by setting up a system of linear equations, one for each station. The equations express the difference between the observed arrival times and those calculated from the previous (or initial) hypocenter, in terms of small steps in the 3 hypocentral coordinates and the origin time. We must also have a mathematical model of the crustal velocities (in kilometers per second) under the seismic network to calculate the travel times of waves from an earthquake at a given depth to a station at a given distance. The system of linear equations is solved by the method of least squares which minimizes the sum of the squares of the differences between the observed and calculated arrival times. The process begins with an initial guessed hypocenter, performs several hypocentral adjustments each found by a least squares solution to the equations, and iterates to a hypocenter that best fits the observed set of wave arrival times at the stations of the seismic network.

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28 Magnitude of Earthquakes Richter scale Devised in 1935 to describe magnitude of shallow, moderately-sized earthquakes located near Caltech seismometers in southern California Bigger earthquake greater shaking greater amplitude of lines on seismogram Defined magnitude as logarithm of maximum seismic wave amplitude recorded on standard seismogram at 100 km from earthquake, with corrections made for distance For every 10 fold increase in recorded amplitude, Richter magnitude increases one number

29 Magnitude of Earthquakes Richter scale With every one increase in Richter magnitude, the energy release increases by about 45 times, but energy is also spread out over much larger area and over longer time Bigger earthquake means more people will experience shaking and for longer time (increases damage to buildings) Many more small earthquakes each year than large ones, but more than 90% of energy release is from few large earthquakes Richter scale magnitude is easy and quick to calculate, so popular with media

30 Magnitude of Earthquakes

31 Magnitude of Earthquakes

32 Magnitude of Earthquakes 21,688 earthquakes recorded by NEIC in

33 Magnitude of Earthquakes 21,688 earthquakes recorded by NEIC in

34 Other Measures of Earthquake Size Richter scale is useful for magnitude of shallow, small-moderate nearby earthquakes Does not work well for distant or large earthquakes Short-period waves do not increase amplitude for bigger earthquakes Richter scale: 1906 San Francisco earthquake was magnitude Alaska earthquake was magnitude 8.3 Other magnitude scale: 1906 San Francisco earthquake was magnitude Alaska earthquake was magnitude 9.2 (100 times more energy)

35 Other Measures of Earthquake Size Two other magnitude scales: Body wave scale (m b ): Uses amplitudes of P waves with 1 to 10-second periods Surface wave scale (m s ): Uses Rayleigh waves with 18 to 22-second periods All magnitude scales are not equivalent Larger earthquakes radiate more energy at longer periods not measured by Richter scale or body wave scale Richter scale and body wave scale significantly underestimate magnitudes of earthquakes far away or large

36 Moment Magnitude Scale Seismic moment (M o ) Measures amount of strain energy released by movement along whole rupture surface; more accurate for big earthquakes Calculated using rocks shear strength times rupture area of fault times displacement (slip) on the fault Moment magnitude scale uses seismic moment: M w = 2/3 log 10 (M o ) 6 Scale developed by Hiroo Kanamori

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38 Foreshocks, Main Shock and Aftershocks Large earthquakes are not just single events but part of series of earthquakes over years Largest event in series is mainshock Smaller events preceding mainshock are foreshocks Smaller events following mainshock are aftershocks Large event may be considered mainshock, then followed by even larger earthquake, so then reclassified as foreshock

39 Magnitude, Fault-Rupture Length and Seismic-Wave Frequencies Fault-rupture length greatly influences magnitude: 100 m long fault rupture magnitude 4 earthquake 1 km long fault rupture magnitude 5 earthquake 10 km long fault rupture magnitude 6 earthquake 100 km long fault rupture magnitude 7 earthquake

40 Magnitude, Fault-Rupture Length and Seismic-Wave Frequencies Fault-rupture length and duration influence seismic wave frequency: Short rupture, duration high frequency seismic waves Long rupture, duration low frequency seismic waves Seismic wave frequency influences damage: High frequency waves cause much damage at epicenter but die out quickly with distance from epicenter Low frequency waves travel great distance from epicenter so do most damage farther away

41 Ground Motion During Earthquakes Buildings are designed to handle vertical forces (weight of building and contents) so that vertical shaking in earthquakes is typically safe Horizontal shaking during earthquakes can do massive damage to buildings Acceleration Measure in terms of acceleration due to gravity (g = 9.8 m/s 2 ) Weak buildings suffer damage from horizontal accelerations of more than 0.1 g In some locations, horizontal acceleration can be as much as 1.8 g (Tarzana Hills in 1994 Northridge, California earthquake)

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43 Periods of Buildings and Responses of Foundations Just as waves have natural frequencies and periods, so do buildings Periods of swaying are about 0.1 second per story 1-story house shakes at about 0.1 second per cycle 30-story building sways at about 3 seconds per cycle Building materials affect building periods Flexible materials (wood, steel) longer period of shaking Stiff materials (brick, concrete) shorter period of shaking

44 Periods of Buildings and Responses of Foundations Velocity of seismic wave depends on material it is moving through Faster through hard rocks Slower through soft rocks When waves pass from harder to softer rocks, they slow down Must therefore increase their amplitude in order to carry same amount of energy greater shaking Shaking tends to be stronger at sites with softer ground foundations (basins, valleys, reclaimed wetlands, etc.)

45 Periods of Buildings and Responses of Foundations If the period of the wave matches the period of the building, shaking is amplified and resonance results Common cause of catastrophic failure of buildings

46 Earthquake Intensity What We Feel During an Earthquake Mercalli intensity scale was developed to quantify what people feel during an earthquake Used for earthquakes before instrumentation or current earthquakes in areas without instrumentation Assesses effects on people and buildings Maps of Mercalli intensities can be generated quickly after an earthquake using people s input to the webpage

47 Earthquake Intensity What We Feel During an Earthquake

48 What To Do Before and During an Earthquake Before an earthquake: Inside and outside your home, visualize what might fall during strong shaking, and anchor those objects by nailing, bracing, tying, etc. Inside and outside your home, locate safe spots with protection under heavy table, strong desk, bed, etc. During an earthquake: Duck, cover and hold Stay calm If inside, stay inside If outside, stay outside

49 Mercalli Scale Variables Mercalli intensity depends on: Earthquake magnitude Bigger earthquake, more likely death and damage Distance from hypocenter Usually (but not always), closer earthquake more damage Type of rock or sediment making up ground surface Hard rock foundations vibrate from nearby earthquake body waves Soft sediments amplified by distant earthquake surface waves Steep slopes can generate landslides when shaken

50 Mercalli Scale Variables

51 Mercalli Scale Variables Mercalli intensity depends on: Building style Body waves near the epicenter will be amplified by rigid or short buildings Low-frequency surface waves are amplified by tall buildings, especially if on soft foundations Duration of shaking Longer shaking lasts, more buildings can be damaged

52 Design of Buildings in Earthquake-Prone Areas Eliminate resonance: Change height of building Move weight to lower floors Change shape of building Change building materials Change attachment of building to foundation Hard foundation (high-frequency vibrations) build tall, flexible building Soft foundation (low-frequency vibrations) build short, stiff building

53 Design of Buildings in Earthquake-Prone Areas Floors, Roofs and Trusses Give horizontal resistance by transferring force to vertical resistance elements Shear Walls Designed to receive horizontal forces from floors, roofs and trusses and transmit to ground Lack of shear walls typically cause structures like parking garages to fail in earthquakes

54 Bracing Design of Buildings in Earthquake-Prone Areas Bracing with ductile materials offers resistance Moment-resisting frames Devices on ground or within structure to absorb part of earthquake energy Use wheels, ball bearings, shock absorbers, rubber doughnuts, etc. to isolate building from worst shaking

55 A Case History of Mercalli Variables: The San Fernando Valley, California, Earthquake of 1971 Earthquake magnitude M 6.6, with 35 aftershocks of magnitude 4.0 or higher Distance from epicenter Bull s-eye damage pattern Foundation materials Not a major factor Building style Soft first-story buildings were major problem Hollow-core bricks at V.A. Hospital caused collapse Collapse of freeway bridges

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57 A Case History of Mercalli Variables: The San Fernando Valley, California, Earthquake of 1971 Duration of shaking Lasted 12 seconds (at that magnitude, can last from 10 to 30 seconds), relatively short time Lower Van Norman Reservoir 11,000 acre-feet of water behind earthen dam, above homes of 80,000 When shaking stopped, only four feet (of original 30) of dam was still standing above water level Another few seconds of shaking might have caused catastrophic flood

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63 Problem Set 1, Journals, Term Paper Problem set 1 and term paper format will be available on WebCT by tomorrow morning. Problem set 1 will now be due on Sept 20, rather than Sept 15. Submit a topic for approval for term paper by Sept 22, if you have not already done so Journals - to reiterate - track 1 event (EQ or V) per week for four weeks and submit a journal on what you find. Length and format is up to you, but all work (other than figures) should be original and all sources cited

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