Lecture: Introduction to Seismology and Ground Motion Parameters

GSC415 Winter 2013 

Engineering Geology II 

Today’s Class 

• Lecture: Introduction to Earthquake Hazards and 

Seismology 

• Homework Exercise: Strong Ground Motion 

Parameters 

• Kramer: Geotechnical Earthquake Engineering 

– Chapters 1-3 

– Appendix B.1-B.5.4 

2/18/13 Cal Poly Pomona 

1



Introduction to Earthquake 

Hazards and Seismology

local agency (city or county); show location of fault investigation trenches; 50-foot setbacks perpendicular from fault 

plane and proposed building footprints. 

9. Geologic Hazard Zones (Liquefaction & Landslides): (If applicable) Show proposed structures in 

relation to CGS official map showing zones of required investigation for liquefaction and landslide, and/or any pertinent 

GSC415 Winter geologic 2013 hazard map from the Safety Element of the local agency (city or county). 


10. Geotechnical Testing of Representative Samples: Broad suite of appropriate geotechnical tests. 

11. Consideration of Geology in Geotechnical Engineering Recommendations: 

Checklist Item or Topic Within Consulting Report 

NA = not applicable 

Discuss California engineering Geological geologic aspects Survey of excavation/grading/fill - Note 48 activities, foundation and support of 

structures. Checklist for the Include Review geologic of Engineering and Geology geotechnical and Seismology inspections Reports and for problems anticipated 16. Site-Specific during Ground grading. Motion Analysis: (If applicable) Required for sites where 

Special California design Public and Schools, construction Hospitals, and provisions Essential for Services bearing Buildings capacity failure and/or footings or foundations 

and deterministic lower limit. See requirements in CBC §1803A.6.2. Provide design response 

founded on weak or expansive January 1, soils. 2011 Consideration of seismic compression of fills; spectrum cut/fill that meets differential 

ASCE 7 §21.3. Also provide SDS and SD1 values that meet ASCE 7 §21.4. 

settlement. 

Note 48 is used by the California Geological Survey (CGS) to review the geology, seismology, and geologic hazards evaluated in 

reports that are prepared under California Code of Regulations (CCR), Title 24, California Building Code. CCR Title 24 applies to California 

Public Schools, Hospitals, Skilled Nursing Facilities, and Essential Services Buildings. The Building Official for public schools is the Division of 

the State Architect (DSA). Hospitals and Skilled Nursing Facilities in California are under the jurisdiction of the Office of Statewide Health 

Planning & Development (OSHPD). The California Geological Survey serves under contract with these two state agencies. 

Seismology & Calculation of Earthquake Ground Motion 

and scaled time histories and response spectra. 

12. Evaluation of Historical Seismicity: Prepare a short description of how historical 

Project Name: ____________________________ 

Location: ____________________________________ 

OSHPD or DSA File #: ____________________ Reviewed By: ________________________________ 

Date 13. Reviewed: Classify __________________________ the Geologic Subgrade California Certified (Site Engineering Class): Geologist 2010 #: _______ CBC Table 1613A.5.2 and 

http://earthquake.usgs.gov/research/hazmaps/design/. 

Project Location 

1. Site Location Map, Street Address, County Name: Correctly plot site on a 

15. 7½-minute Seismic USGS quadrangle Design base-map. Category: Report if S 1 > 0.75 

2. Plot Plan with Exploration Data and Building Footprint: One boring or exploration 

shaft per 5000 ft 2 , with minimum of two for any one building. Exploratory trench locations. 

3. Site Coordinates (Latitude & Longitude): 

grading. 

earthquakes have affected the site. 

effectiveness of options to mitigate landsliding/slope failure effects. Acceptance criteria for ground- 

8. Active Faulting & Coseismic Deformation Across Site: Show conditions proposed structures described in relation to in 2010 CBC §1615A.1.227. apply. Dynamic Provide Site Conditions: probabilistic (If applicable) MCE, deterministic Site response analysis MCE and topographic effects 

Alquist-Priolo Earthquake Fault Zones and/or any potential fault rupture hazard identified from the Safety Element of the 

should be considered, if appropriate. 

local agency (city or county); show location of fault investigation trenches; 50-foot setbacks 

and deterministic 

perpendicular from fault 

lower limit. See requirements 28. in Mitigation CBC §1803A.6.2. Options for Provide Landsliding/Other design response Slope Failure: (If applicable) Discuss 

plane and proposed building footprints. 

spectrum that meets ASCE 7 §21.3. Also provide S DS and S D1 values that meet ASCE 7 §21.4. 

9. Geologic Hazard Zones (Liquefaction & Landslides): (If applicable) Show proposed structures in 

improvement schemes. 

relation to CGS official map showing zones of required investigation for liquefaction and landslide, and/or any pertinent 

geologic hazard map from the Safety Element of the local agency (city or county). 

NR = not addressed by consultant and therefore not reviewed at this time 

conditions described in 2010 CBC §1615A.1.2 apply. Provide probabilistic MCE, deterministic MCE 

17. Deaggregated Seismic Source Parameters: (If applicable) Provide controlling 

magnitude (Mw) and distance to fault, if needed for liquefaction, slope stability analysis or for 

earthquake record selection. 

18. Time Histories of Earthquake Ground Motion: (If applicable) Compute target spectra, 

justify selected earthquake records, scale to target to meet ASCE 7 §16.1.3 or §17.3 and show initial 

Liquefaction/Seismic Settlement Analysis 

19. Geologic Setting for Occurrence of Liquefaction: Perform screening analysis to 

identify where the following conditions apply: 

depth of highest historical ground water surface



Engineering 

Seismology: 

A Simplified 

Picture 

• Earthquake source 

• Seismic wave propagation 

• Ground motion 

• Building response 

2/18/13 Cal Poly Pomona 4



Hazard, Mitigation and Risk 

Seismic Hazard: any physical phenomenon associated 

with an earthquake that may cause damage and loss 

Hazard is studied and evaluated -> 

Mitigation: design actions to reduce loss of life, 

injuries and damages 

Risk: a probability that 

social or economic 

consequences will 

exceed a specified value 


5



Return Period 

Return Period/ 

Recurrence 

Interval: the mean 

time period 

between samesized 

events. 

The larger the event, 

the longer the 

return period. 


6



Very High Risk: 

Tokyo 

• One of the world's most 

densely populated 

metropolitan areas 

• In 1923, it suffered a 

destructive earthquake, the 

Great Kanto quake 

– 143,000 fatalities 

– destroyed two-thirds of 

Tokyo 

• Estimated recurrence time: 

70 years…. 


7



Mitigation: Earthquake Engineering 

• Haiti earthquake, 2010: 

M7.0, 230,000 deaths 

• New Zealand earthquake, 

2010: M7.1, 0 deaths 

Great earthquake disasters 

occur where high population 

density, earthquakes, and 

poor construction coincide. 


8



Fatalities and Damages 

Vary greatly from year to year 

Dominated by rare catastrophes 

Locations of worst damages are different from those of 

fatalities. 

Economic Losses: 

• Destruction of Infrastructure 

• Loss in Productivity 


9



The Economic and Human Impact of Disasters* in the last 12 years 

363 Billion 

214 Billion 

190 Billion 

136 Billion 

0 

46 Billion 

27 Billion 

52 Billion 

69 Billion 

34 Billion 

74 Billion 

46 Billion 

131 Billion 

659 Million 

0 

174 Million 

108 Million 

255 Million 

161 Million 

160 Million 

126 Million 

211 Million 

221 Million 

199 Million 

261 Million 

162 Million 

244,880 

242,191 

308,152 

113,513 

93,076 

0 

39,496 

16,666 21,342 

29,893 

22,424 15,957 

32,816 

http://www.unisdr.org 

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 

KEY 

DISASTER 

EVENTS 

*Disasters refers to Natural Disasters as categorized in EM-DAT 

Data source: EM-DAT: The OFDA/CRED International Disaster Database 

Data version: 10 January 2012 - v12.07 

Humanitarian Symbol Set (2008): http://www.ungiwg.org/map/guideline.php 

South Asia 

July 2002 

Europe 

Aug 2002 

China 

Aug 2002 

Bam (Iran) 

Dec 2003 

Indian Ocean 

Dec 2004 

Kashmir 

Oct 2005 

Katrina 

Aug 2005 

Sidr 

Nov 2007 

Sichuan 

May 2008 

Nargis 

May 2008 

2/18/13 Cal Poly Pomona 10 

Pakistan 

July 2010 

Haiti 

Dec 2010 

Japan 

March 2011



Disaster Magnitude and Frequency 

The occurrence of very 

powerful earthquakes is 

rare, small scale activity 

is common. 


11



• Ground Displacement 

Seismic Hazards 

• Ground Shaking (cause of all other hazards) 

• Structural Hazards 

– Retaining Structure Failures 

– Lifeline Hazards 

• Liquefaction 

• Landslides 

• Tsunami and Seiche Hazards 




Ground 

Displacement 

• Permanent surface offset 

on and close to the fault 




Concrete dam failure resulting from surface fault offset 

during the 1999 M7.6 Chi Chi (Taiwan) earthquake 




Greatest Displacement Measured: 

2011 Tohoku Earthquake 




How To Estimate Source Parameters for 

Future Earthquakes 

• Use empirical relations between source parameters 

compiled for many earthquakes 

• Provide estimate, useful average, but: surprises happen! 




Strength of Ground Shaking 

• Strength and duration of 

shaking depend on: 

– source effects 

• orientation 

• size 

• propagation 

direction 

– path effects 

– site effects 

• local rock layering 

• immediate soil 

conditions 

• 3-D basin/hill 

topography 




Ground Shaking 

• For engineering purposes 

shaking is usually measured 

as acceleration in units of 

% g (acceleration of gravity: 

9.8 m/s 2 = 100% g = 1 g) 

– also used: gal (1 gal = 1 cm/s 2 

= 0.01 m/s 2 ~ 0.1% g) 

• Ground shaking is 

perceptible to humans if 

acceleration exceeds 0.5% g 

– “strong ground motion” 

• Structural damage in 

buildings not designed to be 

resistant usually occurs at 

10% g 




ShakeMaps 




Highest Recorded Acceleration 

At a site 3 km from 

magnitude 7.2 

Nairiku, Japan 

earthquake in 

2008: over 4g! 


20






Christchurch Mw6.3: PGA>2g! 




Highest PGV 




Ground Shaking 

• Maximum recorded 

acceleration for 2008 

M5.4 Chino Hills 

earthquake: 0.44 g (in 

Walnut) 




Liquefaction 

Liquefaction: 

– strength and stiffness of a saturated soil is reduced by 

earthquake shaking 

• shaking can cause water pressure to increase to the point where 

soil particles can readily move with respect to each other 

– soil is unable to support structures or remain stable 


25



Liquefaction Lab Experiment 




Liquefaction Examples 

Sand boils/volcanoes in 

New Zealand after 

2010 earthquake 




Liquefaction Examples 

Niigata earthquake in 1964 




Tokyo 2011 




Overturned 

apartment 

complex 

buildings in 

Niigata in 

1964. 

Settling of left section of 

building causes destruction 

of middle section in Izmit, 

1999. 


30



Haiti Port Damage 




Hazard 

Mapping 

http://www.conservation.ca.gov/ 

cgs/shzp/Pages/Index.aspx 


32



Landslides 

• may be triggered by 

– ground shaking 

• slopes marginally stable 

under static conditions 

– liquefaction 

• may create “quake-lakes” 




Tsunami and 

Seiches 

• Tsunami: long period 

sea waves generated 

by rapid vertical 

displacement of water 

• Seiche: induced waves 

in enclosed bodies of 

water 

• Both can be excited by 

earthquakes, 

landslides, volcanic 

eruptions, etc. 


SAN JU AN CAPISTRAN O 



California Emergency Management Agency 

California Geological Survey 

University of Southern California 

118°15'0"W 

Tsunami Inundation Map for Emergency Planning 

Long Beach Quadrangle 

State of California 

County of Los Angeles 

118°7'30"W 

Tsunami 

Inundation Maps 

33°45'0"N 

33°45'0"N 

TOPATOPA MOUNTAINS 

SANTA PAULA PEAK 

SANTA PAULA 

CAMARILLO 

DEVILS HEART PEAK 

FILLMORE 

MOORPARK 

NEWBURY PARK 

COBBLESTONE MTN 

PIRU 

SIMI VALLEY WEST 

THOUSAND OAKS 

WHITAKER PEAK 

VAL VERDE 

SIMI VALLEY EAST 

CALABASAS 

WARM SPRINGS MOUNTAIN 

NEWHALL 

OAT MOUNTAIN 

CANOGA PARK 

GREEN VA LEY 

MINT CANYON 

SAN FERNANDO 

VAN NUYS 

SLEEPY VA LEY 

AGUA DULCE 

SUNLAND 

BURBANK 

RI TER RIDGE 

ACTON 

CONDOR PEAK 

PASADENA 

PALMDALE 

PACIFICO MOUNTAIN 

CHILAO FLAT 

MT WILSON 

LITTLEROCK 

JUNIPER HILLS 

WATERMAN MTN 

AZUSA 

LOVEJOY BU TES 

VALYERMO 

CRYSTAL LAKE 

GLENDORA 

EL MIRAGE 

MESCAL CREEK 

MOUNT SAN ANTONIO 

MT BALDY 

http://www.consrv.ca.gov/cgs/ 

geologic_hazards/Tsunami/ 

Inundation_Maps/Pages/ 

Statewide_Maps.aspx 

POINT MUGU 

TRIUNFO PASS 

POINT DUME 

MALIBU BEACH 

TOPANGA 

BEVERLY HILLS 

HOLLYWOOD 

LOS ANGELES 

ELMONTE 

BALDWIN PARK 

SAN DIMAS 

ONTARIO 

VENICE 

INGLEWOOD 

SOUTH GATE 

WHITTIER 

LA HABRA 

YORBA LINDA 

PRADO DAM 

REDONDO BEACH 

TORRANCE 

LONG BEACH 

LOS ALAMITOS 

ANAHEIM 

ORANGE 

BLACK STAR CANYON 

118°15'0"W 

2/18/13 118°7'30"W 

Cal Poly Pomona 35 

METHOD OF PREPARATION 

Initial tsunami modeling was performed by the University of Southern California (USC) 

Tsunami Research Center funded through the California Emergency Management Agency 

(CalEMA) by the National Tsunami Hazard Mitigation Program. The tsunami modeling 

process utilized the MOST (Method of Splitting Tsunamis) computational program 

(Version 0), which allows for wave evolution over a variable bathymetry and topography 

used for the inundation mapping (Titov and Gonzalez, 1997; Titov and Synolakis, 1998). 

The bathymetric/topographic data that were used in the tsunami models consist of a 

series of nested grids. Near-shore grids with a 3 arc-second (75- to 90-meters) 

resolution or higher, were adjusted to “Mean High Water” sea-level conditions, 

TSUNAMI INUNDATION MAP 

FOR EMERGENCY PLANNING 

State of California ~ County of Los Angeles 

LONG BEACH QUADRANGLE 

SAN PEDRO 

SEAL BEACH 

NEWPORT BEACH 

MAP EXPLANATION 

TUSTIN 

LAGUNA BEACH 

Tsunami Inundation Line 

Tsunami Inundation Area



Seismology 

• Science of earthquakes and 

related phenomena. -Richter, 

1958 

• Basis for all seismic hazard 

analysis 

• For purpose of engineering 

geology, focus on strong 

motion seismology 

2/18/13 

Cal Poly Pomona 

36



Seismometers 

Seismometers detect and 

record motion (acceleration, 

velocity or displacement) of 

ground (or building) 


37



Seismograms 

• Each seismogram is composite of: 

– Earthquake source effects 

– Propagation and site effects => Earth structure 

• It may therefore be difficult to independently resolve either 


38



Wave 

Parameters 

Seismogram 

• Amplitude 

• Wavelength 

• Period = time between waves in seconds 

• Frequency = number of waves passing a given point in 1 

second (measured in cycles per sec: Hz) 

• Velocity (seismic ~ km/sec, depends on material) 


39



Ground 

Motion Period 

• Seismograms, like white 

light, are composites of 

waves of many different 

frequencies 

• Usually recorded ground 

motion will be 

combination of short 

period motions and long 

period 


40



• Body Waves 

– Travel through Earth’s interior 

– Fastest 

– Dominate at short distances 

– High frequencies/short period 

(1-30 Hz) 

• Surface Waves 

– Travel along Earth’s surface 

– Long period 

– Dominate at larger distances 

– Generated most efficiently by 

shallow earthquakes 

• Peak ground motions are 

produced by body waves at 

distances shorter than ~ 

twice crustal thickness (30 

km) 

Seismic Waves 


41



Body Waves: P-wave 

• Primary wave, first to arrive 

– Used in Early Warning Systems 

• Compressional, no rotation 

• Particle motion in direction of wave 

propagation 

• Relatively little damage potential 


42



Body Waves: S-wave 

• Secondary wave, second to arrive 

• Transverse, shearing, no volume change 

• Particle motion at right angles to wave 

propagation 

• Significant damage potential 


43



Surface Waves: Love waves 

• Horizontal, shearing motion 

• Contribute to damage far from 

source 


44



Surface Waves: Rayleigh waves 

• Backward-rotating, elliptical motion 

• Vertical as well as horizontal motions 

• Contribute to damage far from source 


45






Southern California Faults 

Southern California is traversed 

by numerous faults. Some of 

these, like the San Andreas 

Fault, are major players; others 

are minor and not so well 

known. 


47






Geometric Notation 




Geologic Map 


50



Slip Rate 

Map 

• Dominance of 

SAF, San Jacinto 

fault, and Garlock 

fault. 

• Smaller faults 

branching off tend 

to have moderate 

slip rates, 

decreasing with 

distance from 

major fault zones. 


51



Sense of Slip 

• SAF zone: right lateral 

• Garlock fault zone, largest 

left-lateral strike-slip fault 

• Near Transverse Ranges 

and LA Basin are 

numerous reverse faults 

• North of Garlock fault: 

extension 

– normal faulting 

– Basin and Range tectonic 

province 


52



Earthquake 

Failure 

• Earthquake failure process is often described as rock fracture 

– If rock is subjected to stress, eventually fracture occurs 

• It may be more appropriate to view earthquake faulting as frictional 

sliding 

– sliding surface ~ earthquake fault, formed by long-term geological 

processes, and represents weak zone 


53



Strain Leads to 

Stress: Elastic 

Rebound 

• Both sides of fault are gradually moving past one another, 

whereas fault is locked, accumulating strain 

• This flexure places greater and greater stress on fault 

• When it exceeds strength of fault, fault slips, and surrounding 

rock rapidly snaps back => earthquake 


54



Hazard Analysis: Characteristic Earthquake 

Elastic rebound: individual 

earthquakes on particular fault 

segment are not random 

independent events, but depend on 

build up of stress 

USGS in 1985 predicted M6 along SAF 

near Parkfield, between 1987-1993. 

Monitoring systems were installed. 

Quake occurred in 2004, when most 

equipment had been removed. 


55



Magnitude 

Magnitude 

= 5.0 

• Historically best-known 

measure of earthquake size 

• All magnitude scales are related 

to largest amplitude 

⇒ Easy to measure 

• Richter introduced local 

magnitude, M L , in 1930s 

– Measure A max recorded on Wood- 

Anderson seismograph 

– Empirical formula: 

M L = log 10 A + 2.56log 10 Δ - 1.67 

– Measure maximum displacement 

amplitude A in 10 -6 m 

– Correct for distance, Δ, in km 

• Also possible: use nomograph 


56



• Problems with M L : 

– Defined specifically for southern 

California 

– Depends on outdated Wood- 

Anderson instrument 

• But: instrument period close to 

resonant frequency of many 

buildings (1 Hz) 

• More general global scales were 

developed, all of general form: 

M = log (A/T) + F(h, Δ) + C 

– A = amplitude 

– T = its dominant period 

– F = correction factor for depth and 

distance 

– C = regional scale factor 

Other Scales 


57



Other 

Scales 

More general global scales: 

• Body wave magnitude, m b 

– Dominant period of 1 sec 

– Measured from initial part of P-wave 

• Surface wave magnitude, M S 

– Dominant period of 20 sec 

– Only for shallow events: deep events have greatly reduced surface wave 

amplitudes 

Neither correctly reflects the size of large earthquakes 


58



Magnitude Saturation 

• Measures of earthquake size based on maximum ground 

shaking do not account for longer durations of larger events 

– M S saturates at about 8.3 

– m b at about 6.2 


59



Moment 

Magnitude 

Magnitude saturation helped 

motivate development of 

moment magnitude scale, M w 

M w = (log M 0 )/1.5 - 10.73 

determined for M 0 , moment, in 

dyne-cm 

• 10 7 dyne-cm = 1 N-m 

M 0 = µ D A, where: 

µ : shear modulus 

D : average displacement across 

fault (slip) 

A : area of fault 

Gives magnitude directly tied to 

earthquake source processes, 

scaled to agree with previous 

magnitudes for small events. 


60



Earthquake Intensity 

• Described through scales that are based on 

intensity of effects experienced by people and 

buildings, developed in the late 1800s. 

• Most widely used: 

Mercalli scale 


61






Historic Earthquakes: 

1811/1812 New Madrid 

• Intensity can be inferred 

from human accounts => 

no seismometers are 

needed 

• Historic earthquakes can 

still be analyzed 

• Lines of constant intensity: 

isoseismals 

• Typically, intensity decays 

with distance 


63



Regional Geology 

• For fixed earthquake size, 

region of strong shaking 

can be indication of 

regional geologic structure 

• Old, eastern section of US 

transmits seismic 

vibrations very efficiently 

relative to young California 

coastal region 

=> for equal-size earthquake, 

east is likely to experience 

a wider extent of damage 

than coastal California 


64






Strong Ground Motion



Use of Ground Motion Measurements 

in Reducing Future Losses 

Structural engineers must take into account two 

fundamental characteristics of earthquake shaking: 

1. how ground shaking propagates through the Earth (especially near 

the surface) 

2. how buildings respond to this ground motion 

Recordings of ground motion in urban areas by 

seismographs/seismometers can be used to 

characterize variability of ground shaking 




Ground Motion Range 

Range of ground motions 

of interest to 

seismologists is large, 

because earth 

deformation occurs at 

many different rates 

and scales. 

Different types of 

seismometers are used 

to record ground 

motions. 




Seismograph 

Simple seismographs (and buildings) are Single Degree of 

Freedom (SDOF) Oscillators 

• discrete system whose position can be described by single variable 

This system consists of: 

• mass m, moving on frictionless surface 

• driven by horizontal ground motion with acceleration Ü (dot 

notation) 

• connected to spring with stiffness k and 

• dashpot with coefficient of viscous damping c 

Spring and dashpot are not rigid, so motion of mass is not 

identical to that of ground during earthquake 




Review: Free 

Vibration Without 

Damping 

u 

Force is proportional to amount spring is stretched 

“u” with proportionality constant, k: 

m˙ u ˙ + ku = 0 ! 

If we start system by stretching spring by distance A 

! 

and letting go, mass will oscillate with simple 

harmonic motion u(t) with amplitude A and 

f 

undamped natural n 

= 1 k m˙ u ˙ + ku = 0 ! 

! 

frequency f n 

! 

! 

m˙ ! u ˙ + ku = 0! 

u(t) ! = Acos(2"f n 

t)! 

f n ! = 1 k 

! 

! 

2" m ! 

! 

u(t) = Acos(2"f n 

t)! 

2" 


m ! 

! 

u(t) = Acos(2"f n 

t)! 

f n 

= 1 

2" 

k 

m !



Review: Free 

Vibration With 

Damping 

u 

We now add "viscous" damper to model, with damping 

coefficient c. This adds additional force on mass: 

m˙ u ˙ + c˙ u + ku = 0 ! 

! 

u(t) = Ae "#$ nt cos( 1"# 2 2%f 

Solution depends u(t) on = amount Ae "#$ cos( of damping, 1"# 2 2%f n 

t) ! 

characterized by 

n 

! 

! 

damping ratio: 

" = 

c 

2 km! 

m˙ u ˙ + c˙ u + ku = 0! 

! 

! 

which ! is exactly 1 at critical damping, where system returns 

to equilibrium as quickly as possible without oscillating. 

! 

" = 

c 

2 km ! 

! 

! 




Damping 

If damping is small enough (damping ratio



Free Vibration With Damping 

! 

Solution for underdamped 

system: 

m˙ u ˙ + c˙ u + ku = 0! 

! 

u(t) = Ae "#$ nt cos( 1"# 2 2%f n 

t) ! 

• exponential determines how fast 

system damps down 

" = 

c 

• cosine is oscillation 

2 km ! 

Natural frequency and 

damping determine 

behavior of system both in 

free and forced vibration. 




Forced Vibration With Damping 

! 

! 

We can force SDOF oscillator 

by ground displacement (u g ): 

! 

! 

m˙ u ˙ + c˙ u + ku = "m˙ ˙ 

If u g is uharmonic " with 2 

frequency ω g , displacement response 

= 

ratio u g 

will be: ! 

! 

" = # g 

# 0 

! 

(1# " 2 ) 2 + (2$") 2 ! 

where β is tuning ratio: 

! 

! 

! 

u g 

m˙ u ˙ + c˙ u + ku = "m˙ ˙ 

u 

u g 

= 

" = # g 

u g 


" 2 

(1# " 2 ) 2 + (2$") 2 ! 

# 0 

! 

β = ω g 

ω n



Displacement Response Ratio 

Displacement response 

ratio varies with 

frequency and damping 

• For large β, trace amplitude 

is same as ground motion 

amplitude 

• In lightly damped system 

when ground motion 

frequency 

m˙ 

nears natural 

u ˙ + c˙ 

frequency, amplitude of 

vibration can get very high: 

resonance 

! 

! 

u 

u g 

= 

u + ku = "m˙ ˙ 

" 2 

(1# " 2 ) 2 + (2$") 2 ! 

u g 

2/18/13 ! 

Cal Poly Pomona 75 

# 

β = ω g 

ω n



Forced Vibration 

Three identically damped SDOF 

oscillators, all with natural 

frequency f n =1 Hz, are 

initially at rest. Harmonic 

force is applied to each. 

Driving frequencies of 

applied forces are (matching 

colors): 

f g =0.4 Hz f g =1.01 Hz f g =1.6 Hz 




Example: Wood-Anderson 

• Provided data for early 

southern California 

earthquake catalog. 

• Uses mirror on mass 

suspended by vertical wire : 

when ground moved 

horizontally, wire would 

twist, causing deflection of 

reflected light 

• f n =1.25 Hz 

• ζ=0.7 

• magnification=2080 




Seismometer 

Response Curves 

• One way to 

characterize 

seismometers: 

describe range of 

vibration 

frequencies that 

they can detect 

• Plot of amplification 

versus frequency is 

called seismometer 

instrument response 




• Different recording 

instruments may 

produce different 

measurements of 

ground motion for an 

earthquake due to their 

instrument response 

• Strong ground motion: 

motion of sufficient 

strength to affect 

people and their 

environment 

Ground Motions 




Accelerometer 

• also called accelerograph or strong motion seismometer 

• instrument designed to record large amplitude and 

high-frequency shaking within few tens of kilometers 

near large earthquakes 

• strong motion data is basis for all quantitative 

earthquake resistant design 




! 

Example: SMA-1 Strong Motion 

Accelerograph 

• ζ=0.6 

– damping similar to WA 

• high natural frequency: f n = ω n /2π = 18 Hz 

! 

! 

! 

u ˙ + 2"# ˙ n 

u + # 2 u ˙ + u = $˙ 2"# n 

u ˙ + # 2 n 

u = $˙ ˙ 

n 

– third term dominates: 

u 

u g 

= 

" 2 

(1# " 2 ) 2 + (2$") 2 ! 

=> seismograph trace displacement is proportional to 

acceleration of ground 

" = # g 

# 0 

! 

! 

! 


u g 

! 

! 

! 

u = " 1 

# n 

2 ˙ ˙ u g 

! 

" = # g 

# 0 

! 

u g



Strong Motion Records 

• Usually three components of 

ground motion, two horizontals 

+ one vertical 

• Thousands of acceleration 

values measured at increments 

of ~ 0.01 sec 







Deriving Velocity and Displacement 

• velocity of ground movement can be calculated as 

integral of acceleration record 

• displacement = integral of velocity 







March 10, 1933 

Mw=6.4 Long Beach Earthquake 

First accurate 

record of 

destructive ground 

motions 


86



National Strong 

Motion Array 

http://nsmp.wr.usgs.gov/ 

U.S. Geological Survey National Strong-Motion Project has 

primary Federal responsibility for recording each 

damaging earthquake in US on ground and in man-made 

structures in densely urbanized areas to improve public 

earthquake safety. 


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Urban Networks 

• Rapid proliferation of arrays in recent years, especially in 

urban areas 

• Small scale ground motion variability cannot yet be resolved by 

most existing arrays: insufficient spatial sampling. 




Building Arrays 

• Most seismometers are free 

field (i.e. away from large 

structures), but some are 

located in buildings, dams 

or bridges 

• For example: 

– UCLA Factor Building 

Seismic Array 

• 17-story moment-resisting 

steel frame structure with 

embedded 72-channel 

accelerometer array 

– Bay Bridge 

• 72 accelerometers 







Data 

Availability 

http://www.strongmotioncenter.org/ 

• Many strong motion databases are accessible through 

Internet 

– Parametric data 

– Full waveform data 

– Some in near real-time 

• Format not standardized 




Data Format 

• Most seismogram formats contain: 

– header 

• event information 

• station information: metadata 

– location 

– response 

• time information 

– start time 

– time interval 

– number of points 

– ground motion data

Lecture: Introduction to Seismology and Ground Motion Parameters

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