ْ َ ُ َ َ ْ َّ َ َ ْ َ َ ِون بإذنه ِ يا منِ استقرتِ اْلرض Fundamentals of Earthquake Engineering Engineering Seismology Mojtaba Mahsuli mahsuli@sharif.edu 1 Myth 2 • • • • • Greek: When Poseidon is in a bad mood, he strikes the ground with a trident, causing earthquakes Hindu: When one of the eight elephants that carry the Earth gets tired … Mongolian: When a frog that carries the world moves … African: When the giant on whose head people all live, sneezes or scratches … Japanese: When the attention of Kashima (who looks after the giant catfish Namazu that supports the Earth and prevents it to sink into the ocean) weakens and Namazu moves … • Native American: When the god Maimas decides to count the population in Peru, his footsteps shake the Earth. Then natives run out of their huts and yell: “I’m here, I’m here!” 2 Seismic Waves 3 • Body waves • Travel through the Earth’s interior • Surface waves • Result from the interaction between body waves and the surficial material • Travel along Earth’s surface 3 Seismic Wave Propagation 4 • Seismic wave propagates from the rupture location to all directions 4 Seismic Waves: Body Waves 5 Body waves • p-waves: Primary, compressional, longitudinal waves • Analogues to sound waves • Particle motion is parallel to wave direction • Can travel through fluid and solid • s-waves: Secondary, shear, or transverse waves • Cause shearing deformation • Particle motion is perpendicular to wave direction • Fluids cannot sustain s-waves • Can be divided into two components: SV (vertical plane movement) and SH (horizontal plane movement) • The s-wave on bottom-left (Figure c) is SV, because it causes vertical particle movement • Figure d shows the combination of p- and s-waves travelling towards the ground surface • Geologic material are stiffest in compression: p-waves travel faster than s-waves and are first to arrive at a site • The speed of s-waves is typically around 60% of that of p-waves in any given material • Earthquake advance warning is possible by detecting the non-destructive p-waves that travel more quickly • The time of advance warning depends on the delay between the arrival of the p-wave and other destructive waves → Generally on the order of seconds up to about 60–90 seconds for deep, distant, large earthquakes such as the one Tokyo would have received before the 2011 Tohoku earthquake and tsunami 5 General s-wave SH component (Horizontal plane movement) Particle SV component (Vertical plane movement) 6 • SV and SH components of the s-wave 6 Body Wave Propagation p-wave s-wave 7 • Right: Unidirectional propagation of p- and s-waves • Left: Propagation of a p- and s-waves in a 2D grid 7 Seismic Waves: Surface Waves 8 Surface waves • Result from the interaction between body waves and the surficial material • Amplitude decreases roughly exponentially with depth • More prominent at distances farther from the source of the earthquake • Because of their low frequency, long duration, and large amplitude, they can be the most destructive type of seismic wave • Surface waves are slower than body waves, roughly 90% of the velocity of s-waves for typical homogeneous elastic media • Rayleigh waves: • Interaction of p- and SV-waves with Earth’s surface • Involve both vertical and horizontal particle motion • Similar to waves produced by throwing a rock in a pond • Love waves: • Interaction of SH-waves with a soft surficial layer • No vertical component • Slightly faster than Rayleigh waves 8 Surface Wave Propagation 9 • Top: Propagation of the Rayleigh wave • Bottom: Propagation of the Love wave 9 Wave Arrival 10 • Each ground motion recorded at a station has two horizontal components and one vertical • Note the lower frequency and higher amplitude of the surface waves • Surface waves have lower speeds than s-waves (roughly 10% less); therefore, they arrive at the site later than body waves • Love waves are the most destructive, and appear in the horizontal components of recorded ground motions, but do not appear in vertical components (Q: Why?) • Rayleigh waves do appear in the vertical component, because they involve vertical particle motion as well • Note that surface waves have a lower frequency than body waves, because they are the response of the soil layer to body waves • Therefore, soil damps out the high frequency waves and amplifies the lower frequency waves due to resonance, because the frequency of the latter is closer to the natural frequency of the soil • In this slide, due to the large distance to epicenter (~2000 km), the time difference between arrival times of different waves is large 10 Wave Arrival Up-Down N-S E-W P S Surface waves 11 Q: Identify the waves 11 Earth Layers 12 Chemical Layers: Crust, mantle, outer core, inner core • Crust 24-40km • As thin as 5km beneath oceans • As thick as 60-70km under young mountains • Distinct change in the wave propagation velocity marks the boundary between the crust and the mantle, called Mohorovičić discontinuity, or Moho • Named after Croatian seismologist, who discovered it in 1909 • Moho reflects and refracts the seismic waves • Two types of crust shown on top-right: Continental crust and oceanic crust • Mantle = 2850 km (1770 miles) thick • Upper mantle: About 650 km (404 miles) • Lower mantle: No earthquakes have been recorded in the lower mantle, which appears to be chemically homogeneous • The mantle is cooler near the crust than at greater depths but still has an average temperature 2200°C • As a result, the mantle materials are in a viscous, semi-molten state • They behave as a solid when subjected to rapidly applied stresses, such as those associated with seismic waves, but can slowly flow like a fluid in response to long-term stresses • The mantle material has a specific gravity of about 4 to 5 • Outer core and inner core in the next slide … 12 Earth Chemical Layers 13 Lehman Gutenberg • Outer core, or liquid core = 2260km • As a liquid, it cannot transmit s-waves • Note the drop to zero in Vs • Note the sharp drop in Vp • Boundary between mantle and outer core is called Gutenberg discontinuity • Primarily consists of molten iron, with density of 9-12 • Flow of the outer core produces the Earth’s magnetic field • Inner core, or solid core = 1220 km • Very dense; density up to 15 • Boundary between inner and outer cores: Lehman discontinuity • Nickel-iron material compressed under tremendous pressure • 5000-6000°C 13 Earth Mechanical Layers 14 • Mechanical layers: Lithosphere, Asthenosphere, Mesosphere, outer core, inner core • Lithosphere: Crust + upper parts of mantle • Uppermost 50-100 km • No strict boundary between lithosphere and asthenosphere • Behaves rigidly over very long periods of time • Consists of tectonic plates • Asthenosphere: Weakest part of mantle • Depth of 100-200km, sometimes up to 600 km • Solid in short time scales, fluid in long term • Decouples the tectonic plates from the rest of the mantle • Mesosphere: Hot, but stronger than asthenosphere due to high pressure 14 Reflection and Refraction 15 • Seismic wave paths are shown in this slide, which illustrates reflection and refraction of seismic waves • p- and s-waves can reach the earth's surface between 0° and 103° • Outer core allows only p-waves to reach the surface between 143° and 180° • Shadow zone: Between 103° and 143°, only the few waves that are reflected from the inner core can reach the earth's surface; hence, no significant waves are recorded in this zone 15 Wave Path 16 • Q: The travel path of the waves is curved, because the density increases with depth 16 Continental Drift 17 • All the continents had once been one super-continent (Pangaea), and have since broke apart and drifted, and are still drifting • This would mean that massive continents pushed through the seas and across the ocean floor • However, the ocean floor is too strong to permit such motion, and the theory was originally discredited by most earth scientist • From this background, however, the modern theory of plate tectonics began to evolve 17 Plate Tectonics 18 • • • • Earth's surface consists of a number of large, intact blocks called plates Tectonic plates are large parts of litosphere floating on the astenosphere Plates move with respect to each other Earth's crust is divided into • 6 continental-sized plates: African, American, Antarctic, Australia-Indian, Eurasian, and Pacific • About 14 of sub-continental-sized plates, e.g., Caribbean, Cocos, Nazca, Philippine, etc. • Relative deformation between plates occurs in narrow zones near their boundaries • slowly and continuously (aseismic deformation) • spasmodically in the form of earthquakes (seismic deformation) • Map of seismic activity supports this theory 18 Seismicity since 1980 19 • Only events with Mw > 5.0 are shown • Note that the line of earthquake closely follows the boundaries of the tectonic plates 19 Seismicity in 2002 20 • Again, the line of earthquakes closely follows the boundaries of the tectonic plates 20 Convection in Mantle 21 • Plate tectonics is a kinematic theory • In other words, it explains the geometry of plate movement without addressing its underlying cause • Movement of these huge plates requires gigantic forces • Thermomechanical equilibrium of the earth's materials explains the movement: • Upper mantle is in contact with cool crust, and lower mantle with hot outer core, which produces a temperature gradient • Unstable situation: Denser, cooler material resting on top of less dense, warmer material • Cooler, denser material begins to sink under the action of gravity and the warmer, less dense material begins to rise • Sinking material gradually warms, becomes less dense, moves laterally, and begin to rise again • Cooled material begins to sink • This is called convection • Convection currents in the semi-molten mantle impose shear stresses on the bottom of the plates, which drag them in various directions across the Earth’s surface 21 Convection in Mantle 22 • Video illustrating the convection cells within the mantle 22 Plate Interactions 23 • Convergent: Plates collide or subduct • Divergent: plates move away from each other • Transform: plates slide one past another 23 Plate Tectonics 24 • Kermanshah 2017 M7.3 earthquake epicenter was due to the movement of Arabian plate towards the Eurasian plate at 26 mm/year 24 Plate Interactions 25 • Divergent: Bottom-right • Produces spreading ridges • Molten rock rises and cools • Plates grow at spreading ridges (2-18 cm/year) • Generally weaker earthquakes than subduction • Convergent: Top • One Plate subducts beneath the other • Balances the growth at ridges • Top-left: Continental-continental collision (orogeny) • Forms mountain ranges, e.g., Himalayas, Alps • Top-right: Oceanic-continental collision (subduction) • Near the edge of continents • The denser crust goes underneath the less dense one under its own weight • Produces strong and sometimes very deep earthquakes (up to 700 km) • Deeper earthquakes are more infrequent, because as the plate subducts, it warms and becomes ductile • Huge earthquakes such as the large ones that have occurred in Chile and Japan are produced by this mechanism • Produces volcanoes • Transform: Bottom-left • Movement along transform faults • Weak to strong earthquakes 25 Plate Interactions 26 NOTE • Theory of plate tectonics does not explain all observed tectonic seismicity • For example, it is known that intra-plate earthquakes (earthquakes that occur within a plate, away from its edges) have occurred on most continents 26 Inactive Fracture Zones 27 • Fracture zones may be observed over thousands of kilometers • However, only the segment between the spreading ridges is the transform fault • Motion on the portions that extend beyond the transform fault is in the same direction on either side → No relative motion • These inactive portions of the fracture zone are fossil faults that are not producing earthquakes 27 Faults φ: Strike angle δ: Dip angle λ: Slip angle 28 • • • • • On a smaller scale, the movement at a particular location can be quite complicated Plate boundaries may be broken to platelets or micro-plates trapped between the larger plates Locally, the movement between two portions of the crust will occur on offsets known as faults Maybe obvious, maybe difficult to detect Presence of a fault does not necessarily mean earthquakes are expected → Movement can occur aseismically, or the fault may be inactive • Lack of observable surficial faulting does not imply that earthquakes cannot occur → Fault rupture does not reach the earth's surface in most earthquakes • Fault geometry • Strike: horizontal line produced by the intersection of the fault plane and a horizontal plane • Strike angle: Angle between the strike and the direction of the north • Dip: Downward slope of the fault plane • Dip angle: Angle between the dip and the horizon • For vertical faults: Dip angle = 90 • Foot wall: فرودیواره • Hanging wall: فرادیواره 28 Fault Types 29 • Dip-slip ()شیبلغز: Movement along the dip • Normal fault: Tensile stress, lengthening of crust • Reverse fault: Shortening of crust • Thrust fault: Very small dip angle; it causes very large movements (e.g., Alps) • Strike-slip ()امتدادلغز: Movement along the strike; usually vertical faults that have a dip angle of 90 degrees; cause large movements • Left-lateral: An observer would observe the material on the other side moving to the left • Right-lateral: An observer would observe the material on the other side moving to the right • Oblique-slip: Movement along both the strike and the dip 29 Examples 30 Strike-slip Dip-slip Normal Fault 30 Event Characteristics 31 EMSC (2017) • Kermanshah earthquake rupture mechanism was analyzed by several agencies • They all indicated a reverse, thrust fault as evident from the seismology “beach ball,” which produces significant motions compared to normal or strike-slip faults • In seismology beach balls, material moves from white to black; hence, the beach balls in this slide show compression, which mean reverse faulting • The interface of white and black also shows the direction of rupture • The agencies differed in their estimation of the epicenter, depth, and magnitude: • Epicenter: 34.77N, 45.76E (Geophysics UT), 34.81N, 45.91E (BHRC) → 14.5 km apart • 7.2<M<7.4 in moment magnitude (Richter local saturates at 6.8~7) • 15<Depth<25km • Tehran Geophysics: M7.3 at 18km depth • Energy: 1.8M ton TNT or 89 Hiroshima atomic bomb; 5.6 Peta Joule (peta = 1015) • 5 times the energy of Bam earthquake, which was occurred on Dey 8, 1382, M6.6, Depth of 8.6km, distance to Bam=5km • However, smaller PGAs at Sarpol compared to Bam because of larger distance and depth • Bam: Horizontal PGA: 0.82g, Vertical PGA: 1.01g • Sarpol Zahab: Horizontal PGA: 0.7g, Vertical PGA: 0.36g 31 Elastic Rebound Theory 32 • Elastic rebound theory describes the process of the successive buildup and release of strain energy in the rock adjacent to faults • Relative movement of the plates leads to Elastic strain energy being stored in the materials near the boundary as shear stresses increase on the fault plane • When shear stress reaches the strength of the rock, it fails → Accumulated strain energy is released • Effects of the failure: • Weak and ductile rock: strain energy released relatively slowly → Movement occurs aseismically • Strong and brittle rock: rapid failure; energy released explosively → Heat and stress waves (earthquakes) 32 Fault Rupture START Depth Surface of the earth Distance along the fault plane (100km) 33 33 Fault Rupture Second 2.0 34 34 Fault Rupture Second 4.0 35 35 Fault Rupture Second 6.0 36 36 Fault Rupture Second 8.0 37 37 Fault Rupture Second 10.0 38 38 Fault Rupture Second 12.0 39 39 Fault Rupture Second 14.0 40 40 Fault Rupture Second 16.0 41 41 Fault Rupture Second 18.0 42 42 Fault Rupture Second 20.0 43 43 Fault Rupture Second 22.0 44 44 Fault Rupture Second 24.0 45 45 Fault Rupture Total Slip in the M7.3 Landers Earthquake 46 46 Seismic Moment M0 = AD 2 M w = ( lo g10 ( M 0 ) − 9.1) 3 M 0 in N m 47 • Seismic moment: A measure of the work done by the earthquake • μ: Rupture strength of the material along the fault • A: Rupture area • D: Average amount of slip • Seismic moment is named for its units of force times length • It is a measure of the total amount of energy that is transformed during an earthquake from the built-up stresses to other forms, such as • Cracks and deformation in rocks • Heat • Radiated seismic energy • Only a fraction of the M0 is converted into radiated seismic energy, Es, which is what seismographs register: Es=1.6 M0 ∙ 10-5 • Moment magnitude: • Most magnitude scales are empirical • As the amount of energy released increases, the ground-shaking characteristics do not necessarily increase at the same rate • Saturation: For strong earthquakes, the measured ground-shaking characteristics become less sensitive to the size of the earthquake than for smaller earthquakes • Body wave and Richter local magnitudes saturate at magnitudes of 6 to 7 • Surface wave magnitude saturates at about Ms = 8 • The only magnitude scale that is not subject to saturation is the moment magnitude • This is because it is based on the seismic moment, which is a direct measure of the factors that produce rupture along the fault 47 Magnitude-Duration Correlation 48 • Earthquake duration is highly correlated with the magnitude 48 Magnitude-Fault Length Correlation 49 • Magnitude is highly correlated with the length of the fault 49 Directivity and Fling 50 • Forward directivity: Focusing of wave energy along the fault in the direction of rupture; produces a pulse-like record with a large amplitude and short duration (right figure) • Fling: Pulses of large displacement at sites toward which the rupture is progressing; produced by constructive interference of waves (right figure) • Backward directivity: When rupture propagates away from the site, the arrival of the pulses is distributed in time; produces motions with relatively long duration and low amplitude (left figure) 50 Regional Damage دو یب یب ز یبمتو 4.1±1.6 یبشدید یب م فروریز 4.1±1.6 22.3±3.3 25.7±3.3 700 600 500 10.1±2.5 33.8±4.1 400 300 200 51 100 • This is the result of processing the data of 1198 buildings that experienced the 1396 Kermanshah earthquake • Explain each damage state: • None: 0% • Slight: 2% • Moderate: 10% • Severe: 50% • Total: 100% • Collapse • Most damage in Ezgeleh but in terms of numbers, Sarpol had higher number of damaged and collapsed buildings because it is a much larger city • It is clear that when you go towards east, the damage declines quickly • But towards south and southeast, the directivity caused significant damage and damage does not decay as quickly • This is due to directivity 51 Seismic Gap 52 • Seismic gap: A segment of an active fault that has not slipped in an unusually long time compared with other segments • 1989 Loma-Prieta earthquake occurred on a segment of the San Andreas fault that had previously been identified as a gap 52 Geometric Notation 53 • • • • • • Focus or hypocenter: Point at which rupture begins and the first seismic waves originate Rupture spreads across the fault at velocities of 2 to 3 km/sec Focus is located at some focal depth (or hypocentral depth) below the ground surface Epicenter: Point on the ground surface directly above the focus Epicentral distance: Distance on the ground surface between an observer or site and the epicenter Hypocentral distance: Distance between the observer and the focus 53 Determination of Location d= ts − p 1 / vs − 1 / v p 54 • This is a preliminary method • More refined estimates of the epicentral or hypocentral location are made using multiple seismographs, a three-dimensional seismic velocity model of the earth, and numerical optimization techniques 54 Determination of Location 55 • This is a classic example of an inverse problem • An inverse problem is a general framework that is used to convert observed measurements into information about a physical object or system that we are interested in 55 Path Combination of source, path and site effects 56 Source: Boore D. M. (2004) Journal of Earthquake Engineering 8(1), pp. 1-41 • An earthquake scenario consists of the source, the path, and the site • Source: What we talked about thus far • Path: Travel of waves • Distance: As waves travel away from a seismic source, geometric spreading reduces their amplitude; this is called attenuation • Crustal Structure: Tendency to transmit and absorb the energy in the seismic waves by the crust and mantle (reflection and refraction) • Site (next slide) 56 Site Effect 57 Site Effect • Surface Geology • Motion at the ground surface is the response of the soil layer to the input motion at the bedrock-soil interface • Soil deposits amplify the ground motion • Topography: Presence of topographic features affects the ground motion • Figure from the Instructor’s master’s thesis 57 Soil-Structure Interaction 58 • Soil-structure interaction: Happens when the wave has arrived at the base of the structure • This is the due to the presence of a non-rigid soil under the structure • Kinematic interaction: The structure experiences an average of the motions that are exerted on the foundation; therefore, the input motion to the foundation differs from the “free-field” motion • Inertial interaction: Presence of the soil affects the vibration properties of the system, such as its period and damping; therefore, it affects the response of the structure to the seismic excitation • Figure from the Instructor’s master’s thesis 58 EXTRA SLIDES 59 59 • K: Bulk modulus (Incompressibility) • μ: Shear modulus (Rigidity) • ρ: Density vp = vs = K + 43 60 Thin line is density Notes: • The Vs in inner core is not zero in this graph • There is no jump in Vp at the Lehman discontinuity (see next slide) 1. How different layers were formed? Heavier, more dense material, tended to sink in the early molten mass, while lighter, less dense material, rose toward the surface. Separation into layers was based on density. The separation seems to have taken place shortly after the formation of the planet in an event called the "Iron Catastrophe". http://wiki.answers.com/Q/How_did_Earth_separate_into_different_layers#ixzz28Y21xEcx Therefore, the boundaries between layers are due to presence of different types of materials, which are detected by the change in the wave propagation pattern. 2. Why mantle acts as rigid under sudden stresses? Under tremendous pressure, the solid mantle rock can act like a fluid or a solid. It is plastic. If sudden stresses act upon it, it reacts like a solid, as in the case of s-waves generated by earthquakes. If allowed enough time, when stressed, it will flow upward like heated water flows upward through layers of cooler, denser water. http://www.creationinthecrossfire.com/Articles/CatastrophicPlates3.html 3. Why the wave velocity increases with depth? The increase is a result of the effects of pressure on the seismic wave speed. Although 60 temperature also increases with depth, the pressure increase resulting from the weight of the rocks above has a greater impact and the speed increases smoothly in these regions of uniform composition http://eqseis.geosc.psu.edu/~cammon/HTML/Classes/IntroQuakes/notes/waves_ and_interior.html Since the density of the Earth increases with depth, you would expect the waves to slow down with increasing depth. Why, then, do both p- and s-waves speed up as they go deeper? This can only happen because the incompressibility and rigidity of the Earth increase faster with depth than density increases. http://www.bibliotecapleyades.net/tierra_hueca/inner_earth/inner1.htm 3. Why the waves propagate in curved paths? The waves have curved paths because their velocities increase with depth. http://www.chm.bris.ac.uk/webprojects1997/JohnH/WELCOME.HTM 5. Why the velocity curve has a jagged shape in upper mantle? The shallow part of the mantle contains several important well-established and relatively abrupt velocity changes. In fact, we often divide the mantle into two regions, upper and lower, based on the level of velocity heterogeneity. The region from near 400 to 1000 km depth is called the transition zone and strongly affects body waves that "turn" at this depth and arrive about 20°-30° distant from a shallow earthquake. In this depth range, the minerals that make up the mantle silicate rocks are transformed by the increasing pressure. The atoms in these rocks rearrange themselves into compact structures that are stable at the high pressures and the result of the rearrangement is an increase in density and elastic moduli, producing an overall increase in wave speed. 60 Jump in vp in Inner Core Boundary 61 61
