1/5/11 1 - Cal Poly Pomona

1/5/11 GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsToday’s Class• Lecture:– Seismic Waves• Lab 1 will be handed out on Wednesday• Will need dynamic tables and software from CDfrom textbookSeismic ExplorationFundamental Concepts in SeismicWaves01/06/11 Cal Poly Pomona1GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsSeismic ExplorationBasic principle:• induce disturbance that imparts energy into Earth, which istransmitted in form of seismic waves• make measurements of these seismic waves on Earth’s surface• make deductions about internal structures and compositions01/06/11 Cal Poly Pomona 301/06/11 Cal Poly Pomona 4GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsSimplified ExampleThe “Real” EarthPlanar, homogeneous body of granite.What is needed to be able to determine seismic wavespeed of this material?• distance between instrument and impact (source)• arrival time of wave at instrument• time of impact• Seismic waves generallydo not travel in straightlines, but are deflected, byrefraction or reflection,by layers they encounter=> allows determinationof internal structure• Particularly useful fordetermining position ofroughly horizontalinterfaces between layers01/06/11 Cal Poly Pomona 501/06/11 Cal Poly Pomona 61

1/5/11 GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsWave TerminologyAssume periodic, sinusoidalwave:• wavelength: distance between twoadjacent peaks• amplitude: maximumdisplacement• period: time it takes for twosuccessive wave crests to pass areference point• frequency: repetition rate: 1/Twhere T is the period– measured in units of Hertz (numberof repetitions per second)• speed: V = fλ two different frames of reference01/06/11 Cal Poly Pomona 701/06/11 Cal Poly Pomona 8GSC334 Winter 2011Exploration GeophysicsMeasure Period and Frequency of thisWaveGSC334 Winter 2011Exploration GeophysicsRays andWave fronts• Wave front is surface of all equal travel times from source• In describing wave propagation, vector perpendicular towave front is defined as ray.01/06/11 Cal Poly Pomona 901/06/11 Cal Poly Pomona 10GSC334 Winter 2011Exploration GeophysicsWaves Propagating ThroughHomogeneous Medium (Halfspace)GSC334 Winter 2011Exploration GeophysicsRelating Physical Measurements toSubsurface GeologySo, what determines how fast (and in whatmanner) seismic waves travel through Earth?Material’s elastic propertiesSubsurface rock is subject to stress, changes its shape(undergoes strain) and then returns to its original shape=> elastic behavior01/06/11 Cal Poly Pomona 1101/06/11 Cal Poly Pomona 122

1/5/11 GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsForce and StressF = m a, where:• F: force applied to a body• m: its mass, and• a: acceleration induced byforceStress is force applied perunit area (units?).Normal and Shear Stressnormal stressIf force is perpendicular(normal) to surface, thenstress is called normalstress; if it is tangentialto surface, it is calledshear stress.01/06/11 Cal Poly Pomona1301/06/11 Cal Poly Pomona14GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsStrain• Materials may respond tomoderate forces bychanging their shape:strain• For example: if I stretch arubber band that was 5 cmlong until it is 6 cm long,the strain is 1cm/5cm=0.2or 20%• Strain has no units, isdimensionlessHooke’s Law• Assume Hookean behavior: materials behave elastically andexhibit instantaneous linear relationship between stress andstrain• Illustrated using spring:Suppose we apply force F to stretch spring by length x :F and x are related by Hooke's law: F = k s x– k s : spring constant.01/06/11 Cal Poly Pomona1501/06/11 Cal Poly Pomona16GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsElastic Behavior• Similarly for stress σ and strainε: σ = µε or σ/ε = µ– µ: elastic constant or modulus• Most rocks, when subjected tonear surface conditions, can bedescribed as linear elasticsolids:– strain remains proportional toapplied stress and– strain is reversible• If rock or material is “strong”,would it have a relatively highor low value for the elasticconstant?Elastic Constants• Young’s modulus, E– Defined from uniaxialcompression or tension– σ 3 = Eε 3 – directly relates resultantstrain to given stress– rocks with differentvalues of E have differentseismic velocitiesε = l f− l ol o= Δl• Poisson’s ratio, µ – Ratio betweenelongations– µ

1/5/11 GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsElastic ConstantsElastic Constants• Bulk modulus (orincompressibility), K– Subject material topressure change ΔP– ΔP = -K Δ – measure of howmuch force is neededto change volume ofmaterial withoutchanging its shapeΔ = V f−V oV o19• Rigidity modulus, or shear modulus, G– Deform solid by simple shearσ s= Gγ– Measure of effort needed to change shape ofmaterial, without changing its volume€01/06/11 Cal Poly Pomona€01/06/11 Cal Poly Pomona20GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsElastic Coefficients and Rock TypesE, µ, K and G:• define elastic behavior of subsurface• govern speed with which waves travel through Earthmaterials• values have been determined in lab• are not mutually independent– G and K can be defined in terms of µ and ESeismic Wave TypesEquations of motion can be derived that show thatfor infinite elastic homogeneous body, two typesof waves may be transmitted:• P-waves• S-wavesBoth types are referred to as body waves, as theytravel through body of EarthThey deform rock in different ways, which areresisted by different elastic restoring forces, andtherefore have different velocities01/06/11 Cal Poly Pomona 2101/06/11 Cal Poly Pomona 22GSC334 Winter 2011Exploration GeophysicsBody Waves: P-wave• Primary wave, greatest speed• Compression, changes size and shape• Particle motion in direction of wavepropagation, longitudinal• Can travel through any materialGSC334 Winter 2011Exploration GeophysicsP-Wave Particle Motion• If wave front is canted to horizontal plane, P-waveground surface motion will have horizontal and verticalmotion01/06/11 Cal Poly Pomona2301/06/11 Cal Poly Pomona 244

1/5/11 GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsBody Waves: S-wave• Secondary wave, slower speeds• Transverse, shearing, no volume change• Particle motion at right angles to wavepropagation• Can travel only through solidsS-WaveParticleMotion• Often S-wave particle motion is resolved into twocomponents: one parallel to ground surface (SH) andone in vertical plane containing incident ray (SV)01/06/11 Cal Poly Pomona2501/06/11 Cal Poly Pomona 26GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsMotion and Propagation Direction• In this example, seismic waves are coming up verticallytoward stations (earthquake occurred directly beneath them)– First arrival, P wave, primarily on vertical component– Large later arrival, S-wave, most on horizontalsSurface WavesIf medium is nothomogeneous andinfinite (for example, if ithas surface), anothertype of waves will also begenerated: surfacewaves, which travelalong Earth’s surface• Rayleigh waves• Love waves01/06/11 Cal Poly Pomona2701/06/11 Cal Poly Pomona 28GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsSurface Waves: Love wavesLove Waves• Horizontal, shearing motion, similar to S-waves• Do not travel through water• All particle motion is in horizontal plane• Amplitude decreases downwards01/06/11 Cal Poly Pomona2901/06/11 Cal Poly Pomona 305

1/5/11 GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsSurface Waves: Rayleigh wavesRayleigh Waves• Backward-rotating (retrograde), elliptical motion• Vertical as well as horizontal motions• Travel through both ground and water• Amplitude decays exponentially with depth (greatest atsurface)01/06/11 Cal Poly Pomona31• All particle motion is contained in vertical plane• Strong signal on exploration seismic records, alsoreferred to as ground roll01/06/11 Cal Poly Pomona 32GSC334 Winter 2011Exploration GeophysicsSeismic Wave VelocitiesP- and S-wave velocities depend on elastic properties anddensity of material through which they travelK = bulk modulusG = shear modulusρ = densityV P=K + 4 3 GBecause K and G are both positive, V P > V SG=0 for liquids,€€so shear waves cannot propagate in liquidsρV S=G ρGSC334 Winter 2011Exploration GeophysicsSeismic Waves in Exploration• Routinely used in seismic exploration: P-waves• General rules for velocities:– unsaturated sediments: V P lower than saturated– unconsolidated sediments: V P lower than consolidated– weathered rocks: lower V P than similar rocks that areunweathered– fractured rocks: lower V P than similar rocks that areunfractured• Reasonable values:– 500 m/s for dry unconsolidated materials– 1500 m/s for wet unconsolidated materials– 4000 m/s for sedimentary rocks– 6000 m/s for unweathered igneous and metamorphicrocks01/06/11 Cal Poly Pomona3301/06/11 Cal Poly Pomona 34GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsAir WaveTypical Wavelengths• With hammer blows or explosives near surface,compressional wave will be created that travelsthrough air: air wave.• This wave travels at 331 m/sec, which may beslightly faster than some common surfacematerials.• May be significant signal, that you should beaware of in your interpretation!• Energy sources: f~10-100 Hz• V P ~1500 m/s• Typical wavelength?01/06/11 Cal Poly Pomona 3501/06/11 Cal Poly Pomona 366

1/5/11 GSC334 Winter 2011Exploration GeophysicsPropagation: Rays and WavefrontsGSC334 Winter 2011Exploration GeophysicsWave Propagation Through the RealEarthPoint source seismic disturbance:• Wavefront expands out from this point• Rays: perpendicular to wavefront01/12/09 Cal Poly Pomona37Seismic waves will reflect or refract when they encountersurfaces bounding materials with different elasticcoefficients and densities (interfaces).01/12/09 Cal Poly Pomona 38GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsHuygen’s PrinciplePlane Wave Approximation• All points on wavefront can be consideredpoints sources forgeneration ofsecondary wavelets• Thus we can determineposition of wave frontat time t 2 after time t 1 .01/12/09 Cal Poly Pomona 3901/12/09 Cal Poly Pomona 40GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsFermat’s Principle• Principle of least time• Path of wave between two fixed points is onealong which travel time is least of all possiblepaths between those two points, with respect tonearby possible paths– This may not be shortest distance!Reflection• When planar wave front strikes planar horizontalinterface, it will reflect, with angle of incidence equal toangle of reflection01/12/09 Cal Poly Pomona 4101/12/09 Cal Poly Pomona 427

1/5/11 GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsRefractionFor refracted wave,ratio of sines ofangle of incidenceand angle ofrefraction is equal toratio of velocities oftwo materials:Snell’s lawReflection and Refraction of Waves(Explanation by Huygens' Principle)sinθ 1sinθ 2= v 1v 2• http://www.walter-fendt.de/ph11e/huygenspr.htm01/12/09 Cal Poly Pomona 4301/12/09 Cal Poly Pomona 44€GSC334 Winter 2011Exploration GeophysicsGSC334 Winter 2011Exploration GeophysicsWave Paths Through EarthSnell’s Law• As wave travels through Earth, path depends onvelocity of material• Snell's law determines path wave takes as itrefracts from one rock layer into another• Change in direction depends on ratio of wavevelocities of two different rocks€sinθ iV 1= sinθ rflV 1= sinθ rfrV 2V2>V1!• Seismic rays obey Snell’sLaw (just as in optics)• At interface some ofincident energy isreflected, some istransmitted• If V2 is higher than V1,which is commonly case,ray bends away fromnormal to the interface.• (Simplified picture, incident P-wavewill give rise to a reflected and arefracted S-wave as well)01/12/09 Cal Poly Pomona4501/12/09 Cal Poly Pomona46GSC334 Winter 2011Exploration GeophysicsGeneral Description: Incident P-waveCalculate all angles, for a P-waveincident angle of 20°sinθ i= sinθ rfl P= sinθ rfl S= sinθ rfr P= sinθ rfr SV 1PV 1PV 1SV 2PGSC334 Winter 2011Exploration GeophysicsV 2SIncident S-wave€01/12/09 Cal Poly Pomona 4701/12/09 Cal Poly Pomona 488

1/5/11 GSC334 Winter 2011Exploration Geophysics€sinθ icritV 1sinθ iV 1sinθ icrit= V 1GSC334 Winter 2011Critical RefractionMost commonly: V 2 >V 1= sinθ rfrAs angle of incidence increases, so doesV 2angle of refraction.When incidence angle reaches thecritical angle, rays are refractedparallel to interface: head wave.If it is increased beyond this criticalV 2= sin90°V 2= 1 V 2value, no refraction occurs, and ray istotally reflected.Exploration GeophysicsHead WavesHead waves onlyoccur when a layeroverlies anotherlayer with a higherseismic velocity€01/12/09 Cal Poly Pomona4901/12/09 Cal Poly Pomona 50GSC334 Winter 2011Exploration GeophysicsLayer Over a Halfspace01/12/09 Cal Poly Pomona 519