1/5/11 1 - Cal Poly Pomona
1/5/11 1 - Cal Poly Pomona 1/5/11 1 - Cal Poly Pomona
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
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1/5/<strong>11</strong> GSC334 Winter 20<strong>11</strong>Exploration GeophysicsGSC334 Winter 20<strong>11</strong>Exploration 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/<strong>11</strong> <strong>Cal</strong> <strong>Poly</strong> <strong>Pomona</strong> 701/06/<strong>11</strong> <strong>Cal</strong> <strong>Poly</strong> <strong>Pomona</strong> 8GSC334 Winter 20<strong>11</strong>Exploration GeophysicsMeasure Period and Frequency of thisWaveGSC334 Winter 20<strong>11</strong>Exploration 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/<strong>11</strong> <strong>Cal</strong> <strong>Poly</strong> <strong>Pomona</strong> 901/06/<strong>11</strong> <strong>Cal</strong> <strong>Poly</strong> <strong>Pomona</strong> 10GSC334 Winter 20<strong>11</strong>Exploration GeophysicsWaves Propagating ThroughHomogeneous Medium (Halfspace)GSC334 Winter 20<strong>11</strong>Exploration 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/<strong>11</strong> <strong>Cal</strong> <strong>Poly</strong> <strong>Pomona</strong> <strong>11</strong>01/06/<strong>11</strong> <strong>Cal</strong> <strong>Poly</strong> <strong>Pomona</strong> 122
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