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 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
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1/5/<strong>11</strong> GSC334 Winter 20<strong>11</strong>Exploration GeophysicsGSC334 Winter 20<strong>11</strong>Exploration 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/ph<strong>11</strong>e/huygenspr.htm01/12/09 <strong>Cal</strong> <strong>Poly</strong> <strong>Pomona</strong> 4301/12/09 <strong>Cal</strong> <strong>Poly</strong> <strong>Pomona</strong> 44€GSC334 Winter 20<strong>11</strong>Exploration GeophysicsGSC334 Winter 20<strong>11</strong>Exploration 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 <strong>Cal</strong> <strong>Poly</strong> <strong>Pomona</strong>4501/12/09 <strong>Cal</strong> <strong>Poly</strong> <strong>Pomona</strong>46GSC334 Winter 20<strong>11</strong>Exploration GeophysicsGeneral Description: Incident P-wave<strong>Cal</strong>culate 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 20<strong>11</strong>Exploration GeophysicsV 2SIncident S-wave€01/12/09 <strong>Cal</strong> <strong>Poly</strong> <strong>Pomona</strong> 4701/12/09 <strong>Cal</strong> <strong>Poly</strong> <strong>Pomona</strong> 488
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