Seismic methods: Waves ad rays - II Readig: Today: p7-33 Net Lecture: p33-43 Reflectio ad trasmissio Seismic rays obey Sell s Law (just like i optics) The agle of icidece equals the agle of reflectio, ad the agle of trasmissio is related to the agle of icidece through the velocity ratio. si i si R si r
Reflectio ad trasmissio si i Seismic rays obey Sell s Law (just like i optics) The agle of icidece equals the agle of reflectio, ad the agle of trasmissio is related to the agle of icidece through the velocity ratio. But a coversio from to S or vice versa ca also occur. Still, the agles are determied by the velocity ratios. si R si r si R si r S S S S where p is the ray parameter ad is costat alog each ray. p Amplitudes reflected ad trasmitted The amplitude of the reflected, trasmitted ad coverted phases ca be calculated as a fuctio of the icidece agle usig Zoeppritz s equatios. Simple case: Normal icidece Reflectio coefficiet R C A A R i ρ ρ ρ + ρ Trasmissio coefficiet T C AT A i R C ρ ρ + ρ Reflectio ad trasmissio coefficiets for a specific impedace cotrast These coefficiets are determied by from the product of velocity ad desity the impedace of the material. R C usually small typically % of eergy is reflected.
Reflectio ad trasmissio You ca see: a direct wave, reflected ad trasmitted waves, plus multiples Normal move out (NMO) Reflectio from a sigle horizotal impedace cotrast: Arrival time or ( ) SR T h + T T0 + The arrival time curve is a hyperbola Note: a geophoe spread GG samples RR of the reflector. RR GG /
Normal move out (NMO) Arrival time curve is quadratic T T0 + So, if plot T vs. we ca determie the ad h from the slope ad itercept The importace of NMO Havig determied the layer velocity, we ca use the predicted quadratic shape to idetify reflectors The correct (shift traces) ad stack to ehace sigal to oise T NMO T T 0 T 0 Multiple layers Use Sell s Law to trace ray paths At each iterface si i si r p
NMO for layers Whe the offset is small w.r.t. reflector depth (<<h), the NMO curve is still a hyperbola T T0, + rms, where T 0, rms, k T 0, k k k T T k k k k h k k k k k3 Determie velocity structure oe layer at a time Diffractio From optics A sharp break i a reflector acts as a secodary source of a spherical wavefrot
Critical icidece si i si r whe >, r > i therefore, we ca icrease i util r 90 Whe r 90 i i C the critical agle si i C The critically refracted eergy travels alog the velocity iterface at cotiually refractig eergy back ito the upper medium at a agle i C a head wave Head wave Occurs due to a low to high velocity iterface Eergy travels alog the boudary at the higher velocity Eergy is cotiually refracted back ito the upper medium at a agle i C rovides costraits o the boudary depth e.g. Moho depth
Head wave You ca see: a head wave, trapped surface wave, divig body wave Factors affectig velocity Desity velocity typically icreases with desity (κ ad µ are depedat o ρ ad icrease more rapidly tha ρ) κ + 4 3 µ ρ S µ ρ orosity ad fluid saturatio Icreasig porosity reduces velocity. Fillig the porosity with fluid icreases the velocity. sat φ φ + F M oisso s ratio related to / S This is used to distiguish betwee rock/sedimet types. It is usually more sesitive tha just aloe. The sigificat variatios i sedimets are usually due to porosity variatios ad water saturatio. Water saturatio has o effect o S (for low porosities) but a sigificat effect o.
elocity ad desity Nafe-Drake curve sedimets ad sedimetary rocks igeous ad metamorphic rocks S This curve has bee approimated usig the epressio 4 ρ a (a is a costat: 670 whe ρ i km/m 3 ad i km/s) elocity ad desity Birch s Law A liear relatioship betwee velocity ad desity v aρ + b Three pressures Crust ad matle rock observatios
Typical rock velocity rages Usig velocity aloe to determie rock type is problematic to impossible. Seismic sources Rifles ad gus Cheap Repeatable fire ito water filled hole Shallow targets 0-50m Cosider Eergy iput Repeatability Cost Coveiece Sledge hammer Cheap Repeatable oce plate is stable (ad with traiig!) Targets 5-50m Weight drops Cheap Repeatable automated Targets > 50m
Seismic sources ibroseis No pulse, frequecy sweep Sigificat sigal with stackig/decovolutio Cosider Eergy iput Repeatability Cost Coveiece Eplosives arious sizes target depth Safety ad epese ca be a issue Air gus At sea ery repeatable Large array for big sigal Seismic receivers Geophoes Cylidrical coil suspeded i a magetic field The iertia of the coil causes motio relative to the maget geeratig a electrical sigal Geophoes are sesitive to velocity Istrumet respose The relatio betwee the iput groud motio ad the output electrical sigal Natural frequecy The frequecy which produces the maimum amplitude output Dampig Reduces the amplitude of the atural frequecy respose ad prevets ifiite oscillatios Wat a flat respose Hydrophoes Used at sea Use piezoelectric mierals to sese pressure variatios
Deploymet Importat cosideratios Need good couplig to the groud spike Mii-arrays to reduce surface wave oise Offset of geophoes Small offsets Near-vertical icidece retais -eergy High resolutio of subsurface reflectors Seismic reflectio aalysis Large offsets Improves velocity sesitivity rovides horizotal averages oly Seismic refractio aalysis