VẬT lý địa CHẤN 03 geometry

Reflected, Refracted and Diffracted waves • Reflected wave from a horizontal layer • Reflected wave from a dipping layer • Refracted wave from a horizontal layer • Refracted wave from a dipping layer • Diffracted waves Applications for shallow high resolution Reflection seismic • • • • • Hydrogeological studies of acquifers Engineering geology Shallow faults Mapping Quaternary deposits Ground investigation for pipe and sewerage tunnel detection Applications for Refraction seismic • • • • • Depth of groundwater level Depth and location of hardrock Elastic medium parameters Permafrost Glaciology Refraction seismic • Refracted Waves • Mainly horizontal Wave propagation • Only refracted waves are used (Lower layer must have higher velocity than upper layer) • Distribution of velocity as well as the depth and orientation of interfaces between layers Reflection seismic • • • • Reflected Waves (“Echo lot principal”) Mainly vertical wave propagation Complete seismic recording is used Distribution of the velocity variation Geometrical situation Direct wave Reflected wave Refracted wave Traveltime curve Receivers Source Receivers Direct wave t t= x v x o x x x x v x v= t Velocity of direct wave is derived from the distance and travel time Reflection: Horizontal reflector x A B x o S = 4h + x = t v s h α v h s 4h + x t = v2 x 2 t = t0 + , v 2h t0 = v 2 Reflection: horizontal reflector 2 h + x t = v2 x t = , for x >> h v h t2v2 = 4h2+x2 t2v2 - x2 = 4h2 t2v2 - x2 =1 4h2 4h2 Hyperbola Normal Moveout 0 Difference in traveltime t und t(x): x12 ∆T=t1- t0 ≈ 2v2t0 t2v2=4h2+x2- 4hxcos(90+Θ) X=-2hsinΘ t2v2=4h2+x2+4hxsin(Θ) Hyperbola: ∆Tdip [x+2hsin(Θ)] t2v2 =1 [2hcos(Θ)]2 - [2hcos(Θ)]2 -x x h Θ h x 90+Θ ∆Tdip= tx-t-x = 2xsinΘ v Refraction seismic sin ic v1 v1 = ⇔ sin ic = sin 90 v v2 Propagation of seismic waves Headwave (Roth et al., 1998) Direct wave Reflected wave Refracted wave Traveltime curve h TSG = TSA + TAB + TBG = 2TSA + TAB ( x − 2h tan ic ) h =2 + v1 cos ic v2 x 2h cos ic = + v2 v1 Refraction: horizontal reflector t v1 v2 2 v2 – v 2h x + -t = v2 v1 v ti x xcross x t = - + t i v2 x h v1 v2 v2 + v1 xcross = 2h -v – v1 x sin(θ c + α ) z a cosθ c + td = v1 v1 For small slopes (α < 100): x sin(θ c − α ) zb cosθ c + v1 v1 vd + vu v2 ≈ tu = x sin(θ c + α ) z a cosθ c + td = v1 v1 For small slopes (α < 100): x sin(θ c − α ) zb cosθ c + v1 v1 vd + vu v2 ≈ tu = Huygens’ Principle: Every point on a wavefront can be considered as a secondary source of spherical waves Surface V=1.6 km/s 800 m Reflection/Diffraction Reflection: tr≈ t0+δt h t0=2h/v δt =x2/(4vh) Reflection /Diffraction Diffraction: td≈ t0+2δt Question To find the depth to bedrock in a dam-site survey, traveltimes were measured from the shotpoint to 12 geophones laid out on a straight line through the shotpoint The offsets x range from 15 to 180 m Determine the depth of overburden from the data in the Table X(m) T(ms) 15 30 45 60 75 90 105 120 135 150 165 180 19 29 39 50 59 62 65 68 72 76 78 83 ... ∆T=t 1- t0 ≈ 2v2t0 t2v2=4h2+x 2- 4hxcos(90+Θ) X =-2 hsinΘ t2v2=4h2+x2+4hxsin(Θ) Hyperbola: ∆Tdip [x+2hsin(Θ)] t2v2 =1 [2hcos(Θ)]2 - [2hcos(Θ)]2 -x x h Θ h x 90+Θ ∆Tdip= tx-t-x = 2xsinΘ v Refraction seismic... t2v2 - x2 = 4h2 t2v2 - x2 =1 4h2 4h2 Hyperbola Moveout Difference in travel time t(x1 ) und t(x2 ): x2 2- x12 t 2- t1 ≈ 2v2t0 Normal Moveout 0 Difference in traveltime t und t(x): x12 ∆T=t 1- t0... horizontal reflector t v1 v2 2 v2 – v 2h x + -t = v2 v1 v ti x xcross x t = - + t i v2 x h v1 v2 v2 + v1 xcross = 2h -v – v1 x sin(θ c + α ) z a cosθ c + td = v1 v1 For small