Pre-Critical incidence

Transcription

1 Seismi methods: Refration I Refration reading: Sharma p58-86 Pre-Critial inidene Refletion and refration Snell s Law: sin i sin R sin r P P P P P P where p is the ray parameter and is onstant along eah ray. p Refletion and transmission oeffiients for a speifi impedane ontrast

2 Critial inidene When r P 90 i P i C the ritial angle sin i C P P he ritially refrated energy travels along the veloity interfae at ontinually refrating energy bak into the upper medium at an angle i C a head wave Refletion and transmission oeffiients for a speifi impedane ontrast Post-Critial inidene he angle of inidene > i C No transmission, just refletion Refletion and transmission oeffiients for a speifi impedane ontrast

3 Horizontal interfae raveltime equations Diret wave: Head wave Head wave: SB h osi DD' BD h tan i h a b slope: / interept: gives h Horizontal interfae Crossover distane, o Where the diret and head wave ross. heir travel times are equal: o o o h h Another approah to obtaining layer thikness

4 Horizontal interfae Refletions he ritial refletion is the losest head wave arrival. At shorter offsets there are low amplitude refletions (used in refletion seismology). At greater offsets there are wide-angle refletions. hree-layer model raveltime SA AB BC CD DG SG SG z osθ z z tanθ z tanθ osθ With some manipulation z SG z. Determine,, from slopes. Determine z from st interept. Determine z from nd interept 4

5 Multiple-layered models For multiple layered models we an apply the same proess to determine layer thikness and veloity sequentially from the top layer to the bottom Head wave from top of layer : h Head wave from top of layer : h h Head wave from top of layer n: n hj n j j n j n Horizontal vs. vertial veloity ontrasts A three-horizontal layer model an produe the same traveltime urve as a single horizontal layer over a vertial veloity ontat / / / / / a / b Head wave ontinues into b 5

6 Horizontal vs. vertial veloity ontrasts Use a long-offset shot Leave the geophones fied and move shot to greater offset In horizontal layers ase the shape of the traveltime urve is unhanged, just shifted in spae. In vertial veloity ontrast ase the rossover distane remains fied but is time shifted. Mapping vertial ontats Small offsets A vertial step auses an offset on the traveltime urve he relation of veloity to the slope remains unhanged he offset an be alulated from the time offset, z t Diffrations link the two head wave urves Depth, z, is alulated from the interept in the usual way 6

7 Mapping vertial ontats Infinite/large offsets For infinite/large vertial offsets there is no seondary head wave hree segments Diret wave Head wave Diffrated wave Will have the veloity lose to the diret wave Reverse the line Shooting to the same string of geophones from the other end wo traveltime segments: diret and head wave Head wave generated from energy entering the high veloity layer at the vertial interfae Dipping layers Dipping layers still produe head waves but the traveltimes are affeted by the dip Shooting up-dip: the veloity appears greater Shooting down-dip: the veloity is redued 7

8 Reversing lines shooting to a line of geophones from both ends For horizontal layers the traveltime urves are symmetrial For dipping layers layer veloities appear different for eah end the dip and true veloity an be determined from the updip and down-dip veloities Dipping layer traveltime Down-dip SC CD DS' d hu hd d osi [( h h ) tan i ] u d With trigonometri transformations, an eerise for the lass: Down-dip traveltime sin( i φ) d Up-dip traveltime sin( i φ) u hd osi hu osi Down-dip apparent veloity d sin( i φ) Up-dip apparent veloity u sin( i φ) where is dependene? 8

9 Dipping layer traveltime Given d sin( i φ) u sin( i φ) We an solve for: φ i sin sin sin d d sin u u then obtained from: sin i Finally, the interept times an be used to determine the perpendiular distane to the refletor: hd osi hu osi id iu Dipping layer Eample Diret arrivals eloities from slopes: 780 m/s and 50 m/s average: 05 m/s Head waves Up-dip veloity, u 00 m/s Down-dip veloity, d 870 m/s Using φ sin sin d u i sin sin d u we obtain: φ.8 i 4 9

10 Dipping layer Eample Now obtain from sin i 000 m/s o determine the perpendiular depths, h u and h d, use id hd osi h u 55 m and h d 95 m iu hu osi 0