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Refraction - III -

Refraction - III -. Ali K. Abdelfattah Geology Department Collage of science King Saud University. Delay Time Method. Allows Calculation of Depth Beneath Each Geophone Requires refracted arrival at each geophone from opposite directions Requires offset shots

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Refraction - III -

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  1. Refraction- III - Ali K. Abdelfattah Geology Department Collage of science King Saud University

  2. Delay Time Method • Allows Calculation of Depth Beneath Each Geophone • Requires refracted arrival at each geophone from opposite directions • Requires offset shots • Data redundancy is important

  3. Delay Time Method x V1 V2 • Irregular travel time curves is due to bedrock topography or glacial fill, much analysis is based on delay times. • Total Delay Time is the difference in travel time along actual ray path and projection of ray path along refracting interface.

  4. Delay Time Method x V1 V2

  5. Delay Time Method x V1 V2

  6. Delay Time Method x V1 V2

  7. Delay Time Method x V1 V2 Definition: (1)

  8. But from figure above, . Substituting, we get or

  9. Substituting from Snell’s Law,

  10. Multiplying top and bottom by sin(ic)

  11. Substituting from Snell’s Law, We get (2)

  12. (3)

  13. Reduced Traveltimes x Definition: T’AP = “Reduced Traveltime” at point P for a source at A T’AP=TAP’ Reduced travel times are useful for determining V2. A plot of T’ vs. x will be roughly linear, mostly unaffected by changes in layer thickness, and the slope will be 1/V2.

  14. Reduced Traveltimes x From the above figure, T’AP is also equal to TAP minus the Delay Time. From equation 9, we then get

  15. Reduced Traveltimes x Earlier, we defined to as (1) Substituting, we get (4)

  16. Reduced Traveltimes Finally, rearranging yields (5) The above equation allows a graphical determination of the T’ curve. TAB is called the reciprocal time.

  17. Reduced Traveltimes The first term is represented by the dotted line below:

  18. Reduced Traveltimes The numerator of the second term is just the difference in the traveltimes from points A to P and B to P.

  19. Reduced Traveltimes Important: The second term only applies to refracted arrivals. It does not apply outside the zone of “overlap”, shown in yellow below.

  20. Reduced Traveltimes The T’ (reduced traveltime) curve can now be determined graphically by adding (TAP-TBP)/2 to the TAB/2 line. The slope of the T’ curve is 1/V2.

  21. We can now calculate the delay time at point P. From Equation 4, we see that (4) According to equation 8 (2) So (6) Now, referring back to the equation of refracted waves

  22. It’s fair to say that (7) Combining equations 12 and 13, we get Or (8)

  23. Referring back to equation 3, we see that (3) Substituting into equation 8, we get Or (9) Solving equation 9 for hp, we get (10)

  24. We know that the incident angle i is critical when r is 90o. From Snell’s Law,

  25. Substituting back into equation 16, (10) we get (11) or

  26. In summary, to determine the depth to the refractor h at any given point p:

  27. 1.Measure V1 directly from the traveltime plot.

  28. 2.Measure the difference in traveltime to point P from opposing shots (zone of overlap only).

  29. 3.Measure the reciprocal time TAB.

  30. , 4. From equation 5, divide the reciprocal time TAB by 2.

  31. , 5. From equation 5, add ½ the difference time at each point P to TAB/2 to get the reduced traveltime at P, T’AP.

  32. 6. Fit a line to the reduced traveltimes, compute V2 from slope.

  33. 7. Using equation 15, (9) Calculate the Delay Time DT at P1,P2,P3….PN

  34. 8. Using equation 17, (10) Calculate the Depth h at P1,P2,P3….PN

  35. Faulted Planar Interface ( Diffraction ) • If refractor faulted, then there will be a sharp offset in the travel time curve. • We can estimate throw on fault from offset in curves, i.e. difference between two intercept times, from simple formula:

  36. Blind layer problem • Blind layers occur when there is a low velocity layer (LVL). • Head waves only occur for a velocity increase. Thus, there will be no refraction from the top of the LVL. • The LVL will not be detected on the time-distance plot. • This is described below.

  37. What if V2 < V1? Snell’s Law

  38. What if V2 < V1? If V1>V2, then as i increases, r increases, but not as fast.

  39. If V2<V1, the energy refracts toward the normal. None of the refracted energy makes the rays back to the surface.

  40. Seismic Refraction requires that velocities increase with depth. A slower layer beneath a faster layer will not be detected by seismic refraction. This can lead to errors in depth calculations.

  41. Hidden Layer Problem • Layers may not be detected by first arrival analysis: 1- Travel time curve produces no critical refraction from layer 2 2- Insufficient velocity contrast makes refraction difficult to identify 3- Refraction from thin layer does not become first arrival 4- Geophone spacing too large to identify second refraction

  42. Important: The Length of the Geophone Spread Should be 4-5 times the depth of interest.

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