![Critical Distance and Crossover Distance
Critical Distance A critical distance is the
distance on the offset spread at which reflected
and refracted waves have the same arrival time.
x' = 2h tanθc 2.1
Crossover Distance A crossover distance is the
offset distance when the head wave(refracted
wave) takes over direct wave to become the first
arrival on the seismogram (Sharma, 2018).
xc = 2h [ (v2 + v1) / (v2 – v1)]½ 2.2
Figure 2. Critical Distance & Crossover Distance in refraction
seismology ( Kharal, 2017).](https://image.slidesharecdn.com/ahasanhabibpresentationgeophysics-230121124014-28959444/85/REFRACTION-PATHS-Single-Horizontal-Refractor-4-320.jpg)
![Single Horizontal Refractor
Here, V2 > V1,
MP = x -
(htanθc
+ htanθc ) = x -
2htanθc
OM = z/ cos θc
Where, sin θc
= V1/V2
The equation can be written as, t = (x/V2) +t1 (3.1)
Where, t1 = (2h cos θc) / V1
h= ½ v1 t1 /cosθc (3.2)
The head wave will not be observed at offsets less than
the critical distance.
Critical distance, x' = OQ = 2h tanθc = 2h tan [sin-1
(V1/V2)] = 2h [(V2/V1)2 - 1]½
Figure 3. Relation between reflection and refraction
raypaths and traveltime curves.](https://image.slidesharecdn.com/ahasanhabibpresentationgeophysics-230121124014-28959444/85/REFRACTION-PATHS-Single-Horizontal-Refractor-5-320.jpg)
![Single Horizontal Refractor
Slope of the reflection time-distance curve at x = x',
[dt/dx] = 1/v1[OQ/(OM + MQ)] = 1/v1(½ OQ/OM) =
1/v1 sin θc = 1/ v2
The reflection and refraction curves have the same slope at D,
consequently, the refraction curve is tangent to the
reflection curve at x = x'.
The intercept time t1 for the refraction is less than the arrival
time t0 for the reflection at the source point because,
t1= (2h/v1) cosθc , t0 = 2h/v1 ; hence, t1 < t0
In Fig. 4., refracted and direct wave traveltimes are equal at
the point W. If the offset corresponding to W is xc , we have
xc/v1 = xc / v2 + 2h/ cosθc
So, h =[ xc/2 (1 – v1/v2 )] / cosθc 3.3
This relation is used to find h from measurements of the
velocities and the crossover distance xc . Figure 4. Relation between reflection and refraction
raypaths and traveltime curves.](https://image.slidesharecdn.com/ahasanhabibpresentationgeophysics-230121124014-28959444/85/REFRACTION-PATHS-Single-Horizontal-Refractor-6-320.jpg)
![References
[1] Dondurur, D. ( 2018). Acquisition and Processing of Marine Seismic Data. Elsevier. https://doi.org/10.1016/C2016-0-
01591-7
[2] Encyclopedia. (n.d). A Dictionary of Earth Sciences. Retrieved from
https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releaes
[3] Kharal, N. (2017). Study of hydrogeological setting on Grindalsmoen waterwork ,Elverum. Retrieved from
https://www.researchgate.net/publication/317792448_study_of_hydrogeological_setting_on_Grindalsmoen_waterwork_Elver
um
[4] Sharma, K. (2017, October 8). Seismic Imaging Techniques. Retrieved from
https://www.quora.com/What-is-the-difference-between-critical-distance-and-cross-over-distance-in-seismic-refraction
[5] Surface Search Inc. (n.d.). Seismic Refraction What is it?. Rtrieved From https://surfacesearch.com/seismic-refraction-
what-is-it/
[6] Telford, W.M., Geldart, L.P. & Sheriff, R.E. (1990). Applied Geophysics. (2nd ed.), Cambridge: Cambridge University
Press.](https://image.slidesharecdn.com/ahasanhabibpresentationgeophysics-230121124014-28959444/85/REFRACTION-PATHS-Single-Horizontal-Refractor-8-320.jpg)
REFRACTION PATHS - Single Horizontal Refractor
- 1. REFRACTION PATHS - SINGLE HORIZONTAL REFRACTOR Presented by - Name : Md. Ahasan Habib Roll : 2314 Course Name : Exploration Geophysics Course No : GS 307
- 2. Presentation Outlines • Introduction • Critical Distance and Crossover Distance • Single Horizontal Refractor • Conclusion
- 3. Introduction Head wave A refracted wave which enters and leaves a high-velocity medium at the critical angle. Usually, the term refers to the refracted wave which arrives to give a refraction first break. Direct wave A seismic wave which travels through the ground directly from the source to the detectors without being reflected off or refracted by a subsurface layer. Snell's Law When a wave crosses a boundary between two isotropic media, the wave changes direction such that, sin i / v1 = sin r / v2 (1.1) Figure 1. Head wave (refracted) and direct wave in seismic data acquisition (after Dondurur, 2018).
- 4. Critical Distance and Crossover Distance Critical Distance A critical distance is the distance on the offset spread at which reflected and refracted waves have the same arrival time. x' = 2h tanθc 2.1 Crossover Distance A crossover distance is the offset distance when the head wave(refracted wave) takes over direct wave to become the first arrival on the seismogram (Sharma, 2018). xc = 2h [ (v2 + v1) / (v2 – v1)]½ 2.2 Figure 2. Critical Distance & Crossover Distance in refraction seismology ( Kharal, 2017).
- 5. Single Horizontal Refractor Here, V2 > V1, MP = x - (htanθc + htanθc ) = x - 2htanθc OM = z/ cos θc Where, sin θc = V1/V2 The equation can be written as, t = (x/V2) +t1 (3.1) Where, t1 = (2h cos θc) / V1 h= ½ v1 t1 /cosθc (3.2) The head wave will not be observed at offsets less than the critical distance. Critical distance, x' = OQ = 2h tanθc = 2h tan [sin-1 (V1/V2)] = 2h [(V2/V1)2 - 1]½ Figure 3. Relation between reflection and refraction raypaths and traveltime curves.
- 6. Single Horizontal Refractor Slope of the reflection time-distance curve at x = x', [dt/dx] = 1/v1[OQ/(OM + MQ)] = 1/v1(½ OQ/OM) = 1/v1 sin θc = 1/ v2 The reflection and refraction curves have the same slope at D, consequently, the refraction curve is tangent to the reflection curve at x = x'. The intercept time t1 for the refraction is less than the arrival time t0 for the reflection at the source point because, t1= (2h/v1) cosθc , t0 = 2h/v1 ; hence, t1 < t0 In Fig. 4., refracted and direct wave traveltimes are equal at the point W. If the offset corresponding to W is xc , we have xc/v1 = xc / v2 + 2h/ cosθc So, h =[ xc/2 (1 – v1/v2 )] / cosθc 3.3 This relation is used to find h from measurements of the velocities and the crossover distance xc . Figure 4. Relation between reflection and refraction raypaths and traveltime curves.
- 7. Conclusion Seismic Refraction is a surface geophysics method that utilizes the refraction of seismic waves on geology layers and rock/soil units to characterize subsurface geologic conditions. The method involves a geophysical principle governed by Snell’s Law, which is a formula used to describe the relationship between seismic wave angles of refraction when passing through a boundary between two different isotropic media. Refraction seismology involves the study of head waves using primarily first arrivals, the equivalent of first breaks in reflection seismology. For a head wave to be generated, the velocity below an interface must be higher than that above it. However, this is not always the case, and problems sometimes result from a low-speed layer that never carries a headwave.
- 8. References [1] Dondurur, D. ( 2018). Acquisition and Processing of Marine Seismic Data. Elsevier. https://doi.org/10.1016/C2016-0- 01591-7 [2] Encyclopedia. (n.d). A Dictionary of Earth Sciences. Retrieved from https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releaes [3] Kharal, N. (2017). Study of hydrogeological setting on Grindalsmoen waterwork ,Elverum. Retrieved from https://www.researchgate.net/publication/317792448_study_of_hydrogeological_setting_on_Grindalsmoen_waterwork_Elver um [4] Sharma, K. (2017, October 8). Seismic Imaging Techniques. Retrieved from https://www.quora.com/What-is-the-difference-between-critical-distance-and-cross-over-distance-in-seismic-refraction [5] Surface Search Inc. (n.d.). Seismic Refraction What is it?. Rtrieved From https://surfacesearch.com/seismic-refraction- what-is-it/ [6] Telford, W.M., Geldart, L.P. & Sheriff, R.E. (1990). Applied Geophysics. (2nd ed.), Cambridge: Cambridge University Press.
- 9. Thank You