This document summarizes seismic refraction paths involving a single horizontal refractor. It defines key terms like head waves, direct waves, critical distance, and crossover distance. It describes how Snell's law governs the refraction of seismic waves at boundaries between materials with different velocities. Equations are provided for calculating critical distance, crossover distance, and the depth of the refractor based on measured velocities and distances. In conclusion, the document notes that seismic refraction uses first arrivals to characterize subsurface geology by analyzing how seismic waves refract at boundaries between materials.

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