1. Refractions: Head Waves, Diving Waves, Refraction
Tomography
Velocity
Diving Waves (exist vertical dv/dz>0) z

2. Head Waves vs Diving Waves
Velocity
Head Wave z
Velocity
Velocity
Velocity
Diving Waves (exist vertical dv/dz>0)
Interference Head waves z z

3. Diving Waves, linear V(z) grad. and Triplications
Diving Waves, linear V(z) grad. and Triplications
Velocity x x
Direct Wave
Refraction
Direct Wave
Refraction z z t
p = sin i(z)/v(z) = 1/vmax
A simple velocity gradient produces a refraction that takes a circular path, having a hyperbolic sine (or Error Function) shape in the t-x plot.
V(z)=v + kz o
Velocity x
3 arrivals at dash x
3 arrivals at dash
Direct Wave
Head Wave
Reflection
Direct Wave z t
Reflection
Refraction
p = sin i(z)/v(z) = 1/vmax

4. p = sin i(z)/v(z) = 1/vmax
Limit of thin horizontal layers
Slowness = inverse apparent Vx
P = sinO1/v1 = sinO2/v2=sinO3/v3=1/v4 v1 v2 v3 v4

5. Diving Waves, linear V(z) grad. and Triplications
Diving Waves, linear V(z) grad. and Triplications
Velocity x x
Direct Wave
Refraction
Direct Wave
Refraction z z t
p = sin i(z)/v(z) = 1/vmax
A simple velocity gradient produces a refraction that takes a circular path, having a hyperbolic sine (or Error Function) shape in the t-x plot.
V(z)=v + kz o
Velocity x
3 arrivals at dash x
3 arrivals at dash
Direct Wave
Head Wave
Reflection
Direct Wave z t
Reflection
Refraction
p = sin i(z)/v(z) = 1/vmax

6. Diving Waves, linear V(z) grad. and Triplications
Diving Waves, linear V(z) grad. and Triplications
Velocity x
3 arrivals at dash x
3 arrivals at dash
Direct Wave d d
Direct Wave
Reflection z
Reflection t
Refraction
Head Wave
p = sin i(z)/v(z) = 1/vmax
Direct Wave
Reflection
Refraction
Synthetics
40 s
80 s
10 deg
40 deg
T-dx10 s
Reflection
Direct Wave
Refraction
T-dx10 s
40 s
80 s
10 deg
40 deg
Gulf California Data

7. T(x,z) for a linear V(z) grad.
Identify with circular arc:
Thus:
Source-receiver offset:
Linear velocity variation:
Constancy of apparent horizontal wave-number:

8. T(x,z) for a linear V(z) grad.
Time:
One can solve for
Plugging Eq.(1) and (3) into Eq.(2), we finally get:
From
Asymptote:

9. Layered Medium & Critical Angle
CSG
Model
3 km/s
Sea floor
Post-critical reflection ray
Post-critical reflections
Z (km)
Time (s)
4.0
3.5
1.5 km/s 6 6
X (km)
X (km)

10. Shadow Zones and Caustics
Sahdow Zones:
Shadow Zones and Caustics
Shadow Zone II:
Velocity x F
Shadow Zone
Caustic:Phase change results, large
Amplitude,ray area zero,surface weak focus,
Discontinuity of traveletime slopes z z x t
Shadow Zone: An area on Earth's surface where no direct seismic waves from a particular earthquake can be detected.

11. Shadow Zones and Caustics
Shadow Zones and Caustics
Romaowicz Lecture 1 hour:
Shadow Zone: An area on Earth's surface where no direct seismic waves from a particular earthquake can be detected.

12. Head Wave, Diving Wave, post-Crit. Reflections
Head Waves: Horizontal layered medium Vx = Vrefrac.
Slope dx/dt in data = Vrefract.
More generally: Refraction tomography.
Post Crit. Reflections: Strong Amplitude
More generally: Refraction tomography.
Phase Change
3. Diving Waves: Phase Changes, Triplication
Strong Amplitudes, Interfer. Head Waves, Shadow
Zones, Caustics

13. Refraction Tomography
t1 = L11/v1 + L12/v2 + L13/v3 + ….+ L1n/vn
t2 = L21/v1 + L22/v2 + L23/v3 + ….+ L2n/vn

14. Refraction Tomography
Cool=falling blobs
Cool colors = +v
Hot=rising blobs
Hot colors = -v
670 km discontinuity
Any planet with a radius over ~1500 km cannot conduct its internal heat away within the age of the universe, so it must convect viscously to release its heat, or it would melt and then convect as a fluid.

15. Bedrock Depths from the Wells
3D Marine:
Bedrock Depths from the Wells
here!
Humboldt County
Lander County
The bedrock is expected to be at depth of several hundred meters from ground surface
677m
Buffalo Valley Mine
Pershing County
#124
680ft(200m)
#125
320ft(97m)
3.36km 15

16. Buffalo Valley Buffalo Valley Mine Seismic Line Pershing County
North central Nevada
Buffalo Valley Mine
Seismic Line
Pershing County 16

17. Survey Site 17

18. Seismic Recording Unit18

19. Seismic Source 19

20. Comparison of Tomographic and Seismic Image
Tomographic Image
300
Z (m)
m/s
Seismic Refractor Image
300
2500
Z (m)
X (m)
Amplitude A B C 22

21. Interpretation of Tomogram and Seismic Refractors
m/s
300
2500
Z (m)
X (m) A B C
#124
#125
320ft
(97m)
680ft
(200m)
900 ft
(273m)
845ft
(256m)
2000 m
(ch48 of
Line C)
150 m
off from
the end 23