Introduction to Geophysics

Ali Onceloncel@kfupm.edu.

saDepartment of Earth SciencesKFUPM

Seismic Exploration: Fundamentals 2

Previous Lecture

Huygens's Principle Fermat's Principle Travel-time Graph Estimates of Seismic Velocity Reflected/Refracted waves Model Calculation for simple, horizontal, two layers Ray Paths Snell's law-Critically Refracted Arrival Seismic Refraction Behavior of refracted ray on velocity changes

12°

15°20°

35°

#1 #2 #3

medium 1

medium 2

A ray incident on surface results in 3 reflected and refracted rays. If the seismic velocities in medium 1 are α = 6.5 km/sec, β = 3.8 km/sec, what are the seismic velocities in medium 2? What type of material is medium2? Identify rays #1, #2, #3, #4

as P or S waves.

Homework Due to Wednesday

Refracted Ray and Angle

The angle of refraction increases as the angle of

incidence increases.

Energy Return and Critical Angle

A critically refracted wave, traveling at the top of

the lower layer with velocity V2, leaks energy back

into the upper layer at the critical angle (θ2)

c c c c c c

Lillie, Whole Earth Geophysics, Fig 3.25

Angle of For Incident P wave For Incident S waveIncidence Reflected Refracted Reflected Refracted

P-wave S-wave P-wave S-wave S-wave P-wave S-wave P-wave10 10 6 28 16 10 17 28 5111 11 7 31 18 11 19 31 5812 12 7 34 19 12 20 34 6813 13 8 37 21 13 22 37 8914 14 8 40 23 14 24 40 #NUM!15 15 9 44 24 15 26 44 #NUM!16 16 10 47 26 16 27 47 #NUM!17 17 10 51 28 17 29 51 #NUM!18 18 11 55 30 18 31 55 #NUM!19 19 11 60 31 19 33 60 #NUM!20 20 12 66 33 20 35 66 #NUM!21 21 12 73 35 21 37 73 #NUM!22 22 13 87 37 22 39 87 #NUM!23 23 14 #NUM! 39 23 41 #NUM! #NUM!24 24 14 #NUM! 41 24 43 #NUM! #NUM!25 25 15 #NUM! 43 25 45 #NUM! #NUM!26 26 15 #NUM! 45 26 47 #NUM! #NUM!27 27 16 #NUM! 47 27 49 #NUM! #NUM!28 28 16 #NUM! 49 28 51 #NUM! #NUM!29 29 17 #NUM! 51 29 54 #NUM! #NUM!30 30 17 #NUM! 53 30 56 #NUM! #NUM!

Modified Table 2.3 after Berger, pp.29.V1-P (m/s) 1500

V1-S (m/s) 900V2-P (m/s) 4000V2-S (m/s) 2400

21

22

21

1

2

21VV

VV

hX

Vtrefraction

Total Time of Refraction

Ttotal= T1+T2+T3

Xc=critical distance

Xcr=crossover distance

T1= Intercept time

Travel time for Direct/Refracted Waves

12

2112 VV

VVhxcr

Xc=critical distance

Xcr=crossover distance

T1= Intercept time

Seismic Reflection

Reflection occurs when Z1 differs from Z2, where Z

Acoustic impedance which is product of density and velocityV-shaped ray paths for a compressional wave from a

source to 6 receivers, reflected from a horizontal

interface.

=Z1

=Z2

Lillie, Whole Earth Geophysics, Fig 3.28

Reflection equation for a reflection hyperbolae:

1

2/122 )4(

V

hXtr

Tim

e

Distance

?

Tim

e

Distance

Dire

ct

Tim

e

Distance

?

Tim

e

Distance

Refl

ecte

d

Tim

e

Distance

?

Tim

e

Distance

Refracted or Head Wave

Tim

e

Distance

Direc

tRe

flect

ed

Refracted or Head Wave

?

Tim

e

Distance

Direc

tRefracted or Head Wave

Crossover distance

Tim

e

Distance

Dire

ct

Refle

cted

Refracted or Head Wave

Crossover distance?

Tim

e

Distance

Direc

t

Refle

cted

Refracted or Head Wave

ti

Miller et al. 1995

Records of Ground Motion and Travel-Time Curves

Miller et al. 1995

Miller et al. 1995

These exercises are designed to illustrates some of the basic characteristics of wave propagation in a single layer model use ray-tracing concepts to determine the arrival times of particular events. These exercises require that you construct the time-distance plot for the given model. In addition to

constructing the time-distance plots,

Due to Next Week

INTRODUCTORY RAY TRACING EXERCISESGENERAL INSTRUCTIONS

http://www.mines.edu/fs_home/tboyd/GP311/MODULES/SEIS/NOTES/deriv1.html

Observational DataDistance Direct Refracted Reflected

Arrival Arrivalft ft/sec

0 0.00 0.17 0.20500 0.10 0.22 0.22

1000 0.20 0.27 0.281500 0.30 0.32 0.362000 0.40 0.37 0.452500 0.50 0.42 0.543000 0.60 0.47 0.633500 0.70 0.52 0.734000 0.80 0.57 0.824500 0.90 0.62 0.925000 1.00 0.67 1.02

Single-Layer Model

XV

tdirect

1

1

21

21

21

2 4

V

h

V

Xtreflection

21

22

21

1

2

21VV

VV

hX

Vtrefraction

Equations

Be sure to do the following1) label all plotted curves,2) label all relevant points, and3) in a paragraph or so discuss the significanceand origins of the interrelationships portrayed inthe resultant time-distance plots