Introduction to Geophysics

Ali Onceloncel@kfupm.edu.

saDepartment of Earth SciencesKFUPM

Seismic Exploration: Fundamentals 3

Previous Lecture

Refracted Ray and Angle Energy Return and Critical AngleTotal Time of RefractionTravel Time for Direct/Refracted Waves Seismic Reflection

Figure 3.30 of Lillie,1999

c c c c

Figure 3.31 of Lillie,1999

True Velocity and Apparent Velocity

Refracted arrivals have higher apparent velocities than direct arrivals.

c

c

Figure 3.33 of Lillie,1999

V = k + ( )

p4/3

Question: Nafe-Drake Curves suggesting that compressional wave velocity and density are directly proportional . The below equation:

Implies that P-wave velocity is inversely proportional

to density, Explain the paradox.

Last Homework of the week

Answer: Increasing in seismic velocity versus density is commonly true for rocks (see Nafe-Drake Curve), even the above equation show an inverse relation between velocity and density. As rocks become more dense, they become more incompressible and more rigid; the corresponding elastic constants (k and µ) commonly increase more than the density (ρ).

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

12°

15°20°

35°

#1 #2 #3

medium 1

medium 2

#4

Solution for the Homework

12°

15°20°

35°

#1 #2 #3

medium 1

medium 2

#4

Vp = 6.5 km/sec

Vs= 3.8 km/sec

1. What could you say about in medium 2?A) V2 <V1

B) V2>V1Remember that

Now, you can conclude that V2>V1

For Incident P wave Reflected Refracted P-wave S-wave P-wave S-wave

35 20 12 7

For Incident S wave Reflected Refracted S-wave P-wave S-wave P-wave

35 79 12 21

V1P (m/s)-incident 6500

V1S (m/s)-incident 3800

V2P (m/s)-refracted 2356

V2S (m/s)-refracted 1377

Then, estimate the velocities for two scenarios of incident waves: a) P-wave and b) S-wave

Then, estimate the angles for either reflected or refracted. Then, compare which wave are giving the angles are given in the ray tracing model.

Then, make a conclusion.

P-waveS-wave P-wave

P-wave

Rock Velocities (m/sec)

pp. 18-19 of Berger

V1P (m/s)-incident 6500

V1S (m/s)-incident 3800

V2P (m/s)-refracted 2356

V2S (m/s)-refracted 1377

Figure 3.10 of Lillie, 1999, modified f rom Birch, 1960Figure 3.10 of Lillie, 1999, modified f rom Birch, 1960

Sediments and sedimentary rock

I gneous and metamorphic rock

Solution for the Homework

Using the information in the below figures, Explain the anomalous positions of Vp and Vs for ice.

Anomalous positions of seismic velocity (V) for ice occurs since the elastic modules (k and µ) increase more rapidly than ρ.

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 Tuesday

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

Parks and Plates©2005 Robert J. Lillie

Depths in Kilometers