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- 1. Introduction to Geophysics Ali Oncel [email_address] Department of Earth Sciences KFUPM Seismic Exploration: Fundamentals 1
- 2. <ul><li>Nafe-Drake Curves suggesting that compressional wave velocity and density are directly proportional . The below equation: </li></ul>Implies that P-wave velocity is inversely proportional to density, Explain the paradox. Homework, Due to Wednesday
- 3. Homework due to Wednesday <ul><li>Using the information in the below figures, Explain the anomalous positions of Vp and Vs for ice. </li></ul>
- 4. Previous Lecture Elastic Coefficients and Seismic Waves Birc's Law Nafe-Drake Curve Factors affecting P-wave and S-wave velocity Seismic velocities for Geological Materials Amplitude Changes of Particle Motions Wavefronts and RayPaths Seismic Trace Seismic Wave Types
- 5. Reminder: Seismic Velocity in a homogeneous medium V=(appropriate elastic modulus/density) 1/2 What is relationship of rock density to seismic velocity? Inversely proportional to the square root of the density From Tom Boyd’s WWW Site - http://talus.mines.edu/fs_home/tboyd/GP311/introgp.shtml V = = = k + ( ) + 2 p 4/3 V = = s
- 6. Elastic Moduli <ul><li>Where Shear Modules </li></ul><ul><li> Lame’s lambda constant </li></ul><ul><li>E= Young’s module </li></ul><ul><li>ρ= mass density </li></ul><ul><li>σ = Poisson’s ratio </li></ul>Bulk Module is k = k - = 2 σ E 3 ( 1 + σ ) ( 1 - 2 σ ) k = 2 2 σ υ
- 7. Reminder: k and Bulk Modulus where = dilatation = V/V and P = pressure =k= ( P/ ) Ratio of increase in pressure to associated volume change shear stress = ( F /A) = shear stress shear strain shear modulus shear strain = ( l /L) Force per unit area to change the shape of the material
- 8. Reminder: Poisson’s Ratio Ratio Vp and Vs depends on Poisson ratio: where Poisson’s ratio varies from 0 to ½. Poisson’s ratio has the value ½ for fluids
- 9. Reminder: Seismic Velocities (P-wave)
- 10. Rock Velocities (m/sec) pp. 18-19 of Berger
- 11. Reminder: Influences on Rock Velocities <ul><li>In situ versus lab measurements </li></ul><ul><li>Frequency differences </li></ul><ul><li>Confining pressure </li></ul><ul><li>Microcracks </li></ul><ul><li>Porosity </li></ul><ul><li>Lithology </li></ul><ul><li>Fluids – dry, wet </li></ul><ul><li>Degree of compaction </li></ul><ul><li>…………… </li></ul>
- 12. Huygen’s Principle
- 13. Fermat’s Principle pp. 20 of Burger’s book.
- 14. <ul><li>Travel time graph . The seismic traces are plotted according to the distance (X) from the source to each receiver. The elapsed time after the source is fired is the travel time (T). </li></ul>Travel-Time Graph T=X/V X distance from source to the receiver, T total time from the source to the receiver V seismic velocity of the P, S, or R arrival. <ul><li>Initial wave fronts for P, S and R waves , propagating across several receivers at increasing distance from the source. </li></ul>
- 15. Estimates of Seismic Velocity <ul><li>B) The slope of the travel time for each of the P,S, and R arrivals (see earlier figure) is the inverse of velocity. </li></ul><ul><li>The slope of line for each arrival is the first derivative </li></ul><ul><li>( dT/dX ). </li></ul>
- 16. A) A compressional wave , incident upon an interface at an oblique angle , is split into four phases : P and S waves reflected back into the original medium; P and S waves refracted into other medium. Reflected/Refracted Waves
- 17. Model Calculation Simple, Horizontal Two Layers Direct Wave?
- 18. Selected ray path (a) and travel-time curve 9b) for direct wave. The slope, or first derivative, is the reciprocal of the velocity (V 1 ). Direct Wave
- 19. Model Calculation Simple, Horizontal Two Layers Reflected Wave?
- 20. Model Calculation Simple, Horizontal Two Layers Head Wave or Critically Refracted?
- 21. All Three Arrivals
- 22. Ray paths for direct, reflected, and critically refracted waves, arriving at receiver a distance ( X ) from the source. The interface separating velocity ( V 1 ) from velocity ( V 2 ) material is a distance ( h ) below the surface. Ray paths
- 23. Snell’s Law- Critically Refracted Arrival For a wave traveling from material of velocity V 1 into velocity V 2 material, ray paths are refracted according to Snell’s law . i 1 = angle of incidence i 2 = angle of refraction
- 24. <ul><li>Wave fronts are distorted from perfect spheres as energy transmitted into material of different velocity. Ray paths thus bend (“ refract ”) across an interface where velocity changes . </li></ul>The angles for incident and refracted are measured from a line drawn perpendicular to the interface between the two layers. Seismic Refraction
- 25. Behavior of Refracted Ray on Velocity Changes

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