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Waves in Fluids: Understanding the Elements of 3D Seismology

This presentation provides an overview of waves in fluids, covering topics such as fluid properties, elastic moduli, acoustic solutions, density, and velocity. It also explores different approaches to understanding fluid behavior and the importance of density and velocity in seismic processing.

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Waves in Fluids: Understanding the Elements of 3D Seismology

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  1. Geol 4068 Class presentation to accompany reading of Chapter 2- Waves in Fluids Elements of 3D Seismology, 2nd Edition by Christopher Liner September 6, 2005 Juan M. Lorenzo

  2. Outline • What is a Fluid? • Elastic Moduli • Acoustic Solution to the Wave equation • Density • Velocity

  3. Outline • What is a Fluid? • Elastic Moduli • Acoustic Solution to the Wave equation • Density • Velocity

  4. TYPES OF SEISMIC MATERIALS Fluid (no shear strength) Porous solid (Solid+fluid -BIOT THEORY) Solid (shear strength and high and finite resistance to compressibility

  5. Outline • What is a Fluid? • Elastic Moduli • Acoustic Solution to the Wave equation • Density • Velocity

  6. Key Physical Parameters of the Acoustic Wave Equation (Pa) Bulk Modulus or modulus of incompressibility

  7. Key Physical Parameters of the Acoustic Wave Equation (Pa) Bulk Modulus or modulus of incompressibility

  8. Example: Ocean Water density = 1,035 kg.m^3 Incompressibility modulus is of order 10^9 Pa

  9. Outline • What is a Fluid? • Elastic Moduli • Acoustic Solution to the Wave equation • Density • Velocity

  10. Different Approaches • Hooke’s Law: stress (Pa)= Y (Pa). strain • + Newton’s Law (F=ma) • Lagrangian Mechanics (Energy Relationships)

  11. Outline • What is a Fluid? • Elastic Moduli • Acoustic Solution to the Wave equation • Density • Velocity

  12. Density is given minor importance with respect to velocity. Usually velocity and denisty increase together. Gardner’s Rule (Gardner et a., 1974) density = a .V^0.25, where a=0.31 Salt: 4500-5000 m/s; 2.0-2.1 g/cc

  13. Outline • What is a Fluid? • Elastic Moduli • Acoustic Solution to the Wave equation • Density • Velocity

  14. (… geometric mean)

  15. Mean velocity; traditional Very important for basic seismic processing. Can be obtained directly from seismic field data or GPR field data. Errors ~10%

  16. V=330 m/s, rho =0 z=100000m i=1 i=2 i=3=j s = 200m; V=1000 m/s, rho =1.6 V=1500 m/s, z= 500m rho =1.8

  17. Excel macro

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