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Understanding Snell's Law in Seismic Data Analysis

This document explores Snell's Law, which describes how seismic waves behave at the interface of different media. It details the relationship between the angle of incidence, refraction, and reflection in seismic data through the Northern and Southern P-shot gathers. Key concepts such as critical angle, wave velocities (V1, V2), and densities (ρ1, ρ2) are addressed. By analyzing pre- and post-critical rays, we can better understand seismic wave propagation and improve subsurface imaging techniques in geology and geophysics.

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Understanding Snell's Law in Seismic Data Analysis

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  1. Snell’s Law

  2. Northern Sh Shot-gather Seismic Data
  3. Southern P- Shot-gather Seismic Data
  4. At critical angle of incidence, angle of refraction = 90 degrees=angle of reflection P` critical angle V1,rho1 P`P’ V2,rho2
  5. Pre- and Post-critical Rays x z V1 Critical distance V2> V1 V2 Direct wave Pre-critical reflections Head wave Post-critical reflections
  6. One-layer Refracted Head Wave Xc =? Tc=? Critical distance=Xc x r1 z r3 r1 V1 r2 V2> V1 V2
  7. One-layer Refracted Head Wave Xc =? Tc=? Critical distance=Xc x r1 z r3 r1 V1 z0 r2 V2> V1 V2 (9)
  8. One-layer Refracted Head Wave Xc =? Tc=? Xc + Critical distance=Xc x r1 z r3 r1 V1 z0 r2 V2> V1 V2 (10)
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