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Seismic Wave Travel-Time Curves . Danny Hertel EPS 109 Prof. Militzer. Background/Method.

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seismic wave travel time curves

Seismic Wave Travel-Time Curves

Danny Hertel

EPS 109

Prof. Militzer

background method
  • As seismic waves travel through different mediums in the earth, the different mediums create different wave velocities. With geophones, the amplitude of the wave response can be measured at the surface and overlaid to create travel-time curves that tell what’s underneath.
  • P-waves are compressiona,l but travel under the laws of the wave equation.
  • Discretization of the wave equation:

wave equation in 2D:


(in code, dy=dx)

  • Then I modeled the wave through a medium with different velocity for different depths/distances. Surfed the amplitude
  • To create the travel-time curve, I took the amplitude of the wave at the surface, and for loop: if the iter=100,200 …(every 10 seconds) Z=Z+ iter/10 (1 sec, dt=0.1) a new profile ten seconds above the last. Boundaries around the plot were needed so the wave wouldn’t reflect of the edge of the plot (Mur’s or Perfectly Matched Layer are less memory intense but more math intensive)
  • Did forward and backward models with 3 different medium examples.
  • Yet to be addressed: Head wave diffraction, boundary conditions, earth like velocities up to 3000m/s

Source: Bancroft, John C. “Simple Wave Modeling.” CREWES Research Report-Volume 14. 2002.

2 layer model
2 Layer Model

run: project2layerfinal.m

3 layer model
3 Layer Model

run: project3layerfinal.m

dipping layer model
Dipping Layer Model


underground tunnel
Underground Tunnel