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Modeling seismic wave propagation using paraxial extrapolators


Graves, Robert Wilson (1991) Modeling seismic wave propagation using paraxial extrapolators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/10tz-eh38.


The development of a paraxial extrapolation system to simulate seismic wave field propagation in complex three-dimensional (3-D) media results in a practical approach to address modeling problems that require large computer memory. The paraxial approach applies to wave propagation problems in which most of the energy is traveling within a restricted angular cone about a principle axis of the problem. To set up the paraxial system, the equations of motion are initially cast as a first-order extrapolation system. Approximating the exact one-way extrapolation operator for this system with a truncated series expansion yields a sequence of paraxial extrapolation operators. Using the second-order operator results in a paraxial system which is accurate for propagation angles out to 60° with respect to the extrapolation axis. The acoustic formulation of this system produces excellent results as compared to a full wave field calculation. Formulating an appropriate system for the elastic case is more difficult due to the coupling between P and S energy. Specifying media variations as small perturbations to a homogeneous reference medium leads to a useful formulation of the paraxial system for the 2-D elastic case. Using the acoustic system to model path effects for local earthquakes recorded at two southern California stations indicates the strong influence that the 3-D crustal basins of this region have on the propagation of seismic energy. Although the simulation tracks only acoustic waves, the method is capable of modeling effects due to focusing, diffraction and the generation of multiple reflections and refractions. The modeling results show that the 3-D structure of the Los Angeles, San Fernando and San Gabriel basins create strong patterns of focusing and defocusing for propagation paths coming into the stations located at Pasadena (PAS) and the University of Southern California (USC). These simulations compare well with earthquake data recorded at both stations.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Geology
Degree Grantor:California Institute of Technology
Division:Geological and Planetary Sciences
Major Option:Geophysics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Clayton, Robert W.
Thesis Committee:
  • Harkrider, David G. (chair)
  • Helmberger, Donald V.
  • Clayton, Robert W.
Defense Date:16 November 1990
Record Number:CaltechTHESIS:04112011-093820974
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6283
Deposited By: Tony Diaz
Deposited On:12 Apr 2011 18:53
Last Modified:16 Apr 2021 23:28

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