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Applications of the Kirchhoff-Helmholtz Integral to Problems in Body Wave Seismology


Scott, Patricia Frances (1985) Applications of the Kirchhoff-Helmholtz Integral to Problems in Body Wave Seismology. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/tckd-xm91.


This thesis describes a procedure for evaluating the Kirchhoff-Helmholtz integral and presents applications of it which involve the interpretation of amplitude and travel time anomalies of body waves. The method of integration is a summation of single point evaluations of the integrand and requires that spacing of these evaluations on the surface be small compared to the wavelength of the incident disturbance. The technique predicts amplitudes, travel times and waveforms of acoustic potentials that propagate through a homogeneous medium and interact with three-dimensional curved boundaries. Results from test models compare well with optical solutions for reflections off planar interfaces and rigid spheres and transmissions through planar interfaces.

The reflected integral solution is used to simulate the effect of an idealized mountain on the amplitude and waveforms on pP. This structure causes multiple arrivals, phase shifts, and amplitude anomalies in the synthetic reflection profile. Also the effects of spall on pP waves generated by explosions are simulated by specifying position dependent reflection coefficient on the surface of integration. These experiments predict frequency dependent amplitude anomalies and travel time delays of the reflections.

The transmitted solution is used to model the effect of several idealized crust-mantle boundary structures on teleseismic P waves generated by explosions. The structures are upwarps and product travel time residuals as a function of delta and azimuth which have the same magnitude as residuals observed for NTS tests within Pahute Mesa. The structure causes early complicated low amplitude waveforms and late simple high amplitude waveforms. Thus they cause systematic amplitude variations with azimuth, delta, and source location. The magnitude of predicted variation is less than the observed ab amplitude variation with azimuth of Pahute Mesa tests; however, it is approximately the same as the observed ab variation at a given station as a function of test location within the mesa.

The integral method is extended to include a symmetric velocity function in the medium and is used to model ScS waves which propagate through a JB Earth and reflect off a bumpy core-mantle boundary. Solutions with this extension establish that isovelocity Kirchhoff solutions are sufficient to predict the relative amplitude and travel time anomalies of ScS arising from core-mantle boundary relief. Isovelocity modeling shows that upwarps 300 to 600 kilometers wide and at least 10 kilometers high cause precursors to ScS and amplitude reductions of the same magnitude as the observations. However, the height is not mechanically feasible; therefore, the anomalous observations must originate elsewhere.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Geophysics
Degree Grantor:California Institute of Technology
Division:Geological and Planetary Sciences
Major Option:Geophysics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Kanamori, Hiroo
Thesis Committee:
  • Clayton, Robert W. (chair)
  • Harkrider, David G.
  • Helmberger, Donald V.
  • Silver, Leon T.
  • Kanamori, Hiroo
Defense Date:25 September 1984
Funding AgencyGrant Number
Office of Naval Research (ONR)14-76-C-1070
Record Number:CaltechETD:etd-06062005-132701
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2474
Deposited By: Imported from ETD-db
Deposited On:06 Jun 2005
Last Modified:16 Apr 2021 22:27

Thesis Files

PDF (Scott_pf_1985.pdf) - Final Version
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