Citation
Jordan, Thomas Hillman (1973) Estimation of the radial variation of seismic velocities and density in the earth. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/K0B1PW97. https://resolver.caltech.edu/CaltechTHESIS:08292011141658832
Abstract
An inversion procedure is developed to estimate the radial variations of compressional velocity, shear velocity, and density in the Earth. The radial distributions are defined as spherically symmetric averages of the actual distributions in the laterally heterogeneous Earth, and the nature of the averaging implied by averaging certain sets of eigenperiod and traveltime data is examined. For traveltime data, the spherical averaging yields the Terrestrial Monopole if the data sample a distribution derived from a uniform distribution of sources and receivers. Since this is difficult to obtain for absolute times, differential travel times are used to constrain the velocities. It is shown that the bias inherent in available sets of differential traveltime data is considerably less than that in equivalent sets of absolute traveltime data, if the phase combination is suitably chosen. Observations are presented for the phase combinations PcPP, ScSS, P'(AB)P'(DF), and P'(BC)P'(DF). The inversion algorithm developed is based on a linear approximation to the perturbation equations and is shown to provide a stable method for estimating the radial distributions of velocities and density from a finite number of inaccurate data. The linear inversion theory presented is complete; it allows one to estimate the resolving power of the data and the resolvability of specified features in the model. Three estimates of the radial distributions are derived using an extensive set of eigenperiod and traveltime data. One model, designated model B1, fits 127 of the 177 eigenperiods of the DziewonskiGilbert set within their formal 95% confidence intervals. This model satisfies extensive sets of auxillary data as well. It is shown from resolving power calculations that little information is lost by using differential travel times in lieu of absolute times. It is demonstrated that the nature of the averaging in the estimation procedure for given sets of gross Earth data can be improved by judicious specification of the norm on the space of models.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Geology 
Degree Grantor:  California Institute of Technology 
Division:  Geological and Planetary Sciences 
Major Option:  Applied Mathematics Geophysics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  4 August 1972 
Record Number:  CaltechTHESIS:08292011141658832 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:08292011141658832 
DOI:  10.7907/K0B1PW97 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  6629 
Collection:  CaltechTHESIS 
Deposited By:  INVALID USER 
Deposited On:  29 Aug 2011 22:21 
Last Modified:  09 Nov 2022 19:20 
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