David Dalton

David Dalton
Memorial University of Newfoundland · Department of Earth Sciences

Doctor of Philosophy

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16
Publications
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37
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Publications

Publications (16)
Preprint
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We illustrate properties of guided waves in terms of a superposition of body waves. In particular, we consider the Love and SH waves. Body-wave propagation at postcritical angles--required for a total reflection--results in the speed of the Love wave being between the speeds of the SH waves in the layer and in the halfspace. A finite wavelength of...
Article
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We use the Pareto Joint Inversion, together with the Particle Swarm Optimization, to invert the Love and quasi-Rayleigh surface-wave speeds, obtained from dispersion curves, in order to infer the elasticity parameters, mass densities and layer thickness of the model for which these curves are generated. For both waves, we use the dispersion relatio...
Article
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We examine the Backus average of a stack of isotropic layers overlying an isotropic halfspace to examine its applicability for the quasi-Rayleigh and Love wave dispersion curves, both of which apply to the same model. We compare these curves to values obtained for the stack of discrete layers using the propagator matrix. The Backus average is appli...
Article
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We show that, in general, the translational average over a spatial variable---discussed by Backus \cite{backus}, and referred to as the equivalent-medium average---and the rotational average over a symmetry group at a point---discussed by Gazis et al. \cite{gazis}, and referred to as the effective-medium average---do not commute. However, they do c...
Article
We examine the sensitivity of the Love and the quasi-Rayleigh waves to model parameters. Both waves are guided waves that propagate in the same model of an elastic layer above an elastic halfspace. We study their dispersion curves without any simplifying assumptions, beyond the standard approach of elasticity theory in isotropic media. We examine t...
Article
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Dalton and Slawinski (2016) show that, in general, the Backus (1962) average and the Gazis et al. (1963) average do not commute. Herein, we examine the extent of this noncommutativity. We illustrate numerically that the extent of noncommutativity is a function of the strength of anisotropy. The averages nearly commute in the case of weak anisotropy...
Article
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We examine two types of guided waves: the Love and the quasi-Rayleigh waves. Both waves propagate in the same model of an elastic isotropic layer above an elastic isotropic halfspace. From their dispersion relations, we calculate their speeds as functions of the elasticity parameters, mass densities, frequency and layer thickness. We examine the se...
Article
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We show that the Backus (1962) equivalent-medium average, which is an average over a spatial variable, and the Gazis et al. (1963) effective-medium average, which is an average over a symmetry group, do not commute, in general. They commute in special cases, which we exemplify.
Article
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We postulate that validity of the Backus (1962) average, whose weights are layer thicknesses, is limited to waves whose incidence is nearly vertical. The accuracy of this average decreases with the increase of the source-receiver offset. However, if the weighting is adjusted by the distance travelled by a signal in each layer, such a modified avera...
Article
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In this paper, following the Backus (1962) approach, we examine expressions for elasticity parameters of a homogeneous generally anisotropic medium that is long-wave-equivalent to a stack of thin generally anisotropic layers. These expressions reduce to the results of Backus (1962) for the case of isotropic and transversely isotropic layers. In ove...
Article
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The integral of a time-domain diffraction operator which has an integrable inverse-root singularity and an infinite tail is numerically differentiated to get a truncated digital form of the operator. This truncated difference operator effectively simulates the singularity but is computationally inefficient and produces a convolutional truncation gh...
Article
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We derive exact time-domain solutions for scattering of acoustic waves by a half plane by inverse Fourier transforming the frequency-domain integral solutions. The solutions consist of a direct term, a reflected term and two diffraction terms. The diffracting edge induces step function discontinuities in the direct and reflected, terms at two shado...
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Vita. Thesis (M. Sc.)--University of British Columbia, 1988. Bibliography: leaves 92-95.
Article
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Thesis (M. Sc.)--University of British Columbia, 1988. Includes bibliographical references.

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Project (1)
Project
I'm working on a Ph.D. doing forward modelling and joint inversion of Love and quasi-Rayleigh (like Rayleigh only in layered media) waves, initially for isotropic media but eventually for layered transversely isotropic media, including the case where one of the layers is a Backus averaged equivalent medium of a series of thin isotropic or transversely isotropic layers.