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The three-layer Maxwell half-space model of the Earth and a disk-load approximation of the Weichselian deglaciation history of Fennoscandia are used to calculate glacio-isostatic adjustment for this region. The calculations include the effects of deglaciation-induced geoid perturbations and eustatic sea-level rise and regard (1) lithosphere thickness, (2) asthenosphere viscosity and (3) ice thickness as the free model parameters. Numerical values of parameters (1)-(3) are estimated by calculating the past land uplift and present land-uplift rate observed in central Sweden (glaciation centre) and the past land uplift and past land tilt observed in southern Finland (glaciation margin). The uniqueness of the estimates and their sensitivity to uncertainties in (4) subasthenosphere viscosity, (5) ice cross-section and (6) deglaciation time are also assessed. The principal result of the investigation is that it suggests an upper bound of 80 km on the thickness of the Fennoscandian lithosphere.
ARK: https://n2t.net/ark:/88439/y082218
Permalink: https://geophysicsjournal.com/article/93
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A technique for magnetotelluric (MT) data analysis, known as the canonical decomposition, is developed from first principles. This analysis is based on the canonical decomposition of the impedance tensor Z and explicitly parametrizes Z in terms of eight physically relevant structural parameters which specify the transfer characteristics of the Earth system (i.e. the maximum and minimum principal apparent resistivities and the associated principal phases) as well as the principal or intrinsic coordinate system for Z (i.e. the two principal orthogonal electric and magnetic field polarization states). It is shown that the formulation of canonical decomposition in which the polarization descriptors are specified in terms of elliptic parameters results in the MT impedance tensor analysis presented by LaTorraca et al. The relationships between canonical decomposition and several other forms of magnetotelluric data analysis are explored. Specifically, we compare the canonical decomposition with the "conventional" analysis, the maximum coherency analysis, the associate and conjugate directions analysis developed by Counil et al., Eggers' eigenstate analysis and Spitz's rotation analysis. It is shown that canonical decomposition is a natural generalization of the conventional analysis in that both the rotation and ellipticity properties of Z are utilized in the definition of a principal coordinate system. A generalization of the maximum coherency analysis is shown to yield the same parameters as those extracted in canonical decomposition. By imposing a specific restriction on the generalized maximum coherency analysis, we next show how to extract the parameters (i.e. the directions of maximum and minimum current and induction and the corresponding electric and magnetic sheet impedances) that were obtained by Counil et al. in their associate and conjugate directions analysis. The relationship between canonical decomposition and Eggers' eigenstate analysis is developed and it is shown that the primary deficiency in the eigenstate formulation resides in the incorporation of an artificial field constraint. Spitz's rotation analysis extracts two analytical rotation angles from the matrix factors in the Cayley factorization of Z. It is shown that the Cayley factorization of Z is nothing more than the repackaging of the information in canonical decomposition and, as a consequence, Spitz's rotation analysis is not required to extract a principal or intrinsic coordinate system of Z.
ARK: https://n2t.net/ark:/88439/y078429
Permalink: https://geophysicsjournal.com/article/92
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The domain configuration of primary pyrrhotite in a Devonian diabase was studied using the Bitter pattern technique. Due to the uniaxial symmetry the multidomain grains have a rather simple domain structure. The single-domain — multidomain transition occurs at an average particle diameter of 1.6 μm. In the multidomain grains clusters of inclusions seem to produce pseudo-single-domain effects with complicated domain configurations. Such pseudo-single-domain effects are necessary for the interpretation of the magnetically hard component of remanence which cannot be explained by the observed abundance of true single-domain particles alone.
ARK: https://n2t.net/ark:/88439/y061450
Permalink: https://geophysicsjournal.com/article/91
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For describing transmission of seismic energy through a medium in which seismic waves are intensively scattered, a statistical approach provides an attractive alternative to the conventional, deterministic approach. The energy transmission in such a medium with a given size distribution of scatterers is generally governed by a diffusion equation with a frequency-dependent diffusivity, rather than wave equations as in the conventional approach. By applying this theory, we can explain many unusual characteristics of lunar seismic signals, including those generated by surface impacts at near and far ranges and by continuous movement of the Lunar Rovers. The size distribution of scatterers can be estimated from the frequency dependence of diffusivity. Predominantly rectilinear particle motions observed indicate that the scattered energy is transmitted as body waves. When intensive scattering is limited to only a part of the transmitting medium, as in the case of far impacts on the Moon, a more general theory combining the two approaches is required. The theory is also useful for interpreting certain characteristics of terrestrial seismic signals because, while frequently ignored, appreciable scattering exists even for terrestrial cases.
ARK: https://n2t.net/ark:/88439/y052271
Permalink: https://geophysicsjournal.com/article/90
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A new derivation of the Earth-flattening approximation (EFA) for body waves from geometric ray theory is given which results in an improved version of the EFA. This version agrees with the EFA, derived by Chapman (1973) from wave theory. Moreover, it allows absolute, not only relative, body-wave amplitude calculations for given source time functions. The choice of the density transformation of the EFA is shown, by numerical calculations, to be uncritical for body-wave amplitudes in the period range up to 30 s. An error in an earlier derivation of the EFA (Muller, 1973a) is corrected. This error requires a new investigation of the range of applicability of the EFA, which is performed for the P-wave propagation through a homogeneous sphere. The results are similar to those of the earlier paper: long-period P waves with dominant periods up to about 20s can be treated practically exactly, as long as they do not pass closer than about 800 km to the Earth's center.
ARK: https://n2t.net/ark:/88439/y046102
Permalink: https://geophysicsjournal.com/article/89
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This paper presents a survey of the development and use of first order elastic scattering theory in seismology. The various methods used to provide expressions for scattered waves from variations in structure are shown to lead to a single scattering formula. A ray theory approximation for the incident and scattered waves provides a simple formula from which the radiation patterns of different types of scatterer can be derived. As an illustration, the solution for a homogeneous 'average' structure is given in detail. The statistical properties of the signal in time are clearly related to those of the scatterers in space and, in particular, the correlation time of the signal is related to the correlation distance of the scatterers. The paper ends with a discussion of the possible use of first order (weak scattering) theory in cases when the scattered signals are large.
ARK: https://n2t.net/ark:/88439/y038723
Permalink: https://geophysicsjournal.com/article/88
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The maximum entropy principle as described in the first, introductory part of the paper is applied to 2 problems: the estimation of the power spectrum from a finite number of values of the autocovariance function, and the determination of the density within the Earth from its mass, radius, and moment of inertia. In both cases the available information is given in terms of known values of linear functionals and the maximum entropy principle is used to derive a probability distribution for the values of the unknown function. The expectation value of the probability distribution for the spectral power is shown to be equal to the well-known maximum entropy power spectrum. The expectation value for the density within the Earth is in ― with respect to the few data used ― good agreement with that of accepted Earth models.
ARK: https://n2t.net/ark:/88439/y025164
Permalink: https://geophysicsjournal.com/article/87
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Tunnel waves are long period waves which on overcritical incidence have penetrated through thin high-velocity layers. The generation and propagation of these waves are studied by numerical experiments using synthetic seismograms. Tunnel waves may occur as secondary and primary arrivals, on retrograde and prograde branches. Observations from explosion and teleseismic data with low-frequency tunnel waves are presented. A model of the lower lithosphere with thin high-velocity layers explains not only the occurrence of tunnel waves but also the high-frequency transmission of Pn and Sn waves to teleseismic distances. This model is in accordance with the observation of seismic anisotropy in the upper mantle and suggests refinements of existing petrological models of the lower lithosphere.
ARK: https://n2t.net/ark:/88439/y017705
Permalink: https://geophysicsjournal.com/article/86
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A fast computer program of the Thomson-Haskell matrix formalism is presented for the computation of the P—SV reflection coefficients Rpp, Rps, Rss and Rsp for layered solid media. A matrix formalism and a computer program are also derived for the computation of P reflection coefficients for layered liquid media and of SH reflection coefficients for layered solid media.
ARK: https://n2t.net/ark:/88439/y003056
Permalink: https://geophysicsjournal.com/article/85
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Seismic refraction profiles from Iceland are studied with the aid of synthetic seismograms. The classical layered model of the Icelandic crust is shown to be an unacceptable interpretation of the available data. This is because the layered model does not satisfy the observed amplitude variation. On the other hand, a model which assumes continuously increasing velocity with depth does not contradict the observations and is therefore acceptable although it is not the only possible interpretation. The model represented here shows that the surface value of the P-velocity is variable from 2.0 km/s to 5.0 km/s, depending primarily on the degree of metamorphism. The P-velocity increases rapidly with depth in the velocity interval 2.0-3.5 km/s followed by an approximately constant gradient of about 0.57 s-1. This constant gradient continues down to the 6.5 km/s isovelocity surface below which the P-velocity becomes nearly constant. In view of this, it is more reasonable to divide the Icelandic crust into two parts: the upper crust with velocity continuously increasing with depth (corresponding to layers 0, 1, 2 in the layered model) and the lower crust with almost constant velocity (corresponding to layer 3 in the layered model). The depth to the lower crust is variable and depends on how deep the crust is eroded. A typical depth to the lower crust is 5-6 km for an uneroded basalt pile but can be considerable less where the basalt pile is deeply eroded, especially below extinct central volcanoes.
ARK: https://n2t.net/ark:/88439/y091317
Permalink: https://geophysicsjournal.com/article/84
