| 1. |
- Abreu, Rafael, et al.
(författare)
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Micropolar modelling of rotational waves in seismology
- 2017
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Ingår i: Geophysical Journal International. - : OXFORD UNIV PRESS. - 0956-540X .- 1365-246X. ; 210:2, s. 1021-1046
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Tidskriftsartikel (refereegranskat)abstract
- In this contribution we study elastic wave propagation via the introduction of the micropolar theory. As a generalization of a classical linear elastic medium, a micropolar medium allows each particle to have intrinsic rotational degrees of freedom (spin). We perform numerical experiments using the Pseudospectral method. We find analytical harmonic micropolar solutions for different problem configurations, which result in waveform differences between the classical linear elastic and micropolar media. In contrast to linear elastic media, wave propagation in micropolar media is dispersive. We study how the spin waveform depends on the micropolar elastic parameters and frequency content of the simulation. The micropolar effect on numerical seismograms has a direct implication on the phase, amplitude and arrival time. For frequencies lower than the cut-off frequency, the spin waveform has the same amplitude as the macrorotation field. For frequencies higher than the cut-off frequency, the amplitude of the spin waveform decreases with increasing frequency, so that then it is no longer comparable to the amplitude of macroscopic rotations. When both frequencies are equal there is no wave propagation. This work attempts to clarify the theory of micropolar media for its applications in seismology. We argue that micropolar theory should be further investigated for its potential uses in seismology to, for example, describe energy dissipation, seismograms recorded with rotational seismometers and rupture processes.
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| 2. |
- Kamm, Jochen, et al.
(författare)
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Inversion of airborne tensor VLF data using integral equations
- 2014
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Ingår i: Geophysical Journal International. - : Oxford University Press (OUP). - 0956-540X .- 1365-246X. ; 198:2, s. 775-794
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Tidskriftsartikel (refereegranskat)abstract
- The Geological Survey of Sweden has been collecting airborne tensor very low frequency data (VLF) over several decades, covering large parts of the country. The data has been an invaluable source of information for identifying conductive structures that can among other things be related to water-filled fault zones, wet sediments that fill valleys or ore mineralizations. Because the method only uses two differently polarized plane waves of very similar frequency, vertical resolution is low and interpretation is in most cases limited to maps that are directly derived from the data. Occasionally, 2-D inversion is carried out along selected profiles. In this paper, we present for the first time a 3-D inversion for tensor VLF data in order to further increase the usefulness of the data set. The inversion is performed using a non-linear conjugate gradient scheme (Polak-RibiSre) with an inexact line-search. The gradient is obtained by an algebraic adjoint method that requires one additional forward calculation involving the adjoint system matrix. The forward modelling is based on integral equations with an analytic formulation of the half-space Green's tensor. It avoids typically required Hankel transforms and is particularly amenable to singularity removal prior to the numerical integration over the volume elements. The system is solved iteratively, thus avoiding construction and storage of the dense system matrix. By using fast 3-D Fourier transforms on nested grids, subsequently farther away interactions are represented with less detail and therefore with less computational effort, enabling us to bridge the gap between the relatively short wavelengths of the fields (tens of metres) and the large model dimensions (several square kilometres). We find that the approximation of the fields can be off by several per cent, yet the transfer functions in the air are practically unaffected. We verify our code using synthetic calculations from well-established 2-D methods, and trade modelling accuracy off against computational effort in order to keep the inversion feasible in both respects. Our compromise is to limit the permissible resistivity to not fall below 100 Omega m to maintain computational domains as large as 10 x 10 km(2) and computation times on the order of a few hours on standard PCs. We investigate the effect of possible local violations of these limits. Even though the conductivity magnitude can then not be recovered correctly, we do not observe any structural artefacts related to this in our tests. We invert a data set from northern Sweden, where we find an excellent agreement of known geological features, such as contacts or fault zones, with elongated conductive structures, while high resistivity is encountered in probably less disturbed geology, often related to topographic highs, which have survived predominantly glacial erosion processes. As expected from synthetic studies, the resolution is laterally high, but vertically limited down to the top of conductive structures.
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