Wavefield Polarization Research Articles

Strong Ground Motion in the 2011 Tohoku Earthquake: A One-Directional Three-Component Modeling

Local wave amplification due to strong seismic motions in surficial multilayered soil is influenced by several parameters such as the wavefield polarization and the dynamic properties and impedance contrast between soil layers. The present research aims at investigating seismic motion amplification in the 2011 Tohoku earthquake through a one-directional three-component (1D-3C) wave propagation model. A 3D nonlinear constitutive relation for dry soils under cyclic loading is implemented in a quadratic line finite element model. The soil rheology is modeled by mean of a multi-surface cyclic plasticity model of the Masing-Prandtl-Ishlinskii-Iwan (MPII) type. Its major advantage is that the rheology is characterized by few commonly measured parameters. Ground motions are computed at the surface of soil profiles in the Tohoku area (Japan) by propagating 3C signals recorded at rock outcrops, during the 2011 Tohoku earthquake. Computed surface ground motions are compared to the Tohoku earthquake records at alluvial sites and the reliability of the 1D-3C model is corroborated. The 1D-3C approach is compared with the combination of three separate one-directional analyses of one motion component propagated independently (1D-1C approach). The 3D loading path due to the 3C-polarization leads to multiaxial stress interaction that reduces soil strength and increases nonlinear effects. Time histories and spectral amplitudes, for the Tohoku earthquake, are numerically reproduced. The 1D-3C approach allows the evaluation of various parameters of the 3C motion and 3D stress and strain evolution all over the soil profile.

Directional site effects in a non-volcanic gas emission area (Mefite d’Ansanto, southern Italy): Evidence of a local transfer fault transversal to large NW–SE extensional faults?

The technique of the wavefield polarization is applied to ambient vibrations recorded in the Mefite d’Ansanto area, an important non-volcanic natural emission of low temperature CO2 enriched gases. Twenty-five measurements were performed in the study area, eleven near the emission site and the other fourteen in different sites within an area of 5km. Polarization is assessed both in the frequency and time domain through the individual-station horizontal-to-vertical spectral ratio and covariance-matrix analysis, respectively. We find a significant tendency of ground motion in the gas emission area to be polarized in the horizontal plane, with a N115° predominant trend. This polarization tends to disappear while moving far from the site. According to previous papers in other study areas, such a directional effect is likely caused by fault-induced fractures and tends to be orthogonal to the fracture strike. The predominant NW–SE regional faulting does not fit the N115° polarization direction. To explain observations, we propose an interpretation in terms of a NE–SW oriented, local transfer fault as inferred from the lineament analysis. The intersection of the damage zone of this fault with the regional NW–SE normal fault system could easily be the responsible for the gas emissions since it favors a locally increased crustal weakness.

Evaluation algorithms for multistep measurement of spatially varying linear polarization and phase

Optical components manipulating both polarization and phase of wave fields find more and more applications in today's optical systems. In particular, the polarization orientation may vary across the aperture. New measurement techniques and evaluation algorithms are needed to simultaneously characterize the properties of such elements. In this Letter, a general measurement algorithm for locally linear polarization distributions is presented, extending the methods of phase shifting interferometry to the simultaneous determination of polarization and phase. A class of evaluation algorithms is derived, and some example algorithms are described and tested for their resilience against systematic and stochastic stepping errors.

Modelling strong seismic ground motion: three-dimensional loading path versus wavefield polarization

Seismic waves due to strong earthquakes propagating in surficial soil layers may both reduce soil stiffness and increase the energy dissipation into the soil. To investigate seismic wave amplification in such cases, past studies have been devoted to one-directional shear wave propagation in a soil column (1D-propagation) considering one motion component only (1C-polarization). Three independent purely 1C computations may be performed ('1D-1C' approach) and directly superimposed in the case of weak motions (linear behaviour). This research aims at studying local site effects by considering seismic wave propagation in a 1-D soil profile accounting for the influence of the 3-D loading path and non-linear hysteretic behaviour of the soil. In the proposed '1D-3C' approach, the three components (3C-polarization) of the incident wave are simultaneously propagated into a horizontal multilayered soil. A 3-D non-linear constitutive relation for the soil is implemented in the framework of the Finite Element Method in the time domain. The complex rheology of soils is modelled by mean of a multisurface cyclic plasticity model of the Masing-Prandtl-Ishlinskii-Iwan type. The great advantage of this choice is that the only data needed to describe the model is the modulus reduction curve. A parametric study is carried out to characterize the changes in the seismic motion of the surficial layers due to both incident wavefield properties and soil non-linearities. The numerical simulations show a seismic response depending on several parameters such as polarization of seismic waves, material elastic and dynamic properties, as well as on the impedance contrast between layers and frequency content and oscillatory character of the input motion. The 3-D loading path due to the 3C-polarization leads to multi-axial stress interaction that reduces soil strength and increases non-linear effects. The non-linear behaviour of the soil may have beneficial or detrimental effects on the seismic response at the free surface, depending on the energy dissipation rate. Free surface time histories, stress-strain hysteresis loops and in-depth profiles of octahedral stress and strain are estimated for each soil column. The combination of three separate 1D-1C non-linear analyses is compared to the proposed 1D-3C approach, evidencing the influence of the 3C-polarization and the 3-D loading path on strong seismic motions.

Common-image gathers in the incident phase-angle domain from reverse time migration in 2D elastic VTI media

Reverse time migration (RTM) was implemented with a modified crosscorrelation imaging condition for data from 2D elastic vertically transversely isotropy (VTI) media. The computation cost was reduced because scalar qP- and qS-wavefield separations are performed in VTI media, for the source and receiver wavefields only at the RTM imaging time, to calculate the migrated qP and qS images. Angle-domain common-image gathers (CIGs) were extracted from qPqP and qPqS common-source RTM images. The local incident angle was produced as the difference between the qP-wave phase angle, obtained directly from the source wavefield polarization, and the normal to the reflector, calculated as the instantaneous wavenumber direction via a directional Hilbert transform of the stacked image. Angle-domain CIGs were extracted by reordering the prestack-migrated images by local incident phase angle, source by source. Vector decomposition of the source qP-wavefield was required to calculate the qP-wave phase polarization direction for each image point at its imaging time. RTM and angle-domain CIG extraction were successfully implemented and illustrated with a synthetic 2D elastic VTI example.

Subband decomposition and reconstruction of continuous volcanic tremor

A new method of analyzing volcanic tremor is presented, which uses properties of undecimated wavelet packet transforms to filter, decompose, and recover signals from continuous multichannel data. The method preserves many standard properties that are used to characterize tremor, such as wavefield polarization and seismic energy. In this way, we can better understand the (potentially many) seismic sources that combine to form continuous volcanic tremor, and we can specifically address the problem of what causes changing tremor spectral content. Tests on synthetic data suggest that SDR can recover multiple quasi-continuous signals that differ from one another by an order of magnitude, even in noisy environments. Tests on real data recorded at Erta 'Ale in 2002 suggest that SDR can recover signals with geophysically meaningful interpretations, and corroborates existing seismic and multiparametric work by Harris et al. (2005), Jones et al. (2006), and Harris (2008). We suggest that this algorithm could effectively detect subtle changes in the time-frequency content of volcanic tremor, and recover signals from real seismic sources that appear buried in background noise (and/or partly masked by one another). Such an algorithm could allow volcanologists much greater insight into the dynamics of volcanic systems, and could detect subtle signals that might help address the possibility of unrest.

Whistler spheromaks, instabilities and triggered emission experiments

Whistler instabilities are observed in an EMHD spheromak in a large laboratory plasma. The spheromak slowly propagates along the ambient magnetic field, decays and converts its magnetic energy into electron kinetic energy. Anisotropies in the electron distribution function create magnetic oscillations below the electron cyclotron frequency. These are identified as whistler modes by measuring the frequency spectrum, wave field topology, polarization, helicity and propagation velocity. The instability is triggered by the transient formation of the spheromak but loses coherence in time. In order to investigate spatial and temporal growth a test whistler wave is propagated into the source region. The test wave does not grow but triggers a much larger instability amplitude. The triggered emission has a slightly different frequency from that of the test wave. The field topology of the triggered emission differs from that of the test wave. Space–time measurements in the source region show both convective wave amplification and an absolute instability in the current ring. These laboratory observations complement earlier studies of triggered whistler emissions in space plasmas.

Seismic characteristics of variable convection at Erta ʻAle lava lake, Ethiopia

The active summit lava lake of Erta ʻAle volcano, Ethiopia, offers a unique opportunity to study magma convection. In February 2002, we collected a multiparametric set of seismic, thermal and video data. These data indicate that the lake cycled between periods characterized by low (0.01–0.08 m s − 1 ) and high (0.1–0.4 m s − 1 ) convection rates, typically lasting tens to hundreds of minutes. Three seismometers placed around the active crater recorded continuous tremor with a dominant frequency of 2 Hz, and energy at frequencies from 0.8 to 12 Hz. Here, we characterize the seismic signature of each regime by its spectral content, wavefield polarization, and tremor source location. For both regimes, the wavefield is mostly rectilinear. Azimuths and incidence angles are consistent with P waves originating in one of two locations: the north edge of the active lava lake, or a region 100–150 m ENE of the lava lake. Because both regimes are dominated by a low frequency, rectilinearly polarized wavefield, we investigate the source location using a method that solves for location and isotropic source power by a weighted least-squares amplitude-based inversion of seismic data. We find that tremor source regions are unique to each convective regime, although some location overlap exists when tremor is located in short time windows. Wavefield composition suggests that the convective phases may share a common source process, but their differing locations indicate that either the source region is non-stationary, or a second source skews the location during the high convective phase. Tremor polarization and location suggests that the low-frequency tremor is caused by bubble coalescence and bursting in a conduit whose surface is the lava lake. The higher frequency signal associated with the high convective regime is associated with a scattered, more complex wavefield superimposed on the low-frequency background tremor, caused by bubble bursting and cracking of cooled crust at the lava lake surface.

QS-waves in a vicinity of the axis of symmetry of homogeneous transversely isotropic media

We study propagation of the SV and SH waves, generated by a concentrated force in unbounded transversely isotropic (TI) homogeneous media acting in orthogonal to the symmetry axis direction, in a vicinity of this axis. This problem is known in geophysics as the problem of kiss singularity. Our approach is based on application of the high-frequency asymptotics of the SV and SH waves in TI media in a vicinity of the axis of symmetry obtained earlier in [M.M. Popov, Asymptotics of the wave field in a vicinity of the axis of symmetry of a transversely isotropic homogeneous medium, Zap. Nauchn. Semin. POMI, 275 (2001) 199–211 (in Russian) [Engl. Trans.: J. Math. Sci. 117 (2) (2003) 4001–4007]. These formulas provide smooth transition of the qS-wave field from the vicinity of the axis, where the ray method fails, to the ray formulas for the SV and SH waves which are valid at some distance from the axis. We present time pulse propagation of the coupled SV and SH waves and their splitting with the increasing distance to the symmetry axis. A distortion of the initial time pulse and evolution of the wave field polarization are discussed.

Anomalies in the spectrum of electromagnetic eigenwaves in anisotropic plates

A radical transformation of the spectrum of electromagnetic eigenwaves in anisotropic plates of optically biaxial and uniaxial crystals is investigated for small deviations of the direction of wave propagation from crystallographic orientations. It is demonstrated that, in the case when the sagittal plane and plate faces are the symmetry planes of the permittivity tensor ɛ, there exist four independent families of bulk eigenwaves, each characterized by an infinite set of dispersion curves. Dispersion curves of the independent families intersect one another to form a network structure. Under the action of perturbations, the sagittal plane and the plate faces cease to be the symmetry planes. Moreover, these perturbations lead to interactions between waves belonging to different families, the generation of mixed polarization modes, and divergence of the dispersion curves, i.e., the disappearance of intersection points. In the vicinity of these points, the polarization of wave fields changes drastically even with insignificant variations in the frequency.

Propagation of a VLF electromagnetic wave packet in a magnetoplasma

In this paper the propagation of a VLF electromagnetic wave packet in a magnetoplasma is studied. The wave packet is constructed by superposing a group of spectrum‐weighted characteristic vectors. Accurate to the second order, a set of analytic expressions of the complex amplitude factor and field vectors for a Gaussian packet has been obtained. Based on these expressions, effects of dispersion and anisotropy on the vector property of wave field and the amplitude envelope are simulated. Numerical results show that the polarization of wave fields is varying when the packet moves and somewhat deviates from exact circular polarization in a plane transverse to the carrier wave vector, ko. The Gaussian envelope is found to rotate around the Vg×ko direction and to spread three dimensionally as it propagates. The rotation of the ellipsoidal pulse tends toward a stable direction after a propagation of about 250 periods.

Quantitative determination of phases of X-ray reflections from three-beam diffraction. I. Theoretical considerations

A method of quantitative determination of X-ray reflection phases using three-beam multiple diffraction is described. This method is derived from the dynamical theory of X-ray diffraction. First-order approximation is employed to take care of the multi- beam diffraction situation. Polarization and excitation of wave fields and the Lorentz factor of crystal rotation are considered. For practical purposes, instrumental broadening and crystal mosaicity are included in calculating the diffraction intensity profiles. It is found that in the theoretical formulation the phase-dependent (dynamical) diffraction distribution can be separated from the phase-independent (kinematical) diffraction background. This makes possible the quantitative determination of reflection phases.