Controls on Rayleigh wave amplitudes: attenuation and focusing

A large data set of amplitude measurements of minor and major arc Rayleigh waves in the period range 73–171 s is collected. By comparing these amplitudes with the amplitudes of synthetic waveforms calculated by mode summation, maps of lateral variations in the apparent attenuation structure of the Earth are constructed. An existing formalism for predicting the effects of focusing is employed to calculate amplitude perturbations for the same data set. These perturbations are used to construct 'pseudo‐attenuation' maps and these results are compared with the apparent attenuation maps calculated from the data. It is shown that variations in Rayleigh wave amplitude perturbations in the Earth are dominated by attenuation at long wavelengths (below about degree 8) and by elastic structure at shorter wavelengths. It is also shown that the linear approximation for focusing is successful at predicting Rayleigh wave amplitudes using existing phase velocity maps. These results indicate that future attempts to model the velocity structure of the Earth would be assisted by incorporating amplitude data and by jointly inverting for Q structure.     

Glacial isostatic adjustment in Fennoscandia for a laterally heterogeneous earth

Glaciation and deglaciation in Fennoscandia during the last glacial cycles has significantly perturbed the Earth's equilibrium figure. Changes in the Earth's solid and geoidal surfaces due to external and internal mass redistributions are recorded in sequences of ancient coastlines, now either submerged or uplifted, and are still visible in observations of present‐day motions of the surface and glacially induced anomalies in the Earth's gravitational field. These observations become increasingly sophisticated with the availability of GPS measurements and new satellite gravity missions.
Observational evidence of the mass changes is widely used to constrain the radial viscosity structure of the Earth's mantle. However, lateral changes in earth model properties are usually not taken into account, as most global models of glacial isostatic adjustment assume radial symmetry for the earth model. This simplifying assumption contrasts with seismological evidence of significant lateral variations in the Earth's crust and upper mantle throughout the Fennoscandian region.
We compare predictions of glacial isostatic adjustment based on an ice model over the Fennoscandian region for the last glacial cycle for both radially symmetric and fully 3‐D earth models. Our results clearly reveal the importance of lateral variations in lithospheric thickness and asthenospheric viscosity for glacially induced model predictions. Relative sea‐level predictions can differ by up to 10–20 m, uplift rate predictions by 1–3 mm yr⁻¹ and free‐air gravity anomaly predictions by 2–4 mGal when a realistic 3‐D earth structure as proposed by seismic modelling is taken into account.     

Modelling of ground deformation and gravity fields using finite element method: an application to Etna volcano

Elastic finite element models are applied to investigate the effects of topography and medium heterogeneities on the surface deformation and the gravity field produced by volcanic pressure sources. Changes in the gravity field cannot be interpreted only in terms of gain of mass disregarding the ground deformation of the rocks surrounding the source. Contributions to gravity changes depend also on surface and subsurface mass redistribution driven by dilation of the volcanic source. Both ground deformation and gravity changes were firstly evaluated by solving a coupled axisymmetric problem to estimate the effects of topography and medium heterogeneities. Numerical results show significant discrepancies in the ground deformation and gravity field compared to those predicted by analytical solutions, which disregard topography, elastic heterogeneities and density subsurface structures. With this in mind, we reviewed the expected gravity changes accompanying the 1993–1997 inflation phase on Mt Etna by setting up a fully 3-D finite element model in which we used the real topography, to include the geometry, and seismic tomography, to infer the crustal heterogeneities. The inflation phase was clearly detected by different geodetic techniques (EDM, GPS, SAR and levelling data) that showed a uniform expansion of the overall volcano edifice. When the gravity data are integrated with ground deformation data and a coupled FEM modelling was solved, a mass intrusion could have occurred at depth to justify both ground deformation and gravity observations.     

A reappraisal of postglacial decay times from Richmond Gulf and James Bay, Canada

Decay times inferred from relative sea‐level (RSL) histories of previously glaciated regions provide a potentially important constraint on mantle rheology. We present a new compilation of RSL data from Richmond Gulf and James Bay, Canada. This recompilation reveals errors in previous compilations that led to inaccurate estimates for the Richmond Gulf decay time in a series of recently published articles. We derive updated estimates for the decay time at Richmond Gulf and James Bay using a methodology that incorporates errors in both the age and the height of the sea‐level markers. This exercise is guided by a series of synthetic RSL calculations that show that decay time estimates in the region can be significantly biased if the RSL time‐series are not corrected for global eustatic sea‐level trends, or if the estimates are based on composite RSL histories derived by combining data from both the Richmond Gulf and the James Bay regions. Our decay time analysis for Richmond Gulf applies the pioneering approach of Walcott (1980) to a large database and we derive a value of 4.0–6.6 kyr, where the range is defined by a misfit tolerance 10 per cent higher than the minimum. Our analysis for James Bay is based on the uplift curve derived by Hardy (1976) , and we estimate a decay time of about 2.0–2.8 kyr. The difference between our estimates for Richmond Gulf and James Bay may be due to errors in the observational record from these regions, but could also be influenced by lateral variations in lithospheric structure associated with the assembly of Laurentia.     

Some remarks about the degree-one deformation of the Earth

The degree-one deformation of the Earth (and the induced discrepancy between the figure centre and the mass centre of the Earth) is computed using a theoretical approach (Love numbers formalism) at short timescales (where the Earth has an elastic behaviour) as well as at long timescales (where the Earth has a viscoelastic or quasi-fluid behaviour). For a Maxwell model of rheology, the degree-one relaxation modes associated with the viscoelastic Love numbers have been investigated: the M_o mode does not exist and there is only one transition mode (instead of two) generated by a viscosity discontinuity.
The translations at each interface of the incompressible layers of the earth model [surface, 670 km depth discontinuity, core-mantle boundary (CMB) and inner-core boundary (ICB)] are computed. They are elastic with an order of magnitude of about 1 mm when the excitation source is the atmospheric continental loading or a magnetic pressure acting at the CMB. They are viscoelastic when the earth is submitted to Pleistocene deglaciation, with an order of magnitude of about 1 m. In a quasi-fluid approximation (Newtonian fluid) because of the mantle density heterogeneity their order of magnitude is about 100 m (except for the ICB, which is in quasi-hydrostatic equilibrium at this timescale).     

Off‐great‐circle propagation of intermediate‐period surface waves observed on a dense array in the French Alps

Array analysis is performed on surface waves recorded in the French Alps using a small‐aperture (25 km) temporary array of six broad‐band stations. The analysis shows that both Rayleigh and Love waves deviate relative to the great‐circle path. The deviations are particularly strong, up to 30°, between 20 and 40 s period. To interpret these observations, we first study the effect of large‐scale structures using ray tracing in a smooth, laterally heterogeneous model of the Earth. Second, we evaluate the local effect by considering a model for the French Alps including strong lateral heterogeneities around the array that were not taken into account in the ray tracing. By combining these two possible causes of the observed deviations, we propose an explanation for the general trend in the observed deviations. Finally, we show that by taking into account azimuthal deviations, phase velocities measured at a regional scale can be significantly improved.     

A probabilistic approach to the inversion of data from a seismic array and its application to volcanic signals

Array techniques are particularly well‐suited for detecting and quantifying the complex seismic wavefields associated with volcanic activity such as volcanic tremor and long‐period events. The methods based on the analysis of the signal in the frequency domain, or spectral methods, have the main advantages of both resolving closely spaced sources and reducing the necessary computer time, but may severely fail in the analysis of monochromatic, non‐stationary signals. Conversely, the time‐domain methods, based on the maximization of a multichannel coherence estimate, can be applied even for short‐duration pulses. However, for both the time and the frequency domain approaches, an exhaustive definition of the errors associated with the slowness vector estimate is not yet available. Such a definition become crucial once the slowness vector estimates are used to infer source location and extent. In this work we develop a method based on a probabilistic formalism, which allows for a complete definition of the uncertainties associated with the estimate of frequency–slowness power spectra from measurement of the zero‐lag cross‐correlation. The method is based on the estimate of the theoretical frequency–slowness power spectrum, which is expressed as the convolution of the true signal slowness with the array response pattern. Using a Bayesian formalism, the a posteriori probability density function for signal slowness is expressed as the difference, in the least‐squares sense, between the model spectrum and that derived from application of the zero‐lag cross‐correlation technique. The method is tested using synthetic waveforms resembling the quasi‐monochromatic signals often associated with the volcanic activity. Examples of application to data from Stromboli volcano, Italy, allow for the estimate of source location and extent of the explosive activity.     

Surface-wave polarization data and global anisotropic structure

In the past few years, seismic tomography has begun to provide detailed images of seismic velocity in the Earth's interior which, for the first time, give direct observational constraints on the mechanisms of heat and mass transfer. The study of surface waves has led to quite detailed maps of upper-mantle structure, and the current global models agree reasonably well down to wavelengths of approximately 2000 km. Usually, the models contain only elastic isotropic structure, which provides an excellent fit to the data in most cases. For example, the variance reduction for minor and major arc phase data in the frequency range 7–15 mHz is typically 65–92 per cent and the data are fit to within 1–2 standard deviations. The fit to great-circle phase data, which are not subject to bias from unknown source or instrument effects, is even better. However, there is clear evidence for seismic anisotropy in various places on the globe. This study demonstrates how much (or little) the fit to the data is improved by including anisotropy in the modelling process. It also illuminates some of the trade-offs between isotropic and anisotropic structure and gives an estimate of how much bias is introduced by neglecting anisotropy. Finally, we show that the addition of polarization data has the potential for improving recovery of anisotropic structure by diminishing the trade-offs between isotropic and anisotropic effects.     

Using Vertical Aerial Photography to Estimate Mass Balance at a Point

The mass balance distribution over a 0.5 km² area of the lower part of South Cascade Glacier is obtained from remotely sensed measurements of its geometry and velocity field over two periods, 1992–93 and 1993–94. Vertical aerial photography from late summer 1992, 1993, and 1994 is analyzed photogrammetrically to get surface topography of South Cascade Glacier on a 100-meter square grid. The known bed topography is subtracted from the surface topography to get the ice thickness, and the surface topographies are subtracted from each other to get the thickness change. Annual displacement vectors, determined at points where natural features could be tracked from one year to the next, are contoured by hand and interpolated to the grid. Assuming that the ice follows Glen's flow law with exponent n = 3, and that 10% of the ice flow is due to sliding at the bed, the surface velocity is scaled by 0.82 to get the average velocity in the vertical ice column. The average velocities are combined with the thicknesses to calculate the flux divergence at each of 46 gridpoints on a 100-m square grid, where it is subtracted from the thickness change to get the mass balance.
Use of the same control points from year to year makes any systematic error in photogrammetric coordinates temporally constant, so such error has no effect on the mass balance estimate. Random error in coordinates is assumed to be uncorrelated from coordinate to coordinate, from point to point, from year to year; the standard error is estimated to be 1 m, resulting in a standard error in coordinate differences of about 1.5 m. A 1 m error in a vertical coordinate has nearly twice the effect on the estimated balance that one in a horizontal coordinate has and more than ten times the effect that one in ice thickness has. Compared with measurements at a stake, the estimated balances are about 1 m too negative.     

Storsteinsfjellbreen: Variations in Mass Balance from the 1960s to the 1990s

When the Norwegian State Power Board decided to plan an extensive water power development in the mountainous areas southeast of Narvik in northern Norway, a large mapping project was started. Detailed maps were constructed at a scale of 1:10 000 from aerial photographs taken in 1960. Several hydrometric stations were installed, and three glaciers were selected for mass balance observations. Storsteinsfjellbreen was the largest of these, and a special glacier map with 10 m contours was printed in four colours, to be used in the field work. Mass balance studies were carried out initially during one 5-year period (1964–68), and also later during another 5-year period (1991–95).
Results from these periods are compared with similar data from the Swedish glacier Storglaciären, about 45 km to the southeast. For all the years except one (1968), the net balance of these glaciers shows a similar pattern: positive years and negative years are synchronous.
A new glacier map was made from a special aerial survey in 1993 at the same scale and of similar accuracy as the first map, so a comparison could be made to calculate the change in glacier volume from 1960 to 1993. From digital terrain models it could be shown that the glacier surface had dropped more than 60 m vertically on the tongue, while the thickness increased above the equilibrium line by up to 20 m. The overall mass loss amounted to 16.8×10⁶ m³ water during 33 years, which corresponds to an extra 2.6 l·s⁻¹·km⁻² (litres per sec. per sq. km) delivered to the river, in addition to the "normal" discharge
due to annual precipitation, which is 36 l·s⁻¹·km⁻² in the area.
A copy of the new glacier map is enclosed with this article.     

Local Extremes in the Lidar‐Derived Snow Cover of Alpine Glaciers

Snow deposition and redistribution are major drivers of snow cover dynamics in mountainous terrain and contribute to the mass balance of alpine glaciers. The quantitative understanding of inhomogeneous snow distribution in mountains has recently benefited from advances in measuring technologies, such as airborne laser scanning (ALS). This contribution further advances the quantitative understanding of snow distribution by analysing the areas of maximum surface elevation changes in a mountain catchment with large and small glaciers. Using multi‐annual ALS observations, we found extreme surface elevation changes on rather thin borders along the glacier margins. While snow depth distribution patterns in less extreme terrain have presented high inter‐annual persistence, there is little persistence of those extreme glacier accumulations between winters. We therefore interpret the lack of persistence as the result of a predominance of gravity‐driven redistribution, which has an inherently higher random component because it does not occur with all conditions in all winters. In highly crevassed zones, the lidar‐derived surface elevation changes are caused by a complex interaction of ice flux divergence, the propagation of crevasses and snow accumulation. In general, the relative contribution of gravitational mass transport to glacier snow cover volume was found to decrease for glaciers larger than 5 km² in the investigated region. We therefore suggest that extreme accumulations caused by gravitational snow transport play a significant role in the glacier mass balance of small to medium‐size glaciers and that they may be successfully parameterized by simple mass redistribution algorithms, which have been presented in the literature.     

Deglaciation effects on the rotation of the Earth

Summary. The viscoelastic response of the Earth to the mass displacements caused by late Pleistocene deglaciation and concomitant sea level changes is shown to be capable of producing the secular motion of the Earth's rotation pole as deduced from astronomical observations. The calculations for a viscoelastic Earth yield a secular motion in the direction of 72° W meridian which is in excellent agreement with observed values. The average Newtonian viscosity and the relaxation time obtained from polar motion data are about (1.1 ± 0.6)10²³ poise (P) and 10⁴ (1 ± 0.5) yr. The non-tidal secular acceleration of the Earth can also be attributed to the viscoelastic response to deglaciation and results in an independent viscosity estimate of 1.6 × 10²³ P with upper and lower limits of 1.1 × 10²³ and 2.8 × 10²³ P. These values are in agreement with those based on the polar drift analysis and indicate an average mantle viscosity of 1–2 × 10²³ P.     

ScSp observed on North Island, New Zealand: implications for subducting plate structure

Seismic phase conversions provide important constraints on the layered nature of subduction zone structures. Recordings from digital stations in North Island, New Zealand, have been examined for converted ScS ‐to‐ p ( ScSp ) arrivals from deep (>150 km) Tonga–Kermadec earthquakes to image layering in the underlying Hikurangi subduction zone. Consistent P ‐wave energy prior to ScS has been identified from stations in eastern and southern North Island, where the subducted plate interface is at a depth of between 15 and 30 km. Two ScS precursors are observed. Ray tracing indicates that the initial precursor ( ScSp ₁) corresponds to conversion from the base of an 11–14 km thick subducting Pacific crust. The second precursor is interpreted as a conversion from the top of the subducting plate. The amplitude ratio, ScSp ₁: ScS , increases from 0.10 to 0.19 from northern to southern North Island. This is within the range expected from a simple first‐order velocity discontinuity at an oceanic Moho. A 1–2 km thick layer of low‐velocity sediment at the top of the subducting plate is required to explain the remaining ScSp waveform. Our results imply that the abnormally thick Hikurangi–Chatham Plateau has been subducting beneath New Zealand for at least 2.9 Myr, thus explaining the high uplift rates observed across eastern North Island.     

The three-dimensional shear wave structure in the mantle by overtone waveform inversion - I. Radial seismogram inversion

Summary. The three-dimensional (3-D) shear wave structure of the mantle, down to the depth of about 900 km, is obtained by inverting waveforms of radial component seismograms. Radial component seismograms contain large amplitude overtone signals which circle the Earth as wave packets and are sometimes called X1, X2, X3, … We use data which contain R1, X1 and X2 and filtered between 2 and 10mHz. It is shown that, unless each seismogram is weighted, all seismograms are not fitted uniformly. Only data from large earthquakes are fitted and the final velocity anomalies are biased by the small number of large earthquake data. Resolution is good at shallow depths, becomes worse in the intermediate depth range between about 400 and 500 km and then becomes better at greater depth ranges (600–900km). Even though we use only spheroidal mode data, velocity anomalies in the shallow structure show excellent correlation with the age of the surface rocks of the Earth. In the deeper regions, between about 600 and 900km, South America shows a fast velocity anomaly which may indicate the slab penetration beyond 700 km there. Another region which shows a fast velocity anomaly is the Mariana trench, but other subduction regions do not show such features.     

Ocean-bottom seismograph observations on the Mid-Atlantic Ridge near 45° N

Summary. Rayleigh-wave phase velocities at very long periods (185–290 s) are investigated and regionalized, taking into account the lateral heterogeneities within ocean plates revealed by earlier studies at shorter periods. The two-station method is applied to a few 'pure-age' oceanic paths, and is shown to be compatible with the average Earth model C2 (Anderson & Hart 1976) below depths of 180 km. Under this assumed oceanic model, regionalized for age above 180 km, continental velocities are then derived from a set of experimental great-circle values, both new or taken from previously published studies. The results basically agree with earlier studies (Dziewonski 1970; Kanamori 1970), although they exhibit less scatter than Kanamori's model. Results are successfully checked against a set of values derived by the two-station method from a pure continental path.
Although the shield velocities are substantially different from the mean oceanic ones, they still fall within the range of variation of oceanic velocities with the age of the plate. This makes velocities derived theoretically from Jordan's (1975a, b) models of deep continent—ocean lateral heterogeneities, inconsistent with the present set of experimental data. Finally, we show that Dziewonski's (1971) model S2 reconciles all experimental seismic data relative to shields, without being significantly different from oceanic models below 240 km.     

Further evidence for oceanic excitation of polar motion

While the role of the atmosphere in driving variations in polar motion is well established, the importance of the oceans has been recognized only recently. Further evidence for the role of the oceans in the excitation of polar motion is presented. To estimate the equatorial excitation functions, χ ₁ and χ ₂ , for the ocean, we use velocity and mass fields from a constant-density ocean model, driven by observed surface wind stresses and atmospheric pressure, for the period 1993–1995; comparison with similar functions derived from a more complex density-stratified ocean model indicates the effectiveness of the simple constant-density modelling approach. Corresponding atmospheric excitation functions are computed from NCEP/NCAR re-analyses. Results indicate significant improvements in the agreement with the observed polar motion excitation when the simulated oceanic effects are added to atmospheric excitation. Correlations between the polar motion and the geophysical signals at periods of 15–150 days increase from 0.53 to 0.80 and from 0.75 to 0.88 for χ ₁ and χ ₂ , respectively. The oceanic signals are particularly important for seasonal variations in χ ₁ (correlation increases from 0.28 to 0.85 when oceanic excitation is included). A positive impact of the oceans on more rapid polar motion is also observed, up to periods as short as 5 days. The sensitivity of the results to different forcing fields and different amounts of friction in the oceans is also discussed.     

Strain accumulation along an oblique plate boundary: the Reykjanes Peninsula, southwest Iceland

We use annual GPS observations on the Reykjanes Peninsula (RP) from 2000 to 2006 to generate maps of surface velocities and strain rates across the active plate boundary. We find that the surface deformation on the RP is consistent with oblique plate boundary motion on a regional scale, although considerable temporal and spatial strain rate variations are observed within the plate boundary zone. A small, but consistent increase in eastward velocity is observed at several stations on the southern part of the peninsula, compared to the 1993–1998 time period. The 2000–2006 velocities can be modelled by approximating the plate boundary as a series of vertical dislocations with left-lateral motion and opening. For the RP plate boundary we estimate left-lateral motion  18⁺⁴₋₃ mm yr⁻¹  and opening of  7⁺³₋₂ mm yr⁻¹  below a locking depth of  7⁺¹₋₂ km  . The resulting deep motion of  20⁺⁴₋₃ mm yr⁻¹  in the direction of  N(100⁺⁸₋₆)°E  agrees well with the predicted relative North America–Eurasia rate. We calculate the areal and shear strain rates using velocities from two periods: 1993–1998 and 2000–2006. The deep motion along the plate boundary results in left-lateral shear strain rates, which are perturbed by shallow deformation due to the 1994–1998 inflation and elevated seismicity in the Hengill–Hrómundartindur volcanic system, geothermal fluid extraction at the Svartsengi power plant, and possibly earthquake activity on the central part of the peninsula.     

The Structure of Atmospheric Turbulence and its Application to the Design of Pipe Arrays

Summary Turbulent boundary layers at the surface of the Earth limit the detection of infrasonic waves with periods greater than 1 s. Pipe arrays designed to improve the signal-to-noise ratios of infrasonic waves usually assume that the background noise due to this turbulent boundary layer is incoherent between the array inlets. The power at various points on a surface was measured; coherences between these points were determined and they were found to be significant in the period range 1–100 s. Such coherent noise must be considered when pipe arrays are designed.     

Detrital zircon geochronology: enhancing the quality of sedimentary source information through improved methodology and combined U–Pb and fission‐track techniques

ABSTRACT Zircon is the most widely used mineral in detrital dating studies because it is common to multiple rock types, is chemically and physically resistant, and can endure successive cycles of burial, metamorphism and erosion. Zircon also has the advantage that single grains may be dated by either the fission‐track (FT) or U–Pb method, which, because of their contrasting thermal sensitivities (total resetting occurs at temperatures > 320 °C for FT and > 700–900 °C for U–Pb), can provide unique information about both the age structure and the thermal evolution of a sediment source. However, single method‐based bias and difficulties associated with interpreting measured ages can influence both the quality and the level of useful provenance information. For example, the zircon FT system is sensitive to metamorphic overprinting and hence measured ages alone cannot be interpreted as unambiguously dating formation age of the source rock. In contrast, U–Pb zircon data have high resistance (700–900 °C) to thermal overprinting and therefore recorded formation ages may not relate to an immediate source but may instead reflect a polycyclical history. The focus of this paper is to examine, from a practical standpoint, the provenance potential of detrital zircon fission track data and to investigate the method's complementary role as an aide to the interpretation of high‐temperature detrital U–Pb zircon data by combining U–Pb and FT methods in a single study.     

Coseismic deformation revealed by inversion of strong motion and GPS data: the 2003 Chengkung earthquake in eastern Taiwan

A moderate earthquake of   M _w= 6.8  occurred on 2003 December 10. It ruptured the Chihshang Fault in eastern Taiwan which is the most active segment of the Longitudinal fault as a plate suture fault between the Luzon arc of the Philippine Sea plate and the Eurasian plate. The largest coseismic displacements were 13 cm (horizontal) and 26 cm (vertical). We analyse 40 strong motion and 91 GPS data to model the fault geometry and coseismic dislocations. The most realistic shape of the Chihshang fault surface is listric in type. The dipping angle of the seismic zone is steep (about 60°–70°) at depths shallower than 10 km and then gradually decreases to 40°–50° at depths of 20–30 km. Thus the polygonal elements in Poly3D are well suited for modelling complex surfaces with curving boundaries. Using the strong motion data, the displacement reaches 1.2 m dip-slip on the Chihshang Fault and decreases to 0.1 m near surface. The slip averages 0.34 m, releasing a scalar moment of 1.6E26 dyne-cm. For GPS data, our model reveals that the maximal dislocation is 1.8 m dip-slip. The dislocations decrease to 0.1 m near the surface. The average slip is 0.48 m, giving a scalar moment of 2.2E26 dyne-cm. Regarding post-seismic deformation, a displacements of 0.5 m were observed near the Chihshang Fault, indicating the strain had not been totally released, as a probable result of near-surface locking of the fault zone.