Coupled normal-mode sensitivity to inner-core shear velocity and attenuation

We have studied the response of normal modes to perturbations in inner-core shear velocity and attenuation, using fully coupled mode synthetics. Our results indicate that (i) mode pairs   _n S _l – _{n ±1} S _l   are strongly coupled by anelasticity, (ii) this coupling causes shear velocity perturbations to strongly affect the Q values of modes through exchange of inner-core characteristics, (iii) there is no evidence for a weakly attenuating inner core in shear, and (iv) the discrepancy between attenuation models returned from normal modes and body waves is small. These results suggest that inversions for inner-core attenuation and shear velocity should be performed simultaneously and should take account of the strong cross-coupling due to attenuation.     

Average attenuation of 0.7–5.0 Hz Lg waves and magnitude scale determination for the region bounding the western branch of the East African Rift

The investigation of L g attenuation characteristics in the region bounding the western branch of the East African rift system using digital recordings from a seismic network located along the rift between Lake Rukwa and Lake Malawi is reported. A set of 24 recordings of L g waves from 12 regional earthquakes has been used for the determination of anelastic attenuation, Q _Lg , and regional body-wave magnitude, m _{b Lg} , scale. The events used have body-wave magnitudes, m _b , between 4.6 and 5.5, which have been determined teleseismically and listed in ISC bulletins. The data were time-domain displacement amplitudes measured at 10 different frequencies (0.7–5.0  Hz). Q _Lg and its frequency dependence, η , in the region can be represented in the form Q _Lg = (186.2 ± 6.5)  f  ^(0.78±0.05). This model is in agreement with models established in other active tectonic regions. The L g -wave-based magnitude formula for the region is given by m _{b Lg} = log   A + (3.76 ± 0.38)  log   D − (5.72 ± 1.06), where A is a half-peak-to-peak maximum amplitude of the 1  s L g wave amplitude in microns and D is the epicentral distance in kilometres. Magnitude results for the 12 regional earthquakes tested are in good agreement with the ISC body-wave magnitude scale.     

Evidence of spatial variations of attenuation in the western Pyrenean range

Summary. Spectral attenuation of coda waves has been studied in the range 2–40 Hz from local events recorded in the western Pyrenean range from 1980 to 1982. Q _c was obtained using a single scattering model of S -waves for different segments of the coda. An increase of Q _c with lapse time was found and attributed to a rapid increase of Q _β with depth.
Three groups of events were selected from distinct focal areas. Two data sets are mainly composed of aftershocks of moderate earthquakes of magnitude 5.1 and 4.8, respectively. No moderate earthquake occurred in the third area in the few years preceding or following the selected events. Use of stations close to epicentres allowed sampling of the coda at very short lapse times and then study of small, distinct scattering volumes. Noticeable differences were found between the three studied areas and attributed to spatial rather than temporal variations.
The Q _c frequency dependence was studied according to Q _c= qf ^α. α is found to range from 0.7 to 1.1 and q from 30 to 140. These values are in agreement with those found in other tectonic areas. It is shown that scattering is the dominant attenuation process below 10Hz.     

Run-up from impact tsunami

We report on calculations of the on-shore run-up of waves that might be generated by the impact of subkilometre asteroids into the deep ocean. The calculations were done with the COULWAVE code, which models the propagation and shore-interaction of non-linear moderate- to long-wavelength waves  ( kh < π)  using the extended Boussinesq approximation. We carried out run-up calculations for several different situations: (1) laboratory-scale monochromatic wave trains onto simple slopes; (2) 10–100 m monochromatic wave trains onto simple slopes; (3) 10–100 m monochromatic wave trains onto a compound slope representing a typical bathymetric profile of the Pacific coast of North America; (4) time-variable scaled trains generated by the collapse of an impact cavity in deep water onto simple slopes and (5) full-amplitude trains onto the Pacific coast profile. For the last case, we also investigated the effects of bottom friction on the run-up. For all cases, we compare our results with the so-called 'Irribaren scaling': The relative run-up   R / H ₀=ξ= s ( H ₀/ L ₀)^−1/2  , where the run-up is   R , H ₀  is the deep-water waveheight, L ₀ is the deep-water wavelength, s is the slope and ξ is a dimensionless quantity known as the Irribaren number. Our results suggest that Irribaren scaling breaks down for shallow slopes   s ≤ 0.01  when  ξ < 0.1 − 0.2  , below which   R / H ₀  is approximately constant. This regime corresponds to steep waves and very shallow slopes, which are the most relevant for impact tsunami, but also the most difficult to access experimentally.     

The Influence of Surface Inhomogeneities On Deep Electromagnetic Soundings of the Earth

Summary. Asymptotic expressions for components of the electromagnetic field of a grounded electric dipole are considered for the model consisting of a thin surface-layer overlapping a stratified medium with a highly resistive screen on the roof. It is shown that the method of spatial derivatives makes it possible to obtain proper estimates of the impedance at distances of r ≥|λ₀| from the nearest edge of the surface anomaly (|λ₀| being the effective depth of the field penetration in the underlying section). the magnetotelluric methods allow one to obtain the true values of impedance, provided r ≥ max {|λ₀|, |/( S ⁻¹+ Z ⁻₀|^1/2} where S is the integrated conductivity of the surface layer, is the transverse resistance of the screen, and Z ⁻₀ is the Tikhonov—Cagniard impedance for the medium underlying the surface layer.     

Seismic amplitude tomography for crustal attenuation beneath China

Amplitude tomography reconstructs seismic attenuation directly from recorded wave amplitudes. We have applied the tomography to amplitude data reported in the 'Annual Bulletin of Chinese Earthquakes' and interpreted the regionally varying crustal attenuation in terms of tectonics. The seismic amplitudes were originally recorded for determining the M _L and M _S magnitudes. They generally correspond to the maximum amplitudes of the horizontal components of the short-period S waves and intermediate-period Rayleigh waves. Both sets of measurements are sensitive to crustal structure. The peak amplitudes from M _L amplitudes spread spherically with significant dispersion and scattering. M _S amplitudes show cylindrical spreading with little dispersion. Average crustal Q values for attenuation at 1 Hz are 737 and 505 for M _L and M _S, respectively, with substantial regional variations. Frequency dependence in the attenuation is also indicated. Regions with the lowest attenuation (high Q values) are beneath the south China Block, Sichuan Basin, Ordos Platform, the Daxinganling and the Korea Craton. These tend to be tectonically inactive regions, which are generally dominated by intrusive and cratonic rocks in the upper crust. Regions with the highest attenuation (low Q values) are beneath Bohai Basin, Yunnan, eastern Songpan-Ganzi Terrain, margins of the Ordos platform and the Qilian Shan. These are predominantly active basins, grabens and fold belts. The continental margin also highly attenuates both S and surface waves.     

Numerical simulation of the propagation of P waves in fractured media

We study the propagation of P waves through media containing open fractures by performing numerical simulations. The important parameter in such problems is the ratio between crack length and incident wavelength. When the wavelength of the incident wavefield is close to or shorter than the crack length, the scattered waves are efficiently excited and the attenuation of the primary waves can be observed on synthetic seismograms. On the other hand, when the incident wavelength is greater than the crack length, we can simulate the anisotropic behaviour of fractured media resulting from the scattering of seismic waves by the cracks through the time delay of the arrival of the transmitted wave. The method of calculation used is a boundary element method in which the Green's functions are computed by the discrete wavenumber method. For simplicity, the 2-D elastodynamic diffraction problem is considered. The rock matrix is supposed to be elastic, isotropic and homogeneous, while the cracks are all empty and have the same length and strike direction. An iterative method of calculation of the diffracted wavefield is developed in the case where a large number of cracks are present in order to reduce the computation time. The attenuation factor Q ⁻¹ of the direct waves passing through a fractured zone is measured in several frequency bands. We observe that the attenuation factor Q ⁻¹ of the direct P wave peaks around kd = 2, where k is the incident wavenumber and d the crack length, and decreases proportionally to ( kd ) ⁻¹ in the high-wavenumber range. In the long-wavelength domain, the velocity of the direct P wave measured for two different crack realizations is very close to the value predicted by Hudson's theory on the overall elastic properties of fractured materials.     

Transient and impulse responses of a one-dimensional linearly attenuating medium—II. A parametric study

Summary. We investigate one-dimensional waves in a standard linear solid for geophysically relevant ranges of the parameters. The critical parameters are shown to be T*= t_u/Q_m where t _u is the travel time and Q_m the quality factor in the absorption band, and τ⁻¹ _m , the high-frequency cut-off of the relaxation spectrum. The visual onset time, rise time, peak time, and peak amplitude are studied as functions of T* and τ _m. For very small τ _m , this model is shown to be very similar to previously proposed attenuation models. As τ _m grows past a critical value which depends on T* , the character of the attenuated pulse changes. Seismological implications of this model may be inferred by comparing body wave travel times with a'one second'earth model derived from long-period observations and corrected for attenuation effects assuming a frequency independent Q over the seismic band. From such a comparison we speculate that there may be a gap in the relaxation spectrum of the Earth's mantle for relaxation times shorter than about one second. However, observational constraints from the attenuation of body waves suggest that such a gap might in fact occur at higher frequencies. Such a hypothesis would imply a frequency dependence of Q in the Earth's mantle for short-period body waves.     

Lateral variation and frequency dependence of coda-Q in the southern part of Iberia

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A method based on the coda attenuation law: Q = Q ₀( f/f ₀)^v leads to the determination of the lateral variation of coda- Q in the southern part of the Iberian Peninsula using seismograms belonging to the seismological network of the Cartuja Observatory, located in Granada. The lateral variation of Q ₀ ( Q value corresponding to a reference frequency f ₀ of 1 Hz) and its frequency dependence for the 1 to 5 Hz frequency range are, in general, in agreement with coda- Q values for frequencies less than about 1 Hz, previously determined in the region under study.
To determine the coda- Q values analytical functions have been used to fit the magnification curves of the vertical component short-period seismographs belonging to the Cartuja network. The problem is solved by using least-squares techniques and non-linear inversion. The determined coda- Q ₀ values and its frequency dependence correlate well with several known geophysical parameters in the southern part of the Iberian Peninsula.     

Anelasticity of the Crust and Upper Mantle of South America From the Inversion of Observed Surface Wave Attenuation

Fundamental-mode Rayleigh and Love waves generated by several earthquakes situated along great-circle paths between pairs of seismograph stations have been analysed to obtain coefficients of attenuation, group velocities, phase velocities, and specific quality factors in the period range 18–80s in two regions of the South American continent. One set of paths crosses the shield region which lies on the eastern coast and another set traverses the mountainous region inland. the average attenuation coefficient values are clearly higher in the tectonically active western region throughout the entire period range than in the eastern or shield region.
Inversion of the attenuation data yielded shear wave internal friction ( Q ^-1_β) models as a function of depth in the crust and upper mantle in both regions. A low- Q zone below the lithosphere is prominent in both regions. the results show that substantial variations of Q _β occur in the two regions of South America. the Q_β values were found to be inversely related to the heat flow values or to the temperature.     

Surface motion of a fluid planet induced by impacts

In order to approximate the free-surface motion of an Earth-sized planet subjected to a giant impact, we have described the excitation of body and surface waves in a spherical compressible fluid planet without gravity or intrinsic material attenuation for a buried explosion source. Using the mode summation method, we obtained an analytical solution for the surface motion of the fluid planet in terms of an infinite series involving the products of spherical Bessel functions and Legendre polynomials. We established a closed form expression for the mode summation excitation coefficient for a spherical buried explosion source, and then calculated the surface motion for different spherical explosion source radii a (for cases of   a / R = 0.001  to 0.035, R is the radius of the Earth) We also studied the effect of placing the explosion source at different radii r ₀ (for cases of   r ₀/ R = 0.90  to 0.96) from the centre of the planet. The amplitude of the quasi-surface waves depends substantially on a / R , and slightly on   r ₀/ R   . For example, in our base-line case,   a / R = 0.03, r ₀/ R = 0.96  , the free-surface velocity above the source is 0.26 c , whereas antipodal to the source, the peak free surface velocity is 0.19 c . Here c is the acoustic velocity of the fluid planet. These results can then be applied to studies of atmosphere erosion via blow-off caused by asteroid impacts.     

Stacking for the frequencies and Qs of 0S0 and 1S0

Summary. Using nine IDA records for the Indonesian earthquake of 1977 August 19, we have formed an optimal linear combination of the records and have measured the frequency and Q of ₀ S ₀ and ₁ S ₀. The frequency was measured using the moment ratio method. The attenuation was measured by the minimum width method and by the time-lapse method. The frequency and attenuation were measured simultaneously by varying them to obtain a best fit to the data. A 2000-hr stack, the sum of nine individual records, for ₀ S ₀ gave a frequency of 0.814664 mHz±4 ppm. The values for the Q of ₀ S ₀ for the three different methods of measurement were 5600,5833 and 5700, respectively. The error in the estimates of Q ^-1 is about 5 per cent for the minimum power method. For ₁ S ₀ a 300-hr stack yielded a frequency of 1.63151 mHz±30 ppm. The values of Q for this mode were 1960, 1800 and 1850, respectively, with an error in Q ^-1 of about 12 per cent for the minimum power method.     

Centennial to millennial geomagnetic secular variation

A time-varying spherical harmonic model of the palaeomagnetic field for 0–7 ka is used to investigate large-scale global geomagnetic secular variation on centennial to millennial scales. We study dipole moment evolution over the past 7 kyr, and estimate its rate of change using the Gauss coefficients of degree 1 (dipole coefficients) from the CALS7K.2 field model and by two alternative methods that confirm the robustness of the predicted variations. All methods show substantial dipole moment variation on timescales ranging from centennial to millennial. The dipole moment from CALS7K.2 has the best resolution and is able to resolve the general decrease in dipole moment seen in historical observations since about 1830. The currently observed rate of dipole decay is underestimated by CALS7K.2, but is still not extraordinarily strong in comparison to the rates of change shown by the model over the whole 7 kyr interval. Truly continuous phases of dipole decrease or increase are decadal to centennial in length rather than longer-term features. The general large-scale secular variation shows substantial changes in power in higher spherical harmonic degrees on similar timescales to the dipole. Comparisons are made between statistical variations calculated directly from CALS7K.2 and longer-term palaeosecular variation models: CALS7K.2 has lower overall variance in the dipole and quadrupole terms, but exhibits an imbalance between dispersion in   g ¹₂  and   h ¹₂  , suggestive of long-term non-zonal structure in the secular variations.     

Estimation of uncertainties in eigenspectral estimates from decaying geophysical time series

Summary. The response of many dynamical systems to an impulse is a linear combination of decaying cosines. The frequencies of the cosines have generally been estimated in geophysics by periodogram analysis and little formal indication of uncertainty has been provided. This work presents an estimation procedure by the methods of complex demodulation and nonlinear regression that specifically incorporates in the basic model the decaying aspect of the cosines (periodogram analysis does not). The use of plots of the instantaneous phase as a function of time is shown to greatly enhance resolution. Expressions for the variances of eigenfrequencies, amplitudes, phases and damping constants Q are derived by non-linear least-squares. The results are illustrated, for the problem of the free oscillations of the Earth, by computations with the record made at Trieste of the Chilean earthquake of 1960 May 22. Sample values are periods and standard errors of 737.79 ± 0.13 s, 506.25 ± 0.13 s and 429.60 ± 0.14 s for ₀ T ₈, ₀ T ₁₃ and ₀ T ₁₆ with Q values and standard errors of 200 ± 14, 230 ± 28 and 215 ± 30, respectively.     

Ray-theoretical relations between intrinsic and apparent dissipation factors in the Earth

Summary. A ray-theoretical approach is successfully employed for obtaining the relations between the intrinsic dissipation factors of P - and S -waves, Q _α and Q _β, and the apparent dissipation factors of toroidal and spheroidal oscillations, Q _Tor and Q _SphThese are given in quite simple forms and are expressed, to zero-order approximatiom which neglects the effect of reflection of waves at an interface and/or at a free surface), as where α and β are the P - and S -wave velocities and the integrals are evaluated long the surface to surface P - and S -rays.
Some numerical comparisons support the validity of these formulae for higher modes of toroidal and radial oscillations of a realistic earth model.
A first-order approximation reveals that the existence of a discontinuity in an earth induces a systematic fluctuation in normal-mode Q values for any given phase velocity as a function of frequency (or radial mode number).     

A comparison of annual and seasonal carbon dioxide effluxes between sub-Arctic Sweden and High-Arctic Svalbard

Recent climate change predictions suggest altered patterns of winter precipitation across the Arctic. It has been suggested that the presence, timing and quantity of snow all affect microbial activity, thus influencing CO₂ production in soil. In this study annual and seasonal emissions of CO₂ were estimated in High-Arctic Adventdalen, Svalbard, and sub-Arctic Latnjajaure, Sweden, using a new trace gas-based method to track real-time diffusion rates through the snow. Summer measurements from snow-free soils were made using a chamber-based method. Measurements were obtained from different snow regimes in order to evaluate the effect of snow depth on winter CO₂ effluxes. Total annual emissions of CO₂ from the sub-Arctic site (0.662–1.487 kg CO₂ m^–2 yr^–1) were found to be more than double the emissions from the High-Arctic site (0.369–0.591 kg CO₂ m^–2 yr^–1). There were no significant differences in winter effluxes between snow regimes or vegetation types, indicating that spatial variability in winter soil CO₂ effluxes are not directly linked to snow cover thickness or soil temperatures. Total winter emissions (0.004–0.248 kg CO₂ m^–2) were found to be in the lower range of those previously described in the literature. Winter emissions varied in their contribution to total annual production between 1 and 18%. Artificial snow drifts shortened the snow-free period by 2 weeks and decreased the annual CO₂ emission by up to 20%. This study suggests that future shifts in vegetation zones may increase soil respiration from Arctic tundra regions.     

Focal mechanisms of small earthquakes in the southeastern Brazilian shield: a test of stress models of the South American plate

Focal mechanisms of small earthquakes with magnitudes of about 3 in the SE Brazilian shield are calculated using S / P amplitude ratios. Low attenuation ( Q _p from 400 to 800) in the shield upper-crustal layers allowed sharp S arrivals to be recorded up to distances of 100 km. Besides P -wave polarities, SH -wave first motions were also used to constrain the nodal-plane orientations. Normal and reverse faulting mechanisms with strike-slip components were found. The inversion of four mechanisms to estimate the stress tensor indicated a strike-slip stress regime with roughly E–W-orientated σ ₁ and N–S σ ₃. Both the orientations and the shape factor ( φ =0.7) of the inverted stress are in excellent agreement with theoretical predictions for that part of Brazil from the driving-force model of Coblentz & Richardson (1996) . Good agreement with the nature of the stress, as well as its orientation, was also found for the model of Meijer (1995) . Both of these theoretical models include spreading stresses along the continent/ocean lithospheric transition. Because the earthquakes are more than 300 km from the continental shelf they should not be affected by the local flexural forces caused by sediment load in the marginal basins. The agreement between observed and theoretical stresses then confirms the importance of continental spreading forces in modelling intraplate stresses.     

Generation of the teleseismic P-wave coda from Aleutian earthquakes

We investigate large-amplitude phases arriving in the P -wave coda of broad-band seismograms from teleseisms recorded by the Gräfenberg array, the German Regional Seismic Network and the Global Seismic Network. The data set consists of all events m _b≤ 5.6 from the Aleutian arc between 1977 and 1992. Earthquakes with large-amplitude coda waves correlate with the presence of oceanic crust in the source region. The amplitudes sometimes approach those of the P wave, much larger than predicted by theory. Modelling indicates that phases in the P -wave coda cannot be P -wave multiples beneath the source and receiver, or underside reflections, which precede PP , from upper-mantle discontinuities. Among the events, seismograms are very similar, where the arrival times of the unusual phases agree approximately with the predicted times of S -to- P conversions from the upper-mantle discontinuities under the source. Because the large-amplitude phases in the P -wave coda have little, if any, dependence on event depth and have predominantly an SV -wave radiation pattern towards the receiver, we suggest that they originate as SV and/or Rayleigh waves and are enhanced by lateral heterogeneity and multipathing from the subducting Aleutian slab.     

Oxygen consumption in Macrotrachela musculosa and Trichotria truncata (Rotatoria) from the High Arctic

Oxygen consumption by rotifers Macrotrachela musculosa and Trichotria truncata from Spitsbergen tundra (77°N) was measured using the method of Cartesian divers. The metabolic rate of M. musculosa was: 0.205 10⁻³mm³ 0₂ per g 10⁻⁶ per hour at 2°C, 0.201 10⁻⁶mm³ at 6°C and 0.616 10⁻³mm³ 0₂ per g 10⁻⁶ per hour at 10°C. The metabolic rate of Trichotria truncata at 6° was 0.103 10⁻³mm³ per g 10⁻⁶ per hour. The relation between body weight and oxygen consumption by M. musculosa at 2°C is expressed with the equation R = 0.18W^0.67, with R – oxygen consumption in mm³10⁻³ per individual per hour and W – wet weight of an animal in g 10⁻⁶.