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.     

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.     

Velocity structure of upper-mantle transition zones beneath central eurasia from seismic inversion using genetic algorithms

We present velocity constraints for the upper-mantle transition zones beneath Central Siberia based on observations of the 1982 RIFT Deep Seismic Sounding (DSS) profile. The data consist of seismic recordings of a nuclear explosion in north-western Siberia along a 2600 km long seismic profile extending from the Yamal Peninsula to Lake Baikal. We invert seismic data from the mantle transition zones using a non-linear inversion scheme using a genetic algorithm for optimization and the WKBJ method to compute the synthetic seismograms. A statistical error analysis using a graph-binning technique was performed to provide uncertainty values in the velocity models.
Our best model for the upper-mantle velocity discontinuity near 410 km depth has a two-stage velocity-gradient structure, with velocities increasing from 8.70–9.25 km s⁻¹ over a depth range of 400–415 km, a gradient of 0.0433 s⁻¹, and from 9.25–9.60 km s⁻¹ over a depth range of 415–435 km, a gradient of 0.0175 s⁻¹. This derived model is consistent with other seismological observations and mineral-physics models. The model for the velocity discontinuity near 660 km depth is simple, sharp and includes velocities increasing from 10.15 km s⁻¹ at 655 km depth to 10.70 km s⁻¹ at 660 km depth, a gradient of 0.055 s⁻¹.     

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).     

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.     

Upper crustal shear velocity models from higher mode Rayleigh wave dispersion in Scotland

Summary. Group velocities for first and second higher mode Rayleigh waves, in the frequency range 0.8–4.8 Hz, generated from a local earthquake of magnitude 3.7 M _L in western Scotland, are measured at stations along the 1974 LISPB line. These provide detailed information about the crustal structure west of the line. The data divide the region into seven apparently homogeneous provinces. Averaged higher mode velocity dispersion curves for each province are analysed simultaneously using a linearized inversion technique, yielding regionalized shear velocity profiles down to a depth of 17 km into the upper crust. Shear wave velocity is between 3.0 and 3.4 km s⁻¹ in the upper 2 km, with a slow increase to around 3.8 km s⁻¹. P -wave models computed using these results agree with profiles from the LISPB and LUST refraction experiments.     

Seismic anisotropy within the uppermost mantle of southern Germany

This paper presents an updated interpretation of seismic anisotropy within the uppermost mantle of southern Germany. The dense network of reversed and crossing refraction profiles in this area made it possible to observe almost 900 traveltimes of the P_n phase that could be effectively used in a time-term analysis to determine horizontal velocity distribution immediately below the Moho. For 12 crossing profiles, amplitude ratios of the P_n phase compared to the dominant crustal phase were utilized to resolve azimuthally dependent velocity gradients with depth. A P -wave anisotropy of 3–4 per cent in a horizontal plane immediately below the Moho at a depth of 30 km, increasing to 11 per cent at a depth of 40 km, was determined. For the axis of the highest velocity of about 8.03 km s⁻¹ at a depth of 30 km a direction of N31°F was obtained. The azimuthal dependence of the observed P_n amplitude is explained by an azimuth-dependent sub-Moho velocity gradient decreasing from 0.06 s⁻¹ in the fast direction to 0 s⁻¹ in the slow direction of horizontal P -wave velocity. From the seismic results in this study a petrological model suggesting a change of modal composition and percentage of oriented olivine with depth was derived.     

An investigation of the regional variations and frequency dependence of anelastic attenuation in the mantle under the United States in the 0.5–4 Hz band

Summary. Studies of teleseismic P -and S -wave amplitudes and spectra in the 0.5–4 Hz band show large variations in the attenuative properties of the upper mantle under the United States. The data indicate that attenuation is greatest under the south-western United States including, but not confined to, the Basin and Range province. The lowest attenuation prevails under the north central shield regions. The north-eastern part of the country, consisting of New England and possibly including a larger area along the eastern seaboard, is characterized by moderate attenuation in the mantle.
The level of the high-frequency energy in short-period seismic waves and the differences between Q values derived from short-and long-period data indicate that Q is frequency dependent. The form of frequency dependence of t * compatible with the data in the 0.5–4 Hz range does not allow a rapid decrease of t * with increasing frequency. Rather it supports a gradual decrease covering the broader 0.1–4 Hz range. The curves of t * versus frequency, for shield-to-shield and mixed shield-to-western United States type paths are parallel with an average difference of 0.2 s in t * in the short-period band, but may diverge towards the long-period band. For both curves t *_p is below 1 s. For shield-to-shield paths t *_p must be below 0.5 s at 1 Hz.     

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.     

Seismic moment release during slab rupture beneath the Banda Sea

The highest intermediate depth moment release rates in Indonesia occur in the slab beneath the largely submerged segment of the Banda arc in the Banda Sea to the east of Roma, termed the Damar Zone. The most active, western-part of this zone is characterized by downdip extension, with moment release rates (∼10¹⁸ Nm yr^–1 per 50 km strike length) implying the slab is stretching at ∼10⁻¹⁴ s⁻¹ consistent with near complete slab decoupling across the 100–200 km depth range. Differential vertical stretching along the length of the Damar Zone is consistent with a slab rupture front at ∼100–200 km depth beneath Roma propagating eastwards at ∼100 km Myr^–1. Complexities in the slab deformation field are revealed by a narrow zone of anomalous in-plane P -axis trends beneath Damar, where subhorizontal constriction suggests extreme stress concentrations ∼100 km ahead of the slab rupture front. Such stress concentrations may explain the anomalously deep ocean gateways in this region, in which case ongoing slab rupture may have played a key role in modulating the Indonesian throughflow in the Banda Sea over the last few million years.     

Long-period geomagnetic variations and mantle conductivity: an inversion using Bailey's method

Summary. We have implemented an algorithm which is based on Bailey's solution of the inverse problem of electromagnetic induction in the Earth. The study was motivated by recent determinations of very long period data and also benefited from recent redeterminations of high frequency data. The algorithm has been successfully tested to provide reliable estimates of conductivity down to a depth of 2000 km, using synthetic data in the period range from 4 days to 11 years. Smooth data sets, which are required for the inversion, were constructed from various sources. At a given depth, the range of inverted models is less than one order of magnitude. Due to the lack of high frequency data, the conductivity of the upper 600 km of the mantle, which is found to be of the order of 10⁻¹Ω⁻¹ m⁻¹, may be overestimated. The algorithm performs well in the middle mantle, where conductivity rises steadily from 1 to 50 Ω⁻¹ m⁻¹. The lack of very low frequency data and limitations of the algorithm prevent one from obtaining meaningful estimates in the lower mantle. However, the study of the propagation of the late 1960s secular variation acceleration provides an estimate of the mean conductivity of the whole mantle. Thus, a complete mantle profile can be constructed. It is found that deep mantle conductivity probability does not exceed a few hundred Ω⁻¹ m⁻¹.     

Crustal and upper mantle structure of the northwestern North Island, New Zealand, from seismic refraction data

The crustal and upper mantle structure of the northwestern North Island of New Zealand is derived from the results of a seismic refraction experiment; shots were fired at the ends and middle of a 575 km-long line extending from Lake Taupo to Cape Reinga. The principal finding from the experiment is that the crust is 25 ± 2 km thick, and is underlain by what is interpreted to be an upper mantle of seismic velocity 7.6 ± 0.1 km s⁻¹, that increases to 7.9 km s⁻¹ at a depth of about 45 km. Crustal seismic velocities vary between 5.3 and 6.36 km s⁻¹ with an average value of 6.04 km s⁻¹. There are close geophysical and geological similarities between the north-western North Island of New Zealand and the Basin and Range province of the western United States. In particular, the conditions of low upper-mantle seismic velocities, thin crust with respect to surface elevation, and high heat-flow (70–100 mW m⁻²) observed in these two areas can be ascribed to their respective positions behind an active convergent margin for about the past 20 Myr.     

Crustal model of the Bransfield Rift, West Antarctica, from detailed OBS refraction experiments

The first detailed deep seismic refraction study in the Bransfield Strait, West Antarctica, using sensitive OBSs (ocean bottom seismographs) was carried out successfully during the Antarctic summer of 1990/1991. The experiment focused on the deep crustal structure beneath the axis of the Bransfield Rift. Seismic profile DSS-20 was located exactly in the Bransfield Trough, which is suspected to be a young rift system. Along the profile, five OBSs were deployed at spacings of 50-70 km. 51 shots were fired along the 310 km profile. This paper gives the first presentation of the results. A detailed model of the crustal structure was obtained by modelling the observed traveltimes and amplitudes using a 2-D ray-tracing technique. The uppermost (sedimentary?) cover, with velocities of 2.0-5.5 km s⁻¹, reaches a depth of up to 8 km. Below this, a complex with velocities of 6.4-6.8 km s⁻¹ is observed. The presence of a high-velocity body, with V _p= 7.3-7.7 km s⁻¹, was detected in the 14-32 km depth range in the central part of the profile. These inhomogeneities can be interpreted as a stage of back-arc spreading and stretching of the continental crust, coinciding with the Deception-Bridgeman volcanic line. Velocities of 8.1 km s⁻¹, characteristic of the Moho, are observed along the profile at a depth of 30-32 km.     

Earthquake intensity attenuation pattern in the United States

Summary. Attenuation of earthquake intensities with epicentral distance was studied by analysing the intensity data for 39 earthquakes in the United States. Attenuation of MM intensity ( I ) with distance (Δ km) follows a simple relation of the type log I = log I ₀ - m Δ, where I ₀ is the intensity at the epicentre and m is a constant. Slope m is found to be inversely proportional to the square of the focal depth. Intensity attenuation pattern in the United States in general can be represented by a unified relation I/I ₀= exp [-(0.8999/ h ²+ 0.0014)Δ] where 16km ≤ h ≤ 60km. Intensities were calculated with the help of this equation and a good agreement with the observed intensities were found. A comparative study has also been made between the attenuation relations applicable to India and the United States.     

Crustal structure of the Whipple Mountains, southeastern California: a refraction study across a region of large continental extension

Summary. Closely spaced refraction profiling across the Whipple Mountains metamorphic core complex in southeastern California yields a complex picture of crustal structure in this region of large continental extension. A NE-directed profile, parallel to the extension direction, reveals a high-velocity mid-crustal layer (6.6–6.8 km s⁻¹) at 16-18 km depth, bounded above and below by laterally discontinuous low-velocity zones (<6.0 km s⁻¹). In marked contrast, a NW-directed profile shows a more uniform 6.0 km s⁻¹ crust down to the crust-mantle boundary. The apparent contrast between these two perpendicular profiles may be related not only to a more complex geologic structure in the NW-SE direction, but also to velocity anisotropy associated with mid-crustal mylonites. Despite the differences between the two refraction profiles, both define a flat Moho at 26-27 km depth with an associated upper mantle-velocity of 7.8 km s⁻¹. This observation is significant as it suggests that, although the amount of extension has been highly variable regionally, the crust is no thinner beneath the Whipple Mountains (where extension has been extreme) than the surrounding mountain ranges. Such an observation requires either that the crust was considerably thicker prior to extension, or that lateral flow in the lower crust and/or inflation of the crust via magmatism occurred contemporaneous with extension.     

Size and duration of the high-frequency radiator in the source of the 2004 December 26 Sumatra earthquake

We recover the gross space–time characteristics of high-frequency (HF) radiator of the great Sumatra-Andaman islands earthquake of 2004 December 26 ( M _w= 9.1–9.3) using the time histories of the power of radiated HF P waves. To determine these time histories we process teleseismic P waves at 36 BB stations, using, in sequence: (1) bandpass filtering (four bands: 0.4–1.2, 1.2–2, 2–3 and 3–4 Hz); (2) squaring wave amplitudes, making 'power signals' for each band and (3) stripping the propagation-related distortion ( P coda, etc.) from the power signal and thus recovering source time function for HF power. In step (3) we employ an inverse filter constructed from an empirical Green's function, which is estimated as the power signal from an aftershock. For each ray we thus obtain signals with relatively well-defined end and no coda. From these signals we extract: total duration (joint estimate for all four bands) and temporal centroid of signal power for each band. Through linear inversion, the set of duration values for a set of rays delivers estimates of the rupture stopping point and stopping time. Similarly, the set of temporal centroids can be inverted to obtain the position of the space–time centroid of HF energy radiator. The quality of inversion for centroid is acceptable for lower-frequency bands but deteriorates for higher-frequency bands where only a fraction of stations provide useful data. For the source length and duration the following joint estimates were obtained: 1241 ± 224 km, 550 ± 10 s. The estimated stopping point position corresponds to the northern extremity of the aftershock zone. Spatial HF radiation centroids are located at distances 350–700 km from the epicentre, in a systematic way: the higher is the frequency, the farther is the centroid from the epicentre. Average rupture propagation velocity is estimated as 2.25 km s^–1.     

Imaging the Hikurangi subduction zone, New Zealand, using teleseismic receiver functions: crustal fluids above the forearc mantle wedge

We image the Hikurangi subduction zone using receiver functions derived from teleseismic earthquakes. Migrated receiver functions show a northwest dipping low shear wave feature down to 60 km depth, which we associate with the crust of the subducted Pacific Plate. Receiver functions (RF) at several stations also show a pair of negative and positive polarity phases with associated conversion depths of ∼20–26 km, where the subducted Pacific Plate is at a depth of ∼40–50 km beneath the overlying Australian Plate. RF inversion solutions model these phases with a thin low S -wave velocity zone less than 4 km thick, and an S -wave velocity contrast of more than ∼0.5 km s⁻¹ with the overlying crust. We interpret this phase pair as representing fluids near the base of the lower crust of the Australian Plate, directly overlying the forearc mantle wedge.     

Crust and upper mantle structure of the central Iberian Meseta (Spain)

Summary. Quarry blasts recorded along three lines on the central Iberian Meseta are used in an attempt to interpret the crustal structure. The results of the interpretation of the data, together with published surface wave and earthquake data, suggest a layered structure of the crust having the following features: the basement, in some areas covered by up to 4 km of sediments, has a P -velocity of 6.1 km s⁻¹; a low-velocity layer, between 7 and 11 km depth, seems to exist on the basis of both P and S interpretation of seismic data; a thick middle crust of 12 km has a P -velocity of 6.4 km s⁻¹ and overlies a lower crust with a mean P -velocity of 6.9 km s⁻¹ and a possible slight negative gradient; the mean v _p/ v _s ratio for the crust is about 1.75; the Moho is reached at about 31 km depth and consists of a transition zone at least 1.5 km thick. The P -velocity of the upper mantle is close to 8.1 km s⁻¹ and the S -velocity about 4.5 km s⁻¹, which gives a v _p /v _s ratio of 1.8 for the uppermost mantle. A tentative petrological interpretation of the velocities and composition of the layers is given.     

On the penetration of a hot diapir through a strongly temperature-dependent viscosity medium

Summary. The ascent of a hot spherical body through a fluid with a strongly temperature-dependent viscosity has been studied using an axisymmetric finite element method. Numerical solutions range over Peclet numbers of 10⁻¹– 10³ from constant viscosity up to viscosity variations of 10⁵. Both rigid and stress-free boundary conditions were applied at the surface of the sphere. The dependence of drag on viscosity variation was shown to have no dependence on the stress boundary condition except for a Stokes flow scaling factor. A Nusselt number parameterization based on the stress-free constant viscosity functional dependence on the Peclet number scaled by a parameter depending on the viscosity structure fits both stress-free and rigid boundary condition data above viscosity variations of 100. The temperature scale height was determined as a function of sphere radius. For the simple physical model studied in this paper pre-heating is required to reduce the ambient viscosity of the country rock to less than 10²² cm² s⁻¹ in order for a 10 km diapir to penetrate a distance of several radii.     

The period and Q of the Chandler wobble

Summary. We have extended our calculation of the theoretical period of the Chandler wobble to account for the non-hydrostatic portion of the Earth's equatorial bulge and the effect of the fluid core upon the lengthening of the period due to the pole tide. We find the theoretical period of a realistic perfectly elastic Earth with an equilibrium pole tide to be 426.7 sidereal days, which is 8.5 day shorter than the observed period of 435.2 day. Using Rayleigh's principle for a rotating Earth, we exploit this discrepancy together with the observed Chandler Q to place constraints on the frequency dependence of mantle anelasticity. If Qμ in the mantle varies with frequency σ as σα between 30 s and 14 months and if Qμ in the lower mantle is of order 225 at 30 s, we find that 0.04 ρ^α≤ 0.11; if instead Qμ in the lower mantle is of order 350 near 200 s, we find that 0.11 ≤α≤ 0.19. In all cases these limits arise from exceeding the 68 per cent confidence limits of ± 2.6 day in the observed period. Since slight departures from an equilibrium pole tide affect the Q much more strongly than the period we believe these limits to be robust.