Errors in travel times measured on paper seismograms

Summary. The investigation of temporal variations in seismic velocities sometimes requires the use of paper seismograms. For this reason, an investigation of all of the sources of random error in measuring travel times on seismograms has been undertaken using a mathematical model devised by Jeffreys and some additional results derived using elementary statistics. The most important contribution to the total error is often the error due to linear interpolation between minute markers or other time marks on the seismogram, which can be as high as 0.13 s on smoked paper seismograms recorded at 120 mm min⁻¹, and as high as 0.076 s on short-period seismograms of the Canadian network recorded at 60 mm min⁻¹. For 32 explosions at short distances (< 50 km) recorded on smoked paper, however, the median value of the total error in the travel times was 0.016 s. Interpolation errors are generally insignificant for travel-time studies of teleseisms, but may be important in some special studies of local earthquakes and explosions. The theoretical results are useful, not only in seismology, but wherever the accurate timing of an event relative to two reference time markers on a chart recorder is required.     

The traveltime perturbations for seismic body waves in factorized anisotropic inhomogeneous media

The traveltime perturbation equations for the quasi-compressional and the two quasi-shear waves propagating in a factorized anisotropic inhomogeneous (FAI) media are derived. The concept of FAI media simplifies considerably these equations. In the FAI medium, the density normalized elastic parameters a _ijkl ( X _i ) can be described by the relation a _ijkl ( X _i) = f ²( x _i ) A _ijkl, where A _ijkl are constants, independent of coordinates x _i and f ²( x _i) is a continuous smooth function of x _i . The types of anisotropy ( A _ijkl ) and inhomogeneity [ f ( x _i)] are not restricted. The traveltime perturbations of individual seismic body waves ( q ^P , qS 1 and qS 2) propagating in the FAI medium depend, of course, both on the structural pertubations [δ f ²( x _i)] and on the anisotropy perturbations (δ A _ijkl ), but both these effects are fully separated. The perturbation equations for the time delay between the two qS -waves propagating in the FAI medium are simplified even more. If the unperturbed (background) medium is isotropic, the perturbation of the time delay does not depend on the structural perturbations (δ f ²( x _i) at all. This striking result, valid of course only in the framework of first-order perturbation theory, will simplify considerably the interpretation of the time delay between the two split qS -waves in inhomogeneous anisotropic media. Numerical examples are presented.     

Explicit, approximate expressions for the resolution and a posteriori covariance of massive tomographic systems

We present an approximate method to estimate the resolution, covariance and correlation matrix for linear tomographic systems Ax = b that are too large to be solved by singular value decomposition. An explicit expression for the approximate inverse matrix A ⁻ is found using one-step backprojections on the Penrose condition AA ⁻≈ I , from which we calculate the statistical properties of the solution. The computation of A ⁻ can easily be parallelized, each column being constructed independently.
The method is validated on small systems for which the exact covariance can still be computed with singular value decomposition. Though A ⁻ is not accurate enough to actually compute the solution x , the qualitative agreement obtained for resolution and covariance is sufficient for many purposes, such as rough assessment of model precision or the reparametrization of the model by the grouping of correlating parameters. We present an example for the computation of the complete covariance matrix of a very large (69 043 × 9610) system with 5.9 × 10⁶ non-zero elements in A . Computation time is proportional to the number of non-zero elements in A . If the correlation matrix is computed for the purpose of reparametrization by combining highly correlating unknowns x _i , a further gain in efficiency can be obtained by neglecting the small elements in A , but a more accurate estimation of the correlation requires a full treatment of even the smaller A _ij . We finally develop a formalism to compute a damped version of A ⁻.     

Travel times of Pn -waves in the Aegean and surrounding area

Summary. Based on accurately located 23 very shallow earthquakes ( h = 1–14 km) in northern and central Greece by portable networks of seismic stations and by the joint epicentre method, the travel times of the P_n -waves from the foci of these earthquakes to the sites of 54 permanent stations in the Balkan region have been determined. The travel times of P_n -waves in the central and eastern part of the area (eastern Greece, south-eastern Yugoslavia, the Aegean Sea, Bulgaria, southern Romania, western Turkey) fit a straight line very well with the P_n velocity equal to 7.9 ± 0.1 km s^-1. On the contrary, the travel times of P_n -waves to stations in the western part of the area (Albania, western Greece) do not fit this curve because the P_n -waves travelling to these stations are delayed by more than 1 s due to the thicker crust under the Dinarides–Hellenides mountain range. Time delays for P_n -waves have been calculated for each permanent station in the Balkan area with respect to the mean travel-time curve of these waves in the central and eastern part of the area. Corrections of the travel times for these delays contribute very much to the improvement of the accuracy in the location of the shallow earthquakes in the Aegean and surrounding area.     

Micromonas pusilla (Prasinophyceae) as part of pico-and nanoplankton communities of the Barents Sea

Micromonas pusilla (Butcher) Manton & Parke appears to be a prominent member of the Barents Sea picoplankton community as revealed by the serial dilution culture method. Cell numbers frequently exceeded 10⁷ cells 1⁻¹, though they usually varied between 10³and 10⁶ cells l⁻¹. A number of other identified and unidentified taxa were recorded and quantified. Distribution relative to the marginal ice zone is reported.     

Simultaneous inversion of seismic data

Summary. The resolving power of different data sets, consisting of surface-wave dispersion measurements and S travel times, are compared for a continental structure. The shear velocity in the low-velocity zone can be resolved in some detail with higher-mode phase-velocity data. Sufficient resolution for small density contrasts (0.03 g cm⁻³) until depths of ∼ 300 km can be reached if higher-mode group velocities are available as well, even at a precision as low as 0.10 km/s. At greater depths the density is not resolved, and here travel-time data are superior to higher modes in resolving the shear velocity.     

40Ar/39Ar dates of eastern Iceland lavas

Summary. Twenty-two plateau ages obtained by the ⁴⁰Ar/³⁹Ar step-heating method span most of the time of formation of eastern Iceland. With one exception the dates are consistent with the stratigraphy, the exception having a very unusual argon release pattern. It is concluded that the ⁴⁰Ar/³⁹Ar step-heating method can give correct dates on hydrothermally altered samples the total fusion ages of which are not correct; however, it is not possible to conclude from the results obtained that the method is inherently more accurate than the conventional method using carefully selected samples.
Though it is known from geological evidence that minor irregularities of spreading have occurred the results show that, within the resolution of the dates, spreading has been steady and symmetrical; in particular, neither a large eastward jump nor repetitive westward jumps can have occurred. The average half spreading rate for the period 2Myr to 12 Myr ago was 0.78 ± 0.16 cm yr-¹.     

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.     

Palaeoclimatic record from a loess–soil profile in northeastern Bulgaria—II. Correlation with global climatic events during the Pleistocene

Magnetic susceptibility ( χ ) variations and the behaviour of the ratio of susceptibility to saturation magnetization ( χ/J _s ) along the loess/palaeosol section at Koriten (NE Bulgaria) are used to deduce climatic changes during the Pleistocene in southeastern Europe. A good correlation of susceptibility variations with the astronomically tuned oxygen isotope record from ODP site 677 enables us to propose a more precise dating of the upper part of the Bulgarian loess complex. Close correspondence between susceptibility and δ ^{1 8} O records demonstrates the global significance of the palaeoclimatic signal recorded, although differences in relative amplitudes of χ and χ/J _s and δ ^{1 8} O create difficulties in making quantitative estimates of the climatic humidity in the past. The role of local factors affecting the palaeoclimatic mineral magnetic record deduced from the profile studied in Bulgaria is discussed.     

A near-regional explosion source model for tuff

Summary. A variety of near-regional (300 km) data, including spectral amplitudes of Pg , surface-wave forms, and close-in (5–10 km) accelerograms have been used to build an elastic seismic source model for a 1-Mton explosion in tuff at near-regional distances. The model consists of: (1) a pressure pulse which injects 3 × 10¹² cm³ of volume into the medium, (2) a vertical, upward force impulse that imparts 10¹⁸ dyn-s of momentum to the medium, each source component having a time duration of 0.6 s and a depth of 1.3 km. The force impulse appears to be required by two considerations: (a) the striking similarity, apart from sign, of explosion surface waves with those of their cavity collapses, (b) the observation of considerable SV energy leaving the source of the 1-Mton explosions JORUM and HANDLEY . Scaling curves have been constructed which fit the proposed source model. These scaling curves employ: very slow decrease, as (yield)^−0.10 of the primary corner frequency; decay as (frequency)⁴ or (frequency)³ to high frequency. While these scaling curves are unconventional, they appear to be the only ones which can satisfy the near-regional data. The slow scaling with yield of the spectral carner frequency suggests that it is caused by something other than the equivalent elastic radius, e.g. the time duration of motion at the source. The results, at odds with similar studies at teleseismic distances, suggest that significantly different equivalent elastic sources are required at near-regional (as compared with teleseismic) distances; therefore, the effect of the upward impulse might not be seen at teleseismic distances. Consequently, these results probably do not pertain to the seismic discrimination problem at teleseismic distances.     

Effect of viscosity structure on fault potential and stress orientations in eastern Canada

Previous investigations of the causal relationship between postglacial rebound and earthquakes in eastern Canada have focused on the mode of failure and the observed timing of the pulse of earthquake/faulting activity following deglaciation. In this study, the observational database has been extended to include observed orientations of the contemporary stress field and the rotation of stress since deglacial times. It is shown that many of these observations can be explained by a realistic ice history and a viscoelastic earth with a uniform 10²¹ Pa s mantle.
The effects of viscosity structure on the above predictions are also examined. It is shown that, since most of the above observations are found within the ice margin, they are not very sensitive to lithospheric thickness. Also, the inclusion of a 25 or 50 km ductile layer within the lithosphere will not decouple the seismogenic upper crust. High viscosity (10²² Pa s) in the lower mantle is rejected by the stress orientation and rotation observations. A low-viscosity (6 times 10²⁰Pa s) upper mantle with 1.6 times 10²¹ Pa s in the upper part of the lower mantle and 3 times 10²¹ Pa s in the lower part of the lower mantle below 1200 km depth has been found to give predictions that are in general agreement with the observations.     

Seismic sources with observable glut moments of spatial degree two

Let ζ_Λ and r _Λ. be the hypocentral position and time of an extended indigenous seismic source. Backus showed that the force moment tensors of the source, Γ^{( m +1, n )}(ζ_Λ, r _Λ), determine and are determined by the motion which the source produces. For small m + n , only the long-period motion is relevant. The glut moment tensor Λ^{( m,n )} (ζ_Λ, r _Λ.) can be calculated uniquely from γ^{( m +1, n )}(ζ_Λ r _Λ) only if m = 0 or m = 1. The tensor G =Λ^(2,0)(ζ_Λ) gives the spatial variance tensor W_Λ of the source, and W_Λ. roughly describes the size, shape and orientation of the source region. Therefore the failure of the observed F =Γ^(3,0)(ζ_Λ) to determine G uniquely is of seismological interest. In the present paper we show that F determines G uniquely if we assume the source to be a simple straight line source (SSLS) or an ideal fault in an isotropic medium with isotropic prestress (IFIMIP). We give tests on F which determine whether it can come from a SSLS, from an IFIMIP or from a simple plane surface source (SPSS). If we assume the source to be a SPSS then knowing F and the fault plane determines G to within an unknown scalar multiple of a certain tensor tangent to the fault plane. Moreover F determines the fault plane uniquely unless F can come from a SSLS. If it can, then F determines this virtual source line uniquely, and F permits the fault plane to be any plane containing the virtual source line.     

Crustal structure in the Western Somali Basin

Summary. As part of integrated marine geophysical studies in the Western Somali Basin, we performed 118 sonobuoy experiments to define better the crustal structure of the margins and basin created by the separation of Madagascar and Africa. After using T ²/ X ², conventional slope-intercept methods, and slant-stacked t-p techniques to analyse the data, we combined our solutions with all previous velocity information for the area. Velocity functions were derived for the sediment coiumn, and we detected a high-velocity (4.58 ± 0.29 km s^–1) sediment layer overlying acoustic basement. We confirmed that the crust is indeed seismically oceanic, and that it may be considered either in terms of a layered model – layers 2B (5.42 ± 0.19 km s^–1), 2C (6.23 ± 0.22 km s^–1), 3 (7.03 ± 0.25 km s^–1), and mantle (7.85 ± 0.32 km s^–1) were identified – or a more complex gradient model in which layer 2 is marked by a steeper velocity gradient than underlying layer 3. Integrated igneous crustal thicknesses (1.62 ± 0.22 s, 5.22 ± 0.64 km) are significantly less than what is considered normal. We present a revised seismic transect across the East African margin, as well as total sediment thickness, depth to basement and crustal thickness maps.     

Uplift and heat flow following the injection of magmas into the lithosphere

Summary. The thermal effect of a rapid injection of hot magmas into the lower part of the lithosphere is modelled as an increase in heat production through the invaded region. The change in surface heat flow and the uplift resulting from the thermal expansion are determined in three-dimensional axially symmetric geometry: they are expressed as the space time convolutions of a Green's function with the anomalous heat production.
The anomalies with shorter wavelength (compared to the lithospheric thickness) are attenuated. This filtering affects the surface uplift more than the heat flow anomaly; the attenuation effect is larger when only the lower part of the lithosphere is invaded.
The uplift time constant is of the same order as the heat conduction time if the lower lithosphere is invaded by magmas at a moderate rate (i.e. the rate of injection does not exceed the equivalent of 0.1 per cent of the lithospheric volume in 10⁶yr). Fifty per cent of the total uplift takes place in about 80 × 10⁶yr for a lithosphere 100 km thick. The uplift is slightly faster when the whole lithosphere is invaded. The heat flow anomaly is delayed when the lower part of the lithosphere is invaded.
The spatial extent and the timing of the uplift and heat flow anomalies are critical in determining the mechanism's feasibility. Magma injections explain rapid uplifts [> 100 m (10⁶ yr)⁻¹] only if the magma is supplied at a very high rate (i.e. at least 10 per cent of the lithosphere volume per 10⁶yr). It is a feasible mechanism for uplifts that occur over longer periods of time (≊ 30 × 10⁶yr) such as those that seem to have occurred when the African plate came to rest with respect to the mantle.     

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.     

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.     

Surface vertical displacements, potential perturbations andgravity changes of a viscoelastic earth model induced by internal point dislocations

Using the viscoelastic correspondence principle, we utilize the surface coseismic spheroidal deformation fields (i.e. vertical displacements, potential perturbations and gravity changes) of SNREI earth models caused by four typical types of point dislocation, derived by Sun & Okubo (1993 ), to deduce the fundamental formulas for spheroidal fields relevant to viscoelastic earth models. In computations, we employ a strike-slip dislocation on a vertical plane buried at the bottom of the lithosphere to estimate the maximal viscous relaxation responses to this kind of source that possibly exist on the surface of the earth. We take the seismic moment as 10²²  N  m, which is characteristic of an average large earthquake. The numerical results demonstrate that, if we take the viscosity as 10¹⁹  Pa  s in the asthenosphere, and 10²¹  Pa  s in the other mantle layers, the rates of surface vertical displacements and gravity changes within about 2.5° for the 10 postseismic years are respectively 1.5–8.1  cm  yr⁻¹ and 4.0–14.9  μgal  yr⁻¹ : the viscous relaxation for this mantle viscosity profile proceeds much faster than for a constant mantle viscosity of 10²¹  Pa  s.     

Stability of output fluxes of large rivers in South and East Asia during the last 2 million years: implications on floodplain processes

We compare the present-day sediment discharge (solid phase) of some of the largest rivers in Asia to the average discharge deduced from the mass accumulated in several sedimentary basins during the Quaternary. There is a very good correlation, especially for the largest rivers: the Ganges–Brahmaputra, the Changjiang, the Huanghe and, to a lesser extent, the Indus and the Zhujiang. This suggests that present-day average discharge at the outlet has remained constant throughout the Quaternary at least for very large rivers (drainage area of the order of 10⁵–10⁶ km²). This, in turn, suggests either that continental denudation of large Asian catchments has remained on average constant, implying a strong tectonic control on erosion during the Quaternary, or that the river network has the ability to buffer changes in hillslope erosion or in sea-level in order to conserve the total discharge at the outlet. We show how this buffering capacity relies on the characteristic reaction time-scale of Asian alluvial plains (of the order of 10^5–6 years), that is, much higher than the time-scales of the Quaternary climate oscillations (of the order of 10⁴ years). A short-term perturbation originating in hillslopes will be diluted by the floodplain. At the outlet the signal should have a longer time span and a smaller amplitude. In the same manner, an alluvial plain should not instantaneously react to a 10⁴-year sea-level drop because of its inertia. Along with long-term tectonic control we infer this buffering to be the main cause for the average constancy of sediment yield of large Asian rivers during the Quaternary.     

Axial Intrusion Zone beneath the Median Valley of the Mid-Atlantic Ridge at 37°N Detected by Explosion Seismology

Summary. Four seismic refraction lines, three of which had shots every 250 m, were shot across, along and parallel to the median valley of the Mid-Atlantic Ridge at 37° N. A method has been developed for calculating the effect on the travel times of the rough sea-floor relief beneath the profiles and has been used to correct all the travel times for this effect. Most arrivals were from a main refractor of apparent velocity 5·4 to 6·3 km s⁻¹; only beyond 35 km were faster arrivals observed from an 8·09 ± 36 km s⁻¹ refractor. The main refractor corresponds in depth, at least approximately, to the top of Layer 3 of the ocean basins but its velocity is significantly less than normal for Layer 3, perhaps due to dip. A study of time residuals along two profiles across the median valley indicates the presence of a 2 to 3 km wide low velocity zone (about 3·2 km s⁻¹) beneath the median valley floor. This zone extends over the upper 2·5 km of the crust and is believed to represent a zone of intrusion through which magma passes on its way to the sea floor.     

FIR filter effects and nucleation phases

The symmetric impulse response of linear phase Finite Impulse Response (FIR) filters most commonly used in modern seismic recording systems produces precursory signals to impulsive arrivals. These acausal filter-generated artefacts may result in misinterpretations of various onset properties. Prior to any onset interpretation, these effects have to be removed from the seismic record. This can be achieved without loss of bandwidth by post-filtration of the digital seismograms if the filter coefficients and the decimation ratios are known. We have analysed numerous signals from different instruments and sampling rates for precursory phases and found that—in contrast to commonly held beliefs—FIR-filter-related precursory signals are not always easy to recognize visually from their waveform signature. Furthermore, they can exhibit surprisingly similar properties to those reported for nucleation phases, although the majority of nucleation phases reported in the past have been obtained on instruments with a causal response. We demonstrate examples of filter-related precursory signals for events scanning nine orders of moment, from 10¹⁰ N m to 10¹⁹ N m. Surprisingly, the lower bound of the artefact durations as a function of seismic moment scales close to the cube root of the seismic moment. We interpret this as being caused by the fact that above a certain seismic moment, the attenuated source signal acts as a causal lowpass filter of a smaller bandwidth than the FIR filter. Assuming an ω^-2 source model, constant stress drop and an empirical relationship between the maximum artefact duration and the cut-off frequency of the FIR filter, the artefact durations are expected to scale proportional to the 1/2.5 power of the seismic moment, in comparison to 1/3 as proposed for nucleation phases.