Showing papers in "Geophysical Journal International in 1982"

A thin viscous sheet model for continental deformation

Abstract: Summary. For the purposes of describing its large-scale and long-term deformation, the continental lithosphere is regarded as a continuum, obeying a Newtonian or a power law rheology. The flow of a thin sheet of power law material overlying an inviscid substrate is studied under the assumption that vertical gradients of the horizontal velocity are negligible. A numerical model is used to investigate the deformation of such a sheet under conditions approximating those of continent-continent collision. The material flows in response to forces applied to its boundaries (for example, the indenting of one continent by another) and to forces in its interior arising from gradients in crustal thickness. The horizontal divergence of the flow produces changes in the crustal thickness and hence a time-dependent form to the flow itself. For a given set of boundary conditions, the flow depends on the stress exponent in the power law rheology, n, and on the Argand number& which is a measure of the ratio between the stress arising from crustal thickness contrasts and the stress required to deform the material at the ambient strain rates. When the effective viscosity of the medium is very high (Ar-+O), crustal thickness variations do not influence the flow. If the material is Newtonian (n = l), the deformation associated with an influx of material (approximating an indenter) is of much greater lateral dimension than the width of the indenter, whereas when material has a power law rheology (n = 3, 5 are used), the deformation is confined to a region of lateral extent comparable to that of the indenter. As Ar increases, the forces arising from crustal thickness contrasts exert more influence on the flow, and the maximum crustal thickness that can be sustained by a given influx of material is related by a simple expression to the effective viscosity of the medium at the ambient strain rates. In the limit of a very weak medium (Ar> 10) the lithosphere is unable to sustain appreciable crustal elevation contrasts. The results of these numerical experiments show that systems in which the effective viscosities are such that the maximum deviatoric stresses are between 1 kbar

Computation of wave fields in inhomogeneous media — Gaussian beam approach

Abstract: Summary. An asymptotic procedure for the computation of wave fields in two-dimensional laterally inhomogeneous media is proposed. It is based on the simulation of the wave field by a system of Gaussian beams. Each beam is continued independently through an arbitrary inhomogeneous structure. The complete wave field at a receiver is then obtained as an integral superposition of all Gaussian beams arriving in some neighbourhood of the receiver. The corresponding integral formula is valid even in various singular regions where the ray method fails (the vicinity of caustic, critical point, etc.). Numerical examples are given.

Viscous gravitational relaxation

Abstract: Summary. This paper is concerned with a detailed examination of the response of Maxwell models of the planet to surface mass loads. Particular attention is devoted to an examination of the factors which determine the isostatic response since the understanding of this response is crucial in a number of different geodynamic problems. One particular example which we discuss in detail is concerned with the prediction of free air gravity anomalies produced by large-scale deglaciation events. Using the methods developed here we are able to provide the first direct assessment of the importance of initial isostatic disequilibrium on the observed relative sea-level variations and free air gravity anomalies forced by the melting of the Laurentide ice sheet. We are therefore able to estimate the extent to which such initial disequilibrium might influence the inference of mantle viscosity from isostatic adjustment data. Our calculations establish that free air gravity data, although they are sensitive to the degree of initial disequilibrium, provide an extremely high quality constraint upon the viscosity of the lower mantle.

Analysis of palaeomagnetic inclination data

Abstract: Summary The analysis of palaeomagnetic data where only inclinations are available is considered. Maximum likelihood estimates for the mean inclination I0 and Fisher's precision parameter k are derived. It is shown that they are in all cases biased although the bias is small for low inclinations. The case of steep inclinations and small values of k is examined and it is shown that in this region I0 and k are not separable as distinct variables, because the lack of declination information in this region leads to fundamental ambiguities. Unbiased estimates for I0 and (1/k) are derived for the case where the portion of the distribution folded about the vertical is insubstantial. A worked example of the method, with calculation of confidence limits, is appended.

Inversion of field data in fault tectonics to obtain the regional stress — I. Single phase fault populations: a new method of computing the stress tensor

Abstract: Summary. We attempt a general definition of the inverse problem of computing the components of the regional stress tensor from a set of field data including the measurements of the strike and dip of several faults, and the directions and senses of relative motion along these faults (as indicated by slickenslides). In previous treatments of this problem, no experimental errors could be taken into account except those in measuring the pitch of slickenslides; thus, errors in the orientation of the fault (strike and dip), which have considerable practical importance, were neglected. In our work, all experimental errors in the field measurements are taken into account, so that the agreement between the computed stress tensor and the set of field measurements can be rigorously checked.

Constraints on yield strength in the oceanic lithosphere derived from observations of flexure

Abstract: Summary. The wavelength and amplitude of outer rises seaward of sub-duction zones and arches surrounding islands and seamounts are used to parameterize flexure profiles in terms of the moment and curvature at the first zero crossing. The data show the clear age dependence in the mechanical thickness of the lithosphere up to 60–100Myr. Saturation of moment at large curvature is interpreted in terms of a depth-dependent yield strength for the lithosphere using relations adopted from laboratory experiments of rock deformation. A comparison of theoretical curves with observed moments indicates that old oceanic lithosphere has no long-term strength below about 40 km depth, with no difference between 100 and 165 Myr old crust. Moderate axial loading forces (±200 MPa) can explain most variations in the moment/curvature observations, except in the case of the Kuril Trench which appears anomalous given the age of the crust. Regional tension causes greater variability in moment as compared to regional compression because of the greater slope in the brittle failure envelope under tension. The observations point to a lithosphere weaker than the prediction from experimental deformation of rocks. Of the possible weakening mechanisms, elevated pore-fluid pressure on faults does not predict the correct age dependence and is incompatible with earthquake focal mechanisms. Our favoured explanation is that the activation energy, Q, appropriate for ductile flow at geological strain rates is lower than the values derived from laboratory extrapolations of dry olivine data taken at high temperatures. If recent oceanic geotherms are reliable, Q in the lower lithosphere must be lower than 100kcal mol−1. The method used here is most appropriate for trench profiles with curvatures greater than 10−7m−1. For lower curvatures, such as along seamount profiles, small errors in the curvature estimate cause large changes in rheological parameters.

Mantle convection as a boundary layer phenomenon

Abstract: Summary. The boundary layer nature of vigorous thermal convection is explored using high resolution numerical solutions to the governing hydrodynamic equations. These solutions are obtained for a series of idealized models of the Earth’s mantle in which the viscosity is assumed to be constant. A detailed analysis of the local energy balance within the horizontal and vertical thermal boundary layers is presented in terms of which a test of the fundamental assumptions of boundary layer theory is provided. The results of this test have important geophysical consequences since the asymptotic predictions of boundary layer theory have been employed extensively in the context of thermal history modelling. Although boundary layer theory closely predicts the correct power-law behaviour of various quantities it does not determine their absolute values accurately. Vertical advection is shown to play an important role in the energy balance within horizontal boundary layers at all Rayleigh numbers. Horizontal and vertical advection dominate the energy balance within vertical plumes while horizontal diffusion plays a very minor role. When heating is partially from within the fluid, vertical advection into the upper thermal boundary layer can produce significant departures in the thermal structure from that found when heating is entirely from below. For a free upper boundary this results in a relative flattening of the variations of surface topography and heat flow across the convection cells. For a constant velocity upper boundary (similar to plate motion) the bathymetry flattens but the heat flow does not; this result agrees with marine observations. Rigidity of the thermal boundary layer below the upper surface is not included explicitly in the model, and it is not known whether the inclusion of this feature in future models would significantly alter the topographic expression. If not, the observed departure of the oceanic bathymetry from a 6 dependence at old ocean floor ages could be attributed to a small amount of internal heating in a mantle-wide convective circulation.

On the evolution of rifted continental margins: comparison of models and observations for the Nova Scotian margin

Abstract: Summary. A model for the formation and evolution of rifted continental margins based on lithospheric extension during rifting and its thermal and mechanical consequences is proposed. Model predictions are then compared with geological and geophysical observations from a transect of the ∼185 Ma old rifted margin off Nova Scotia through the Scotian Basin. Three kinematic models of the rifting process are discussed. These are: (1) the uniform extension model, in which the amount of extension is uniform with depth but varies with position across the margin; (2) the uniform extension and melt segregation model which has similar properties, but also provides an explanation for the properties of the extended continental crust and its transition to oceanic crust by postulating that basaltic melt segregates from the asthenosphere and migrates to the crust, and; (3) the depth-dependent extension model in which the first-order consequences of rapidly changing rheological properties with depth in the lithosphere are included by decoupling the lithosphere into two zones with depth, each of which undergoes differing amounts of extension. These rift models predict the form of crustal and lithospheric thinning, subsidence and temperature change once the amount of extension has been determined. This is estimated from seismic measurements of present crustal thickness on the assumption that the crust had a uniform thickness, equal to that currently measured in the adjacent continental region, before rifting occurred. Rifting is also considered to occur instantaneously. A time-stepping thermo-mechanical model is used to predict the cooling of rifted margin, additional thermal contraction subsidence and its amplification by water and sediment loading. Thermal aspects are calculated using a finite difference model of time-dependent conductive heat transport, whereas regional isostatic response to loading is calculated by a finite element model. The models are coupled because the temperature distribution is used to define a rheological lithosphere (an elastic region with thickness that varies in time and space as the model evolves) for flexural calculations in the mechanical model. Secondary coupling occurs through perturbations to the temperature field by sedimentary thermal blanketing and advection of heat during isostatic adjustment. The model predictions of: (1) sedimentary basin stratigraphy, (2) Moho position, (3) free air gravity anomaly, (4) age—depth relations for deep exploratory wells and (5) subsidence and temperature histories agree well with observations from the Scotian Basin. Additional effects due to sedimentary and crustal radiogenic heat production, lateral heat transport and the possible existence of a near surface brittle listric faulted region created during rifting are also considered. It is concluded that a model in which rifting occurred by depth-dependent extension, and which includes a finite thickness for the rheological lithosphere, radiogenic heat production in the sediments and crust, and a brittle listric faulted crustal layer affords an accurate description of the first-order processes that occur during rifting and evolution of this margin.

Determination of source parameters by wavefield extrapolation

Abstract: Summary The extrapolation of an observed (seismogram) wavefield backward in time produces an image, in both time and space, of the source. This concept is implemented through a finite difference solution of the two-dimensional acoustic wave equation. The seismograms themselves are used as time-dependent boundary values that drive the finite difference mesh, Numerical examples illustrate the determination of hypocentre location and origin time for point sources and of source extent, orientation and rupture velocity for finite sources in both homogeneous and heterogeneous media. Spatial resolution of source parameters is typically one-half wavelength of the dominant frequency generated by the source.

Optimal estimation of scalar seismic moment

Abstract: Summary. For any seismic source specified by a frequency-dependent moment-rate tensor M(ω), we define the total moment MT(ω) =||M||/2 and the isotropic moment MI(ω) =|trM|/6. A method is presented for estimating these scalar seismic moments from noisy seismic data when the source mechanism is uncertain or completely unknown. Our formulation exploits the linear relation between squared moment M2 (total or isotropic) and the product of two seismic spectra; in a particular frequency band, an estimate M2 is constructed as a linear combination of power and cross-spectra integrated across the band. The coefficients yielding an exact estimate from perfect data are the solution to a linear system of equations involving spectral integrals of the transfer functions that relate M to the seismograms. The failure to solve this system exactly induces an error in M2 whose statistics can be calculated from a likelihood function for the source mechanism, which we model using the hyperspherical normal distribution and its Gaussian approximation and generalizations. We also develop expressions for the bias and variance induced in M2 by ambient seismic noise and by transfer-function errors due to aspherical heterogeneity. To optimize the estimate, the coefficients specifying M2 are computed by minimizing a non-negative-definite quadratic form constructed from these statistics. We have applied the method to IDA records of the deep-focus Honshu earthquake of 1978 March 7 and the shallow-focus Oaxaca earthquake of 1978 November 29. For each event, estimates of MT have been obtained with good precision over disjunct 1-mHz bands spanning the frequency interval 1—11mHz; their relative standard deviations range from 10 to 22 per cent. Our best estimate of MT averaged over the entire 1–11mHz interval is 0.43 ± 1027 dyne cm for Honshu and 2.8 ± 1027 dyne cm for Oaxaca. The isotropic component of the Oaxaca event, as measured by the ratio, is negligibly small (< 0.1). In the case of Honshu, however, this ratio averages about 0.34; all six estimates at frequencies greater than 5 mHz are significantly greater than zero at the 90 per cent confidence level, and four of the six are significant at the 95 per cent level. This observation lends credence to the conjecture made previously by seismologists that isotropic compression accompanies some deep-focus earthquakes.

Diffracted waves and displacement field over two-dimensional elevated topographies

Abstract: Summary The Aki-Larner technique is used to perform, in both the time and frequency domains, an analysis of the effects of two-dimensional elevated topography on ground motion. Incident plane SH-, SV- and P-waves are considered and the respective influences of surface geometry, elastic parameters and the incident wave characteristics, as long as they remain within the limits of applicability of the A-L technique, are investigated in some detail. Besides the well-known amplification/deamplfication effect related to the surface curvature, wave scattering phenomena on the convex parts of the surface are shown to contribute significantly to the disturbances in the displacement field around the topographic structure. These scattered waves are SH in the case of incident SH-waves, and mainly Rayleigh waves in the P case, while both Rayleigh and horizontal P-waves, sometimes of large amplitude, develop in the SV case. The frequency dependence of this scattering, though complex, seems to be mainly controlled by the horizontal scale of the topographic structure. The parameter study points out the regular and intuitive behaviour of this wave scattering in both SH and P cases, while it exhibits a puzzling complexity for incident SV-waves, which is interpreted as resulting from the importance of the S-P reflections on mountain slopes in that case. As to the ground motion, some general features may be pointed out. The amplification on mountain tops, which is systematically greater for incident S-waves than for P-waves, generally decreases as the average slope decreases or as the angle of incidence increases. Mountain slopes undergo either amplification or deamplification depending on site location, frequency and incidence angle, but they always undergo strong differential motion due to the lateral propagation of the scattered waves and their interference with the primary wave. Finally, all these effects may be greatly enhanced in the case of complex topographies, which moreover give rise to a significant prolongation of ground motion because of the large number of scattered waves.

The effects of the atmosphere and oceans on the Earth's wobble — I. Theory

Abstract: Summary The theory of wobble excitation for a non-rigid earth is extended to include the effects of the earth's fluid core and of the rotationally induced pole tide in the ocean. The response of the solid earth and oceans to atmospheric loading is also considered. The oceans are shown to be affected by changes in the gravitational potential which accompany atmospheric pressure disturbances and by the load-induced deformation of the solid earth. These various improvements affect the excitation equations by about 10 per cent. Atmospheric and oceanic excitation can be computed using either an angular momentum or a torque approach. We use the dynamical equations for a thin fluid to relate these two methods and to develop a more general, combined approach. Finally, geostrophic winds and currents are shown to be potentially important sources of wobble excitation, in contrast to what is generally believed.

Surface waves and free oscillations in a regionalized earth model.

Abstract: The linearized equation is derived which relates observed long-period seismic waveforms to the aspherical perturbations of a spherically symmetric earth model. This is accomplished by formulating the theory of spectral splitting in the time domain. It is shown to be possible greatly to simplify the resulting equations in a way which makes it apparent that for each modal multiplet the ‘scattered’ field depends only upon three local functionals of earth structure. The effect of regional structural variations may then be quantified in a manner analogous to that assumed in the ‘pure path technique’, but without making the usual asymptotic approximations. These results are used to investigate the validity of the asymptotic result for the locations of the centroids of spectral peaks in individual recordings, for a regionalized model of the Earth. A technique is suggested for retrieving information about geographical structural variations from low-frequency waveform data.

Upper mantle anisotropy - Evidence from free oscillations

Abstract: Isotropic earth models are unable to provide uniform fits to the gross Earth normal mode data set or, in many cases, to regional Love-and Rayleigh-wave data. Anisotropic inversion provides a good fit to the data and indicates that the upper 200km of the mantle is anisotropic. The nature and magnitude of the required anisotropy, moreover, is similar to that found in body wave studies and in studies of ultramafic samples from the upper mantle. Pronounced upper mantle low-velocity zones are characteristic of models resulting from isotropic inversion of global or regional data sets. Anisotropic models have more nearly constant velocities in the upper mantle. Normal mode partial (Frediet) derivatives are calculated for a transversely isotropic earth model with a radial axis of symmetry. For this type of anisotropy there are five elastic constant. The two shear-type moduli can be determined from the toroidal modes. Spheroidal and Rayleigh modes are sensitive to all five elastic constants but are mainly controlled by the two compressional-type moduli, one of the shear-type moduli and the remaining, mixed-mode, modulus. The lack of sensitivity of Rayleigh waves to compressional wave velocities is a characteristic only of the isotropic case. The partial derivatives of the horizontal and vertical components of the compressional velocity are nearly equal and opposite in the region of the mantle where the shear velocity sensitivity is the greatest. The net compressional wave partial derivative, at depth, is therefore very small for isotropic perturbations. Compressional wave anisotropy, however, has a significant effect on Rayleigh-wave dispersion. Once it has been established that transverse anisotropy is important it is necessary to invert for all five elastic constants. If the azimuthal effect has not been averaged out a more general anisotropy may have to be allowed for.

Magnetic properties and opaque mineralogy of drilled submarine intrusive rocks

Abstract: Summary Measurements of natural remanent magnetization (nrm), Curie temperature, ferrimagnetic and paramagnetic susceptibility, saturation induced and remanent magnetizations, coercive forces, alternating field properties and viscous magnetization are reported for 50 submarine intrusive rocks drilled during Legs 30, 37 and 45 of DSDP. The collection includes doleritic sill rocks, fresh and serpentinized cumulate gabbros and serpentinized cumulate peridotites, and serpentinized lherzolites believed to have originated in Layers 2B, 3B and 4 respectively. Magnetite, with a Curie temperature between 520 and 580°C, is the principal magnetic mineral in all samples. There is no indication of maghemitization or of metamorphism to greenschist facies or above. The magnetite in the doleritic and cumulate gabbros is a product of deuteric alteration of titanomagnetite and pyroxene; the stable nrm is a primary trm. The magnetite in the serpentinized rocks is a secondary product of serpentinization; the stable nrm is a crm. In most rock types, the magnetite is of single-domain or pseudo-single-domain size and soft components of nrm are small. The magnetite grain size in some of the doleritic gabbros is much coarser; these rocks acquire large viscous magnetizations, which however are readily removed by alternating field cleaning. The cleaned nrms of Legs 30 and 45 rocks have approximately dipole inclinations but the nrms of most of the mutually intruded Leg 37 units have been dispersed by tectonic rotations. The doleritic gabbros and the serpentinized peridotites have stable, directionally coherent nrms ≳ 10-3emu cm-3 in intensity. Their counterparts in Layers 2B and 3B/4 are likely contributors to oceanic magnetic anomalies. Layer 3B cumulate gabbros and tectonic serpentinites in the middle and upper crust are less likely anomaly sources.

Reflection—refraction of general P-and type-I S-waves in elastic and anelastic solids

Abstract: Summary. The reflection and refraction of general (homogeneous or inhomo-geneous) plane P and type-I S(SV) body waves incident on plane boundaries are considered for general linear viscoelastic solids. Reflection—refraction laws, physical characteristics of the waves, and the nature of critical angles are examined in detail at welded boundaries and a free surface. General visco-elasticity with no low-loss approximations predicts that contrasts in intrinsic absorption at boundaries give rise to inhomogeneous reflected and refracted waves with elliptical particle motions, velocities and maximum attenuations that vary with frequency and angle of incidence, energy propagation at speeds and directions different from phase propagation, phase propagation that in general is parallel to the boundary for at most one angle of incidence, and reflection—transmission coefficients dependent on energy flow due to wave interaction. None of these physical characteristics are predicted for waves incident on boundaries that respond instantaneously.

Stable regions in the Earth's liquid core

Abstract: Summary. Slow cooling of the whole Earth can be responsible for the convection in the core that is required to generate the magnetic field. Previous studies have assumed the cooling rate to be high enough for the whole core to convect. Here we study the effects of a low rate of cooling by assuming the temperature at the base of the mantle to remain constant with an initially entirely molten, adiabatic core. We argue that, in such a situation, convection would stop at the top of the core, and calculate the consequent thermal evolution. A stable, density stratified layer grows downwards from the core mantle boundary reaching a thickness of 100-1000 km in a few thousands of millions of years. There is some geomagnetic evidence to support belief in the existence of such a stable layer.

Dispersion and attenuation of mantle waves through waveform inversion

Abstract: Summary. We propose a new approach to the determination of elastic and anelastic parameters of the Earth’s structure from seismic data. Instead of measuring such functionals of the medium response as the phase delay or spectral ratios, we perturb parameters of the model to satisfy the observed waveforms. The advantage of our waveform inversion technique (WIT) is that it uses the properties of the Earth as a smoothing filter. Also, because the Earth’s structure is the common denominator, the method allows simultaneous interpretation of different functionals of this structure; for example, the waveforms of Rayleigh and Love waves for the same source-receiver pair. Following extensive testing of the method on synthetic and actual data, we subject results of our analysis of 37 recordings for various sources and stations to ‘pure path’ decomposition. The period range of analysis extends from 160 to 630s. We distinguish four types of regions: stable continents, areas tectonically active within the last 400Myr, ocean floors younger than 38 Myr, and old ocean floors older than 38 Myr. The results indicate significantly different responses of the oceanic and continental areas at long periods. Stable continental and tectonic regions have nearly the same dispersion for periods greater than 300-35Os, and then diverge rapidly, with stable continents showing higher velocities. The young and old oceans, on the other hand, become distinct at periods as long as 500 s; the old oceans are faster. In terms of shear velocity models, the data are consistent with a difference of about 4 per cent between the young and old oceans in a depth range from 400 to 670 km, while the continental regions are similar and close to the global average. At shallower depths our structures are conceptually similar to those inferred from previous ‘pure path’ analyses and short-period surface wave studies. While we cannot, yet, establish statistically significant differences in Q for the four regions, such differences are obtained if one distinguishes only between continents and oceans: the Q for the latter is 10-20 per cent lower in the period range of the analysis.

Grain-size dependence of initial susceptibility and saturation magnetization-related parameters of four natural magnetites in the PSD?MD range

Abstract: Summary. Initial susceptibility, coercive force and several types of remanent coercive forces were measured on a set of artificial rock specimens containing grain-size fractions of a natural magnetite and titanomagnetite, both of which are optically homogeneous and a natural titanomagnetite and titanomaghemite, both of which show exsolution phenomena. It was found subsequently that the optically homogeneous titanomagnetite contains some submicroscopic Fe-rich inclusions. These inclusions are magnetically screened in coarse grains; only for the lower grain sizes studied they have an appreciable influence on the data. The size of the fractions varied from < 5 to 250 μm. The parameters and several parameter ratios are plotted as a function of grain size. Several of these parameters can be used as mineralogical and grain-size indicators. The varying degree of exsolution of the minerals is reflected in the gradients of the plots. From plots of initial susceptibility versus grain size it is concluded that the shape of the grains does not play a dominant role in determining the change of this parameter with grain size. Variation of the various parameters with grain size is explained in terms of a gradual transition from large PSD grains to MD grains without there being any sharp transition. For titanomagnetite (x= 0.55) the transition takes place at grain sizes that are about 15 μm larger than for magnetite.

Normal modes of the viscoelastic earth

Abstract: Summary A uniformly valid linear viscoelastic rheology is described which takes the form of a ‘generalized’ Burgers' body and which appears capable of reconciling the behaviour of the Earth's mantle across the complete spectrum of geodynamic time-scales. This spectrum is bracketed by the short time-scales of body wave and free oscillation seismology on which anelastic effects are dominant, and the long time-scale of mantle convection on which the Earth behaves viscously. The parameters of the model which control the viscous response are fixed by post-glacial rebound data whereas those which govern the anelasticity are to be determined by fitting the model to observations of seismic Q. The paper is concerned primarily with a discussion of the normal mode spectrum of the Earth as a generalized Burgers' body. Focusing upon the homogeneous model, it includes an initial analysis of the accuracy of first-order perturbation theory as a method of calculating the respective Qs of the elastic gravitational free oscillations. Also considered are the quasi-static modes of relaxation which only exact eigenanalysis can reveal. The importance of these modes is assessed within the context of a discussion of the effect of viscoelasticity upon the efficiency of Chandler wobble excitation.

Detransformation of the British geomagnetic secular variation record for Holocene times

Abstract: In this note we replot the British post-glacial secular variation curve in terms of actual values of declination and inclination, rather than the ‘transformed’ declination and inclination system used in our original paper (Turner & Thompson 1981). This should facilitate the comparison of our record with contemporaneous European archaeomagnetic data. Our composite record was obtained by averaging the dated records from 10 cores of lake sediment. The sequence of unit vectors describing the magnetic direction record of each core was rotated so as to place its mean direction (the mean over the section of core dated between 0 and 7000 BP, the time span of the shortest core) at zero transformed declination and inclination (dT = O”, IT = 0”). The transformed coordinate frame of each core is thus derived from its mean direction, assumed to represent the mean geomagnetic field direction over the 7000 yr period, rather than from the core tube and its orientation during coring. Hence the problem of not knowing the azimuthal orientation and inclination of the corer during core collection is avoided, and the 10 records can be averaged in this coordinate system. Transformed coordinates then, provide a convenient, generalised method of plotting averaged sediment records. However, in the archaeomagnetic method, sample orientation is straightforward, and the results can readily be plotted as absolute declination and inclination values. So for consistency when comparing the two, we have attempted here to ‘detransform’ our record. The following procedures, assumptions and approximations were taken to produce the detransformed magnetograms and Bauer-type plots of Figs 1 and 2. (1) Amplitude correction. Although the combination of 10 data sets produces a good estimate of the signature of the geomagnetic variations, the following factors contribute to an overall loss of amplitude in both declination and inclination. (a) The quality of magnetic recording varies widely between different sediments, depending on the porosity of the sediment, the size and shape distributions and the nature of the magnetic carrier (Verosub 1979). The Loch Lomond sediments carry a good, high amplitude pattern of remanent directions, of which the most recent closely follow the London observatory records. The much wetter and less compacted sediments of Llyn Geirionydd, on the

On the electrical crust—mantle structure in Fennoscandia: no Moho, and the asthenosphere revealed?

Abstract: Summary. An interpretation of the geomagnetic inductive response function, C(ω, 0), observed at Kiruna in northern Sweden, is herein undertaken. The bounds of acceptable solutions are initially discovered by a Monte-Carlo random search procedure, and the best-fitting solutions are examined by the application of linear theory to the problem. The data are shown to have a higher degree of internal consistency than that described by the estimated variances of each datum. A further Monte-Carlo inversion of the variance- reduced data set gives solutions with well defined model parameters. The two major features of the models are: (1) a small, or non-existent, electrical conductivity variation across the seismic Moho boundary, and (2) the unequivocal existence of an electrical asthenosphere, under the Fenno- scandian shield, beginning at a depth of between 155–185 km, and of 60km minimum thickness. Both of these observations have seismic counterparts. Finally, possible mantle temperature profiles are deduced which depend on the assumptions and laboratory data employed.

Explosive volcanic eruptions — V. Observations of plume dynamics during the 1979 Soufrière eruption, St Vincent

Abstract: Summary. During the 1979 eruption of the Soufritre of St Vincent, West Indies, a 14min period of explosive activity occurred on April 22. The first three minutes of this activity were filmed. Five individual explosions formed distinct plumes which fed an eruption column which eventually ascended to a height of over 18 km. The ascent velocities of the fronts of these plumes ranged from 8.5 to 61.7m s-'. The half-angle of spreading of the plume fronts ranged from 21.5 to 24". One of the plumes was observed to 8 km height and decelerated steadily from 5 1.5 to 23 m s-l. The main column fed by individual explosions was, however, observed to accelerate from 8.5 to 58 m s-l in the same height interval. A theoretical treatment of volcanic plume motion is presented. Measurements of dimensions, velocities and spreading rates from the film are used to estimate plume parameters such as temperature, particle content and volume discharge rate of magma from the theoretical relationships. These calculations show that the individual plumes became hotter and richer in juvenile ash with time. The acceleration of the main eruption column was the result of being fed by increasingly hotter and more ash-rich explosions. An average volume discharge rate of 12600m3s-' is estimated from the analysis of the plume motions. This value agrees closely with an estimate of discharge rate based on the heat flux required to form an 18 km high column. This agreement suggests that theories of convective motions in plumes can be successfully adapted to the volcanic case, as long as the effect of hot entrained ash particles is considered.

The 1978 earthquake sequence near Thessaloniki (northern Greece)

Abstract: Summary. This paper presents a detailed study of teleseismically and locally recorded foreshocks and aftershocks of the 1978 Thessaloniki earthquake sequence and discusses the relations between the locations and mechanisms of these shocks and the three-dimensional geometry of faulting in the source region. Sixteen teleseismically recorded events were relocated using a relative relocation method and positioned geographically using the accurate (locally determined) location of the largest aftershock. All these shocks had depths shallower than 15 km. The spatial distribution of the foreshocks showed that the activity was initiated at the central part of the epicentral region, progressed westwards, and for about 20 days clustered in the region of the imminent mainshock. No teleseismically recorded foreshock was located west of the mainshock location. In less than 1 hr after the mainshock large aftershocks occurred west of it and, in later stages, spanned the entire western part of the epicentral region. No teleseismically recorded aftershocks were located east of the mainshock. Locally recorded aftershocks were accurately located and provided a more detailed picture of the seismic deformation. They occurred at depths between 3 and 12 km and in three distinct clusters, separated by well-defined gaps. The largest foreshock, on May 23, had a moment of 5.6 × 1024dyne cm and a mean displacement of 31cm. The mainshock, on June 20, had a moment of 5.2 × 1025dyne cm, a strain drop of 4.0 × 10−5 (static stress drop of 12 bar) and a mean displacement of 64 cm. These values are for one of the two possible interpretations of the aftershock distribution, which suggests that the largest earthquakes of the sequence occurred on two different, but adjacent, fault segments. The first (Event 1, on May 23) occurred along the central fault segment and was followed 28 days later by the second (Event 2, on June 20) along a western fault segment. Finally, 61 days later another smaller earthquake (Event 3) occurred along another fault, east of Event 1.

Tides and the evolution of the Earth—Moon system

Abstract: Summary. A model of the tides in a hemispherical ocean is used to investigate the effect of changes in the Earth's rotation rate on the power dissipated by the ocean tides. The results obtained are then used in an idealized astronomical model to investigate how they affect the history of the Earth—Moon system. Using the tidal model it is found that at rotation rates higher than that of the present Earth, the power dissipated by the semi-diurnal tides in the ocean drops off rapidly as a result of the increased tidal frequency. Thus if the Earth's rotation rate is doubled from its present value, then the rate of energy dissipation in the ocean is reduced to approximately one-third of its present value and the tidal torque is reduced by a factor of about 6. The present value for secular acceleration of the Moon, calculated from the results of the tidal model is -30.5 arcsec century-2. Using this value in the astronomical model, which has the Moon and Sun in circular orbits above the equator, and assuming that the tidal torque is independent of the tidal frequency, the Gerstenkorn event is predicted to have occurred 1.3 × 109 yr ago. When the astronomical model is run with a torque determined at all times from the tidal model, the reduction in the energy dissipated early in the history of the system, leads to a Gerstenkorn date of 5.3 × 109 yr ago. However, dissipation within the solid earth is found to be important early in the history of the system and when this effect is included it gives a date for the Gerstenkorn event of 3.9 × 109 yr ago.

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

Abstract: 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.

Instabilities of fluid conduits in a flowing earth — are plates lubricated by the asthenosphere?

Abstract: Summary. A laboratory and theoretical study of the stability of conduits of buoyant fluid in a viscous shear flow has been conducted. The object of the study is to explain the formation of discrete islands in island chains such as the Hawaiian Emperor seamount chain, and to investigate a new method by which the variation of shear with depth in the mantle may be determined. The conduits were made by injecting oil into a more viscous oil of greater density. Initially a growing chamber of lower viscosity oil formed near the injector, but when the chamber got sufficiently large it rose as a buoyant spheroid. Behind this trailed a vertical cylindrical conduit through which fluid could continue to rise to the surface as long as the source continued. If the more viscous fluid was sheared laterally the conduit was gradually rotated to a more horizontal position. The diameter of the conduit increased with time due to a decreasing component of gravitational force along the axis of the conduit. When the conduit was tilted to more than 60" with the vertical, it began to go unstable by developing bumps which ultimately initiated a new chamber which rose to a new spot. In addition, if the Reynolds number of the conduit was greater than approximately ten, an axisymmetric wavy instability appeared in the walls of the conduit and the conduit had to be tilted less before a new chamber was initiated. If shear under the Pacific plate has to tilt buoyant mantle plumes to as much as 60" to form the relatively regular island chains associated with hot spots, most of the shear would be found in a zone with a vertical extent of less than 200 km.

Crustal structure and isostatic compensation near the Kane fracture zone from topography and gravity measurements—I. Spectral analysis approach

Abstract: Summary. Six gravity and bathymetry profiles perpendicular to the Kane fracture zone, each more than 300 km long, were gathered to study the variation in crustal structure in the vicinity of a major fracture zone and the gravitational edge effect at the contact between lithosphere of two different ages. A spectral analysis of the gravity and bathymetric series as a function of wavelength shows that the gravitational edge effect is only significant at the longest wavelengths. For remaining wavelengths the admittance, the ratio of the amplitude of the gravity anomaly to the amplitude of the bathymetry, is best explained by a model of isostasy in which topographic loads are partially supported by the flexural rigidity of an elastic plate, about 6 km in thickness. After subtracting the gravitational attraction of the bathymetry and its compensation, substantial isostatic anomalies remain. We interpret these anomalies as being caused by variations in crustal thickness which have little correlation with surface topography, except at very long wavelengths. The apparent crustal thickness varies by as much as a factor of 2, but there is no evidence indicating systematic thinning of the crust beneath the fracture zone. Our data do suggest that such density variations within the plate are also compensated by the isostatic response of an elastic plate but with very different effect from those at the surface. This indicates that there are two different modes of crustal formation with different gravity and topographic signatures: effusive volcanism which loads the surface of the elastic plate producing both topographic relief and coherent gravity anomalies, and intrusive volcanism or underplating producing gravity anomalies but little topographic relief.

Modelling the effect of atmospheric pressure variations on gravity

Abstract: Summary. A model is developed to describe the effects of local and global atmospheric pressure fluctuations on local gravity. The calculated admittance of gravity to the pressure tides S1-S4 at Pinon Flat, California is compared to those measured using the superconducting gravimeter. The theoretical and measured admittances are in good agreement for the S3 and S4 tides. The difference between theory and observation at S2 can probably be explained by the ocean tide at that frequency while the discrepancy at S1 remains unexplained. Techniques for the removal of random pressure variations from gravity records are described. Using statistics derived from spherical harmonic decompositions of the Earth's pressure field, it is shown that more than 80 per cent of the pressure induced gravity variations should be removed from a gravity record by employing a single barometer and least-squares procedure. It is further shown that adding a ring of barometers should increase the effectiveness to about 90 per cent. The amount of barometric pressure ‘noise’ which remains after subtracting the simultaneous record of two gravimeters is calculated as a function of their separation and indicates that significantly less noise is present in the difference than in the individual records for separations of up to 17° of arc.

Tectonic history from vitrinite reflectance

Abstract: Summary. The degree of organic metamorphism of carbonaceous matter is expressed in terms of the reflectance of vitrinite. Vitrinite reflectance is a function of temperature and time. A model relating vitrinite reflectance to temperature and time is proposed from published vitrinite reflectance—temperature—time nomograms. A plot of the logarithm of vitrinite reflectance versus depth gives a linear curve (for vitrinite reflectance greater than 0.3 per cent) in a sedimentary basin which has had a constant geothermal gradient throughout its tectonic history; the geothermal gradient (°C km−1) is equal to the slope of the curve multiplied by 194.8. The model is also applied to sedimentary basins with decreasing geothermal gradient with time (i.e. cooling continental-margin basins). The vitrinite reflectance model is demonstrated to be consistent with observed reflectance data and tectonic information from the Sydney, Bowen-Surat and Gippsland basins in eastern Australia.