Showing papers in "Geophysical Journal International in 1974"

Numerical Modelling of Instantaneous Plate Tectonics

Abstract: Assuming lithospheric plates to be rigid, we systematically invert 68 spreading rates, 62 fracture zones trends and 10^6 earthquake slip vectors simultaneously to obtain a self-consistent model of instantaneous relative motions for eleven major plates. The inverse problem is linearized and solved iteratively by a maximum likelihood procedure. Because the uncertainties in the data are small, Gaussian statistics are shown to be adequate. The use of a linear theory permits (1) the calculation of the uncertainties in the various angular velocity vectors caused by uncertainties in the data, and (2) quantitative examination of the distribution of information within the data set. The existence of a self-consistent model satisfying all the data is strong justification of the rigid plate assumption. Slow movement between North and South America is shown to be resolvable. We then invert the trends of 20 linear island chains and aseismic ridges under the assumptions that they represent the directions of plate motions over a set of hot spots fixed with respect to each other. We conclude that these hot spots have had no significant relative motions in the last 10 My.

The Interpretation of Lava Flow Morphology

Abstract: Summary It is postulated that lavas are non-Newtonian liquids with a yield stress and that it is the yield stress which determines flow dimensions. An appropriate theory was developed for the unconfined flow of ideal Bingham liquids on inclined planes. The occurrence of structures similar to IevCes on lava flows was predicted. The theory was verified by laboratory measurements on flows of suspensions of kaolin. These flows showed similarities to lava flows. Data from lava flows was also found to be in general agreement with the theory which was then used to interpret the shapes of two lunar lava flows. It was possible to estimate yield stresses and flow rates for these lavas. 1. Effects limiting the flow of lava Lava flows show great variations in size, shape and surface features. The final form of a flow must be determined by the physical properties of the lava, its temperature and rate of extrusion and local conditions such as gravitational field strength and topography. The aim of the work presented in this paper is to isolate the parameters which have the greatest effect on flow morphology and to elucidate the relationship between the conditions at the start of a flow and the final form of the flow. At present there is no detailed knowledge of this kind but, were it available, the value of air- and satellite-photographs of lava flows would be greatly enhanced. The hypothesis on which this work is based is that flowing lava is a non-Newtonian liquid and it is its non-Newtonian properties which are mainly responsible for the shapes of flows. If lava were an ideal Newtonian liquid it would flow downhill and would continue to flow even after the supply at the vent had ceased until it ponded in a depression. Furthermore the flow would spread laterally until it was restricted by topography or until surface tension prevented spreading by which time it would be extremely thin. Observations show that lava does not behave like this. Commonly it comes to rest on a slope as soon as the supply of fresh lava ceases and many flow fronts are high and steep although unconfined by topographic features. It is clear that there is some process which limits the flow of lava, brings it to rest on slopes and prevents its lateral spreading. The most obvious and apparently generally accepted process is the solidification of lava due to cooling. For this to be a feasible process the time taken for the development of a strong enough skin to prevent lateral motion must be realistic. The solid skin of a flow experiences an outward force due to the hydrostatic pressure of the lava and this must be balanced by an inward force which is the result of tension in the curved skin. If the skin can withstand the tension the lava will not flow laterally.

On the Penetration of Water into Hot Rock

Abstract: Summary This paper develops a theory for the mechanism of penetration of water into hot rock by considering the simplest possible one-dimensional model. The concept of a cracking front is used to separate the convective regime in cracked porous rock from the conductive boundary layer below it. Rock in the boundary layer cools, shrinks and builds up horizontal tensile stress as resistance to creep rises. Cracking occurs when the tensile stress slightly exceeds the overburden pressure and results in the stable downward propagation of a polygonal pattern of sub-vertical cracks. Further cooling shrinkage opens these cracks to the percolation of water so that the effective bulk permeability is a strong function of both crack spacing and temperature. The critical crack spacing is determined by the competing processes of pattern enlargement through stress relief by favoured cracks and the subdivision of columns due to the radial temperature gradients associated with cooling through the cracks themselves. A rudimentary treatment of the transient creep associated with the thermal contraction of virgin rock suggests cracking temperatures between 800 and 1000 °K at depths of several kilometres and a similar treatment of thermally activated crack propagation produces a relationship between front velocity and crack spacing. That permits an approximate solution of the whole problem, resulting in a formula for front velocity where φ is a fudge factor and the temperatures are: TW—hot hydrothermal, Tφ—overburden cancelling creep stress, T0—sink, T1—original. Maximizing through TW permits the calculation of u and all dependent parameters for any given Tφ, itself close to the cracking temperature. If Tφ= 800 °K, the front velocity is 32m/yr, the crack spacing is 4.8cm and the hot hydrothermal temperature is about 462 °K. The power output of the convecting system is about 5 kWm−2. Downward propagation of the cracked region seems to be limited by static fatigue failure of the columns under stress, some distance behind the front. The qualitative aspects of the model are in general agreement with ridge crest heat-flow and seismic data, though the sheeted dike complex near the surface of new crust is created by rapid cooling of each new dike by water circulation rather than by a process comparable to the one-dimensional model. Subsequent, deeper, water penetration may occur by processes similar to those described in the model.

Gravity Anomalies Seaward of Deep-Sea Trenches and their Tectonic Implications*

Abstract: Summary Studies of free-air gravity anomaly profiles across island arcs show an important belt of positive anomalies seaward of deep-sea trenches. This belt of positive anomalies is called the Outer Gravity High. The Outer Gravity High is well developed seaward of the central and eastern Aleutian, Kuril, Japan, northern Bonin and Philippine Trenches where it correlates with a regional rise in topography of a few hundred metres. The Outer Gravity High can be most satisfactorily explained by a stress system associated with the convergence of lithospheric plates at island arcs. The computed gravity effect of simple models of flexure of an oceanic plate approaching an island arc generally explain both the amplitude and wavelength of the Outer Gravity High. The Outer Gravity High seaward of the central and eastern Aleutian, Kuril, Japan, northern Bonin and Philippine Trenches can be explained by a horizontal compressive stress of the order of a few kilobars acting on the oceanic plate. The Outer Gravity High seaward of the southern Bonin and Mariana Trenches, however, can be explained in the absence of horizontal compressive stresses. These conclusions are consistent with differences in the stress field of island arcs as indicated by the seismicity and regional tectonics of the north-western Pacific. The Outer Gravity High is considered an important part of the regional gravity field of island arcs and the field derived from satellite observations. The close correlation of the Outer Gravity High with regional topography seaward of trenches suggest that the gravity effect of a dense downgoing slab beneath island arcs may be small and confined in lateral extent to the region of the island arc and trench. The prominent positive anomalies in island arc areas derived from satellite observations therefore owe a major part of their existence to causes other than the gravity effect of a dense downgoing slab.

The Galapagos Spreading Centre: Lithospheric Cooling and Hydrothermal Circulation

Abstract: Summary The spatial pattern of cooling near a spreading ridge crest was investigated with a suite of 71 precisely-navigated heat-flow stations on the Galapagos spreading centre, East Pacific, near 86"W longitude. Stations are on crust less than 1.0 My old on which bathymetry and sediment distribution are well known. Values vary from near zero to greater than 30 HFU (10-6 cal cm-2 s-1). The average over the entire region is significantly less than that predicted by theoretical conduction models of a cooling lithosphere. We observe a regular variation of the heat-flow pattern with a wavelength of 6 & 1 km approximately normal to the ridge crest. Heat-flow maxima are characteristically located near faults and local topographic highs. The locations of fields of small sediment mounds, apparently hydrothermal vents, are also restricted to these faulted, elevated areas of high heat flow. Near-axis, bottom water temperature anomalies of several hundredths "C were detected. The low average, the low minima in the heat-flow pattern, and the water temperature anomalies suggest that hydrothermal circulation accounts for approximately 80 per cent of the geothermal heat released near the ridge crest. We conclude that the hydrothermal circulation pattern is controlled by one or more of the following physical properties of the system : highly developed cellular convection, discrete zones of high permeability, variation in the strength of heat sources near the base of the crust, or bottom topography. Our results imply that heat-flow studies near active oceanic ridges will be of most value if they are sufficiently detailed and well navigated to define the systematic small-scale variations that appear to be caused by hydrothermal circulation.

Surface Waves in a Laterally Varying Layered Structure

Abstract: Sum17zur.y A kind of ray theory is developed for surface waves in a layered elastic medium in which there are gradual lateral variations in the thicknesses of the layers and in the elastic parameters characterizing each layer. An approximation equivalent to the JWKB approximation is used, and equations governing the slow variations in amplitude, frequency and wavenumber in a nearly uniform sinusoidal wavetrain are deduced. In the first approximation these equations are found to be those given by Whitham’s average Lagrangian method. An equation governing the slow variation in phase is also deduced. The solution of these equations by the method of characteristics gives ray-tracing equations and an amplitude equation similar to those given by standard ray theory for body waves. The analysis also leads to a straightforward method for finding the total energy flux and energy density of the waves without performing an integration over the depth co-ordinate.

Spatial Power Spectrum of the Main Geomagnetic Field, and Extrapolation to the Core

Abstract: Summary The spatial ‘power’ spectrum of the main geomagnetic field has been estimated for harmonics up to n= 500. It is shown to consist of two components, long wavelengths being dominated by fields originating in the core, and short wavelengths by fields originating in the crust; the cross-over occurs at n≥ 11, a wavelength ≤ 3600 km. The core field is often approximated by a set of spherical harmonic coefficients. It is shown that at present main field coefficients for n≤ 9, and secular variation coefficients for n≤ 6, are not known with significant accuracy. Estimates are made of the standard deviations of the IGRF coefficients, and the standard deviation of the IGRF field deduced. This field is known to about 0.5 per cent at the surface but only to about 10 per cent at the core. Its time variation is known only to about 20 per cent at the surface, and is very uncertain at the core.

A New Method of Determining the Magnitude of the Palaeomagnetic Field: Application to five historic lavas and five archaeological samples

Abstract: Summary A new method for determining the magnitude of the palaeomagnetic field (palaeofield), By has been developed and applied to five historic lavas and five archaeological samples. The palaeofield was determined for four lavas. The fifth gave no result. The palaeofield was determined for all five archaeological samples. The Thellier method had previously been applied to three of these samples and the results are compared. A new method for determining the palaeofield, B*, has been developed. The method has been tested on five recent lavas, that had been extruded in the known geomagnetic field, and on five archaeomagnetic samples of known age. The palaeofield is usually determined by comparing the natural remanent magnetization (NRM) with a laboratory thermoremanent magnetization (TRM) (Thellier 8z Thellier 1959), produced in a known field (Blab). The palaeofield (B,,,), is given by equation (I), which is valid for small constant magnetic fields of up to T (Nagata 1943). Usually the TRM does not have the same coercive force spectrum as the NRM, because of changes that occur during the laboratory heating of the sample when producing the TRM. Therefore the direct comparison of the NRM and the TRM (equation (1)) can produce very large errors. In the new method described in this paper only that part of the coercive force spectrum which has not been altered by the (TRM) heating, is used to determine the palaeofield. Empirically, this always lies in the high coercive force region and is therefore not likely to be affected by viscous components of magnetization. 2. The method The method involves comparing two ARM'S created before and after heating. The comparison permits selection of a coercive force region within which the heating * The IAGA (Kyoto 1973) recommended that values of the geomagnetic field be expressed in terms of B. 1T = lo4 G.

Gravity Anomalies and Flexure of the Lithosphere along the Hawaiian-Emperor Seamount Chain

Abstract: Summary Simple models for the flexure of the lithosphere caused by the load of the Hawaiian-Emperor Seamount Chain have been determined for different values of the effective flexural rigidity of the lithosphere. The gravity effect of the models have been computed and compared to observed free-air gravity anomaly profiles in the vicinity of the seamount chain. The values of the effective flexural rigidity which most satisfactorily explain both the amplitude and wavelength of the observed profiles have been determined. Computations show that if the lithosphere is modelled as a continuous elastic sheet, a single effective flexural rigidity of about 5 x loz9 dyne-cm can explain profiles along the Hawaiian-Emperor Seamount Chain. If the lithosphere is modelled as a discontinuous elastic sheet an effective flexural rigidity of about 2 x lo3' dyne-cm is required. Since the age of the seamount chain increases from about 3 M y near Hawaii to about 70 My near the northernmost Emperor seamount these results suggest there is apparently little decrease in the effective flexural rigidity of the lithosphere with increase in the age of loading. This suggests the lithosphere is rigid enough to support the load of the seamount chain for periods of time of at least several tens of millions of years. Thus the subsidence of atolls and guyots along the chain is most likely to be regional in extent and is unlikely to be caused by an inelastic behaviour of the lithosphere beneath individual seamounts.

A Model for Oceanic Crystal Structure Developed

Abstract: Summary The plastic upward flow of asthenosphere at mid-ocean ridge crests implies a linear basaltic magma chamber at the base of the ocean crust at ridge crests. This in turn implies a mature oceanic crust composed of a unit of lavas and dykes, overlying a unit of isotropic gabbro, formed by upward cooling of the magma chamber, overlying a unit of cumulate gabbros and ultramafics, overlying residual mantle from which the basaltic magma has been removed. Analysis of this structure shows that it is asymmetric, with lavas and cumulates dipping towards the spreading centre, and dykes predominantly chilled away from the spreading centre. Increase in spreading rate leads to an increase in lava dips, to a separation of lavas and dykes into distinct units, to a thinning of the dyke unit, and to a narrowing of individual dykes. Metamorphic facies and seismic layering may, but do not necessarily, correspond with this lithological layering. The degree of rifting of oceanic crust and the depth of the median valley are related to an interplay of spreading rate and viscosity of the rising asthenospheric material. Measurement of such parameters as direction and extent of one-way chilling of dykes, dyke thickness, lava dip, and degree of separation of lavas and dykes, in sequence-type ophiolite complexes should allow the determination of direction and rate of spreading at the mid-ocean ridges at which they were formed. The model implies cogenetic liquid-solid relationships between ocean-floor rocks, and suggests changes in the shape of the liquid-solid phase diagram over the pressure range 0.5–2 kb, as well as extensive development of ocean-floor metamorphic rocks.

Green'sFunction for Lamb'sProblem

Abstract: Summary The complete solution to the three-dimensional Lamb'sproblem, the problem of determining the elastic disturbance resulting from a point force in a half space, is derived using the Cagniard-de Hoop method. In addition, spatial derivatives of this solution with respect to both the source co-ordinates and the receiver co-ordinates are derived. The solutions are quite amenable to numerical calculations and a few results of such calculations are given.

Earth Structure from Free Oscillations and Travel Times

Abstract: An extensive set of reliable gross Earth data has been inverted to obtain a new estimate of the radial variations of seismic velocities and density in the Earth. The basic data set includes the observed mass and moment of inertia, the average periods of free oscillation (taken mainly from the Dziewonski-Gilbert study), and five new sets of differential travel-time data. The differential travel-time data consists of the times of PcP-P and ScS-S, which contain information about mantle structure, and the times of P′_(AB) - P′_(DF) and P′_(BC)-P′_(DF) which are sensitive to core structure. A simple but realistic starting model was constructed using a number of physical assumptions, such as requiring the Adams-Williamson relation to hold in the lower mantle and core. The data were inverted using an iterative linear estimation algorithm. By using baseline-insensitive differential travel times and averaged eigenperiods, a considerable improvement in both the quality of the fit and the resolving power of the data set has been realized. The spheroidal and toroidal data are fit on the average to 0·04 and 0·08 per cent, respectively. The final model, designated model B1, also agrees with Rayleigh and Love wave phase and group velocity data. The ray-theoretical travel times of P waves computed from model B1 are about 0·8s later than the 1968 Seismological Tables with residuals decreasing with distance, in agreement with Cleary & Hales and other recent studies. The computed PcP, PKP, and PKiKP times are generally within 0·5 s of the times obtained in recent studies. The travel times of S computed from B1 are 5–10 s later than the Jeffreys-Sullen Tables in the distance range 30° to 95°, with residuals increasing with distance. These S times are in general agreement with the more recent data of Kogan, Ibrahim & Nuttli, Lehmann, Cleary, and Bolt et al. Model B1 is characterized by an upper mantle with a high, 4·8 km s^(−1), S_n velocity and a normal, 3·33 g cm^(−3), density. A low-velocity zone for S is required by the data, but a possible low-velocity zone for compressional waves cannot be resolved by the basic data set. The upper mantle transition zone contains two first-order discontinuities at depths of 420 km and 671 km. Between these discontinuities the shear velocity decreases with depth. The radius of the core, fixed by PcP-P times and previous mode inversions, is 3485 km, and the radius of the inner core-outer core boundary is 1215 km. There are no other first-order discontinuities in the core model. The shear velocity in the inner core is about 3·5 km s^(−1).

The Tau Method for Inversion of Travel Times-I. Deep Seismic Sounding Data

Abstract: Summary A new method for solving the inverse problem of seismology is described in this paper. The problem is formulated as follows: the travel times of body waves are given at a discrete set of points, and we are required to find in the (V, Y) plane (V being the velocity and Y the depth) the closed area which contains all velocity-depth curves corresponding to the given data. The method is based on the use of the function τ(p) =T(p)–pX(p), p being the ray parameter, T the travel time, and X the epicentral distance. This method has the following advantages: it does not necessarily involve the estimation of p by numerical differentiation of the travel times; and it does not involve any interpolation of the travel-time curve between actual observations. Only two assumptions are made: spherical symmetry of the structure (the absence of horizontal inhomogeneities), and the postulation of a lower limit for the velocity in low velocity zones. The function τ(p) is estimated directly from the observed (Ti, Xi) as a singular solution of the Clairaut equation with free term (T(X)). Application of the method is illustrated using data from deep seismic sounding in Turkmenistan.

An Integral Equation Approach to Three-Dimensional Modelling

Abstract: Summary An integral equation method is used to derive the electromagnetic response of a three-dimensional heterogeneity in a three-layer medium The method consists of replacing the heterogeneity with point dipole scattering currents The kernel of the integral equation is a tensor Green's function which is derived for the three-layer case It is shown how the use of iteration methods and Simpson's rule integration might significantly reduce computing requirements The problem of initial estimates is discussed The method is extended to include the case of a simultaneous conductivity and permeability anomaly

The Scalar Equations of Infinitesimal Elastic-Gravitational Motion for a Rotating, Slightly Elliptical Earth

Abstract: Summary We derive the infinite set of coupled ordinary differential equations over radius that govern the infinitesimal free elastic-gravitational oscillations of a rotating, slightly elliptical Earth with an isotropic perfectly elastic constitutive relation and a hydrostatic prestress field. We show how the symmetries of such a body restrict the most general form of the displacement eigenfunctions. We discuss situations in which finite sets of coupled equations may yield good approximate eigenfunctions and describe the sense in which the solution to such a set approximates the solution of the infinite set. Finally we describe in some detail the equations governing a particular class of finite expansions and show how these may be put in a form convenient for numerical solution. The method used to convert tensor equations to scalar equations is an extension of the generalized surface spherical harmonic expansion of Phinney & Burridge and should be useful in other non spherically-symmetric applications.

Numerical Modelling of Tectonic Flow behind Island Arcs

Abstract: Suniniary High heat flow in marginal basins and island arc volcanism are explained by numerical modelling of flow induced by the downgoing slab. The hypothesis that frictional heating above the slab causes thermal diapirs to rise is mechanically unfeasible since the region above the slab must be fluid enough to convect thermally, yet so viscous that the motion of the slab produces over 2 kilobars of stress. The calculation of induced flow is two-dimensional, time dependent, with a variable viscosity dependent on temperature and pressure. A yield stress was used to approximate fault dislocations. The calculation is very sensitive to the material properties and to localized flow near the base of the interface between the slab and the landward plate. The highest stress occurred at the base of the slab interface. This area ablated creating a narrow channel necessary for separating melt from mostly crystalline mush to establish a source of volcanic magmas. In the marginal basin area, tensile yielding occurred in the plate causing it to thin and raise the heat flow significantly. The yielding continued until a complete rift occurred. Induced flow is, then, a likely explanation for island arc volcanics and high heat flow in marginal basins.

The Galapagos Spreading Centre: A Near-Bottom Geophysical Survey

Abstract: Summary A near-bottom geophysical survey of the Galapagos spreading centre at 86"W shows the highly lineated nature of oceanic crust generated at a fastspreading ridge. The bathymetric relief is dominated by small blocks which tilt slightly away from the spreading centre and which are bounded by inward-facing scarps. This relief is similar to that found on slow-spreading ridges, but on a smaller scale, and when covered with a thin layer of sediments, it looks like typical abyssal hill terrain. The magnetization distribution, sediment pattern and the fine-scale bathymetric structure are used to locate the centre of spreading and the region in which the upper portion of the crust is being formed. Recent volcanic activity is primarily occurring within 2 km of the centre, a region which is nearly sediment-free and which contains a highly magnetized ridge. Possible models of ridge crest mechanics are constrained by these observations over a ridge spreading with a half-rate of 35 mm/yr. There appears to be a small median valley which has a width of 16 km and a depth of 150 m. Most of the near-surface volcanism appears to cease when the rigid blocks are initially faulted apart from the central crustal generation zone at about 2 to 4 km from the centre. The central block is fairly level with a relief which appears to have been formed by constructional volcanism while the rigid blocks on either side of this central one already are tilted slightly outwards and are bounded by inward facing scarps.

On the 'Nearly Diurnal Wobble' of the Earth

Abstract: Summary Serious confusion is evident in the original literature and several review articles from the past decade which have claimed that a second free wobble of the Earth, stemming from gyroscopic coupling with our core fluid, has been detected marginally from latitude or time data The confusion is betrayed even by the recent labelling of that mode as a nearly diurnal wobble In fact such a conceivable free mode, as implied for instance by the analysis of Molodenskii, consists fundamentally of a 460-day retrograde nutation in space of the supposedly misaligned angular momenta of the core and the mantle This slow spatial coning of even the mantle axis has to have an amplitude roughly 460 times greater than that of the associated body-related wobble; a motion as large as that would have been noticed long ago if the recent claims of detection of the wobble were sound Besides helping to rectify that oversight, the present article (i) comments on the somewhat incomplete theories of such a fluid mode in a realistic Earth, (ii) determines that its combined viscous and magnetic time of damping can hardly exceed 103 years, and (iii) estimates the effects of such friction also upon our forced, astronomical nutations In particular, it appears that the kinematic viscosity of the uppermost core fluid cannot exceed lo5 stokes without affecting excessively our observed 186-year principal nutation Furthermore, the tidal deceleration of the spin rate of the Earth must have carried us through an exact annual resonance with the free nutation roughly 200 My ago; however, even such resonant coning would probably have had an amplitude only comparable to that of the above principal nutation

The Structure of the Upper Mantle under the United States from the Dispersion of Rayleigh Waves

Abstract: Summary Seismograms from vertical-component, long-period instruments of the World-Wide Standard Seismographic Network (WWSSN) within the United States have been analysed to determine the dispersion of Rayleigh waves by the two-station method. Phase velocities from fundamental mode Rayleigh waves over the period range 20–250s have been obtained to study the structure of the upper mantle of the continent. The phase velocities show systematic variations in specific sub-regions of the United States. The phase velocities observed along five representative paths have been inverted into sub-surface structural cross-sections by the Hedgehog method. The results of the inversion indicate that there are significant regional variations in S-wave velocities, particularly from the Moho down to about 400km. We make no statement about lateral variations in structure at greater depths. The aseismic south-central part of the continent and the tectonically active western Cordillera are characterized by a well-developed low-velocity channel for S waves in the upper mantle. The north-central United States has dispersion data which are consistent with structures which either have a low velocity channel of marginal properties or no low velocity channel at all; if a channel is present for this region, the velocity contrast with the layers of the mantle above and below it is very small.

Spherical Harmonic Analyses of the Geomagnetic Field for Eight Epochs between 1600 and 1910

Abstract: Summary The data for epochs between 1600 and 1910 in the catalogue of Veinberg and Shibaev have been analysed and two sets of spherical harmonic models of the geomagnetic field have been derived. Two methods are used to overcome the shortage of intensity data for the earlier epochs. In the first set of models the ratios of the harmonic coefficients to gIo are determined using both D and I data. The second set uses assumed values of 8,’ for these epochs. In contrast to previous analyses based on this catalogue, the data are weighted according to the number of original observations contributing to the catalogue mean and allowance is made for the oblateness of the Earth. The dipolar nature of the field in the Pacific region is investigated and the positions of the geomagnetic poles are derived. The variation of the position of the eccentric dipole with time is studied.

The Anelasticity of the Inner Core

Abstract: Summary Spectral ratios of short-period core phases with common source and receiver and with nearly the same ray paths in the mantle have been formed to derive a Q-structure for 1 Hz compressional waves in the inner core. Data from one large array (NORSAR) have been used to extract the relevant phases, including the pairs (PKIKP, PKiKP), (PKIKP, PKP(BC)), (PKIIKP, PKiKP), (PKIIKP, PKKP(BC)). An array is needed in particular to separate PKIKP and PKiKP and to identify PKIIKP. In forming the spectral ratios, techniques like spectraforming and instantaneous spectral analysis have been employed. The data have been inverted using a number of different velocity models. The essential features of the resulting Q-models are the same: Q rises from a value of about 200 near the inner core boundary to about 600 at 400 km depth penetration. Below 450 km depth the Q-structure is not well constrained, but probably is below a value of 2000. It is suggested that the temperature at the inner core boundary is close to the melting point of iron and that partial melting occurs in at least part of the inner core. The low Q-structure greatly affects the amplitudes of phases like PKIIKP and PKJKP. It is verified that PKIIKP is observable only in exceptional cases and arguments are presented that PKJKP is too small to be observed.

Rayleigh Wave Phase Velocities in the Atlantic Ocean

Abstract: Summary The phase velocities of Rayleigh waves are found for many paths in the north Atlantic. The single station technique is used with earthquakes in the Mid-Atlantic Ridge. The major contributor to the error in phase velocity is the uncertainty in epicentral location and origin time. Focal depth and mechanism are sufficiently well controlled for these events that they do not significantly add to the phase velocity error. The resulting uncertainty is ± 0.02 km s−1 for the period range 20-100 s. The ocean is regionalized into ridge and basin. Both ray theory and Rytov's method are used to extract the dispersion characteristics of each region from the observations. Large lateral variations of the basin dispersion suggest a further subdivision. These variations can be explained entirely by variations in sediment thickness. The deduced upper mantle model of the ocean basin is characterized by a shear velocity reversal at 40 km depth with a lid shear velocity of 4.7 km s−1. The lowest shear velocities are centered at a depth of 125 km. The lid shear velocity can be reduced to 4.6 km s−1 only if both the thickness of the lid increases and the density increases. Phase velocities for the Mid-Atlantic Ridge imply that the upper mantle shear velocity under the ridge is significantly lower than that under the ocean basin at depths greater than 20 km.

On the Static Deformation of an Earth Model with a Fluid Core

Abstract: Summary The concept of a purely static deformation of an Earth model, although strictly a highly artificial physical situation, nevertheless provides a useful idealization in certain problems. We derive a computational algorithm which allows one to determine any geophysically observable aspect of the purely static deformation of a non-rotating, spherically symmetric Earth model which has an elastic mantle and a compressible fluid core. In particular, we show how to compute the static perturbation to the density, the gravitational potential, and the fluid pressure at every point within the core, as well as every aspect of the deformation in the solid elastic mantle. Because of the artificiality of the concept of a purely static deformation, the static Lagrangian particle displacement in the fluid core is indeterminate.

Heat Flow in the Aegean Sea

Abstract: Summary Heat flow measurements taken in the Aegean Sea indicate a high heat flow in the northern and central Aegean. Nine stations at which a linear thermal gradient was measured give a mean value of 2-08 HFU. Four stations in the southern Aegean at which the gradient was non-linear gave limits to the heat flow in this area of between 1.0 and 1.6 HFU. Two high values in the north are associated with a deep bathymetric feature and intense magnetic anomalies. The high heat flow in the Aegean Sea is considered to be due to underthrusting of oceanic crust similar to that which occurs in the marginal basins of the north-west Pacific.

The Role of Pigment and Specularite in the Remanent Magnetism of Red Sandstones

Abstract: Summary The origin of the remanent magnetism of red sandstones has been investigated by separating the polycrystalline haematite grains (specularite) from rocks and comparing the properties of the remanent magnetism of the specularite, the residual pigment-quartz separate and the original rock. From the results it is possible to determine the relative importance of the two haematite forms as carriers of the remanent magnetization in different rocks and to suggest probable magnetization processes.

Earthquake Prediction: Modification of the Earth Tide Tilts and Strains by Dilatancy

Abstract: Summary Numerical solutions for the earth tide on a model earth with elastic dilatant crustal inclusions indicate that up to 60 per cent changes in the tilt and strain tides result from a 15 per cent reduction of Vp, the seismic p velocity, in the inclusion. The fractional changes in the tilt and strain tide amplitudes are proportional to the changes in Poisson's ratio and inverse areal bulk modulus of the inclusion and are not proportional to the Vp/Vs ratio. Further, detectable changes in the tidal amplitude will occur to a distance of 1.5 times the typical dimension of the dilatant inclusion. Monitoring the earth tide is therefore suggested as a sensitive and continuous method of earthquake prediction if such dilatancy precedes earthquakes. The time dependence of the tidal signal, due to dilatancy, will be the same as that of the Vp/Vs ratio if the dilatant material is elastic. A search of the tidal strain data from the laser strain meters at the Pinon Flat Geophysical Observatory reveals no evidence of anomalous changes in the tidal signal during the past three years. The limits of detection for changes in the tidal admittance are ±2 per cent for a 696 hr averaging period.

Limits on the Constitution of the Lower Mantle

Abstract: Summary The limits on the constitution of the lower mantle which can be inferred from currently available data are investigated. The density and elasticity of the mantle are compared to those of various model mineral assemblages at zero pressure and at high pressures, the former case using extrapolations of mantle properties. The models are based on equations of state of MgO (periclase), SiO2 (stishovite) and FeO (wustite), and of the Twin Sisters and Mooihoek dunite high-pressure phases. The bounds on the elastic properties of mixtures are discussed. The properties of hypothetical phases denser than their isochemical simple oxide mixtures are estimated relative to those of the oxide mixtures. The uncertainties in all quantities are discussed and the interdependence of some inferred mantle characteristics is considered. The inferred silica content, temperature and phase assemblage are strongly interdependent. The inferred FeO content depends to a small extent on the phase assemblage and temperature corrections and more strongly on the presence of iron in the ‘low spin’ electronic state. Models which best fit the data used range between (1) an oxide mixture, or phase assemblage with similar properties, with pyroxene composition and 9 mole per cent FeO, and (2) a phase assemblage about 5 per cent denser than an isochemical simple oxide mixture with olivine composition and 6 mole per cent FeO. Combining all uncertainties and interdependences allows the FeO content to vary between about 3 and 14 mole per cent, and the temperature to vary beyond the independently estimated bounds of 2000 °K and 6000 °K. The possibilities of an isentropic temperature gradient, chemical homogeneity, or some iron enrichment in the lower mantle relative to the upper mantle are allowed, but not required, by the data.

Elastic Dislocations in a Layered Half-Space—I. Basic Theory and Numerical Methods

Abstract: Summary This paper is the first of a series that will examine the effect of earth structure on earthquake displacement, strain and tilt fields at the Earth's surface. Its purpose is to develop the numerical techniques to be applied in the papers that foliow. A general computational procedure for the evaluation of the integral expressions for the surface displacements due to an arbitrary point dislocation source in a layered medium is described. It is shown to be rapid and inexpensive to use, and its accuracy appears to be entirely adequate for practical purposes.

Microearthquakes on the Galapagos Spreading Centre and the Seismicity of Fast‐Spreading Ridges*

Abstract: Summary Fast-spreading centres such as the East Pacific Rise and the Galapagos spreading centre often show hiatuses hundreds of kilometres in length in WWSSN (World Wide Standardized Seismic Network) recorded seismic activity. Sonobuoys were deployed over a seismically quiet segment of the Galapagos spreading centre to measure the seismicity at close range. During 45 h of reliable recording time we detected an average of 15 microearthquakes per hour with a maximum of 80 microearthquakes in one hour. The events were part of a swarm which occurred within a few kilometres of the ridge crest axis. Magnitudes ranged from m = -0.4 to m = $0.8. Although fast-spreading ridges have few large earthquakes, they may be the sites of significant microearthquake and earthquake swarm activity.

Synthetic Seismogram Computation by Expansion in Generalized Rays

Abstract: Summary The exact formulation of generalized ray theory computations of synthetic seismograms for realistic Earth models is relatively complex and expensive. The expense can be reduced considerably by a proper organization of the computational procedures. The expense is reduced far more dramatically by introducing an approximation of the transmission coefficients and a careful selection of the rays to be included. The incorporation of such procedures leads to programmes which are economically feasible to use as an aid in the interpretation of body waves and near source surface and leaky mode waves.