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.     

Effects of the free surface on shear wavetrains

Summary. The behaviour of shear-waves is of great importance in identifying and investigating seismic anisotropy in the Earth. However, shear wavetrains recorded at the Earth's surface do not always reflect the motion at depth, introducing practical problems of interpretation. Shear wavetrains incident on the surface of an isotropic half-space at angles less than critical (about 35°) are broadly preserved, but at greater angles substantial distortions can occur. For stations situated close to the source, as in local earthquake studies, the local SP phase, a radially polarized precursor to S , may occur. The behaviour at the surface of an anisotropic half-space is further complicated by the divergence of phase and energy propagation vectors. All of these complications suggest that detailed seismogram modelling is essential to any study of shear wave propagation in the Earth, and in particular to investigations of anisotropy-induced shear-wave splitting.     

The Zihuatanejo, Mexico, earthquake of 1994 December 10 (M= 6.6): source characteristics and tectonic implications

An analysis of the Zihuatanejo, Mexico, earthquake of 1994 December 10 ( M = 6.6), based on teleseismic and near-source data, shows that it was a normal-faulting, intermediate-depth ( H = 50 ± 5 km) event. It was located about 30 km inland, within the subducted Cocos plate. The preferred fault plane has an azimuth of 130°, a dip of 79° and a rake of −86°. The rupture consisted of two subevents which were separated in time by about 2 s, with the second subevent occurring downdip of the first. The measured stress drop was relatively high, requiring a Δσ of about a kilobar to explain the high-frequency level of the near-source spectra. A rough estimate of the thickness of the seismogenic part of the oceanic lithosphere below Zihuatanejo, based on the depth and the rupture extent of this event, is 40 km.
This event and the Oaxaca earthquake of 1931 January 15 ( M = 7.8) are the two significant normal-faulting, intermediate-depth shocks whose epicentres are closest to the coast. Both of these earthquakes were preceded by several large to great shallow, low-angle thrust earthquakes, occurring updip. The observations in other subduction zones show just the opposite: normal-faulting events precede, not succeed, updip, thrust shocks. Indeed, the thrust events, soon after their occurrence, are expected to cause compression in the slab, thus inhibiting the occurrence of normal-faulting events. To explain the occurrence of the Zihuatanejo earthquake, we note that the Cocos plate, after an initial shallow-angle subduction, unbends and becomes subhorizontal. In the region of the unbending, the bottom of the slab is in horizontal extension. We speculate that the large updip seismic slip during shallow, low-angle thrust events increases the buckling of the slab, resulting in an incremental tensional stress at the bottom of the slab and causing normal-faulting earthquakes. This explanation may also hold for the 1931 Oaxaca event.     

Source process and tectonic implications of the great 1975 North Atlantic earthquake

Summary. The Atlantic segment of the Africa–Europe plate boundary has usually been interpreted as a transform boundary on the basis of the bathymetric expression of the Gloria fault and dextral strike-slip first-motion mechanisms aligned along the Azores–Gibraltar line of seismicity. The 1975 May 26 earthquake ( M _s=7.9) was assumed to fit into this framework because it occurred in the general area of this line and has a similar first-motion focal mechanism (strike=288°, dip=72°, slip angle=184°). However, several anomalies cast doubt on this picture: the event is abnormally large for an oceanic transform event; a sizeable tsunami was excited; the aftershock area is unusually small for such a large event; and most significantly, the epicentre is 200 km south of the presumed plate boundary. The Rayleigh wave radiation pattern indicates a change in focal mechanism to one with a significant dip-slip component. The short duration of the source time history (20 s, as deconvolved from long-period P -waves), the lack of directivity in the Rayleigh waves, and the small one-day aftershock area suggest a fault length less than 80 km. One nodal plane of the earthquake is approximately aligned with the trace of an ancient fracture zone.
We have compared the Pasadena 1-90 record of the 1975 earthquake to that of the 1941 North Atlantic strike-slip earthquake (200 km to the NNW) and confirmed the large size of the 1941 event ( M =8.2). The non-colinear relationship of the 1975 and 1941 events suggests that there is no well-defined plate boundary between the Azores and Gibraltar. This interpretation is supported by the intraplate nature of both the 1975 event and the large 1969 thrust event 650 km to the east. This study also implies that the largest oceanic strike-slip earthquakes occur in old lithosphere in a transitional tectonic regime.     

Random walk of the Earth's pole related to the Chandler wobble excitation

Summary. The equation governing the polar motion shows that the polar secular drift and the Chandler wobble amplitude are related to each other. In particular, a drift of the mean pole position comes out as a consequence of the maintenance of the Chandler wobble by possible step perturbations of the Earth's inertia tensor.
The minimum excitation functions necessary to explain the Chandler wobble amplitude variations for the period 1901–84 are derived from the Chandler term, with the hypothesis that the excitations follow a uniform random distribution in time. It is shown that they have the statistical properties of the steps of a two-dimensional random walk. These functions are then used to derive, from a statistical simulation, a lower limit of the secular drift which may result from the excitation of the Chandler wobble.
The drift generated by the random walk is of the same order of magnitude as the observed secular drift for the period 1901–84, but their time dependence is different. This indicates that the observed secular drift cannot be explained as the consequence of an excitation of the Chandler wobble by random steps of the Earth's inertia tensor. However, the possible contribution of the Chandler wobble excitation to the polar drift has to be taken into account when other mechanisms, such as lithospheric rebound related to deglaciation, are proposed.     

Effect of 3-D viscoelastic structure on post-seismic relaxation from the 2004 M= 9.2 Sumatra earthquake

The 2004 M = 9.2 Sumatra–Andaman earthquake profoundly altered the state of stress in a large volume surrounding the ∼1400 km long rupture. Induced mantle flow fields and coupled surface deformation are sensitive to the 3-D rheology structure. To predict the post-seismic motions from this earthquake, relaxation of a 3-D spherical viscoelastic earth model is simulated using the theory of coupled normal modes. The quasi-static deformation basis set and solution on the 3-D model is constructed using: a spherically stratified viscoelastic earth model with a linear stress–strain relation; an aspherical perturbation in viscoelastic structure; a 'static' mode basis set consisting of Earth's spheroidal and toroidal free oscillations; a "viscoelastic" mode basis set; and interaction kernels that describe the coupling among viscoelastic and static modes. Application to the 2004 Sumatra–Andaman earthquake illustrates the profound modification of the post-seismic flow field at depth by a slab structure and similarly large effects on the near-field post-seismic deformation field at Earth's surface. Comparison with post-seismic GPS observations illustrates the extent to which viscoelastic relaxation contributes to the regional post-seismic deformation.     

Revised value of the dynamical ellipticity of the Earth

Summary. A new value of the Earth's dynamical ellipticity H , defined as the ratio of the difference between the Earth's polar and mean equatorial moments of inertia to its polar moment of inertia, is derived from the most recent, and accurate, values of the Earth's equinoxial precession, the Earth—Moon mass ratio μ and other appropriate data, and a re-evaluation of the numerical procedures involved. This value is an order of magnitude more accurate than its previous values and yields an equivalent improvement in accuracy in other geodynamical quantities derived from H . The new value is consistent with the new System of Astronomical Constants and the new Geodetic Reference System 1980 and is suitable for use in the many astronomical, geophysical and geodetic applications of H .     

A diurnal resonance in the ocean tide and in the Earth's load response due to the resonant free 'core nutation'

Summary. The luni-solar forced nutations and body tide are believed to be resonant at frequencies near (1 + 1/460) cycle sidereal day⁻¹ as seen from the rotating Earth. This resonance is due to the Earth's rotating, elliptical fluid core. We show here that tides in the open ocean and the Earth's response to those tides must also be resonant at (1 + 1/460) cycle day⁻¹. We examine these resonant oceanic effects on the Earth's nutational motion and on the body tide. Effects on the forced nutations might be as large as 0.002 arcsec at 18.6 yr. The effects on the observed resonance in the body tide are more important. For tidal gravity, for example, the difference between K ₁ and 0 ¹ which is usually used to determine the resonance, can be perturbed by 30 per cent or more due to the oceanic resonance effects.     

Palaeomagnetism of the Lower Ordovician Orthoceras Limestone, St. Petersburg, and a revised drift history for Baltica in the early Palaeozoic

Palaeomagnetic investigation of Lower Ordovician limestone in the vicinity of St. Petersburg yields a pole position at latitude 34.7°N, longitude 59.1°E ( dp / dm =5.7°/6.4°). A probable primary remanence origin is supported by the presence of a field reversal. The limestone carries one other remanent magnetization component associated with a Mesozoic remagnetization event.
An apparent polar wander path is compiled for Baltica including the new result, ranging in age from Vendian to Cretaceous. Ages of the published Lower to mid-Palaeozoic palaeomagnetic pole positions are adjusted in accordance with the timescale of Tucker & McKerrow (1995). The new Arenig result is the oldest of a series of Ordovician and Silurian palaeomagnetic pole positions from limestones in the Baltic region. There are no data to constrain apparent polar wander for the Tremadoc, Cambrian and latest Vendian. If the Fen Complex results, previously taken to be Vendian in age ( c . 565 Ma), are reinterpreted as Permian remagnetizations, an Early Ordovician–Cambrian–Vendian cusp in the polar wander path for Baltica is eliminated. The apparent polar wander curve might then traverse directly from poles for Vendian dykes on the Kola peninsula ( c . 580 Ma) towards our new Arenig pole ( c . 480 Ma). The consequence of this change in terms of the motion of Baltica in Cambrian times is to reduce significantly a rotational component of movement.
The new Arenig pole extends knowledge of Ordovician apparent polar wander an increment back in time and confirms the palaeolatitude and orientation of Baltica in some published palaeogeographies. Exclusion of the Fen Complex result places Baltica in mid- to high southerly latitudes at the dawn of the Palaeozoic, consistent with faunal and sedimentological evidence but at variance with some earlier palaeomagnetic reconstructions.     

Gravitational torque on the inner core and decadal polar motion

A decadal polar motion with an amplitude of approximately 25 milliarcsecs (mas) is observed over the last century, a motion known as the Markowitz wobble. The origin of this motion remains unknown. In this paper, we investigate the possibility that a time-dependent axial misalignment between the density structures of the inner core and mantle can explain this signal. The longitudinal displacement of the inner core density structure leads to a change in the global moment of inertia of the Earth. In addition, as a result of the density misalignment, a gravitational equatorial torque leads to a tilt of the oblate geometric figure of the inner core, causing a further change in the global moment of inertia. To conserve angular momentum, an adjustment of the rotation vector must occur, leading to a polar motion. We develop theoretical expressions for the change in the moment of inertia and the gravitational torque in terms of the angle of longitudinal misalignment and the density structure of the mantle. A model to compute the polar motion in response to time-dependent axial inner core rotations is also presented. We show that the polar motion produced by this mechanism can be polarized about a longitudinal axis and is expected to have decadal periodicities, two general characteristics of the Markowitz wobble. The amplitude of the polar motion depends primarily on the Y ¹₂ spherical harmonic component of mantle density, on the longitudinal misalignment between the inner core and mantle, and on the bulk viscosity of the inner core. We establish constraints on the first two of these quantities from considerations of the axial component of this gravitational torque and from observed changes in length of day. These constraints suggest that the maximum polar motion from this mechanism is smaller than 1 mas, and too small to explain the Markowitz wobble.     

The 2004 May 28 Baladeh earthquake (Mw 6.2) in the Alborz, Iran: overthrusting the South Caspian Basin margin, partitioning of oblique convergence and the seismic hazard of Tehran

We use teleseismic waveform analysis and locally recorded aftershock data to investigate the source processes of the 2004 Baladeh earthquake, which is the only substantial earthquake to have occurred in the central Alborz mountains of Iran in the modern instrumental era. The earthquake involved slip at 10–30 km depth, with a south-dipping aftershock zone also restricted to the range 10–30 km, which is unusually deep for Iran. These observations are consistent with co-seismic slip on a south-dipping thrust that projects to the surface at the sharp topographic front on the north side of the Alborz. This line is often called the Khazar Fault, and is assumed to be a south-dipping thrust which bounds the north side of the Alborz range and the south side of the South Caspian Basin, though its actual structure and significance are not well understood. The lack of shallower aftershocks may be due to the thick pile of saturated, overpressured sediments in the South Caspian basin that are being overthrust by the Alborz. A well-determined earthquake slip vector, in a direction different from the overall shortening direction across the range determined by GPS, confirms a spatial separation ('partitioning') of left-lateral strike-slip and thrust faulting in the Alborz. These strike-slip and thrust fault systems do not intersect within the seismogenic layer on the north side, though they may do so on the south. The earthquake affected the capital, Tehran, and reveals a seismic threat posed by earthquakes north of the Alborz, located on south-dipping thrusts, as well as by earthquakes on the south side of the range, closer to the city.     

The Gulf of Aqaba earthquake swarm of 1983 January-April

Summary. In the period 1983 January 21 -April 20, more than 500 local earthquakes ( M _L≤ 4.85) occurred in the Gulf of Aqaba area between latitudes 29°00'and 29°25'and longitudes 34°30'and 34°45'. Most of the activity including the largest shocks was restricted to the area between latitudes 29°07'and 29° 15'and longitudes 34°33'and 34°42'where the NW Atiya regional dyke crosses the area and is horizontally displaced by NE strike-slip faults. The first-motion directions of four large shocks, including the largest, at both UNJ and HLW stations are in agreement with a strike-slip mechanism at a NE-trending fault in this area. The b value showed a temporal increase with time from 0.43 to 0.69. This, together with other geological and geophysical observations may indicate that subsurface magmatic activity has affected the stressed crustal rocks, thus triggering earthquake activity.
This swarm and historical information indicate that the Gulf of Aqaba-Dead Sea Jordan transform is characterized by both swarm and foreshock-aftershock types of seismic activity and therefore the relatively large proportion of non-seismic slip along the southern part of this transform may actually be higher if swarm-type activities are considered.     

On the latitude of the Sq(H) focus at sunspot minimum

Summary. The latitude of the Sq ( H ) focus along the 0° longitude meridian in the northern hemisphere has been determined for all the quiet days, as determined from the aa indices, for the sunspot minimum years 1963–64–65. It is shown that: (a) most of the large variability of the focus latitude is due to the effect of a superposed northward magnetic field that is present on AQDs and which tends to move the apparent focus latitude poleward in the northern hemisphere, and (b) a smaller equatorward motion is caused by the negative AQD events that occur in the 0830–1330 LT range. When these two classes of days are removed from the data set, the focus latitude is found to be completely contained within the range 36°-48° for the months March-October
with an average value of 41.5 ± 2.3, whilst in winter the range is larger with an average value of 36.7 ± 3.4. However, since the magnitude of the superposed northward field is longitude-dependent, it may be present even on days not classed as AQDs. It is shown that much of the variability in the focus latitude of the normal days along the 0° longitude meridian is caused by variations in the amplitude of the superposed northward field.     

Present-day deformation of the Dauphine Alpine and Subalpine massifs (SE France)

The positions of 20 geodetic points surveyed in 1946-1952 by the Institut Géographique National in the Grenoble area (western Alps) were remeasured in 1993-1994 using GPS. We evaluate the displacements of the common points of the networks between the two surveys, and calculate the strain-rate tensors for different sets of three adjacent points. The significant N70° shortening direction observed at the boundary of the Belledonne and Taillefer massifs suggests that the dextral strike-slip motion between the External Crystalline Massifs (ECM) and the Subalpine domain is still active. Geological evidence suggests that this deformation, which is compatible with the few focal mechanisms available for the area, occurred throughout the late Neogene. Our data also suggest a roughly 3-5 mm yr⁻¹ active shortening concentrated at the external front of the Subalpine chains. This thrust motion results in a principal axis of compression orientated N130°, oblique to the direction of shortening observed in the ECM. This change in direction is also seen in in situ stress measurements. This motion may mark the southward continuation of the active fault observed in the Jura mountains by Jouanne, Ménard & Darmendrail (1995).     

Is the Earth contracting?

The fossil record of the variation of the solar day and the synodic month with geological time is examined for evidence of the steady contraction of the Earth postulated by Lyttleton to explain a discrepancy between the apparent secular accelerations of the Sun and Moon. Data for the Phanerozoic and the Precambrian agree in showing that a change in the Earth's moment of inertia as large as that suggested by Lyttleton is only consistent with the fossil record if the secular change in the gravitational constant Ġ/ G ≥+ 4 × 10^–11/yr. A variation of G of this magnitude appears to be ruled out by a recent analysis of lunar occultation observations utilizing Atomic Time.     

A model for energy dissipation at the mantle—core boundary

Summary. An existing experimentally verified model for energy dissipation in a processing spherical cavity filled with liquid assumed to be in a semirigidized state except for a viscous Ekman boundary layer is applied to the Earth's liquid core to assess energy dissipation magnitudes. Application of the model to the best available Earth data occurs at the derived energy dissipation maximum for the model. Other existing research showing that the Earth's atmosphere appears to adjust to a state of maximum dissipation led to generic models for systems of maximum dissipation. The maximum dissipation mantle—core model with core motion driven by Earth precession alone, coupled to the mantle only by viscous shear stresses, and with a spherical mantle—core boundary leads to energy dissipation rates on the order of 10⁴ times those necessary for an Earth dynamo. The maximum dissipation model also leads to excessive magnetic field drift rates and to excessive retardation of the Earth's rotation rate. Effects of the mantle—core ellipticity and of magnetic field coupling are briefly discussed and are used to help develop a less than maximum dissipation model also driven by precession alone but using the additional coupling to yield a model more consistent with observed phenomena.     

The forced nutations of an elliptical, rotating, elastic and oceanless earth

Summary. We compute the luni-solar forced nutations of an elliptical, rotating, self-gravitating, elastic, hydrostatically prestressed and oceanless earth. Several recent structural models are considered, each possessing a fluid outer core and solid inner core. Complete results are given for the nutation of the 'axis of figure for the Tisserand mean surface' which best represents the observational effects of the Earth's nutational motion. Differences between results for different structural models are observationally insignificant. Differences between our results and Molodensky's are as large as ∼ 0.002 arcsec at six month and at 18.6 yr.     

Core–mantle boundary deformations and J2 variations resulting from the 2004 Sumatra earthquake

The deformation at the core–mantle boundary produced by the 2004 Sumatra earthquake is investigated by means of a semi-analytic theoretical model of global coseismic and postseismic deformation, predicting a millimetric coseismic perturbation over a large portion of the core–mantle boundary. Spectral features of such deformations are analysed and discussed. The time-dependent postseismic evolution of the elliptical part of the gravity field ( J ₂) is also computed for different asthenosphere viscosity models. Our results show that, for asthenospheric viscosities smaller than 10¹⁸ Pa s, the postseismic J ₂ variation in the next years is expected to leave a detectable signal in geodetic observations.     

Geophysical model of the dynamical flattening of the Earth in agreement with the precession constant

The dynamical flattening of the Earth, as observed by geodetic techniques, is different by about 1 per cent from the value associated with the PREM density profile with hydrostatic equilibrium. In this paper, we compute a new dynamical flattening H induced by PREM mean density with hydrostatic equilibrium, to which we add lateral heterogeneities associated with (1) seismic velocity variations observed by tomography and (2) internal boundary topographies. First, we compute mantle circulation associated with the density anomalies derived from a tomography model. The flow-induced boundary deformations are then converted into additional mass anomalies which are added to the tomography model for computing the associated perturbation to the Earth's inertia tensor. Finally, we show that it is possible to obtain a dynamical flattening from the total inertia tensor (i.e. the sum of the PREM inertia tensor and of the perturbation) in agreement with that observed.