The frozen-flux hypothesis for the Earth's liquid core assumes that convective terms dominate diffusive terms in the induction equation governing the behaviour of the magnetic field at the surface of the core. While highly plausible on the basis of estimates of physical parameters, the hypothesis has been questioned in recent work by Bloxham, Gubbins & Jackson (1989), who find it to be inconsistent with their field models for most of the century. To study this question we improve the method of Constable. Parker & Stark (1993), which tests the consistency of magnetic observations with the hypothesis by constructing simple, flux-conserving core-field models fitting the data al pairs of epochs. We introduce a new approach that fixes the patch configurations at each of the two epochs before inversion, so that each configuration is consistent with its respective data set but possesses the same patch topology. We expand upon the inversion algorithm, using quadratic programming to maintain the proper flux sign within patches; the modelling calculations are also extended to include data types that depend non-linearly on the model.
Every test of a hypothesis depends on the characterization of the observational uncertainties; we undertake a thorough review of this question. For main-field models, the primary source of uncertainty comes from the crustal field. We base our analysis on one of Jackson's (1994) statistical models of the crustal magnetization, adjusted to bring it into better conformity with our data set. The noise model permits us to take into account the correlations between the measurements and requires that a different weighting be given to horizontal and vertical components. It also indicates that the observations should be fit more closely than has been the practice heretofore. We apply the revised method to Magsat data from 1980 and survey and observatory data from 1915.5, two data sets believed to be particularly difficult to reconcile with the frozen-flux hypothesis. We compute a pair of simple, flux-conserving models that fit the averaged data from each epoch. We therefore conclude that present knowledge of the geomagnetic fields of 1980 and 1915.5 is consistent with the frozen-flux hypothesis.
Resonant coupling between the Earth and the atmosphere at frequencies where the solid Earth modes overlap the fundamental modes of the atmosphere allows for the triggering of oscillatory acoustic perturbations by ground excitation and vice-versa. Here, we describe oscillatory perturbations observed in the solid Earth (from volumetric borehole strainmeter data) and in the atmosphere (from GPS-derived
ionospheric Total Electron Content) following the July~13, 2003,
Soufri\`ere Hills Volcano explosion (Montserrat, Lesser Antilles).
Spectral analysis shows an amplitude peak at 4~mHz for both datasets, with similar waveforms and signal duration. Using a normal mode summation technique, we show that both signals are explained by a single explosive source in the atmosphere. Similarities in waveforms, in particular a double wave train also reported after several other explosion-triggered atmospheric perturbations, result from the superposition of the dominant (fundamental) atmospheric modes that trigger resonant coupling with the solid Earth around 4 mHz.
We report palaeointensity estimates obtained from three Oligocene volcanic sections from the Kerguelen Archipelago (Mont des Ruches, Mont des Tempetes, and Mont Rabouillere). Of 402 available samples, 102 were suitable for a palaeofield strength determination after a preliminary selection, among which 49 provide a reliable estimate. Application of strict a posteriori criteria make us confident about the quality of the 12 new mean-flow determinations, which are the first reliable data available for the Kerguelen Archipelago. The Virtual Dipole Moments (VDM) calculated for these flows vary from 2.78 to 9.47 10e22 Am2 with an arithmetic mean value of 6.15+-2.1 10e22 Am2. Compilation of these results with a selection of the 2002 updated IAGA palaeointensity database lead to a higher (5.4+-2.3 10e22 Am2) Oligocene mean VDM than previously reported, identical to the 5.5+-2.4 10e22 Am2 mean VDM obtained for the 0.3-5 Ma time window. However, these Kerguelen palaeointensity estimates represent half of the reliable Oligocene determinations and thus a bias toward higher values. Nonetheless, the new estimates reported here strengthen the conclusion that the recent geomagnetic field strength is anomalously high compared to that older than 0.3 Ma.
We show that it is possible to capture the oscillatory ground motion induced
by the Tohoku-Oki event for periods ranging from 3 to 100s using Precise Point
Positioning (PPP). We find that the ground motions of the sedimentary basins of
Japan were large (respectively > 0.15m/s and >0.15m/s2 for velocity and
acceleration) even for periods larger than 3s. We compare geodetic observables
with a Ground Motion Prediction Equation (GMPE) designed for Japan seismicity
and find that the Spectral Acceleration (SA) is well estimated for periods
larger than 3s and distances ranging from 100 to 500km. At last, through the
analysis of the displacement attenuation plots, we show that the 2011
Tohoku-Oki event is likely composed of multiple rupture patches as suggested
before by time-reversal inversions of seismic data.
When a seismic record containing multiple sets of world-circling surface waves generated by a major earthquake is auto-correlated, the resulting time function is composed of groups of correlated waves whose phase delay functions are proportional to the difference between the corresponding epicentral distances. Phase information sufficient to calculate the dispersion of waves which travelled exactly one Earth circumference is available from that portion of the auto-correlogram related to the differential distance of interest. This new method also features an enhanced signal to noise ratio because of the superposition of these correlated waves and the simultaneous cancellation of uncorrelated random noise.
The auto-correlation method has been applied to the measurement of phase and group velocities of Rayleigh and Love waves for two great circle paths characterized by similar oceanic and continental portions (two-thirds and one-third, respectively) and by negligible tectonic segments. For Path I, three-component recordings were analysed for two Australian stations of the World Wide Standard Seismograph Network which were collinear with respect to the Kurile Islands earthquake of 1963 October 13. The Matsushiro Observatory vertical component recording of the 1960 May 22 Chilean shock was used for Path II. Phase velocities derived from these auto-correlograms were compared with those derived from the spectral peaks of the corresponding periodograms. The data for the auto-correlograms are more reliable at shorter periods, while spectral analysis leads to better results at the longer periods.
The estimated error of measurement for the trigonometrically smoothed phase velocities of Rayleigh and Love waves is 0.003 km s⁻¹ in the period range from 180 s to 450 s. The total period interval for these new measurements extends from 100 s to 900 s for both types of waves.
An important test of the correctness of the entire set of data processing operations is performed by the comparison of group velocities derived from the trigonometrically smoothed free period and phase velocity data with velocities directly measured by the multiple filter technique. The discrepancies between the group velocities determined by these two methods are usually of the order of 0.02 km s⁻¹ or less.
A number of free periods of the first and second spheroidal overtones were found, using a statistical approach which involved the summation of information from the spectral analyses of five seismograms. The observed higher mode phase velocities, with the exception of the gravest orders of the first overtone, are similar to dispersion curves for a spherical non-rotating Gutenberg—Bullen A′ model.
A number of features are common to the deviations of trigonometrically smoothed Rayleigh wave phase velocities derived from (a) the filtered auto-correlograms, (b) the corresponding periodograms, and (c) the free periods compiled by Pekeris in 1966, when these data are subtracted from values calculated for the non-rotating spherical Gutenberg—Bullen A′ Earth model. The deviations are negative for T > 500 s, slightly positive for 370 < T < 500 s, and again negative for T < 370 s. A negative minimum of ≃ 0.025 km s⁻¹ occurs for T = 250 s, and the present measurements indicate a local decrease in the negative deviations near 180 s. Rayleigh wave group velocity deviations are positive for T > 450 s, and are generally negative for shorter periods with a sharp minimum of ≃ 0.08 km s⁻¹ near 325 s and a local maximum near 225 s. Deviations of the trigonometrically smoothed Love wave phase velocities are negative for T > 350 s and positive for T < 350 s, rising to approximately 0.06 km s⁻¹ near 150 s. The corresponding group velocity deviations change from negative to positive as T becomes less than 500–600 s; they then increase continually, reaching ≃ 0.1 km s⁻¹ near 250 s and remaining near this value for periods as short as 100 s.
The deviations found for T > 225 s may well be world-wide phenomena which indicate that revisions will be required at corresponding depths within the Earth, taking proper account of the required corrections for ellipticity and rotation discussed by Dahlen in 1968. Shear velocities lower than those of the Gutenberg distribution will be needed at depths in the vicinity of 200–500 km, but alterations of both signs may be required at other depths when all of the data are considered. Short period dispersion, group velocities, overtone measurements and body wave observations should prove useful for this task.
The problem of determining the magnetic field originating in the earth's core in the presence of remanent and induced magnetization is considered. The effect of remanent magnetization in the crust on satellite measurements of the core magnetic field is investigated. The crust as a zero-mean stationary Gaussian random process is modelled using an idea proposed by Parker (1988). It is shown that the matrix of second-order statistics is proportional to the Gram matrix, which depends only on the inner-products of the appropriate Green's functions, and that at a typical satellite altitude of 400 km the data are correlated out to an angular separation of approximately 15 deg. Accurate and efficient means of calculating the matrix elements are given. It is shown that the variance of measurements of the radial component of a magnetic field due to the crust is expected to be approximately twice that in horizontal components.
A global estimate of the absolute oceanic general circulation from a geostrophic inversion of in situ hydrographic data is tested against and then combined with an estimate obtained from TOPEX/POSEIDON altimetric data and a geoid model computed using the JGM-3 gravity-field solution. Within the quantitative uncertainties of both the hydrographic inversion and the geoid estimate, the two estimates derived by very different methods are consistent. When the in situ inversion is combined with the altimetry/geoid scheme using a recursive inverse procedure, a new solution, fully consistent with both hydrography and altimetry, is found. There is, however, little reduction in the uncertainties of the calculated ocean circulation and its mass and heat fluxes because the best available geoid estimate remains noisy relative to the purely oceanographic inferences. The conclusion drawn from this is that the comparatively large errors present in the existing geoid models now limit the ability of satellite altimeter data to improve directly the general ocean circulation models derived from in situ measurements. Because improvements in the geoid could be realized through a dedicated spaceborne gravity recovery mission, the impact of hypothetical much better, future geoid estimates on the circulation uncertainty is also quantified, showing significant hypothetical reductions in the uncertainties of oceanic transport calculations. Full ocean general circulation models could better exploit both existing oceanographic data and future gravity-mission data, but their present use is severely limited by the inability to quantify their error budgets.
Gravity anomalies over the Alps and the Molasse Basin are examined, focusing on the relationship between the anomalies and the tectonic processes beneath the region. Bouguer gravity anomalies measured in France, Germany, Italy, and Switzerland are analyzed. No large isostatic anomalies are observed over the Alps and an elastic model is unable to account for gravity anomalies over the Molasse Basin. These results suggest that the dynamic processes that flexed the European plate down, forming the Molasse Basin and building the Alpine chain, have waned. It is proposed that the late Cenozoic uplift of the region may be due to a diminution or termination of downwelling of mantle material.
Many Ground Penetrating Radar (GPR) profiles acquired in dry aeolian
environment have shown good reflectivity inside present-day dunes. We show that
the origin of this reflectivity is related to changes in grain size
distribution, packing and/or grain shape in a sandy material. We integrate
these three parameters into analytical models for bulk permittivity in order to
predict the reflections and the velocity of GPR waves. We consider two GPR
cross-sections acquired over Aeolian dunes in the Chadian desert. The 2D
migration of GPR data suggests that dunes contain different kinds of bounding
surfaces. We discuss and model three kinds of reflections using reasonable
geological hypothesis about Aeolian sedimentation processes. The propagation
and the reflection of radar waves are calculated using the 1D wavelet modelling
method in spectral domain. The results of the forward modelling are in good
accordance with real observed data.
We carried out a detailed and continuous paleomagnetic sampling of the reversed to normal geomagnetic transition recorded by some 60 consecutive flow units near the base of the Lesotho Basalt (183 1 Ma). After alternating field or thermal cleaning the directions of remanence are generally well clustered within flow units. In contrast, the thermal instability of the samples did not allow to obtain reliable paleointensity determinations. The geomagnetic transition is incompletely recorded due to a gap in volcanic activity attested both by eolian deposits and a large angular distance between the field directions of the flows underlying or overlying these deposits. The transition path is noticeably different from that reported in the pioneer work of van Zijl et al. (1962). The most transitional Virtual Geomagnetic Poles are observed after the volcanic hiatus. Once continents are replaced in their relative position 180 Ma ago, the post-hiatus VGP cluster over Russia. However, two successive rebounds from that cluster are found, with VGP reaching repeatedly Eastern Asia coast. Thus, the VGP path is not narrowly constrained in paleolongitude. The decrease in intensity of magnetization as the field deviates from the normal or reversed direction suggests that the decrease in field magnitude during the reversal reached 80-90%. We conclude that although the reversal is of a dipole of much weaker moment than that which existed on average during Cenozoic time, the characteristics of the reversing geodynamo seem to be basically similar. Comment: Paper No GD124 submitted to Geophysical Journal International. Received in original form 20/01/2003, accepted 09/04/2003
Over the southern African region the geomagnetic field is weak and changes rapidly. For this area series of geomagnetic field measurements exist since the 1950s. We take advantage of the existing repeat station surveys and observatory annual means, and clean these data sets by eliminating jumps and minimising external field contributions in the original time series. This unique data set allows us to obtain a detailed view of the geomagnetic field behaviour in space and time by computing a regional model. For this, we use a system of representation similar to harmonic splines. Initially, the technique is systematically tested on synthetic data. After systematically testing the method on synthetic data, we derive a model for 1961 to 2001 that gives a detailed view of the fast changes of the geomagnetic field in this region. Comment: submitted to GJI
Shear deformation of partially molten rock in laboratory experiments causes
the emergence of melt-enriched sheets (bands in cross-section) that are aligned
at about 15-20 degrees to the shear plane. Deformation and deviatoric stress
also cause the coherent alignment of pores at the grain scale. This leads to a
melt-preferred orientation which may give rise to an anisotropic permeability.
Here we develop a simple, general model of anisotropic permeability in
partially molten rocks. We use linearised analysis and nonlinear numerical
solutions to investigate its behaviour under simple shear deformation. In
particular, we consider implications of the model for the emergence and angle
of melt-rich bands. Anisotropic permeability affects the angle of bands and, in
a certain parameter regime, it can give rise to low angles consistent with
experiments. However, the conditions required for this regime have a narrow
range and are unlikely to be met by experiments. Although anisotropic
permeability may shape the behaviour of partially molten rocks, it is not the
primary control on band angles observed in experiments.
Microphones and seismographs were co-located in arrays on Skidaway Island, Georgia, for the launchings of Apollo 13 and 14, 374 km to the south. Simultaneous acoustic and seismic waves were recorded for both events at times appropriate to the arrival of the acoustic waves from the source. The acoustic signal is relatively broadband compared to the nearly monochromatic seismic signal; the seismic signal is much more continuous than the more pulse-like acoustic signal; ground loading from the pressure variations of the acoustic waves is shown to be too small to account for the seismic waves; and the measured phase velocities of both acoustic and seismic waves across the local instrument arrays differ by less than 6 per cent and possibly 3 per cent if experimental error is included. It is concluded that the seismic waves are generated by resonant coupling to the acoustic waves along some 10 km of path on Skidaway Island.
Alfvén waves propagate in electrically conducting fluids in the presence of a magnetic field. Their reflection properties depend on the ratio between the kinematic viscosity and the magnetic diffusivity of the fluid, also known as the magnetic Prandtl number Pm. In the special case, Pm = 1, there is no reflection on an insulating, no-slip boundary, and the incoming wave energy is entirely dissipated in the boundary layer.
We investigate the consequences of this remarkable behaviour for the numerical modelling of torsional Alfvén waves (also known as torsional oscillations), which represent a special class of Alfvén waves, in rapidly rotating spherical shells. They consist of geostrophic motions and are thought to exist in the fluid cores of planets with internal magnetic field. In the geophysical limit Pm ≪ 1, these waves are reflected at the core equator, but they are entirely absorbed for Pm = 1. Our numerical calculations show that the reflection coefficient at the equator of these waves remains below 0.2 for Pm ≥ 0.3, which is the range of values for which geodynamo numerical models operate. As a result, geodynamo models with no-slip boundary conditions cannot exhibit torsional oscillation normal modes.
Approximately one year's worth of altimeter-derived sea-surface heights are compared with global sea-level pressure fields to verify the open ocean inverted barometer response (-1 cm mb-1). When pressure is fit to the sea-surface height along individual altimeter tracks, the response is found to be only 60-70% of the theoretical response or approximately -0.6 to 0.7 cm mb-1. Fits at fixed geographic locations show a clear dependence on latitude. There is a steady decrease in the absolute value of the regression coefficient between 70° and 20°, and then an abrupt increase again closer to the equator. A simple error analysis demonstrates that errors in the pressure data would reduce the along-track regression values, as is observed, and could produce a similar latitude dependence. But, the errors are unlikely to be large enough to explain the entire departure from inverted barometer. We estimate that pressure errors are apt to perturb the along-track track results by no more than about 0.1-0.2 cm mb-1. -from Authors
High-density (about 2-km profile spacing) Geosat/GM altimetry profiles were obtained for Antarctic waters (6-deg S to 72 deg S) and converted to vertical gravity gradient, using Laplace's equation to directly calculate gravity gradient from vertical deflection grids and Fourier analysis to construct gravity anomalies from two vertical deflection grids. The resultant gravity grids have resolution and accuracy comparable to shipboard gravity profiles. The obtained gravity maps display many interesting and previously uncharted features, such as a propagating rift wake and a large 'leaky transform' along the Pacific-Antarctic Rise.
The phase lag by which the earth's body tide follows the tidal potential is estimated for the principal lunar semidiurnal tide M(sub 2). The estimate results from combining recent tidal solutions from satellite tracking data and from Topex/Poseidon satellite altimeter data. Each data type is sensitive to the body-tide lag: gravitationally for the tracking data, geometrically for the altimetry. Allowance is made for the lunar atmospheric tide. For the tidal potential Love number kappa(sub 2) we obtain a lag epsilon of 0.20 deg +/- 0.05 deg, implying an effective body-tide Q of 280 and body-tide energy dissipation of 110 +/- 25 gigawatts.
We use analytical examples and asymptotic forms to examine the mathematical
structure and physical meaning of the seismic cross correlation measurement. We
show that in general, cross correlations are not Green's functions of medium,
and may be very different depending on the source distribution. The modeling of
noise sources using spatial distributions as opposed to discrete collections of
sources is emphasized. When stations are illuminated by spatially complex
source distributions, cross correlations show arrivals at a variety of time
lags, from zero to the maximum surface-wave arrival time. Here, we demonstrate
the possibility of inverting for the source distribution using the energy of
the full cross-correlation waveform. The interplay between the source
distribution and wave attenuation in determining the functional dependence of
cross correlation energies on station-pair distance is quantified. Without
question, energies contain information about wave attenuation. However, the
accurate interpretation of such measurements is tightly connected to the
knowledge of the source distribution.
We report a survey carried out on basalt flows from Amsterdam Island in order to check the presence of intermediate directions interpreted to belong to a geomagnetic field excursion within the Brunhes epoch, completing this paleomagnetic record with paleointensity determinations and radiometric dating. The directional results corroborate the findings by Watkins and Nougier (1973) : normal polarity is found for two units and an intermediate direction, with associated VGPs close to the equator, for the other two units. A notable result is that these volcanic rocks are well suited for absolute paleointensity determinations. Fifty percent of the samples yields reliable intensity values with high quality factors. An original element of this study is that we made use of the PTRM-tail test of Shcherbakova et al. (2000) to help in the interpretation of the paleointensity measurements. Doing thus, only the high temperature intervals, beyond 400 degres C, were retained to obtain the most reliable estimate of the strength of the ancient magnetic field. The normal units yield Virtual Dipole Moments (VDM) of 6.2 and 7.7 10e22 Am2 and the excursional units yield values of 3.7 and 3.4 10e22 Am2. These results are quite consistent with the other Thellier determinations from Brunhes excursion records, all characterized by a decrease of the VDM as VGP latitude decreases. 40Ar/39Ar isotopic age determinations provide an estimate of 26+-15 Kyr and 18+-9 Kyr for the transitional lava flows, which could correspond to the Mono Lake excursion. However, the large error bars associated with these ages do not exclude the hypothesis that this event is the Laschamp.
Progressive deformation of upper mantle rocks via dislocation creep causes
their constituent crystals to take on a non-random orientation distribution
(crystallographic preferred orientation or CPO) whose observable signatures
include shear-wave splitting and azimuthal dependence of surface wave speeds.
Comparison of these signatures with mantle flow models thus allows mantle
dynamics to be unraveled on global and regional scales. However, existing
self-consistent models of CPO evolution are computationally expensive when used
in 3-D and/or time-dependent convection models. Here we propose a new method,
called ANPAR, which is based on an analytical parameterisation of the
crystallographic spin predicted by the second-order (SO) self-consistent
theory. Our parameterisation runs approximately 2-3 x 10^4 times faster than
the SO model and fits its predictions for CPO and crystallographic spin with a
variance reduction > 99%. We illustrate the ANPAR model predictions for three
uniform deformations (uniaxial compression, pure shear, simple shear) and for a
corner-flow model of a spreading ridge.
The vast majority of the microearthquakes recorded occurred to the east: on the Huaytapallana fault in the Eastern Cordillera or in the western margin of the sub-Andes. The sub-Andes appear to be the physiographic province subjected to the most intense seismic deformation. Focal depths for the crustal events here are as deep as 50 km, and the fault plane solutions, show thrust faulting on steep planes oriented roughly north-south. The Huaytapallana fault in the Cordillera Oriental also shows relatively high seismicity along a northeast-southwest trend that agrees with the fault scarp and the east dipping nodal plane of two large earthquakes that occurred on this fault in 1969. The recorded microearthquakes of intermediate depth show a flat seismic zone about 25 km thick at a depth of about 100 km. This agrees with the suggestion that beneath Peru the slab first dips at an angle of 30 deg to a depth of 100 km and then flattens following a quasi-horizontal trajectory. Fault plane solutions of intermediate depth microearthquakes have horizontal T axes oriented east-west.
Equatorial atmospheric angular momentum (AAM) excitation functions and polar motion excitation functions (derived by Kalman filtering Very Long Baseline Interferometry polar motion estimates) are compared with the times of 1984-mid-1988 large earthquakes (magnitude greater than or equal to 7.5). There is a moderate correlation between times of large earthquakes and peaks in polar motion excitation. A strong correlation exists between the times of large earthquakes and large peaks in equatorial AAM amplitude; such a correlation is evident for six out of the eight large earthquakes occurring over the studied time interval. The AAM results indicate potential for the temporal prediction of large/great earthquakes.
The problem of inferring the speed of sound in a contained spherically symmetric fluid solely from its natural frequencies of vibration is considered. An investigation of the case in which the data consist of the two spectra associated with the angular numbers 0 and 1, suggests the possibility that a one-parameter family of slowness profiles can be constructed. These profiles are compatible with the data, up to first order in the non-uniformity of the fluid. It is conjectured that for other angular numbers, the loss of information increases as the difference between them increases.
Laboratory experiments in which synthetic, partially molten rock is subjected
to forced deformation provide a context for testing hypotheses about the
dynamics and rheology of the mantle. Here our hypothesis is that the aggregate
viscosity of partially molten mantle is anisotropic, and that this anisotropy
arises from deviatoric stresses in the rock matrix. We formulate a model of
pipe Poiseuille flow based on theory by Takei and Holtzman [2009a] and Takei
and Katz . Pipe Poiseuille is a configuration that is accessible to
laboratory experimentation but for which there are no published results. We
analyse the model system through linearised analysis and numerical simulations.
This analysis predicts two modes of melt segregation: migration of melt from
the centre of the pipe toward the wall and localisation of melt into
high-porosity bands that emerge near the wall, at a low angle to the shear
plane. We compare our results to those of Takei and Katz  for plane
Poiseuille flow; we also describe a new approximation of radially varying
anisotropy that improves the self-consistency of models over those of Takei and
Katz . This study provides a set of baseline, quantitative predictions to
compare with future laboratory experiments on forced pipe Poiseuille flow of
partially molten mantle.
Numerical simulations of the 3D MHD-equations that describe rotating
magnetoconvection in a Cartesian box have been performed using the code
NIRVANA. The characteristics of averaged quantities like the turbulence
intensity and the turbulent heat flux that are caused by the combined action of
the small-scale fluctuations are computed. The correlation length of the
turbulence significantly depends on the strength and orientation of the
magnetic field and the anisotropic behavior of the turbulence intensity induced
by Coriolis and Lorentz force is considerably more pronounced for faster
rotation. The development of isotropic behavior on the small scales -- as it is
observed in pure rotating convection -- vanishes even for a weak magnetic field
which results in a turbulent flow that is dominated by the vertical component.
In the presence of a horizontal magnetic field the vertical turbulent heat flux
slightly increases with increasing field strength, so that cooling of the
rotating system is facilitated. Horizontal transport of heat is always directed
westwards and towards the poles. The latter might be a source of a large-scale
meridional flow whereas the first would be important in global simulations in
case of non-axisymmetric boundary conditions for the heat flux.