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.
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.
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.
Isotropic earth models are unable to provide uniform fits to the gross Earth normal mode data set or, in many cases, to regional Love-and Rayleigh-wave data. Anisotropic inversion provides a good fit to the data and indicates that the upper 200km of the mantle is anisotropic. The nature and magnitude of the required anisotropy, moreover, is similar to that found in body wave studies and in studies of ultramafic samples from the upper mantle. Pronounced upper mantle low-velocity zones are characteristic of models resulting from isotropic inversion of global or regional data sets. Anisotropic models have more nearly constant velocities in the upper mantle.
Normal mode partial (Frediét) derivatives are calculated for a transversely isotropic earth model with a radial axis of symmetry. For this type of anisotropy there are five elastic constant. The two shear-type moduli can be determined from the toroidal modes. Spheroidal and Rayleigh modes are sensitive to all five elastic constants but are mainly controlled by the two compressional-type moduli, one of the shear-type moduli and the remaining, mixed-mode, modulus. The lack of sensitivity of Rayleigh waves to compressional wave velocities is a characteristic only of the isotropic case. The partial derivatives of the horizontal and vertical components of the compressional velocity are nearly equal and opposite in the region of the mantle where the shear velocity sensitivity is the greatest. The net compressional wave partial derivative, at depth, is therefore very small for isotropic perturbations. Compressional wave anisotropy, however, has a significant effect on Rayleigh-wave dispersion. Once it has been established that transverse anisotropy is important it is necessary to invert for all five elastic constants. If the azimuthal effect has not been averaged out a more general anisotropy may have to be allowed for.
Longitudinal, seasonal, and altitude-dependent variability of magnetic fields is investigated in equatorial latitudes to determine their effect on the isolation of lithospheric Magsat magnetic anomalies. An estimate of ‘ionospheric effect’ was compiled by averaging the total intensity Magsat anomalies as a function of dip latitudes (called ‘dip-latitude averages’) from dawn and dusk data sets grouped according to longitudes, time (months), and altitudes. Unanticipated seasonal variations were observed in dusk Magsat data over the Indian sector that may contribute to an improved understanding of the equatorial electrojet.
The amplitudes of the dawn dip-latitude averages are small in comparison to the dusk averages and they are of opposite sign as anticipated from the westward and eastward flowing currents at the dip equator at dawn and dusk time, respectively. However, longitudinal variation in the equatorial amplitudes of the dawn diplatitude averages is not entirely consistent with present knowledge of the electrojet field. In the past, dawn Magsat anomalies have been considered to be largely free of ionospheric fields. However, in the preparation of the lithospheric component maps, neglecting to remove the dawn dip-latitude averages from dawn Magsat data set leaves conspicuous E-W trending anomaly artifacts in certain regions of the world. Removal of both the dawn and the dusk dip-latitude averages from their respective data sets substantially improves the agreement between the separately prepared dawn and dusk lithospheric component Magsat maps. Despite the agreement between the resultant lithospheric anomaly maps, dip-latitude averages do appear to contain some contribution from the lithospheric fields. Thus, processing of the data with the aid of the dip-latitude averages unavoidably removes a small degree of E-W oriented lithospheric signal as well.
Adopting the formalism of Parsons and Daly (1983), analytical integral equations (Green's function integrals) are derived which relate gravity anomalies and dynamic boundary topography with temperature as a function of wavenumber for a fluid layer whose viscosity varies exponentially with depth. In the earth, such a viscosity profile may be found in the asthenosphere, where the large thermal gradient leads to exponential decrease of viscosity with depth, the effects of a pressure increase being small in comparison. It is shown that, when viscosity varies rapidly, topography kernels for both the surface and bottom boundaries (and hence the gravity kernel) are strongly affected at all wavelengths.
A two-dimensional FEM is used to investigate the flow driven by the horizontal temperature gradient at a fracture zone and to calculate the resulting geoid and topography anomalies. Using a three-layered viscosity structure for the upper mantle, results are presented for the effects of varying: (1) the viscosity contrast between the fluid layers: (2) the Rayleigh number based on the viscosity of the bottom layer; and (3) the thickness of the low-viscosity channel. Good agreement is obtained with the results of geoid anomalies over the Udintsev fracture zone when the viscosity of the top layer is greater than one order of magnitude less than post-glacial rebound values.
We describe three approaches for computing a gravity signal from a density
anomaly. The first approach consists of the classical "summation" technique,
whilst the remaining two methods solve the Poisson problem for the
gravitational potential using either a Finite Element (FE) discretization
employing a multilevel preconditioner, or a Green's function evaluated with the
Fast Multipole Method (FMM). The methods utilizing the PDE formulation
described here differ from previously published approaches used in gravity
modeling in that they are optimal, implying that both the memory and
computational time required scale linearly with respect to the number of
unknowns in the potential field. Additionally, all of the implementations
presented here are developed such that the computations can be performed in a
massively parallel, distributed memory computing environment. Through numerical
experiments, we compare the methods on the basis of their discretization error,
CPU time and parallel scalability. We demonstrate the parallel scalability of
all these techniques by running forward models with up to $10^8$ voxels on
1000's of cores.
A variety of evidence suggests that at least some hotspots are formed by quasi-cylindrical mantle plumes upwelling from deep in the mantle. Such plumes are modeled in cylindrical, axisymmetric geometry with depth-dependent, Newtonian viscosity. Cylindrical and sheet-like, Cartesian upwellings have significantly different geoid and topography signatures. However, Rayleigh number-Nusselt number systematics in the two geometries are quite similar. The geoid anomaly and topographic uplift over a plume are insensitive to the viscosity of the surface layer, provided that it is at least 1000 times the interior viscosity. Increasing the Rayleigh number or including a low-viscosity asthenosphere decreases the geoid anomaly and the topographic uplift associated with an upwelling plume.
The gravitational potential and field anomalies for thin mass layers are derived using the technique of matched asymptotic expansions. An inner solution is obtained using an expansion in powers of the thickness and it is shown that the outer solution is given by a surface distribution of mass sources and dipoles. Coefficients are evaluated by matching the inner expansion of the outer solution with the outer expansion of the inner solution. The leading term in the inner expansion for the normal gravitational field gives the Bouguer formula. The leading term in the expansion for the gravitational potential gives an expression for the perturbation to the geoid. The predictions given by this term are compared with measurements by satellite altimetry. The second-order terms in the expansion for the gravitational field are required to predict the gravity anomaly at a continental margin. The results are compared with observations.
The geological utility of satellite magnetic observations is limited by orbital altitude variations which may be as large as a few hundred kilometres. This study investigates the use of fast and elegant statistical procedures for altitude normalization and gridding of magnetic anomaly data as an alternative to more commonly used equivalent source inversion procedures involving computationally extensive and complex least-squares matrix methods.
A standard statistical approach for gridding satellite magnetic anomalies is to recompute numerically averaged values from three-dimensionally distributed observations which are within two standard deviations of an initially determined averaged anomaly estimate. the errors of this procedure for geological analysis are investigated using orbital anomaly simulations of lithospheric sources over a spherical earth. the simulations suggest that numerical averaging errors constitute small and relatively minor contributions to the total error-budget of higher orbital estimates (≳400 km), whereas for lower orbital estimates the error of averaging may increase substantially.
A more complex statistical procedure involving least-squares collocation in 3-D is found to produce substantially more accurate anomaly estimates as the elevation of prediction is decreased towards the lithospheric sources. Moreover, 3-D collocation is computationally much more efficient and faster to apply than equivalent source inversion methods for altitude-normalizing and gridding magnetic anomaly data. Application of this procedure to MAGSAT magnetic observations of South America demonstrates its utility for producing accurately gridded magnetic anomalies at constant elevation for geological analysis.
Study of the deviations of P and S travel times from the J-B tables at teleseismic distances has shown that there are regional differences in travel time. Both P and S are early in the central and eastern United States, late in the western United States. The differences have a range of about three seconds for P and eight seconds for S.
It can be deduced from the relation between the travel time residuals (1) that the change in shear velocity is approximately one and one-quarter times the change in P velocity, (2) that the observations imply a difference in Poisson's ratio between the two regions, and (3) that a model in which the shear modulus, μ, alone varies, the compressibility, k, remaining sensibly constant, fits the data best. It can be shown also that the differences between the P travel time residuals and the gravity anomalies in the central and western United States are not consistent with the Birch relation between velocity and density.
Typical geophysical inversion problems are ill-posed, non-linear and non-unique. Sometimes the problem is trans-dimensional, where the number of unknown parameters is one of the unknowns, which makes the inverse problem even more challenging. Detecting the shape of a geophysical object underneath the earth surface from gravity anomaly is one of such complex problems, where the number of geometrical parameters is one of the unknowns. To deal with the difficulties of non-uniqueness, ill-conditioning and nonlinearity, a statistical Bayesian model inference approach is adopted. A reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is proposed to overcome the difficulty of trans-dimensionality. Carefully designed within-model and between-model Markov chain moves are implemented to reduce the rate of generating inadmissible geometries, thus achieving good overall efficiency in the Monte Carlo sampler. Numerical experiments on a 2-D problem show that the proposed algorithm is capable of obtaining satisfactory solutions with quantifiable uncertainty to a challenging trans-dimensional geophysical inverse problem. Solutions from RJMCMC appear to be parsimonious for the given prior, in the sense that among the models satisfactorily represent the true model, models with higher posterior probabilities tend to have fewer number of parameters. The proposed numerical algorithm can be readily adapted to other similar trans-dimensional geophysical inverse applications. Keywords: trans-dimensional geophysical inversion, reversible jump Markov chain Monte Carlo; gravity anomaly.
In this research note, we re-evaluate the mechanism proposed by Wunsch to explain pole tide observations in the North Sea. That mechanism included bottom topography and bottom friction; with a constant drag coefficient and the Sea shallowing to the south, the dynamics yielded an eastward intensification of the tide height reminiscent of observations. Errors subsequently brought to light have left the proposal with uncertain status.
We have found that a general solution to the tide equations is possible without approximation, after slight modification of Wunsch's model. The unknown coefficients of the solution are determined through a boundary condition at the open edge of the Sea which corresponds to forcing by a non-equilibrium pole tide in the adjacent Atlantic. However, although the boundary condition is physically plausible, as a constraint for these tide equations it allows multiple determination of the coefficients. In every case, dissipation by the tidal currents greatly exceeds the total dissipation of Chandler wobble energy. The extreme dissipation and the solution non-uniqueness both reflect the inability of the solution to satisfy the open-boundary condition, and imply that the original tidal equations themselves provide an inadequate description of North Sea dynamics.
The nature of the difficulties suggests an analogy with Stokes' paradox, and implies that resolution of the problem may be achieved by inclusion of inertial terms in the tidal equations.
Natural open joints in rocks commonly present multi-scale self-affine
apertures. This geometrical complexity affects fluid transport and heat
exchange between the flow- ing fluid and the surrounding rock. In particular,
long range correlations of self-affine apertures induce strong channeling of
the flow which influences both mass and heat advection. A key question is to
find a geometrical model of the complex aperture that describes at best the
macroscopic properties (hydraulic conductivity, heat exchange) with the
smallest number of parameters. Solving numerically the Stokes and heat equa-
tions with a lubrication approximation, we show that a low pass filtering of
the aperture geometry provides efficient estimates of the effective hydraulic
and thermal properties (apertures). A detailed study of the influence of the
bandwidth of the lowpass filtering on these transport properties is also
performed. For instance, keeping the information of amplitude only of the
largest Fourier length scales allows us to reach already an accuracy of 9% on
the hydraulic and the thermal apertures.
The geoid is the true physical figure of the Earth, a particular
equipotential surface of the gravity field of the Earth that accounts for the
effect of all subsurface density variations. Its shape approximates best (in
the sense of least squares) the mean level of oceans, but the geoid is more
difficult to determine over continents. Satellite missions carry out distance
measurements and derive the gravity field to provide geoid maps over the entire
globe. However, they require calibration and extensive computations including
integration, which is a non-unique operation. Here we propose a direct method
and a new tool that directly measures geopotential differences on continents
using atomic clocks. General Relativity Theory predicts constant clock rate at
sea level, and faster (resp. slower) clock rate above (resp. below) sea level.
The technology of atomic clocks is on the doorstep of reaching an accuracy
level in clock rate that is equivalent to 1 cm in determining equipotential
surface (including geoid) height. We discuss the value and future applicability
of such measurements including direct geoid mapping on continents, and joint
gravity and geopotential surveying to invert for subsurface density anomalies.
Our synthetic calculations show that the geoid perturbation caused by a 1.5 km
radius sphere with 20% density anomaly buried at 2 km depth in the crust of the
Earth is already detectable by atomic clocks of achievable accuracy. Therefore
atomic clock geopotential surveys, used together with relative gravity data to
benefit from their different depth sensitivities, can become a useful tool in
mapping density anomalies within the Earth.
Gravity inversion allows us to constrain the interior mass distribution of a
planetary body using the observed shape, rotation, and gravity. Traditionally,
techniques developed for gravity inversion can be divided into Monte Carlo
methods, matrix inversion methods, and spectral methods. Here we employ both
matrix inversion and Monte Carlo in order to explore the space of exact
solutions, in a method which is particularly suited for arbitrary shape bodies.
We expand the mass density function using orthogonal polynomials, and map the
contribution of each term to the global gravitational field generated. This map
is linear in the density terms, and can be pseudo-inverted in the
under-determined regime using QR decomposition, to obtain a basis of the affine
space of exact interior structure solutions. As the interior structure
solutions are degenerate, assumptions have to be made in order to control their
properties, and these assumptions can be transformed into scalar functions and
used to explore the solutions space using Monte Carlo techniques. Sample
applications show that the range of solutions tend to converge towards the
nominal one as long as the generic assumptions made are correct, even in the
presence of moderate noise. We present the underlying mathematical formalism
and an analysis of how to impose specific features on the global solution,
including uniform solutions, gradients, and layered models. Analytical formulas
for the computation of the relevant quantities when the shape is represented
using several common methods are included in the Appendix.
A theoretical analysis of the earthquake prediction problem in space-time is presented. We find an explicit structure of the optimal strategy and its relation to the generalized error diagram. This study is a generalization of the theoretical results for time prediction. The possibility and simplicity of this extension is due to the choice of the class of goal functions. We also discuss issues in forecasting versus prediction, scaling laws versus predictability, and measure of prediction efficiency at the research stage. Comment: 21 pages, 1 figure
We have developed a new spherical harmonic algorithm for the calculation of the loading and self-gravitating equilibrium pole tide. Based on a suggestion of Dahlen, this approach minimizes the distortions in tide height caused by an incomplete representation of the ocean function. With slight modification our approach easily could be used to compute self-gravitating and loading luni-solar tides as well.
Using our algorithm we have compared the static pole tide with tide observations at a variety of locations around the world. We find statistically significant evidence for pole tide enhancements in mid-ocean as well as the shallow seas.
We have also re-investigated the effect of the static tide on the Chandler wobble period. The difference between the wobble period of an oceanless, elastic earth with a fluid core (Smith & Dahlen) and the period of an earth minus static oceans yields a 7.4-day discrepancy. We conclude from tide observations that much of the discrepancy can probably be accounted for by non-equilibrium pole tide behaviour in the deep oceans.
We obtain stresses for Newtonian viscous flow in simple geometries (e.g. corner flow, bending flow) in order to study the effect of imposed velocity boundary conditions. Stress for a delta function velocity boundary condition decays as 1/r²; for a step function velocity, stress goes as 1/r; for a discontinuity in curvature, the stress singularity is logarithmic. For corner flow, which has a discontinuity of velocity at a certain point, the corresponding stress has a 1/r singularity. However, for a more realistic circular-slab model, the stress singularity becomes logarithmic. Thus the stress distribution is very sensitive to the boundary conditions, and in evaluating the applicability of viscous models of trench topography it is essential to use realistic geometries.
Topography and seismicity data from northern Honshu, Japan, were used to construct a finite element model, with flow assumed constant speed and tangent to the top of the grid, for both Newtonian and non-Newtonian flow (power law 3 rheology). Normal stresses at the top of the grid are compared to the observed trench topography. There is poor agreement. Purely viscous models of subducting slabs with simple, geometrically consistent velocity boundary conditions do not predict normal stress patterns compatible with observed topography. Elasticity and plasticity appear to be important in determining trench topography.
Chapman pointed to the importance of thermal diffusion effects in plasmas. When applied to the Earth's magnetosphere, thermal diffusion, in addition to electrostatic force effects, can produce very marked deviations from local thermodynamic equilibrium; therefore it becomes possible for appreciable concentrations of multiply‐ionized atoms to exist in a low temperature plasma. The concentration of O++, O+, He++, and other ions has been calculated for a variety of assumptions concerning the thermal gradient and the recombination coefficient. Under some conditions, the concentration of O++ may dominate at distances of several Earth radii and produce interesting geophysical consequences.
An attempt has been made to invert a large set of attenuation data for Love waves and toroidal oscillations in the earth, using a recent method by Backus and Gilbert. The difficulty in finding an acceptable model of internal friction which explains the data, under the assumption that the internal friction is independent of frequency, casts doubt on the validity of this assumption. A frequency-dependent model of internal friction is presented which is in good agreement with the seismic data and with recent experimental measurements of attenuation in rocks.
By using 1 min average data from the US–Canada IMS network stations (Alaska, east—west and Fort Churchill chains) and also standard magnetograms from stations in the polar-cap region and in the auroral zone, we have examined the development of polar-cap currents and the relationship of their development to the evolution of auroral electrojects during individual polar geomagnetic disturbances. Characteristics that have been determined include the following:
(1) Even when auroral electrojet activity is weak, polar-cap currents producing fields of magnitude approximately 100-200 nT almost always exist. Examination of the main features of these polar-cap currents and the available interplanetary magnetic field data show that, in addition to the IMF-dependent polar-cap currents, a normal convection current system exists quasi-persistently in the polar cap during extended quiet or weakly disturbed periods of auroral electrojet activity, and that the polar-cap currents cannot all be completely ascribed to a single source mechanism.
(2) After an extended weakly disturbed period of auroral electrojet activity, some drastic changes occur in the polar-cap currents, which are followed by three phases; growth, expansion and recovery: (a) the growth phase is characterized by the development of a large-scale sunward convection current which prevails almost everywhere over the polar cap and is associated with an eastward auroral electrojet on the duskside and a westward auroral electrojet on the dawnside. The growth phase lasts ∼30–60 min, prior to the development of a distinct westward auroral electrojet in the pre-midnight to early morning sector, with the two-cell convection current system expanding gradually equatorward. (b) The expansion phase is characterized by the occurrence of distinct westward auroral electrojets in the pre-midnight to early morning sector that are almost separated from the polar-cap convection current and that exhibit a poleward expansion of the concentrated current region. In the evening sector, on the other hand, the polar-cap convection current system (associated with an eastward auroral electrojet) develops and expands equatorward; this current usually lasts ∼2–3 hr. The polar-cap convection current system develops more stably in the afternoon–evening sector, while in the morning sector, it is soon (within ∼ 1 hr) overtaken by the distinct westward auroral electrojets that expand poleward. (c) The recovery phase is characterized by the new development of multiple eastward auroral electrojets in the noon-afternoon sector, which have time-scales of ∼1 hr and which are discretely separated by a few degrees in latitude. Each of these electrojets move poleward. The conventional idea of the development of auroral electrojets that seeks the primary cause only in the midnight region does not seem to be compatible with the observed characteristics of polar geomagnetic disturbances.
The earth's equatorial principal moments of inertia are given as A and B, where A is less than B, and the corresponding principal axes are given as a and b. Explicit formulas are derived for determining the orientation of a and b axes and the difference B - A using C(22) and S(22), the two gravitational harmonic coefficients of degree 2 and order 2. For the earth, the a axis lies along the (14.93 deg W, 165.07 deg E) diameter, and the b axis lies perpendicular to it along the (75.07 deg E, 104.93 deg W) diameter. The difference B - A is 7.260 x 10 to the -6th MR2. These quantities for other planets are contrasted, and geophysical implications are discussed.
The equations of Willis and Young (1987) for the field lines of an arbitrary axisymmetric multipole are generalized to an arbitrary linear combination of multipoles, i.e., to an arbitrary axisymmetric magnetic field B outside a sphere of radius a, S(a), centered on the origin, and containing all the sources of B. For this field, axisymmetric Stokes stream function is expressed in terms of the Gauss coefficients. It is shown that if only one Gauss coefficient is nonzero, the field line equations are identical to those obtained by Willis and Young.
The study of the earth's gravitational field has provided one of the principal methods for the determination of the structure of the outer layers of the earth. A project has been undertaken which involves the systematic examination of the relationship between the earth's gravity field and topography in each of the earth's major ocean basins. The first part of the project was concerned with the compilation, reduction, and analysis of the available surface-ship gravity and bathymetry and satellite-derived geoid data in the oceans of the earth. The present paper has the objective to summarize the principal results which have been obtained so far in the Pacific Ocean.
The inverse problem in empirical geomagnetic modeling is investigated, with critical examination of recently published studies. Particular attention is given to the use of Bayesian inference (BI) to select the damping parameter lambda in the uniqueness portion of the inverse problem. The mathematical bases of BI and stochastic inversion are explored, with consideration of bound-softening problems and resolution in linear Gaussian BI. The problem of estimating the radial magnetic field B(r) at the earth core-mantle boundary from surface and satellite measurements is then analyzed in detail, with specific attention to the selection of lambda in the studies of Gubbins (1983) and Gubbins and Bloxham (1985). It is argued that the selection method is inappropriate and leads to lambda values much larger than those that would result if a reasonable bound on the heat flow at the CMB were assumed.