J. L. Le Mouël

A statistical approach to the Earth's main magnetic field

Abstract Based mainly on historical magnetic data and following indications derived from paleomagnetic data, we suggest that the Earths main magnetic field can be described as a two scale process. The first scale is characterized by a mainly axial dipolar geometry and long time constants (much longer than several hundred years). It could be maintained at the core-mantle boundary by diffusion from within the core as the likely tangentially geostrophic flow at the top of the core gives special status to this axial dipole field. The second scale is characterized by a far more complex geometry and short time constants (of the order of a couple of hundred years). It encompasses the observed non-dipole field, possibly the equatorial dipole field and is a likely signature of the convective term in the induction equation. Most of the observed axial dipole secular variation is probably also related to it. The stationary isotropic statistical model defined describes the behaviour of the field in statistical terms. This model provides a pertinent formalism for characterizing both the main field and secular variation spectra, and makes it possible to define ‘typical correlation times’, thus allowing a discussion of the two scale process we propose. It also makes it clear that historical data do not support the separation between dipole and quadrupole families, a view which has sometimes been advocated.

Outer-core geostrophic flow and secular variation of Earth's geomagnetic field

In studies of the temporal variations of the main internal geomagnetic field (the secular variation or SV), it is usual to consider separately the variations of the dipolar and non-dipolar parts which appear to have different time constants. The mechanism that is generally invoked to explain the generation of SV is the advection of the lines of force of the main field by the highly conducting fluid at the top of the core. Such a mechanism involves the main field as a whole and it is not clear a priori why its two parts should behave separately. I show here that the Coriolis force will probably dominate the force budget at the top of the core and that, in such a case, the motion of the fluid involves the two parts of the field in a different way; in particular, the existing axial dipolar component is not re-engaged in the process which builds up the SV.

Motions at core surface in the geostrophic approximation

Abstract Motions at the top of the core which generate the observed Secular Variation (S.V.) field are computed. To reduce the well known ambiguity of the solution, two constraints are added: the flow is a large scale one and is geostrophic. The computed flow then has a very simple geometry; its poloidal part is roughly axisymmetrical with respect to an equatorial diameter. This geometry is almost unchanged from 1970 to 1980 while the intensity of the velocity is nearly doubled.

Propagation of an accreting plate boundary: a discussion of new aeromagnetic data in the Gulf of Tadjurah and southern Afar

Abstract A detailed aeromagnetic survey of the Republic of Djibouti and immediate surroundings was performed in 1977. This paper summarizes the reduction techniques which are used in order to produce a magnetic anomaly map and discusses the accuracy of this map, which is presented as an insert at a scale of 1/250,000. Two distinct magnetic styles are recognized: linear anomalies with both large amplitude and short wavelength, considered to be typical of oceanic lithosphere, contrast with areas of lower-amplitude longer-wavelength anomalies, which are found mostly in the northern part of the survey. This quiet zone of subdued magnetic style is thought to have undergone major tectonic deformation in the last millions of years. The general morphology of magnetic anomalies is interpreted in terms of a propagating crack model, as proposed by Courtillot [23]. The crack propagates westwards at approximately 3 cm/yr and the crack tip is thought to lie close to Lake Asal, both on the basis of the magnetic data and of other geophysical evidence. The land section of the survey is a central topic of this paper and is interpreted in terms of the crack propagation model in the light of other available geological, geochemical and geophysical data.

The 1975–1977 crisis of la Soufriere de Guadeloupe (F.W.I): A still-born magmatic eruption

On July 8, 1976, eruptive activity broke out at la Soufriere de Guadeloupe (F.W.I) after about one year of increasing seismic activity. Seismic activity continued to increase until August 1976, reaching more than 1500 events (a 200-fold increase over the preceding quiet period of a few years) and an energy output of about 1017 ergs in a day. A total of 26 major phreatic eruptions similar to the July 8 outburst took place during an eight-months period. The steam blasts that characterized the eruptions gave rise to particle- and sometimes block-charged plumes that deposited an estimated 106 m3 of solids. The H2O-rich gases emitted during the blasts presumably contained other gases (H2S, SO2, CO2...) that were partly adsorbed on solid particles. All material was erupted at temperatures of the order of 100° to 200°C. The observation of vertical migration of earthquake foci in less than a few hours and over about 6 km depth, and of abnormal variations of the geomagnetic field, indicate a deep energy source for the phreatic eruptions. A small proportion of the gases adsorbed on solid particles had a magmatic origin. However, most of the steam and the tephra seemed to originate from superficial levels of a hydrothermal system. Similar phreatic eruptions have occurred several times in recorded history. In the case of la Soufriere, the origin of the phreatic eruptions is best described by an abnormal energy input (versus steady-state) from a crustal magma chamber. The occurrence of truly magmatic eruptions is presumably inhibited by an extensive hydrothermal system. The abrupt release of more power from the magma chamber could have resulted in an explosive pyroclastic eruption. Substantial improvement of the Guadeloupe volcano observatory has followed the 1975–1977 crisis. Permanent telemetered geophysical networks and regular geochemical observations have provided a five year data base of the volcano behavior in its noneruptive state which can be compared to crisis situations.

Physical properties at the top of the core and core surface motions

Abstract Changes of the Earths magnetic field, with time constants of 5–100 years, have been used to constrain the fluid motions at the top of the core. We recall arguments to support the hypothesis that the horizontal components of the Navier-Stokes equation reduce, at the top of the core, to a geostrophic equilibrium. The Navier-Stokes equation then allows us to derive the fluid pressure from the flow υ, and the density heterogeneity from both the flow υ and its shear ∂υ ∂r at the top of the core. The radial shear of the flow cannot be inferred from the secular variation of the magnetic field; only the radial component of the induction equation can be used to constrain the motions and the shear plays no part in this radial component, so the density heterogeneities linked with the motion cannot be calculated this way. Finally, the geostrophic formalism is shown to be compatible with a possible stable stratification of the upper core which might imply strong dependence of the flow on the radius.

Core-mantle topographic torque: a spherical harmonic approach and implications for the excitation of the Earth's rotation by core motions

Abstract The interaction of the fluid pressure over the topography of the core mantle boundary generates a torque that leads to perturbations in the Earths rotation. A general formulation of this topographic torque is proposed with the help of a development in spherical harmonics of the pressure and shape. Various implications of this coupling mechanism are discussed according to the symmetry properties of the dynamic pressure field at the core surface and the distribution of the topographical deviations (bumps) of the core mantle boundary inferred from seismology. Specifically, it is shown that different interaction terms contribute to the equatorial torque; although their sum cannot be precisely quantified using present knowledge, it could be sufficient to excite the Earths wobble. The axial torque contribution seems to be too large to explain the decade fluctuations of the Earths rotation rate, suggesting the existence of a mechanism which reduces the axial resulting torque without altering the equatorial one.

Geomagnetic secular variation, core motions and implications for the Earth's wobbles

Abstract Motions at the top of the core are known to be responsible for the secular variation of the Earths magnetic field. If this flow is supposed geostrophic, the associated pressure field can have an appropriate geometry to exert a pressure torque upon the elliptical core-mantle boundary and, besides, to alter the elastic products of inertia in such a way as to excite the Earths and core wobbles. We consider some schematic excitation functions and the resulting amplitudes of the Earths and core rotational motions. The proposed mechanism is shown to be efficient for exciting the long-period Markowitz wobble of the rotation axis and also the Chandler wobble if the variations in the pressure field have the right time scales, as indeed suggested by the available secular variation data.

The Recent Secular Variation and the Motions at the Core Surface

The Earth’s magnetic field has been undergoing a remarkably systematic variation during the last 30 years. This variation can be described by a constant time derivative and a step-function second derivative. These parameters are smoothly distributed over the Earth’s surface. The step occurred in 1969 and caused the second derivative to change signs for all of the components at most of the magnetic observatories. Similar but less well documented behavior had been observed around 1900; it seemed to correlate with a jump in the acceleration of the Earth’s rotation. We have investigated the motions at the top of the Earth’s core that are responsible for the recent magnetic variations by inversion procedures. The motions responsible for the time derivative of the magnetic field can be reasonably well assessed and are dominated by a westward drift term of approximately 0.2°/year, although important poloidal motions are also inferred. The data for the jump in the second derivative are much noisier and the motion accelerations are not as well resolved. The poloidal acceleration terms are still fairly well resolved, but the toroidal motions, especially the zonal motions, are very poorly resolved. No firm conclusion about an acceleration of the westward drift can be given on the basis of this analysis. The inversions give evidence that the motions for the lower modes are a strongly decreasing function of their order.

Magnetic observations made on la soufriere volcano (guadeloupe) during the 1976–1977 crisis

Abstract An array of fourteen stations for measurement of the total intensity ( B ) of the earths magnetic field was installed on the Soufriere volcano during the 1976 seismovolcanic crisis. Measurements were performed daily from September 1976 to April 1977. Differences between values of the total intensity measured at each station and values of B measured continuously at a reference station (located near the summit of the volcano) have been computed. For each value of the difference, an estimate of an upper bound of the reduction error has been obtained. The effect of lateral conductivity anomalies has been directly measured for four stations and estimated for the others. The main conclusions of these experiments are the following: 1. (1) Significant variations are found in the differences in intensity with characteristic time constants of a few days. These variations are very small for stations located near the summit and within 5 km of the reference station; they reach an amplitude of 15 nT for the more remote stations and often show good correlation from station to station. 2. (2) The amplitude of these variations decreased with the end of the seismovolcanic crisis, at the end of March 1977.