David Crossley

Network of superconducting gravimeters benefits a number of disciplines

A global network of superconducting gravimeters (SGs) is compiling significant data for a range of important studies spanning a number of disciplines concerned with the Earths gravity, tides, environment, and geodetics. Among phenomena being looked at are seismic normal modes, the Slichter triplet, tidal gravity, ocean tidal loading, core nutations, and core modes. Hydrologists and volcanologists also may benefit from SG data. The network was set up by the Global Geodynamics Project (GGP),an international program of observations of temporal variations in the Earths gravity field. Observations began in 1997 and will continue until 2003. Eighteen SGs currently are in operation in the network (see Figures 1 and 2).

Effective barometric admittance and gravity residuals

Abstract In the analysis of surface gravity signals that may originate from the Earths core, the step of correcting for the atmospheric pressure fluctuations is one that must be done carefully. We apply two techniques for determining the local, or effective, barometric admittance function between simultaneous observations of surface gravity and pressure. The first is a frequency domain fit that computes the admittance on a band-by-band basis. Using data from both the Canadian and French superconducting gravimeters we determined that the magnitude of the local, or background, admittance increases smoothly and monotonically from about 0.2 μgal mbar−1 at long periods (> 10 days) to about 0.35 μgal mbar−1 at frequencies greater than 3 cycles per day (c.p.d.); the phase lag is within a few degrees of 180°. By comparison, the effective admittances of the large-scale harmonics of the solar heating tide (S1S7) are much smaller, between 0.1 and 0.3 μgal mbar−1, for most of the harmonics of a day. In the second approach we fit a symmetrical time domain admittance function having lengths between 1 and 19 h using both a standard least-squares fit to a white noise residual and a new, and clearly superior, fit assuming a brown noise residual. Both time and frequency domain approaches give comparable results and contribute to a significant lowering of the residual level in non-tidal bands.

Determination of crustal interface topography from potential fields

We present a method for determination of the topography of an interface separating two uniformly but differently magnetized media. The technique is developed within the framework of discrete linear inverse theory and exploits the quasi‐linearity of the problem to derive a simple, efficient algorithm suitable for use on large gridded data sets. Variation of auxiliary parameters allows a suite of acceptable models to be produced rapidly; these parameters can be appraised in light of available geologic and geophysical evidence. Because very large matrices are involved when large amounts of data are interpreted, approximate resolution measures requiring no matrix inversion provide useful information concerning averages of the constructed topography.

A search for the Slichter triplet in superconducting gravimeter data

Abstract There have been several investigations in the past for weak harmonic signals in the residual spectrum of superconducting gravimeter (SG) data. Recently, a stack of four European SG records led to the claim of the detection of the Slichter mode of translation of the inner core (Smylie, Science, 1992, 255: 1678–1682). We attempt to verify the presence of the Slichter triplet by two methods. We re-analyse the four European SG records with a spectral method differing from that used by Smylie et al. (Phys. Earth Planet. Inter., 1993, 80: 135–157) and compare the results to two homogeneous 2 year data sets from the French and Canadian SG. We find three weak peaks in the European stack coincident with the claimed triplet using a product spectrum, but these disappear when a cross spectrum is used which takes into account phase information. Further we find no evidence of the triplet in the 2 year data sets, where the noise level in the core-mode band is one order of magnitude lower than in the European stack. Moreover various synthetic tests (e.g. pure harmonics in random white noise; damped harmonics in brown noise) lead to the conclusion that a simulated Slichter triplet with characteristics similar to that claimed, would be easily detectable in our less noisy data, especially in cross spectral estimates.

Slichter modes and Love numbers

The recent claim by Smylie [1992] to have detected the Slichter modes of the Earths inner core rests on what appears to be a remarkable agreement between theory and observation. However the theoretical eigenperiods which are used by Smylie conflict significantly with all previously published periods for the Slichter modes, both for non-rotating and rotating Earth models. A closer examination of the theory used in these calculations reveals the use of static Love numbers to represent the response of the inner core and mantle to dynamics in the liquid core. We here show that the use of dynamic Love numbers restores the eigenperiods to those obtained using standard seismological theory and consequently destroys agreement between these periods and the claimed observations.

On the excitation, detection and damping of core modes

Abstract We continue work on the possibility that internal oscillations in the Earths core might be detectable by a gravity meter at the surface. As a possible excitation mechanism we use earthquakes and for the damping we consider the contribution of anelasticity in both solid and liquid parts of the Earth. The calculation of the eigenfunctions is restricted in this paper to a non-rotating Earth model. We first review the spectrum of modes for degrees l up to 20 using a stably stratified fluid core based on the Preliminary Reference Earth Model (PREM) and compute the earthquake excitation and Q values using standard seismic theory. We then show that the effects of boundary rigidity and both Boussinesq and subseismic approximations in the core have little effect on the eigenfrequencies of the core modes. The rigid boundary core solutions are then extended into both the mantle and inner core by making use of a generalised internal load Love number approach. This method yields good approximations to the elastic eigenfunctions throughout the Earth, the agreement with full theory improving as the degree l increases. Thus we have confidence that this method can be extended successfully to models with rotation.

Time Variations In Gravity And Inferences On The Earth's Structure And Dynamics

This paper reviews how the study of the surface gravity changes is able to provide useful information on the Earths structure and global dynamics. The spectral range which is observable with superconducting gravimeters is broad and goes from the seismic frequency band to periods longer than one year. We first investigate the seismic and sub-seismic bands with a special attention paid to the gravity detection of core modes in the liquid core and to the Slichter mode of translation of the solid inner core. In the tidal bands, we show how accurate measurements allow us to infer constraints on various phenomena such as mantle (an-)elasticity, as well as ocean and atmospheric loading. The observation of the Free Core Nutation resonance in the diurnal frequency band is reviewed and indirectly suggests an increase in the ellipticity of the core-mantle boundary with respect to its hydrostatic value. A similar resonance is also theoretically predicted in the diurnal band for the rotation of the solid inner core (Free Inner Core Nutation) but we show that its detection is much more difficult because of the small amplitude and lack of a nearby tidal frequency. Oceanic and atmospheric loading mechanisms induce gravity changes over a wide spectral range and we present some recent progress in this field. Finally, because superconducting gravimeters have high calibration stability and small long-term instrumental drift, they can easily measure longperiod gravity variations due to polar motion and hydrogeology.

Noise limitations in the core-mode band of superconducting gravimeter data

Abstract In recent years, several claims of detection of weak harmonic signals in the sub-tidal band of frequencies of high-quality gravimeter data have been made. Here, we review our attempts at confirming Smylies claim of detection of the Slichter mode of inner-core oscillation using the same four data sets he and his colleagues used. We further examine the homogeneous 2 year data sets obtained from the superconducting gravimeters sited in Strasbourg and at Cantley, Quebec. We show that the power spectra of tidal-reduced, pressure and slew-corrected gravity residuals from these data are indistinguishable from a random walk process except in narrow bands dominated by residual earth tides and by harmonics of the diurnal thermal-atmospheric tide. Such a random ‘brown’ residual could result from mechanical instabilities and electronic noise in the instruments themselves, from site-specific tectonic noise, from local hydrological variations and pier instabilities or it could derive from unaccounted for variability in the atmospheric pressure in the vicinity of the instruments. We argue that the homogeneous 2 year data sets show no evidence whatever of Slichter harmonics even though our preprocessing methods reduce ‘apparent noise levels’ in the core-mode band by almost an order magnitude in comparison with the four data sets originally employed by Smylie et al. and, in their first attempted confirmation of his claimed discovery, by Jensen et al.

Oscillatory flow in the liquid core

Abstract There has been renewed interest lately in the possibility that at least a part of the Earths liquid core may be stably stratified. A gravitationally stable region would permit the existence of inertia-gravity or gravity-inertia waves in addition to the Rossby and Kelvin waves which exist due to rotational effects and which are well known in oceanography and atmospheric dynamics. These wave motions are of interest because their periods are dependent on the density stratification as specified by the buoyancy frequency N which in turn determines the amplitude of large-scale radial motions in the core. The waves have too high a frequency to be connected dynamically to the magnetic field in the core, but if they do exist they may be detectable by sensitive long-period gravimeters at the Earths surface. This paper examines the available evidence for the frequency regimes, excitation and damping mechanisms of the core waves. It is concluded that although the waves may exist theoretically, their detection and interpretation as a method for determining N is a difficult proposition.

Global Earth dynamics and induced gravity changes

We consider the elastogravitational deformation of an Earth model with a liquid outer core and a surficial fluid layer modeling the oceans or the atmosphere. The surface gravity changes caused by planetary-scale dynamical phenomena can be expressed in terms of generalized gravimetric factors. Each of these factors is related to a specific boundary condition (in normal or transverse traction, in potential and derivative) which has to be considered at the different interfaces (inner core-outer core, outer core-mantle, surface) according to the problem. We apply this formalism to express in a self-consistent and uniform manner the gravity disturbances due to various sources: tides, Earth rotation, loading process, inner and outer core dynamics, with special attention paid to possible resonance effects.