Slichter Triplet Research Articles

Potential Slichter Triplet Detection Using Global Superconducting Gravimeter Data

The eigenperiods of the translational oscillation modes of the Earth’s solid inner core, also referred to as the Slichter modes or Slichter triplet, are the key parameters that constrain the density jump across the inner core boundary (ICB). Definite observations of the Slichter triplet are still open. Here, we discuss and investigate this problem using the current most extensive superconducting gravimeter (SG) data, which include 49 records from 35 global stations, altogether spanning about 22 years. Two multi-station stacking methods are employed to process the available SG data, including full-time data and data collected before and after seven major earthquakes, corresponding to persistent and intermittent excitations, respectively. Based on the relationship between the theoretical Slichter periods and the density jump at the ICB, several sets of candidates that could serve as the Slichter triplet are suggested. We identified a complete triplet set that almost coincides with different predictions made based on the PREM Earth model. The synthetic experiments show that Slichter signals excited by continuous sources of excitation may achieve an amplitude of at least 0.04 nGal, which can be detected using our full-time SG data, and the large earthquakes ( $$M_{\mathrm w}\ge 8.4$$ ) that occurred during our detection period might not excite the Slichter modes to a detectable level.

The Slichter mode of the Earth: Revisit with optimal stacking and autoregressive methods on full superconducting gravimeter data set

AbstractThe Slichter mode is the triplet oscillational mode of the 3‐D translation of the Earth's solid inner core; despite much effort it has so far eluded observation. Here we revisit the search by applying new data processing methods upon the latest set of available superconducting gravimeter (SG) data. The new methods are the AR‐z spectrum that is sensitive in detecting weak harmonic signals, and the OSE data stacking scheme proven to be effective in identifying seismic normal mode singlets. The SG data consist of 19 records from 14 worldwide stations spanning up to 15 years. We arrive at three candidate sets of frequencies for the Slichter triplet that satisfy the theoretical splitting rule, namely (3.952, 4.432, 4.908) cpd, (5.136/5.032/5.020, 5.592, 6.040) cpd, and (5.704, 6.208, 6.748) cpd, of which the first set is regarded to be the more likely. A series of synthetic experiments shows that the Slichter triplet signals with RMS received amplitude of ~0.3 nGal (10−11m/s2) can be detected to the extent of the present combination of data and methodology.

Feasibility analysis of searching for the Slichter triplet in superconducting gravimeter records

The search for the elusive Slichter triplet requires elaborate analysis of the elastic-gravitational mode characters and the non-stationary behavior of noisy time-series. A typical question is that it is difficult to characterize the excitations with attenuation by diffusion when their intensity is low compared to noise. Thus the theory for deriving the modes' frequencies is still controversial, and various scholars tried to search for the Slichter triplet in superconducting gravimeter (SG) records, but failed. One of the main causes might be due to the inappropriate use of datasets. We present in this paper synthetic experiments on the selection of record length, sampling rate and number of SG records under the Global Geodynamics Project (GGP) to detect the damped harmonic signals hidden in noises based on the optimal sequence estimation (OSE) method. Moreover, our results show that the existing observation conditions arouse restrictions and it might be impossible to detect the Slichter triplet excited by single excitation source based on Fourier spectrum analysis. Thus we suggest a stacking way of combining several seismic events in the case that the excitation mechanism has so far been unclear.

Detection of the inner core translational triplet using superconducting gravimetric observations

Based upon seven superconducting gravimeter (SG) records of 20 000 h length after the 2004 Sumatra earthquake, four methods, namely the ensemble empirical mode decomposition (EEMD), the multi-station experiment (MSE) technique, the autoregressive (AR) method and the product spectrum analysis (PSA) method, are chosen jointly together to detect the inner core translational modes (1S1). After the conventional pretreatment, each of the seven simultaneous residual gravity series is divided into five segments with an 80% overlap, and then EEMD is applied to all the 35 residual SG series as a dyadic filter bank to get 35 filtered series. After then, according to different stations and different time windows, five new simultaneous gravity datasets are obtained. After using MSE for each of the five new datasets, the AR method is used to demodulate some known harmonic signals from the new sequences that obtained by using MSE, and three demodulated product spectra are obtained. Then, according to two criterions, two clear spectral peaks at periods of 4.548 9±2.3×10−5 and 3.802 3±3.2×10−5 h corresponding respectively to the singlets m=−1 and m=+1 are identified from various spectral peaks, and they are close to the predictions of the 1066A model given by Rieutord (2002), but no spectral peak corresponding to the singlet m=0 is found. We conclude that the selected two peaks might be the observed singlets of the Slichter triplet.

Search for the Slichter modes based on a new method: Optimal sequence estimation

AbstractThe inner core translational mode (1S1), known as the Slichter triplet, can provide important information particularly on the Earth's inner core and its dynamics. A time domain spectral analysis method, the optimal sequence estimation (OSE), is devised and applied to search for the Slichter modes. Applications of the OSE and the multistation experiment (MSE) technique for detection of the singlets of 3S1 and 2S1 show that both OSE and MSE can isolate their singlets, but OSE provides a higher signal‐to‐noise ratio. OSE also can completely isolate the modes 0S2 and 1S2. Using two superconducting gravimeter data sets from nine Global Geodynamic Project stations before and after the 2004 Sumatra earthquake, we search for the possible Slichter triplet via OSE and provide a simple validation using the product spectrum. We set two preliminary criteria in order to identify possible signals; results show three signals as candidates for the Slichter triplet, more likely in the data after the 2004 Sumatra earthquake. While choosing the most reasonable criteria needs further studies, we emphasize here the effectiveness of the OSE in searching for the Slichter modes rather than claiming actual detections.

Experimental detection of the inner core translational triplet

The translational oscillation of the solid inner core is one of the Earth’s fundamental normal modes, which is also called Slichter mode. The normal mode should be split to form a triplet due to the Earth’s rotation and ellipticity. In this study, according to the splitting pattern of Slichter mode, an attempt has been made to detect the possibility of Slichter triplet’s existence by using the product spectra of the long-term continuous gravity measurements from the superconducting gravimeters (SG) at 6 globally-distributed permanent stations in the Global Geodynamics Projects network. The results indicate that the background noise level of the global SG observations is 0.0158 nms−2 and the magnitude threshold of any global harmonic signals, which may be detected by the global SG, is 0.0152 nms−2 in the subtidal frequency band from 0.162 to 0.285 cph in which Slichter triplet may occur. it implies that the signatures, related to the triplet, may be identified in the global SG observations, if they exist. It is found that there is a group of global harmonic signatures with the periods of 5.310, 4.995 and 4.344 h emerging significantly from the background noise in the global SG observations. They are in good agreement with the splitting pattern of Slichter mode. It implies that this group of signatures may be related to the inner core translational oscillations. The associated density contrast across the inner core boundary may be deduced as between the values provided in the Earth models of the PREM and 1066 A.

Least squares self-coherence for sub-nGal signal detection in the superconducting gravimeter records

Abstract In this paper, we use superconducting gravimeter (SG) data recorded at three stations of the global geodynamics project (GGP) network, with good geographical distribution, to search for possible significant peaks in the gravity spectrum that are in the assumed period range of the Slichter triplet. Seven-year long series from Cantley (Canada), and four-year long series from both Canberra (Australia) and Moxa (Germany) stations are used. First, a solid Earth and ocean tide model is subtracted from the data, followed by a local atmospheric pressure correction based on a frequency-, and location-dependent admittance estimated by the least squares response method. Subsequently, the residual series are filtered with a Parzen-based bandpass filter with a passband (12 h–78 s). A sub-nGal detection level is confirmed by injecting an artificial sine wave of different amplitudes. The Least Squares Self-Coherency spectrum shows the existence of many apparently statistically significant peaks at the 95% confidence level in the band (3–8 h). Although a few peaks are close to the claimed Slichter periods in previous research, the large number of candidate peaks may be related to other mechanisms such as global pressure variations, or hydrology.

Connecting a Quanterra Data Logger Q330 on the GWR C021 Superconducting Gravimeter

Below 1.5 mHz the superconducting gravimeters (SGs; Figure 1) are competitive with the best spring gravimeters and seismometers and can achieve the lowest noise level at frequencies lower than ∼1.0 mHz (Van Camp 1999; Rosat et al. 2003; Widmer-Schnidrig 2003; Park et al. 2005). SGs can therefore make a significant contribution to the illumination of long-wavelength density heterogeneities in the Earth's mantle (Widmer-Schnidrig 2003). For reasons of price and complexity, the number of SGs is small compared to the number of sensors deployed in the Global Seismic Network (GSN). However, the potential of a sparse network of gravimeters for normal-mode research has been demonstrated by the International Deployment of Accelerometers (IDA) network (Agnew et al. 1986). Another point worth noting is the stability and accuracy (∼0.1% level) of the calibration factor of SGs (Francis et al. 1998) requested to validate Earth and ocean tide models using tidal gravity measurements (Baker and Bos 2003). This compares well with seismic networks, where results are barely better than 1% (http://ida.ucsd.edu/pdf/DMSSC\_2005\_10.pdf; Park et al. 2005; Davis et al. 2005). Such accuracy is quite unacceptable for geodesy. Since 1997, most of the SG data have been collected under the framework of the Global Geodynamics Project (GGP) global network (Crossley et al. 1999) that presently includes about 25 instruments. The GGP aims to look at seismic normal modes, the Slichter triplet, tidal gravity, ocean tidal loading, core nutations, core modes, and hydrology. Up to now the data have been gathered in an ad hoc database, using the ASCII PRETERNA format, which acts as a standard for tidal analysis (Wenzel 1996). These data are available to non-GGP members after a six-month delay. In order to promote the SG data among the seismic community, contacts between the Royal Observatory of Belgium and the …

A wavelet-based detection and characterization of damped transient waves occurring in geophysical time-series: theory and application to the search for the translational oscillations of the inner core

Geophysical time-series with non-stationary behaviour which contain transient excitations need specific tools to be analysed. Especially, it is difficult to detect and characterize transient excitations with attenuation by diffusion when their intensity is low compared to noise. This is a typical question in the search for the elusive translational motion of the inner core, the so-called Slichter triplet. This detection remains a non-trivial problem since the amplitude of the Slichter triplet is expected to be weak. Moreover, the characteristics (period, time of excitation and quality factor) of these low-intensity damped transient waves are poorly constrained. To improve the detection and characterization of such causal damped transient waves, we introduce a new continuous wavelet-based method using correlations with causal damped sinusoids that serve as the wavelet basis. This causal damped wavelet (CDW) method presents the advantage to give a direct estimate of the quality factor of the transient wave. After some synthetic tests, we present an application of the method to the time-varying gravity data recorded by superconducting gravimeters in the search for the Slichter triplet. No evidence of the Slichter triplet has been found in the 1-yr gravity data considered. However, we show that, thanks to the 3-D representation of our CDW method, it is possible to have a complete overview of the data set content and to constrain the detected events in terms of amplitude, quality factor, frequency and time.

Least-squares self-coherency analysis of superconducting gravimeter records in search for the Slichter triplet

We develop a new approach for the spectral analysis of the superconducting gravimeter data to search for the spheroidal oscillation 1 S 1 of the Earth solid inner core. The new method, which we call least- squares ( LS) self- coherency analysis, is based on the product of the least-squares spectra of segments of the time series under consideration. The statistical foundation of this method is presented in the new least- squares product spectrum theorem that establishes rigorously confidence levels for detecting significant peaks. We apply this approach along with a number of other innovative ideas to a 6-year long gravity series collected at the Canadian Superconducting Gravimeter Installation (CSGI) in Cantley, Canada, by splitting it into 72 statistically independent monthly records. Each monthly record is analysed spectrally and all monthly LS spectra are multiplied to construct the self- coherency spectrum of the 6-year gravity series. The self-coherency spectrum is then used to detect significant peaks in the band 3–7 h at various significant levels with the aim to identify a triplet of periods associated with the rotational/ellipsoidal splitting of 1 S 1 (Slichter triplet). From all the Slichter periods predicted by various researchers so far, Smylie's triplet appears to be the most supported one, albeit very weakly, both, before and after the atmospheric pressure effect is removed from the series. Using the viscous splitting law [Smylie, D.E., 1992. The inner core translational triplet and the density near Earth's center. Science 255, 1678–1682] as guide, we can also see one interesting and statistically significant triplet with periods A = {4.261 h, 4.516 h, 4.872 h}, which changes slightly to A′ = {4.269 h, 4.516 h, 4.889 h} after the atmospheric pressure correction is applied to the gravity series.

A search for the Slichter triplet with superconducting gravimeters: Impact of the density jump at the inner core boundary

Knowledge of the Earth's inner and outer core structure can be considerably improved by the observation of the translational motion of the inner core, the so-called Slichter triplet. The theory for deriving the elastic-gravitational mode frequencies is still controversial and many observational attempts to detect the triplet have so far been unsuccessful. The period of the Slichter modes depends directly of the value of the density jump at the inner core boundary (ICB). We propose a detection method based on the seismological theory for the splitting of the modes. Depending on the density jump at ICB, new theoretical periods for the Slichter modes are computed and the corresponding frequency splittings are used to detect possible candidates. The scanning of the product spectrum obtained after stacking five time-varying gravity records from superconducting gravimeters after the 2001 Peruvian earthquake has confirmed the detection of the 2 S 1 seismic mode, but the application after stacking one-year datasets has not led to any convincing candidate for the Slichter triplet at this stage.

DETECTION AND STUDY OF THE TRANSLATIONAL OSCILLATIONS OF THE EARTH’S SOLID INNER CORE

The advances of the theoretical modeling and detection with the superconducting gravimeters (SGs), related to the Slichter triplet, are systematically introduced in this paper. The translational oscillations of the Earth’s solid inner core, which is usually called as the Slichter modes in honor of the scientist who firstly pointed out its theoretical existence, are a triplet of the principle normal modes of the Earth. The triplet is primarily driven by the gravitational forces and has eigenperiods of several hours. From the theoretical modeling, it is found that the eigenperiods of the Slichter modes are most sensitive to the density contrast across the inner core boundary (ICB), and are only slightly disturbed by the viscosity of the fluid near the ICB, the transitional zone between the outer and inner cores, Lorentz forces and some others effects. Therefore, study and detection of the Slichter modes may provide significant information about the structure of the Earth’s deep interior. Due to less knowledge to the Earth’s deep interior, there exists great uncertainty in the results of theoretical modeling based on the present Earth’s models. It is necessary to detect the signatures related to the Slichter modes by using the ground-based observations. Smylie (1992) claimed that the weak gravity resonance signatures, coming from the Slichter triplet, were found in the SG data from plural stations in the central Europe. Based on the results, the density and viscosity near the ICB have been evaluated. However, thses results were questioned by the other scientists. Recently, we have comprehensively analyzed and treated the continuous long-term SG data from!the worldwide network of the Global Geodynamics Projects. It is found that there is no evidence to support the existence of the resonance related to the Slichter triplet as what Smylie claimed. On the contrary, it is found that there are eight significant spectral peaks related to some globally geodynamical phenomena, and the Slichter triplet is one of their possible resources.

Detection of Long-Period Core Modes by Using the Data from Global Superconducting Gravimeters

Possibility of detection of the long-period core modes has been discussed in this paper by using the long-term gravity observations recorded with 13 superconducting gravimeters (SGs) in a worldwide network of the Global Geodynamics Projects. Identical techniques are used to remove the luni-solar gravity tides, the long-term trends of instrument drift, and the effects of atmospheric pressure from all 13 SG data sets. The power spectral density of each data set, as well as the product spectral density of all the data sets, is evaluated. The background noise levels in various non-tidal bands are estimated and analyzed. The results indicate that the background noise level of the global SG observations is 0.0649nm/s2 in inter-tidal band from 0.047 to 0.075cph, 0.0350nm/s2 in another inter-tidal band from 0.089 to 0.117cph, and 0.0138nm/s2 in the sub-tidal band from 0.172 to 0.333cph. The magnitude thresholds of any global harmonic signals, which may be detected by the global SGs, in these three non-tidal bands are 0.0416, 0.0231 and 0.0098nm/s2, respectively. It implies that the signals, related to the long-period core modes, may be identified in the global SG observations, if they exist. The spectral peaks of the global harmonic signals with periods of 16.55, 15.79, 11.00 and 10.09h are detected in the two inter-tidal bands of the global SG records, and they may come from the long-period oscillations in the fluid outer core of the Earth. In the sub-tidal band, there are no obvious peaks relating to the Slichter triplet claimed by Smylie in 1992. Instead, 8 spectral peaks of global harmonic signatures significantly emerge from the background noise. Comparing their periods with those of the Slichter triplet predicted theoretically, it may be concluded that the Slichter triplet is the possible sources of three peaks of them. Of course, a more certain conclusion cannot be drawn now until further knowledge of the deep interior of the Earth is obtained and more acceptable theoretical technique for the dynamic study of the fluid outer core is developed.

Results from 44 months of observations with a superconducting gravimeter at Moxa/Germany

Abstract Results for more than 42 months of observations with the superconducting gravimeter CD-034 at the Geodynamic Observatory Moxa are discussed. Moxa observatory is one of the newer stations within the ‘Global Geodynamics Project’ (GGP). A special feature of the gravimeter at Moxa is its dual sensor system; differences in the results obtained from the two sensor recordings are generally well within the standard deviations of the tidal analysis. One significant difference concerns the slightly different drift rates of 31 and 49.5 nm/s2 per year for upper and lower sensor; both sensor drifts can be fitted by a linear function. We find that the noise levels are close to the ‘New Low Noise Model’ for the seismic-modes and are also low in the tidal bands. Due to this low noise, Moxa is a station well suited to search for small geodynamic signals. The long-period variation in the gravity residuals correlates well with the polar motion. The difference signal between the two sensor recordings has a peak-to-peak amplitude of about 6 nm/s2 and shows systematic variations. Its spectrum is characterised by instrumental noise between 0.2 and 0.4 cph. The noise level of the difference and of the sum of the two residual datasets are clearly lower, respectively, higher than the noise contents of the gravity residuals themselves. This is a strong indication for the existence of broadband signals common to the two residual datasets, leading to the conjecture that the reduction of environmental effects is still not sufficient. Our results once more emphasize the necessity to correct the data for barometric pressure effects when analyzing the data for seismic modes. The reduction visibly increases the signal-to-noise ratio in the low frequencies of the mode band and helps to avoid misinterpreations of peaks. Besides the well known barometric pressure influence we can establish hydrological effects in the data which are probably caused by soil moisture and groundwater table variations as well as by batch-wise water movement within the weathering layer. As the major part of the observatory surroundings is above gravimeter level, an anticorrelation between hydrological and gravity changes is observed. In addition, it can be shown that global hydrological effects reach an order of magnitude that makes it necessary to consider these effects when analyzing long-period signals like polar motion. Vice versa these effects are large enough to be detectable in the gravity data. A first joint analysis of five datasets from the GGP network shows no indications for signals related to the Slichter triplet or core modes.

Performance of superconducting gravimeters from long-period seismology to tides

Abstract The first phase (1997–2003) of the Global Geodynamics Project (GGP) has now been completed. Data from superconducting gravimeters (SGs) within GGP have shown great capabilities in a wide spectrum of geophysical applications from the tidal studies to the long-period seismology. Here, we compare the noise levels of the different contributing stations over the whole spectrum. We use three different processing procedures to evaluate the combined instrument-plus-site noise in the long-period seismic band (200–600 s), in the sub-seismic band (1–6 h) and in the tidal bands (12–24 h). The analysis in the seismic band has demonstrated that SGs are particularly well suited for the studies of the long-period normal modes and thus are complementary to long-period seismometers. In the sub-seismic band, the power spectral densities, computed over a period of 15 continuous days for every GGP station, cross the New Low Noise Model of Peterson from T = 16 min to T = 4.6 h. SG data are therefore appropriate for studying long-period seismic and sub-seismic modes. In the tidal bands, the noise comparison is realised by a least-squares fit to tides, local air pressure and instrumental drift, leading to gravity residuals where we estimate a standard deviation and average noise levels in different tidal frequency bands. Tidal gravity observations using SGs have also shown to be an independent validation tool of ocean tidal models, and they are therefore complementary to tide gauge and altimetric data sets. Knowledge of the noise levels at each station is important in a number of studies that combine the data to determine global Earth parameters. We illustrate it with the stacking of the data in the search for the gravity variations associated with the sub-seismic translational motions of the inner core, the so-called Slichter triplet.

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 Earth's 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 Earth's 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).

The subseismic approximation in core dynamics-II. Love numbers and surface gravity

SUMMARY This paper extends our earlier examinations of the utility of various approximations for treating the dynamics of the Earth’s liquid core on time-scales of the order of lo4 to lo8 s. We discuss the effects of representing the response of the mantle and inner core by static (versus dynamic) Love numbers, and of invoking the subseismic approximation for treating core flow, used either only in the interior of the liquid core (SSA-1) or also at the boundaries (SSA-2). The success of each approximation (or combinations thereof) is measured by comparing the resulting surface gravity effects (computed for a given earthquake excitation), and (for the Slichter mode) the distribution of translational momentum, with reference calculations in which none of these approximations is made. We conclude that for calculations of the Slichter triplet, none of the approximations is satisfactory, i.e. a full solution (using dynamic Love numbers at elastic boundaries and no core flow approximation) is required in order to avoid spurious eigenfrequencies and to yield correct eigenfunctions (e.g. conserving translational momentum) and surface gravity. For core undertones, the use of static Love numbers at rigid boundaries is acceptable, along with SSA-1 (i.e. provided the subseismic approximation is not invoked at the core boundaries). Although the calculations presented here are for a non-rotating earth model, we argue that the principal conclusions should be applicable to the rotating Earth. Shortcomings of the subseismic approximation appear to arise because both SSA-1 and SSA-2 lower the order of the governing system of differential equations (giving rise to a singular perturbation problem), and because SSA-2 overdetermines the boundary conditions (making it impossible for solutions to satisfy all continuity requirements at core boundaries).

A search for the Slichter triplet in superconducting gravimeter data

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.