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

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.     

利用全球超导重力仪数据检测长周期核模

采用全球地球动力学计划观测网中13台超导重力仪长期连续观测资料,探讨了长周期核模检测的可能性。采用相同的方法剔除了所有13个观测序列中的重力潮汐信号、仪器漂移和大气重力信号,估计了各个序列的功率谱密度及其积谱密度,估计并分析了非潮汐不同频段背景噪声。结果表明,在两个潮汐间频段（0.047~0.075cph和0.089~0.117cph)和亚潮汐频段(0.172~0.333cph),全球超导重力仪的平均噪声水平分别为0.0649,0.0350nm/s2和0.0138nm/s2,可以检测到的全球谐信号幅度极限分别为0.0416,0.0231nm/s2和0.0098nm/s2,表明全球超导重力仪观测资料基本可以识别长周期核模信号.在全球超导重力观测中,在潮汐间频段发现周期分别16.55,15.79,11.00h和10.09h的全球谐信号谱峰,可能来自于液核长周期振荡;在亚潮汐频段没有Smylie 1992年发现的Slichter模信号,但存在8个全球谐信号的谱峰,参考现有的理论模拟结果,Slichter模是这些信号可能的来源之一.     

Performance of superconducting gravimeters from long-period seismology to tides

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.     

Scientific achievements from the first phase (1997–2003) of the Global Geodynamics Project using a worldwide network of superconducting gravimeters

This paper aims to review the main scientific achievements which were obtained in the first phase (1997–2003) of the Global Geodynamics Project (GGP) consisting of a worldwide network of superconducting gravimeters (SG) of about 20 instruments. We show that the low noise levels reached by these instruments in various frequency bands allow us either to investigate new signals of very small amplitude or to better determine other signals previously seen. We first report new results in the long-period seismic band with special emphasis on the detection of the ₂S₁ normal mode and the splitting of the fundamental spheroidal mode ₂S₀ after the magnitude 8.4 Peru earthquake in 2001. We also discuss briefly the ‘hum’, which consists of a sequence of fundamental normal modes existing between 2 and 7 mHz even in the lack of any seismic excitation, and was first discovered on the Syowa (in Antarctica) instrument in 1998. We will comment on the search for the Slichter mode ₁S₁ of degree 1 which is associated with a translational motion of the inner core inside the liquid core. Atmospheric effects are reviewed from the local to the global scale and the improvement due to pressure loading computations on residual gravity signals is shown. An interesting study exhibiting the gravity consequence due to sudden rainfall and vertical mass motion in the atmosphere (without ground pressure change) is presented. The precision of the SGs leads to some convincing results in the tidal domain, concerning the fluid core resonance effect (free core nutation (FCN)) on diurnal tides or various loading effects (linear, non-linear) from the oceans. In particular, SGs gravity measurements are shown to be useful validating tools for ocean tides, especially if they are small and/or confined to coastal regions. The low instrumental drift of the SGs also permits to investigate non-tidal effects in time-varying gravity, especially of annual periodicity. Hydrology has also a signature which can be seen in SG measurements as shown by several recent studies. At even lower frequency, there is the Chandler motion of 435-day period which leads to observable gravity changes at the Earth's surface. We finally report on the progress done in the last years in the problem of calibrating/validating space satellite data with SG surface gravity measurements.     

Internal waves and temperature fronts on slopes

Time series measurements from an array of temperature miniloggers in a line at constant depth along the sloping boundary of a lake are used to describe the ‘internal surf zone” where internal waves interact with the sloping boundary. More small positive temperature time derivatives are recorded than negative, but there are more large negative values than positive, giving the overall distribution of temperature time derivatives a small negative skewness. This is consistent with the internal wave dynamics; fronts form during the up-slope phase of the motion, bringing cold water up the slope, and the return flow may become unstable, leading to small advecting billows and weak warm fronts. The data are analysed to detect ‘events’, periods in which the temperature derivatives exceed a set threshold. The speed and distance travelled by ‘events’ are described. The motion along the slope may be a consequence of (a) instabilities advected by the flow (b) internal waves propagating along-slope or (c) internal waves approaching the slope from oblique directions. The propagation of several of the observed ‘events’ can only be explained by (c), evidence that the internal surf zone has some, but possibly not all, the characteristics of the conventional ‘surface wave’ surf zone, with waves steepening as they approach the slope at oblique angles.     

3-D Non-linear Travel-time Tomography: Imaging High Contrast Velocity Anomalies

In this paper we present an approach for 3-D travel-time tomography, which works well in reconstructing high contrast velocity anomalies in both location and strength. It uses a revised ‘irregular’ approach to the shortest-path method as the ray tracer and a damped minimum norm, and constrained least-squares CG approach as the inversion solver. In ray tracing, the advantages of the revised ‘irregular’ over the ‘regular’ approach are that the secondary nodes introduced on the cell surfaces significantly improve accuracy of computed travel times, without dramatically increasing the total number of cells and nodes; the tri-linear velocity function defined across the cell guarantees accurate ray tracing in a high velocity contrast medium; and the capacity to calculate a relatively large 3-D model, due to the fast run speed (at least one order of magnitude over the ‘regular’ approach) and less number of total nodes. The introduction of ‘soft’ and ‘hard’ bounds into the inversion process changes the conditioning and makes the solution meaningful in a physical sense. Thus the artifacts caused by noise and high velocity contrasts are substantially suppressed and the image quality is considerably improved, making the solution realistic with noisy or inconsistent travel-time data. Several numerical tests indicate that we can obtain good quality images even for high velocity contrast anomalies (say more than 20%) in the target region. This means the inversion algorithm is an efficient and effective procedure. Meanwhile, the inversion procedure is not very sensitive to the quality of the travel-time data, which is promising for practical usage.     

ELF wave generation in the ionosphere using pulse modulated HF heating: initial tests of a technique for increasing ELF wave generation efficiency

This paper describes the results of a preliminary study to determine the effective heating and cooling time constants of ionospheric currents in a simulated modulated HF heating, ‘beam painting’ configuration. It has been found that even and odd harmonics of the fundamental ELF wave used to amplitude modulate the HF heater are sourced from different regions of the ionosphere which support significantly different heating and cooling time constants. The fundamental frequency and its odd harmonics are sourced in a region of the ionosphere where the heating and cooling time constants are about equal. The even harmonics on the other hand are sourced from regions of the ionosphere characterised by ratios of cooling to heating time constant greater than ten. It is thought that the even harmonics are sourced in the lower ionosphere (around 65 km) where the currents are much smaller than at the higher altitudes around 78 km where the currents at the fundamental frequency and odd harmonics maximise.     

Analysis of observations with dual sensor superconducting gravimeters

Among the 21 superconducting gravimeters presently operating worldwide four instruments exist that are equipped with two vertically aligned sensor units. Three of the instruments are installed in Germany (Bad Homburg, Moxa, Wettzell) and one in South Africa (Sutherland). Comparisons of the data sets obtained with the dual sensor systems yield information on instrumental effects and sensitivity as well as on the efficiency of reductions of environmental effects applied to the data. The latter is an important constraint when looking for small geodynamic signals like Slichter and core modes or aperiodic variations.From analyses of the two data sets of each instrument a small but significant difference of 1-3% in the response of the sensor units on barometric pressure variations is found. Likewise, the records of lower and upper sensor vary slightly but not systematically with regard to the noise levels in the different frequency ranges. The tidal analyses yield an agreement of the tidal parameters generally well within the standard deviations determined from the least squares adjustment in the tidal analysis. The deviations are in the range between 0×10⁻⁴ and 3×10⁻⁴ for the amplitude factor and the phases differ between 0.0005° and 0.01° for the four main tidal constituents O1, K1, M2, and S2.The comparison of the gravity residuals of the two sensors with each other as well as with their sum and difference in the time and frequency domain shows the existence of identical signals in the records of the two sensors in the whole range of observation. This probably means that either the environmental reductions applied are not sufficient or there are additional disturbing effects in the data which have not been taken care of yet. From the study it emerges that it is not possible to get entirely rid of the tidal signals in the data. This is probably also due to the fact that despite reductions the data sets contain additional signals and slightly different noise at tidal frequencies which affect the result of the tidal analysis.     

海拉尔地震台SSQ-2I水平摆与VP垂直摆观测数据对比分析

基于SSQ-2I型数字石英水平摆与VP型垂直摆倾斜仪2种摆式倾斜仪不同的工作原理,对2018—2020年海拉尔地震台2套仪器的观测数据连续率与完整率、倾斜量年飘零与年变幅、数据观测精度、噪声水平、映震能力等进行对比分析,以对2套仪器的效能进行综合评价。结果表明,SSQ-2I水平摆仪器效能优于VP垂直摆。     

The search for weak harmonic signals in a spectrum with application to gravity data

When considering the search for discovery or amplitude estimation of a spectral line with a probabilistic approach, great attention must be paid to the meaning of each step. We give the probability law for the amplitude of a spectral peak in the presence of random noise appearing in a periodogram and discuss the effective probability of the existence of the corresponding wave. We find that the estimated amplitude of a spectral peak is biased and should be corrected when the signal-to-noise ratio is small. As a first application to gravity data, it results in a re-estimation of the gravimetric amplitude factors (delta factors) provided by least-squares tidal analysis. We also estimate the probability of observing a spectral line above a given level in the spectrum of a purely random noise. This allows us to compute for given spectrum the number of peaks expected to overcross the classical levels used in statistical analysis (like nσ, where σ is the standard deviation of the temporal noise distribution and n is an integer with typical values equal to 2 or 3). A specific application to real data is investigating the gravity spectrum derived from a 5 year record of the French superconducting gravimeter and we show that the predicted statistics are indeed in agreement with the observations. We also show the statistical consequence of using longer observing periods to obtain the spectral estimations. The problem of detecting translational motion of the Earth's solid inner core (Slichter modes) in a gravity spectrum is analyzed and the probabilities of having a triplet of random peaks thresholding specific levels in a given frequency window are computed. We show that, in the case of a typical gravity spectrum (1 year of hourly data and a frequency window of 0.03 cycle h⁻¹), the probability of having a random set of three peaks exceeding a level of 3 σ, is very high. This emphasizes the need for a very careful analysis of spectral lines before inferring the existence of a true physical signal.     

蓟县地震台重力仪观测数据质量与水文响应分析

对天津蓟县地震台2套相对重力仪2018—2019年观测数据进行潮汐分析和提取非潮汐重力残差处理,研究水文变化所引起的重力响应。结果表明,蓟县地震台2套重力仪精度较高;GS-15重力仪重力残差与水文变化间存在较好的相关性,具体表现为降水时重力减少,降水结束后重力增大,水位下降时重力减少,水位上升时重力增大,但其间都存在延迟对应关系。     

The Black Forest Observatory, Schiltach

The purpose of the geoscientific Observatory at Schiltach in the Black Forest in SW-Germany is to measure and monitor motions and deformations of the earth in a frequency band as broad as possible. The spectrum of geodynamic signal contains

• - the short period waves (up to 40 Hz) of near earthquakes,

• - the longer period body and surface waves from teleseismic events,

• - the free oscillations of the earth excited by giant earthquakes,

• - the earth tide deformations caused by the gravitational forces of the moon and the sun having periods of 12 h and longer,

• - deformations of the earth in a wide period range from other sources (e.g. atmosphere).

Besides providing high quality data with some continuity using ‘standard’ sensors, the observatory must be considered as an experimental station and research facility where new instruments and techniques can be tested.     

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

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.     

Effective barometric admittance and gravity residuals

In the analysis of surface gravity signals that may originate from the Earth's 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.     

利用超导重力数据探测Slichter模三重分裂信号

本文基于2004苏门答腊地震后全球地球动力学计划观测网中9台超导重力仪13200h的连续重力观测数据,联合利用整体经验模态分解(EEMD)、最优序列估计(OSE)、积谱密度分析(PSA)和自回归估计(AR)方法,探测地球固态内核平动振荡模态(Slichter模)的三重分裂信号.利用EEMD提取常规预处理后的重力残差中包含目标频段的本征模态函数(IMFs)作为最终的重力残差之后,将每个台站的重力残差平均分成无重叠的3个子数据块,再应用OSE和PSA方法获取Slichter模三重分裂谱线的积谱密度,并采用AR方法估计各积谱中弱共振信号的中心频率及其误差.结果表明,结合OSE和PSA方法探测到三个清晰的谱峰,周期分别为5.8307±7.1×10-4h、5.2161±8.1×10-4 h和4.7536±5.2×10-4 h,分别对应Slichter模三重分裂谱线m=-1、m=0和m=+1,且三个谱峰的周期与Crossley(1992)、Rochester和Peng(1993)、Peng(1997)和Rogister(2003)基于PREM地球模型给出的Slichter模理论周期非常接近,也与Ding和Shen(2013)建议的"可能的观测结果"较为接近.参考现有的理论和观测结果,本文认为这三个信号可能是Slichter模三重分裂谱线.     

Evolution of accelerographs, data processing, strong motion arrays and amplitude and spatial resolution in recording strong earthquake motion

This paper presents a review of the advances in strong motion recording since the early 1930s, based mostly on the experiences in the United States. A particular emphasis is placed on the amplitude and spatial resolution of recording, which both must be ‘adequate’ to capture the nature of strong earthquake ground motion and response of structures. The first strong motion accelerographs had optical recording system, dynamic range of about 50 dB and useful life longer than 30 years. Digital strong motion accelerographs started to become available in the late 1970s. Their dynamic range has been increasing progressively, and at present is about 135 dB. Most models have had useful life shorter than 5–10 years. One benefit from a high dynamic range is early trigger and anticipated ability to compute permanent displacements. Another benefit is higher sensitivity and hence a possibility to record smaller amplitude motions (aftershocks, smaller local earthquakes and distant large earthquakes), which would augment significantly the strong motion databases. The present trend of upgrading existing and adding new stations with high dynamic range accelerographs has lead to deployment of relatively small number of new stations (the new high dynamic range digital instruments are 2–3 times more expensive than the old analog instruments or new digital instruments with dynamic range of 60 dB or less). Consequently, the spatial resolution of recording, both of ground motion and structural response, has increased only slowly during the past 20 years, by at most a factor of two. A major (and necessary) future increase in the spatial resolution of recording will require orders of magnitude larger funding, for purchase of new instruments, their maintenance, and for data retrieval, processing, management and dissemination. This will become possible only with an order of magnitude cheaper and ‘maintenance-free’ strong motion accelerographs. In view of the rapid growth of computer technology this does not seem to be (and should not be) out of our reach.     

Analysis of Rayleigh waves in saturated porous elastic media by finite element method

A numerical procedure for the analysis of Rayleigh waves in saturated porous elastic media is proposed by use of the finite element method. The layer stiffness matrix, the layer mass matrix and the layer damping matrix in a layered system are presented for the discretized form of the solid-fluid equilibrium equation proposed by Biot. In order to consider the influence of the permeability coefficient on the behavior of Rayleigh waves, attention is focused on the following states: ‘drained’ state, ‘undrained’ state and the states between two extremes of ‘drained’ and ‘undrained’ states. It is found from computed results that the permeability coefficient exerts a significant effect on dispersion curves and displacement distributions of Rayleigh waves in saturated porous media.     

Fuzzy neural network models for liquefaction prediction

Integrated fuzzy neural network models are developed for the assessment of liquefaction potential of a site. The models are trained with large databases of liquefaction case histories. A two-stage training algorithm is used to develop a fuzzy neural network model. In the preliminary training stage, the training case histories are used to determine initial network parameters. In the final training stage, the training case histories are processed one by one to develop membership functions for the network parameters. During the testing phase, input variables are described in linguistic terms such as ‘high’ and ‘low’. The prediction is made in terms of a liquefaction index representing the degree of liquefaction described in fuzzy terms such as ‘highly likely’, ‘likely’, or ‘unlikely’. The results from the model are compared with actual field observations and misclassified cases are identified. The models are found to have good predictive ability and are expected to be very useful for a preliminary evaluation of liquefaction potential of a site for which the input parameters are not well defined.     

Experimental evidence for the exsolution of cratonic peridotite from high-temperature harzburgite

Phase equilibrium experiments were performed on typical ‘oceanic’ and ‘cratonic’ peridotite compositions and a Ca, Al-rich orthopyroxene composition, to test the proposal that garnet lherzolites exsolved from high-temperature harzburgites, and to further our understanding of the origin of ancient cratonic lithospheres. ‘Oceanic’ peridotites crystallize a garnet harzburgite assemblage at pressures above 5 GPa in the temperature range 1450–1600°C, but at 5 GPa and temperatures less than 1450°C, crystallize clinopyroxene to become true lherzolites. ‘Cratonic’ peridotites crystallize a garnet harzburgite assemblage at pressures above 5 GPa in the temperature range 1300–1600°C. Garnet-free harzburgite crystallizes from both ‘cratonic’ and ‘oceanic’ peridotite at temperatures above 1450°C and pressures below 4.5–5 GPa. Phase relations for the high Ca, Al-rich orthopyroxene composition essentially mirror those for ‘oceanic’ peridotite.The complete solution of garnet and clinopyroxene into orthopyroxene observed in all three starting compositions at temperatures near or above the mantle solidus at pressures less than 6 GPa supports the hypothesis that garnet lherzolite could have exsolved from harzburgite. The inferred cooling path for the original high-temperature harzburgite protoliths of garnet lherzolites differs depending on bulk composition. The precursor harzburgite protoliths of garnet lherzolites and harzburgites with ‘cratonic’ bulk compositions apparently experienced simple isobaric cooling from formation temperatures near the peridotite solidus to those at which most of these peridotites were sampled in the mantle (< 1200°C). The cooling histories for harzburgite protoliths of sheared garnet lherzolites with ‘oceanic’ compositional affinity are speculated to have involved convective circulation of mantle material to depths deeper than those at which it was originally formed.Phase equilibria and compositional relationships for orthopyroxenes produced in phase equilibrium experiments on peridotite and komatiite are consistent with an origin for ‘cratonic’ peridotite as a residue of Archean komatiite extraction, which has since cooled and exsolved clinopyroxene and garnet to become the common low-temperature, coarse-grained peridotite thought to comprise the bulk of the mantle lithosphere beneath the Archean Kaapvaal craton.     

A note on distribution of uncorrected peak ground accelerations during the Northridge, California, earthquake of 17 January 1994

This paper presents a summary of uncorrected peak ground accelerations recorded during the Northridge, California, earthquake of 17 January 1994 and a preliminary analysis of these data. The presented contours of recorded accelerations agree well with observed patterns of damage. The paper also addresses the issue of how ‘unusual’ and ‘unexpected’ the recorded accelerations are relative to earlier predictions.