Earth Tides Research Articles

The dynamics of a long-lasting effusive eruption modulated by Earth tides

Deciphering eruptive dynamics in near-real time is essential when dealing with hazard assessment and population evacuation. Recognition of specific patterns in time-series measured during volcanic activity may help decipher distinctive behavior at active volcanoes, providing insights into the underlying driving mechanisms. Multi-parameter data sets usually agree on the overall trend characterizing the temporal evolution of an eruption providing insights into the first-order eruptive dynamics. However, second-order variations detected in different data sets remain often poorly understood. The 2014-2015 Holuhraun eruption (Iceland) offers an excellent opportunity to investigate the dynamics of a long-lasting effusive eruption. We analyze the seismic tremor and the volcanic radiated power emitted by the lava field during the 6 months of the eruption using Singular Spectrum Analysis (SSA). In both geophysical time-series, we identify periods from ∼5 to ∼32 days coinciding with periods of Earth tides. Here we show that ∼50% of both signals are composed of tidal periods suggesting that magma movements follow frequencies imposed by lunisolar forces within the crust and at Earth's surface.

Temporal changes of hydraulic properties of overburden aquifer induced by longwall mining in Ningtiaota coalfield, northwest China

Characterizing the mining induced temporal changes of hydraulic properties of the overburden aquifer is significant for groundwater resource protection. Conventional hydrogeological methods (e.g. hydraulic test, physical model test and numerical simulation) of determining hydraulic properties of the overburden aquifer cannot quantitatively analyze the temporal changes of the hydraulic properties induced by mining disturbances. This paper demonstrates a quantitative determination for the temporal changes of parameters (compressibility, porosity and specific storage) in the overburden aquifer influenced by the mining processes, based on in-situ continuous measurements of groundwater level that was affected by earth tide, atmospheric loading and mining disturbances. The results showed that, when working face reached a certain distance (127 m from borehole J6 in this study), those parameters (compressibility, porosity and specific storage) of overburden aquifer began to show gradual decrease, with approximately up to two order of magnitudes. After the working face passed by the observation borehole J6, those properties of overburden aquifer recovered in about 80 days, which might reflect the characteristic of elastic deformation of the aquifer. Those findings of the mining induced parameters’ temporal changes could improve our understanding of the mining effects on aquifer system and could be meaningful in groundwater resource protection.

Simulation Study of Moon-Based InSAR Observation for Solid Earth Tides

The observation of solid earth tides (SET) provides an important basis for understanding the structure of the earth’s interior, and has long been the focus of research in geoscience. However, actually, there still exist some limitations in capturing its global-scale information only with ground stations. Remote sensing technology can realize large-scale deformation monitoring of high point density constantly. However, it is still difficult for the artificial satellite system to meet the requirements of SET monitoring in terms of field of view and temporal resolution now. In this work, the moon is hypothesized as a new platform for SET observation combined with interferometric synthetic aperture radar (InSAR) technology. Based on the tidal model and lunar ephemeris, the spatial and temporal characteristics of the SET from the lunar view were analyzed. Furthermore, the calculations demonstrate that more abundant SET information can be observed in this view. After comparing various observation modes, the single-station with repeat-pass differential InSAR was selected for this simulation. We mainly considered the restriction of observation geometry on moon-based InSAR under three signal bandwidths, thereby providing a reference for the sensor design. The results demonstrate that the moon-based platform offers the potential to become an optimal SET observation method.

Presentation of a Wavelet‑Based Harmonic Model for Tidal Level Forecasting at Sabah and Sarawak

The world’s tides are a result of the combined forces of celestial forces and centrifugal force exerted by the Earth‑Moon and the Sun acting on the water body, earth tides and the atmospheric tides. Harmonic analysis is the most popular and widely accepted method used for the processing and expression of tidal behavior as well as its characteristics. Despite its strengths, harmonic analysis has a few drawbacks when short data are involved for long term‑prediction. However, to enhance the accuracy of the popular methodology of harmonic analysis (HA), this study presents a wavelet‑based harmonic model for tidal analysis and prediction. Six months of water level heights at four tide gauge stations in Sabah and Sarawak of Malaysia were employed. The results obtained agrees with the original data when a comparison was made. The root mean square error (RMSE) and Pearson correlation coefficient (r) are the statistical index tools applied to test the functioning of the model. The residual error is the deviation between the original data and the predicted data which was also computed in this study. The new wavelet‑based harmonic model improves the accuracy of prediction. Moreover, the model is efficient and feasible for tidal analysis and prediction.

Spatiotemporal Ocean Tidal Loading in InSAR Measurements Determined by Kinematic PPP Solutions of a Regional GPS Network

The coastal crustal deformation caused by ocean tidal loading (OTL) varies spatially and temporally, and this spatiotemporal variation in satellite-based interferometric synthetic aperture radar (InSAR) measurements needs to be determined. In this article, we propose a spatiotemporal modeling method to estimate the OTL displacements in InSAR measurements using the kinematic precise point positioning (PPP) solutions of a regional GPS network. We tested the method through an experiment using 25 Sentinel-1B images and long-term observations of 172 GPS reference sites from Southern California. The experimental results suggest that there are significant OTL and solid Earth tide effects in the differential InSAR interferogram, which is greater than 40 mm. We find that the spatial characteristics of OTL variations can be expressed as a high-order polynomial in the two variables of latitude and longitude, and the spatiotemporally modeled PPP tidal estimates of the high-density GPS sites can provide high precision OTL correction for all the pixels in the interferogram. In the last part of the study, we show that the spatial large-scale signals in the differential interferograms of Sentinel-1B data are mainly atmospheric delay, solid Earth tidal, and OTL effect, and demonstrate the importance of the tidal correction in the InSAR measurements.

Groundwater net discharge rates estimated from lake level change in Badain Jaran Desert, Northwest China

Over a hundred sizable lakes, some even larger than ~1 km2, are distributed across the lowlands between megadunes in the southeastern Badain Jaran Desert (BJD), northwest China. With rather limited precipitation and hardly any surface runoff, these lakes are fed mainly by groundwater. However, the source of the groundwater and the groundwater discharge rates to these lakes are poorly understood. Water level and temperature of four representative lakes in the southeastern BJD were monitored continuously between 2013 and 2017. Water surface evaporation and rainfall in this area were also measured. Combining these acquired data, groundwater discharge rates were estimated using water balance models. The results show that the four lakes have similar recharge and discharge patterns, but at different average net groundwater discharge rates ranging from 1.79 to 3.09 mm d−1. The lake level variation mainly depends on groundwater discharge and lake surface evaporation. We found that diurnal lake level variation may be controlled by earth tide and atmospheric pressure change, and is five times greater than the evaporation. The desert precipitation and deep confined groundwater with high temperature were found also recharging the desert lakes. An Empirical Mode Decomposition (EMD) method was used to identify the lake level trend. All lake levels increased over the last four years, except one decreased in 2015 and 2016. The lake levels’ increasing trend is synchronously similar with the precipitation in north China. This study analyzes annual and seasonal lake level variations, and also finds the diurnal water cycle between the groundwater and lake water for the first time.

Heterogeneous Permeability Changes along a Fault Zone Caused by the Xingwen M5.7 Earthquake in SW China

AbstractEarthquakes can change permeability. Continuous monitoring of the response of water level to solid Earth tides or changes in barometric pressure provides an opportunity to document how earthquakes influence permeability. Here we document spatial variations in changes in a fault zone in SW China. The response of the water level to barometric pressure and the Earth tide in four observation wells was used to calculate the relative changes in permeability at different locations on the fault before and after the Xingwen M5.7 earthquake. The results revealed that the earthquake resulted in a spatial heterogeneity in permeability changes along the Huarongshan fault. Moreover, permeability changes in the horizontal and vertical directions differed from one another at the same well location; that is, there was anisotropy at each location. These findings will help to enhance the understanding of earthquake‐induced changes of permeable fault structure and fault segment deformation.

Response of leaky aquifers to Earth tides – Interpreted with numerical simulation

The response of aquifers to Earth’s solid tides (Earth tides) has increasingly been used as a tool for monitoring the hydraulic properties of groundwater systems. Recent studies of the tidal response of the Arbuckle aquifer opened to a USGS deep well in Oklahoma (Wang et al., 2018; Barbour et al., 2019), which has been injected with an enormous amount of toxic wastewater, showed evidence that this aquifer may be leaking. Quantitative interpretation of the tidal response of this aquifer was made with a one-dimensional analytical solution (Wang et al., 2018) that showed that substantial leakage is occurring. However, the analytical model has inherent simplifications such as conductivity isotropy, small aquifer thickness, absence of aquitard storage, and no basement leakage. In this study we revisit the tidal response of leaky aquifers with a finite-element, multi-layered model where such simplifications are removed. We found that the simplifications in the analytical model lead to overly conservative estimates of leakage. We revisit the tidal response of the Arbuckle aquifer in Oklahoma with the numerical simulation and estimate an average vertical hydraulic conductivity of 2×10-6to7×10-5 m/s for the aquitard overlying the Arbuckle. Thus the ‘aquitard’ above the Arbuckle is not confining at this location but is as conductive as the aquifer itself. Given the fast rise of fluid level in many Arbuckle wells in response to the injection of hundreds of millions of barrels of wastewater into this aquifer across Oklahoma and Kansas, the present result calls for vigilant monitoring of leakage of wastewater from the Arbuckle aquifer into the overlying freshwater reservoirs and the surface environment. Plain Language SummaryEarthquakes can damage the confinement of groundwater aquifers and thus can cause seismic hazard by letting freshwater in some aquifers to be contaminated or stored toxic wastewater in other aquifers to leak out into the environment. Thus it is important to monitor possible leakage of aquifers in earthquake countries. Analysis of the aquifer response to Earth’s solid tides in a USGS deep well in Oklahoma (Wang et al., 2018; Barbour et al., 2019), which has been used as the repository of an enormous amount of injected toxic wastewater, shows that the aquifer may be leaking. An analytical solution (Wang et al., 2018) that contains several simplifications was used to quantify the aquifer leakage from the tidal response. Here we use a two-dimensional, multilayered numerical simulation without these simplifications to explore the limitations of the analytical model. We find that aquitard storage and basement leakage have important effects on the tidal response of aquifers and the omission of these factors in the analytical solution may have caused underestimation of the aquifer leakage. We then apply the numerical model to interpret the tidal response of water level documented in a USGS deep monitoring well installed in the Arbuckle aquifer in Oklahoma, where an enormous amount of toxic wastewater has been stored. With reasonable estimates of the aquitard storage, our simulations yield an estimate of 2×10-6to7×10-5 m/s for the vertical hydraulic conductivity of the aquitard. Thus the ‘aquitard’ is not at all confining but is as conductive as the aquifer itself. Given the fast rise of fluid level in many Arbuckle wells in response to the injection of hundreds of millions of barrels of wastewater into this aquifer across Oklahoma and Kansas, the present result calls for vigilant monitoring of leakage of wastewater from the Arbuckle aquifer into the overlying freshwater reservoirs and the surface environment.

Interaction between seismicity and deformation on different time scales in volcanic areas: Campi Flegrei and Stromboli

Abstract. We study oscillations recorded at Stromboli and Campi Flegrei by different sensors: seismometers, strainmeters and tiltmeters. We examine both the high-frequency (>0.5 Hz) portion of the spectrum and very long period signals up to tidal scales. In this context, seismicity and deformation are investigated on different time scales (from minutes to days/years) in order to identify the basic elements of their interaction, whose understanding should provide new insights on the predictive models. In this work, the strict relation of tides and volcanic processes is shown. At Stromboli, indeed the transition from the stationary phase to the non-stationary phase seems to have a tidal precursor that is related to the duration of the crisis. The subsequent volcanic activity is interpreted as the response of the volcano to restore the equilibrium condition. The moveout from equilibrium produces, first, variations in the standard statistics of explosions, then leads to effusive stage and to a pressure drop in the shallow feeding system. That process induces the nucleation of a gas bubble and the excitation of low frequencies. Campi Flegrei seismicity shows a correlation between the diurnal solar solid tide and the energy released by the long period signals, indicating that the whole mechanism is modulated on a tidal scale. In other words, in the case of Stromboli, a departure from the equilibrium state is marked by solid tide variations in a certain frequency band. On the other hand, at Campi Flegrei diurnal to annual solid tides modulate an increase of volcanic activity.

A study of the solid earth tides, ocean and atmospheric loadings using an 8-year record (2010–2018) from superconducting gravimeter OSG-060 at Djougou (Benin, West Africa)

We investigate a nearly 8-year record (2010–2018) of the superconducting gravimeter OSG-060 located at Djougou (Benin, West Africa). We first perform a tidal analysis with ET34-ANA v7.1 software that leads to the gravimetric amplitude and phase factors for all separable waves according to the available time duration. We test nine different ocean tide models for the main eleven tidal constituents (Ssa, Mm, Mf, Q1, O1, P1, K1, N2, M2, S2, K2). After correction for ocean tidal loading we obtain the real and imaginary parts of the residual vector. We also investigate atmospheric loading which is dominated in this equatorial location by the thermal waves S1 and S2 that are modulated in amplitude by annual and semi-annual components. After correction for ocean loading, we test different air pressure corrections on the tidal gravimetric factors for the waves Sa, Ssa, S1 and S2. We show the rather large discrepancy that exists between the classical single admittance pressure reduction and a hybrid model using global atmospheric models everywhere except in the local zone where the model pressure is replaced by the observed pressure.

Calculation of Tidal Displacements and Tilts for a Nonelastic Rotating Earth

A technique for calculating tidal displacements and tilts for the Earth both with the ocean and without it is presented in this work. This technique mainly follows the technique described in the International Earth Rotation Service Conventions and differs from it in small corrections in formulas for the calculation of displacements for diurnal (21) and semidiurnal (22) waves, as well as in an another set of usual and load Love numbers. Values of the gamma factors for the Earth without the ocean are also presented. Our results can be used for the processing of GNSS and tilt-measuring observations. The obtained results are compared with works by other authors, and the calculation technique is implemented in the new version of the ATLANTIDA3.1_2017 program for predicting parameters of Earth tides.

Changes in Physical Properties of Inland Streamwaters Induced by Earth and Atmospheric Tides

Earth and atmospheric tides create oscillations in water parameters of inland rivers, mainly due to the similar behavior of groundwaters. Tidal oscillations of inland rivers were termed orthotides and were detected in fluctuations of water level and specific conductivity of some rivers. However, few things are understood about orthotides because of their recent discovery. Here, we show that orthotidal signals exist in streamwater temperature too. Wavelet and T_TIDE analyses are used to study streamwater temperature and specific conductivity. We found solar and lunar semidiurnal orthotides (S2 and M2) in Alapaha River (USA) water temperature and Wybong River (Australia) water specific conductivity with amplitudes of up to 0.6 °C and 11.3 µS/cm. We demonstrate that the tidal semidiurnal cycles have statistical significance and are caused by similar cycles in groundwater. Oscillations found in water temperature time series for some new moon time intervals have shapes that correlate with the gravitational tides. Diurnal and fortnightly tidal cycles were found and overlapped with other natural cycles with similar periodicities. The inclusion of more water parameters to the list of orthotidally sensitive parameters indicates the wider than expected environmental impact of the small periodic natural changes.

Topography and Tilt at Volcanoes

For optimal monitoring of the deformation of a volcano, instrumentation should be deployed at the location most sensitive to changes at the suspected deformation source. The topographic effect on tilt depends strongly on the orientation of the deformation field relative to the surface on which the instrument is deployed. This fact has long been understood and corrected for in tilt measurements related to body tides and referred to as “cavity” or “topographic effects” (Harrison, 1976). Despite this, and whilst topography at volcanoes is often significant, until now the topographic effect on tilt at volcanoes has not been systematically explored. Here, we investigate the topographic effect on tilt produced by either the pressurization of a reservoir or conduit, or shear stress as magma ascends through a conduit, using 2D axisymmetric and 3D finite element deformation modeling. We show that topography alone can amplify or reduce the tilt by more than an order of magnitude, and control the orientation of the maximum tilt. Therefore, a decrease in tilt can even be caused by an increase in deformation at the source. Hence, inverting for the source stress using simple analytical models that neglect topography could potentially lead to a misinterpretation of how the volcanic system is evolving. Since topographic features can amplify the tilt signal, they can be exploited when deciding upon an installation site.

Frequency dependence of the polar motion resonance

SUMMARY The nutation of the Celestial Intermediate Pole can be considered as a retrograde diurnal polar motion. As the common polar motion, it presents a resonance, but with period TPM and quality factor QPM differing from the ones characterizing the Chandler wobble (TCW = 430.2−431.6 d, QCW in the interval (56 255) according to Nastula & Gross): according to the nutation analysis presented in a separate paper, this period is about TPM = 380 d and the quality factor becomes −10. In this study, we aim to revisit the geophysical interpretation of this result. Two complementary factors account for the observed values: the non-equilibrium response of the ocean to the pole tide potential in the diurnal band, and the resonance of the solid Earth tide at the free core nutation period. This leads to a resonance of TPM in the vicinity of the free core nutation period, confirmed by estimates derived from nutation analysis.

Improvements in seismic resolution and current limitations in the Global Seismographic Network

SUMMARYStation noise levels play a fundamental limitation in our ability to detect seismic signals. These noise levels are frequency-dependent and arise from a number of physically different drivers. At periods greater than 100 s, station noise levels are often limited by the self-noise of the instrument as well as the sensitivity of the instrument to non-seismic noise sources. Recently, station operators in the Global Seismographic Network (GSN) have deployed several Streckeisen STS-6A very broad-band borehole seismometers. These sensors provide a potential replacement for the no-longer-produced Streckeisen STS-1 seismometer and the GeoTech KS-54 000 borehole seismometer. Along with showing some of the initial observational improvements from installing modern very broad-band seismometers at depth, we look at current limitations in the seismic resolution from earth tide periods 100 000 s (0.01 mHz) to Nyquist at most GSN sites (0.02 s or 50 Hz). Finally, we show the potential for improved observations of continuously excited horizontal Earth hum as well as the splitting of very long-period torsional modes. Both of these observations make use of the low horizontal noise levels which are obtained by installing very broad-band borehole seismometers at depth.

A high-sensitivity MEMS gravimeter with a large dynamic range

Precise measurement of variations in the local gravitational acceleration is valuable for natural hazard forecasting, prospecting, and geophysical studies. Common issues of the present gravimetry technologies include their high cost, high mass, and large volume, which can potentially be solved by micro-electromechanical-system (MEMS) technology. However, the reported MEMS gravimeter does not have a high sensitivity and a large dynamic range comparable with those of the present commercial gravimeters, lowering its practicability and ruling out worldwide deployment. In this paper, we introduce a more practical MEMS gravimeter that has a higher sensitivity of 8 μGal/√Hz and a larger dynamic range of 8000 mGal by using an advanced suspension design and a customized optical displacement transducer. The proposed MEMS gravimeter has performed the co-site earth tides measurement with a commercial superconducting gravimeter GWR iGrav with the results showing a correlation coefficient of 0.91.

Toward Absolute Phase Change Recovery With InSAR: Correcting for Earth Tides and Phase Unwrapping Ambiguities

Radar interferograms provide a map of the phase difference between the reference and repeat acquisitions modulo ${2\pi }$ . Under ideal conditions, the phase can be unwrapped to provide an absolute phase connection across the map, although there is always an unknown integer phase ambiguity (i.e., ${N2\pi }$ ) for the entire map. Here, we demonstrate a practical time series method to solve for these integer ambiguities in order to recover the absolute phase change between the first and last SAR images. An important first step is to correct the phase of each SAR image for the well-known solid earth tide, which typically produces a line of sight offset ±150 mm, as well as, trends along and across each image of ~20 mm. This tide correction significantly reduces the noise in the InSAR time series, especially at the L-band. These tidally corrected interferograms are then unwrapped and used to solve for a set of integer ambiguities that achieves phase closure when summing around loops in the stack. There is an infinite number of ambiguity combinations that achieve loop closure; thus, regularization is required. In contrast to previous studies that use a least-squares approach to find the ambiguities, we adopt an ${L}_{1}$ -norm approach to find the minimum number of ambiguity corrections needed to achieve loop closure. We note that the split-spectrum ionospheric correction can introduce ${N\pi }$ ambiguities and suggest two approaches for correcting both ${N2\pi }$ and ${N\pi }$ ambiguities.

THE PRESENCE OF GEOPHYSICAL LOADINGS IN GPS OBSERVATIONS USING GENERAL LEAST SQUARES APPROACHES

Abstract. The earth’s crust undergoes natural deformation due to the geophysical loadings that consist of the earth body tide, ocean tide loading, atmospheric pressure loading and pole tide. This periodic displacement is generated by the changes of the gravitational attraction between the moon and the sun acting upon the earth’s rotation, along with the temporal atmospheric changes and the variability of the ocean tide. The study of the geophysical loadings is important in the geodesy field as the magnitude of the signals is significant and can contribute to errors in space geodetic measurements such as Global Positioning System (GPS), Very-Long Baseline Interferometry (VLBI) and Altimeter. This study is conducted to evaluate the percentage of geophysical loadings in GPS observations by adopting general least square approaches. The presence of the geophysical loadings indicates that as many as 76% to 93% of the geophysical loadings signal are contained in the GPS time series. The findings reveal that earth body tide signals are more significant if compared to ocean tide loading signals because the magnitude of the earth body tide is greater than that of the ocean tide loading and it affects the coordinate system particularly at up component. Results illustrated the potential of GPS to provide the local parameters of the geophysical loadings that are beneficial for earth tidal modelling and that can be used to improve the quality of space geodetic measurements.

Comparison of aquifer parameters inferred from water level changes induced by slug test, earth tide and earthquake – A case study in the three Gorges area

Hydraulic conductivity plays an important role in groundwater systems, but the estimation of hydraulic conductivity has many difficulties (the costs, feasibility and the scale-dependent results). In this study, we compared the hydraulic conductivity inferred from the conventional method (slug test) and the natural perturbation methods (tidal response and post-seismic water level recovery methods) at two confined wells, DJP well and MP well. The results show that the hydraulic conductivities estimated by the conventional method and the natural perturbation methods deviate somewhat from each other. The reason for the difference in hydraulic conductivities inferred from three methods is the variations of wellbore skin. By analyzing the uncertainty of estimation, we conclude that the different assumptions of the models cause inherent uncertainty and that the parameter uncertainty is secondary. The calculation results of these methods represent the different scales of the aquifer properties: 5–10 m for the slug test and 10–25 m for the tidal response and the post-seismic water level recovery methods, averaged by the hydraulic properties of the fault zone. The calculation errors of the three methods are 25% for the slug test, less than 10% for the tidal analysis and larger than 10% for the third method. Based on these comparisons, we conclude that the tidal response method is the most favorable way to infer aquifer parameters in this study. Both the tidal response and post-seismic water level recovery method provide a way to estimate aquifer properties as well as the mechanism of the co-seismic water level responses.

Lunar Tide in the F Region Ionosphere

AbstractIn this paper the magnetic latitude (±50°) and longitude, local solar time (LST), and month‐to‐month variability of the M2 lunar semidiurnal tide in the ionosphere is revealed through analysis of topside F region electron density measurements by the Planar Langmuir Probe instrument on the CHAMP satellite during the two 5‐year periods 2001–2005 and 2005–2009. The local time precession rate of CHAMP is such that 5 years is required to obtain full LST coverage for every month of the year at each latitude of interest. Thus, each 5‐year period is compressed into one equivalent year. M2 amplitudes, expressed in terms of percent residuals from a background value, range between about 3% and 20% and vary considerably with LST and magnetic longitude. Longitude variations in principle arise from zonal asymmetries in lunar tidal forcing due to Earth and ocean tides, as well as magnitude of Earth's magnetic field. The O1 diurnal tide is also discussed in the context of CHAMP and other measurements of the F region ionosphere.