Fundamental statistical techniques for the analysis of earth tides

1971 ◽  
Vol 61 (1) ◽  
pp. 203-215
Author(s):  
Cheh Pan
Keyword(s):  
Computer Technology ◽  
Earth Tide ◽  
Power Spectra ◽  
Correlation Coefficients ◽  
Earth Tides ◽  
Statistical Techniques ◽  
The Earth ◽  
Tidal Data ◽  
Instrumental Drift ◽  
Phase Differences

abstract Recent advances in instrumentation, digital computer technology and mathematical theory promote the error analysis of Earth-tide data. Various statistical techniques developed and used in other fields are applicable in the study of Earth tides, and the accuracy of the Earth's rigidity constants determined from the tides will be greatly improved with the help of these techniques. The fundamentals of the statistical techniques of autocorrelation, crosscorrelation, convolution, statistical means, bandpass filtering, correlation coefficients, power spectra, coherency and equalization are described, and their principal applications in the Earth-tide analysis summarized. Examples of effective application of these techniques in the elimination of the errors in the tidal data such as those introduced from instrumental drift, phase differences between the observed and predicted tides, etc. are discussed. This work is an attempt to introduce statistical analysis into the Earth-tide study.

Identification of the Earth Tide’s Influences and its Main Influencing-Components on Groundwater Level in an Unconfined-Aquifer

2020 ◽  
Author(s):  
Jian Guo ◽  
Mo Xu ◽  
Haoxin Shi ◽  
Jianhong Ge
Keyword(s):  
Groundwater Level ◽  
Cross Correlation ◽  
Earth Tide ◽  
Unconfined Aquifer ◽  
Earth Tides ◽  
Groundwater Levels ◽  
Monitoring Well ◽  
The Earth ◽  
Cross Correlation Analysis ◽  
Periodic Changes

<p>It is well known that various kinds of factors are causing the fluctuation of the groundwater level. The influence of earth tide on groundwater is first observed in confined-aquifer, while in unconfined-aquifer, understanding the influence of earth tide on the micro-fluctuation of the water level is crucial for obtaining key geo-hydrological parameters of the aquifer. In this study, the groundwater level of a monitoring well in Kualiangzi Village, Zhongjiang County, Deyang, as well as the data of local earth tides and rainfall were collected. And then the identification of the earth tide’s influences and its main influencing-components on groundwater level were studied by means of spectral analysis, cross-correlation analysis and harmonic analysis. The results show that the local groundwater levels are featured periodic changes of 1-day, 1/2 day and 1/3 day, which are corresponded to the earth tide. Moreover, the amplitude of the groundwater levels are negatively correlated with the earth tide, and there is no obvious hysteresis between them. The main influencing-components of earth tide are K1 diurnal wave and S2 semidiurnal wave.</p>

scholarly journals A Simple Theory on the Dynamical Effects of a Stratified Fluid Core Upon Nutational Motion of the Earth

1980 ◽  
Vol 78 ◽  
pp. 165-183 ◽  
Author(s):  
Tetsuo Sasao ◽  
Shuhei Okubo ◽  
Masanori Saito
Keyword(s):  
Linear Equations ◽  
Earth Tide ◽  
Outer Core ◽  
Stratified Fluid ◽  
Earth Tides ◽  
Momentum Balance ◽  
Earth Model ◽  
The Earth ◽  
Fluid Core ◽  
Whole Earth

The theory of Molodensky (1961) on dynamical effects of a stratified fluid outer core upon nutations and diurnal Earth tides is reconstructed on a new and probably much simpler ground. A theory equivalent to Molodensky's is well represented on the basis of two linear equations for angular-momentum balance of the whole Earth and the fluid outer core, which differ from the well-known equations of Poincaré (1910) only in the existence of products of inertia due to deformations of the whole Earth and fluid outer core. The products of inertia are characterized by four parameters which are easily computed for every Earth model by the usual Earth tide equations. A reciprocity relation exists between two of the parameters. The Adams-Wiliamson condition is not a necessary premise of the theory. Amplitudes of nutations and tidal gravity factors are computed for three Earth models. A dissipative core-mantle coupling is introduced into the theory qualitatively. The resulting equations are expressed in the same form as those of Sasao, Okamoto and Sakai (1977). Formulae for secular changes in the Earth-Moon system due to the core-mantle friction are derived as evidences of internal consistency of the theory.

scholarly journals Radial variation of whistler-mode chorus: first results from the STAFF/DWP instrument on board the Double Star TC-1 spacecraft

2005 ◽  
Vol 23 (8) ◽  
pp. 2937-2942 ◽  
Author(s):  
O. Santolík ◽  
E. Macúšová ◽  
K. H. Yearby ◽  
N. Cornilleau-Wehrlin ◽  
H. StC. K. Alleyne
Keyword(s):  
Cyclotron Frequency ◽  
Power Spectra ◽  
Double Star ◽  
Electron Cyclotron ◽  
Radial Variation ◽  
Whistler Mode ◽  
Electron Cyclotron Frequency ◽  
The Earth ◽  
First Results ◽  
Initial Results

Abstract. We use the first measurements of the STAFF/DWP instrument on the Double Star TC-1 spacecraft to investigate whistler-mode chorus. We present initial results of a systematic study on radial variation of dawn chorus. The chorus events show an increased intensity at L parameter above 6. This is important for the possible explanation of intensifications of chorus, which were previously observed closer to the Earth at higher latitudes. Our results also indicate that the upper band of chorus at frequencies above one-half of the electron cyclotron frequency disappears for L above 8. The lower band of chorus is observed at frequencies below 0.4 of the electron cyclotron frequency up to L of 11-12. The maxima of the chorus power spectra are found at slightly lower frequencies compared to previous studies. We do not observe any distinct evolution of the position of the chorus frequency band as a function of L. More data of the TC-1 spacecraft are needed to verify these initial results and to increase the MLT coverage.

scholarly journals Evaluation of global ocean tide models based on tidal gravity observations in China

2020 ◽  
Author(s):  
Hongbo Tan ◽  
Chongyong Shen ◽  
Guiju Wu
Keyword(s):  
High Precision ◽  
Earth Tide ◽  
Global Ocean ◽  
Ocean Tide ◽  
Ocean Tides ◽  
Ocean Tide Model ◽  
Tidal Forces ◽  
The Earth ◽  
Gravity Observation ◽  
Ocean Tide Models

<p>Solid Earth is affected by tidal cycles triggered by the gravity attraction of the celestial bodies. However, about 70% the Earth is covered with seawater which is also affected by the tidal forces. In the coastal areas, the ocean tide loading (OTL) can reach up to 10% of the earth tide, 90% for tilt, and 25% for strain (Farrell, 1972). Since 2007, a high-precision continuous gravity observation network in China has been established with 78 stations. The long-term high-precision tidal data of the network can be used to validate, verifying and even improve the ocean tide model (OTM).</p><p>In this paper, tidal parameters of each station were extracted using the harmonic analysis method after a careful editing of the data. 8 OTMs were used for calculating the OTL. The results show that the Root-Mean-Square of the tidal residuals (M<sub>0</sub>) vary between 0.078-1.77 μgal, and the average errors as function of the distance from the sea for near(0-60km), middle(60-1000km) and far(>1000km) stations are 0.76, 0.30 and 0.21 μgal. The total final gravity residuals (Tx) of the 8 major constituents (M<sub>2</sub>, S<sub>2</sub>, N<sub>2</sub>, K<sub>2</sub>, K<sub>1</sub>, O<sub>1</sub>, P<sub>1</sub>, Q<sub>1</sub>) for the best OTM has amplitude ranging from 0.14 to 3.45 μgal. The average efficiency for O<sub>1</sub> is 77.0%, while 73.1%, 59.6% and 62.6% for K<sub>1</sub>, M<sub>2</sub> and Tx. FES2014b provides the best corrections for O<sub>1</sub> at 12 stations, while SCHW provides the best for K<sub>1 </sub><sub>,</sub>M<sub>2</sub>and Tx at 12,8and 9 stations. For the 11 costal stations, there is not an obvious best OTM. The models of DTU10, EOT11a and TPXO8 look a litter better than FES2014b, HAMTIDE and SCHW. For the 17 middle distance stations, SCHW is the best OTM obviously. For the 7 far distance stations, FES2014b and SCHW model are the best models. But the correction efficiency is worse than the near and middle stations’.</p><p>The outcome is mixed: none of the recent OTMs performs the best for all tidal waves at all stations. Surprisingly, the Schwiderski’s model although is 40 years old with a coarse resolution of 1° x 1° is performing relative well with respect to the more recent OTM. Similar results are obtained in Southeast Asia (Francis and van Dam, 2014). It could be due to systematic errors in the surroundings seas affecting all the ocean tides models. It's difficult to detect, but invert the gravity attraction and loading effect to map the ocean tides in the vicinity of China would be one way.</p>

scholarly journals On Investigations of the Tidal Waves Mf and Mm

1979 ◽  
Vol 82 ◽  
pp. 315-316
Author(s):  
G. P. Pil'nik
Keyword(s):  
Solid Earth ◽  
Elastic Properties ◽  
Earth Tides ◽  
Love Number ◽  
Astronomical Observations ◽  
Tidal Waves ◽  
The Earth ◽  
Astronomical Time ◽  
Solid Earth Tides

The comparison of astronomical time observations with the theory of solid-Earth tides makes it possible to determine the Love number, k, which characterizes the elastic properties of the Earth. In addition, the comparison of values of k determined from different tidal waves allows us to judge the accuracy of the nutational theory in astronomical observations since both tides and the Earth's nutation are produced by the same causes.

scholarly journals On the link between Earth tides and volcanic degassing

2019 ◽  
Author(s):  
Florian Dinger ◽  
Stefan Bredemeyer ◽  
Santiago Arellano ◽  
Nicole Bobrowski ◽  
Ulrich Platt ◽  
...  
Keyword(s):  
Quantitative Model ◽  
Earth Tides ◽  
Bubble Coalescence ◽  
Magmatic System ◽  
Volcanic Emissions ◽  
Volcanic Gas ◽  
Tidal Variation ◽  
Magma Flow ◽  
Volcanic Degassing ◽  
The Earth

Abstract. Long-term measurements of volcanic gas emissions conducted during the recent decade suggest that under certain conditions the magnitude or chemical composition of volcanic emissions exhibits periodic variations with a period of about two weeks. A possible cause of such a periodicity can be attributed to the Earth tidal potential. The phenomenology of such a link has been debated for long, but no quantitative model has yet been proposed. The aim of this paper is to elucidate whether a causal link from the tidal forcing to variation in the volcanic degassing can be traced analytically. We model the response of a simplified magmatic system to the local tidal gravity variations and derive a periodical vertical magma displacement in the conduit with an amplitude of 0.1–1 m, depending on geometry and physical state of the magmatic system. We find that while the tide-induced vertical magma displacement has presumably no significant direct effect on the volatile solubility, the differential magma flow across the radial conduit profile may result in a significant increase of the bubble coalescence rate in a depth of several kilometres by up to several ten percent. Because bubble coalescence facilitates separation of gas from magma and thus enhances volatile degassing, we argue that the derived tidal variation may propagate to a manifestation of varying volcanic degassing behaviour. The presented model provides a first basic framework which establishes an analytical understanding of the link between the Earth tides and volcanic degassing.

scholarly journals Observational evidences for the speed of the gravity based on the Earth tide

2012 ◽  
Vol 58 (4-5) ◽  
pp. 474-477 ◽  
Author(s):  
KeYun Tang ◽  
ChangCai Hua ◽  
Wu Wen ◽  
ShunLiang Chi ◽  
QingYu You ◽  
...  
Keyword(s):  
Earth Tide ◽  
The Earth

A Pump-Probe Analysis of Nonlinear Elastic Behavior on the San Andreas Fault

2020 ◽  
Author(s):  
Andrew Delorey
Keyword(s):  
San Andreas Fault ◽  
Earth Tides ◽  
Elastic Behavior ◽  
Fracture Networks ◽  
Pump Probe ◽  
San Andreas ◽  
The Earth ◽  
Probe Analysis ◽  
Highly Nonlinear ◽  
Nonlinear Elastic

<p>Fracture networks in the subsurface influence nearly every aspect of earthquakes and natural hazards.  These aspects, including stress, permeability and material failure, and are important for hazard assessment. However, our ability to monitor fracture behavior in the Earth is insufficient for any type of decision-making regarding hazard avoidance.  I propose a new method for probing the evolution of fracture networks in situ to inform public safety decisions and understand natural systems. </p><p>In heterogeneous, fractured materials, like those found in the Earth, the relationship between stress and strain is highly nonlinear.  This nonlinearity in the upper crust is almost entirely due to fractures.  By measuring to what extent Earth materials exhibit nonlinear elastic behavior, we can learn more information about them.  Directly, measuring physical properties may be more useful than just detecting that fractures are present or how they are shaped and oriented.  We measure nonlinearity by measuring the apparent modulus at different strains. </p><p>In this study we use a pump-probe analysis, which involves continuously probing velocity (as a proxy for modulus) while systematically straining the material.  We will use solid Earth tides as a strain pump and empirical Green’s functions (EGF) as a velocity probe.  We apply this analysis to the San Andreas Fault near Parkfield, California.  We chose Parkfield because there is a long-term deployment of borehole seismic instruments that recorded before and after a M6 earthquake.  We find evidence that nonlinear behavior is correlated with the seismic cycle and therefore it may contain information on the both the evolution and current state of stress on faults. </p>

The Relationship Between Electron-Only Magnetic Reconnection and Turbulence in Earth’s Magnetosheath

2020 ◽  
Author(s):  
Julia E. Stawarz ◽  
Jonathan P. Eastwood ◽  
Tai Phan ◽  
Imogen L. Gingell ◽  
Alfred Mallet ◽  
...  
Keyword(s):  
Magnetic Reconnection ◽  
Power Spectra ◽  
Theoretical Work ◽  
Small Scale ◽  
Current Sheets ◽  
The Earth ◽  
Recent Theoretical Work ◽  
Magnetospheric Multiscale ◽  
Scale Turbulence ◽  
The Relationship

<p>The Earth’s magnetosheath is filled with small-scale current sheets arising from turbulent dynamics in the plasma. Previous observations and simulations have provided evidence that such current sheets can be sites for magnetic reconnection. Recently, observations from the Magnetospheric Multiscale (MMS) mission have revealed that a novel form of “electron-only” reconnection can occur at these small-scale, turbulence-driven current sheets, in which ions do not appear to couple to the reconnected magnetic field to form ion jets. The presence of electron-only reconnection may facilitate dissipation of the turbulence, thereby influencing the partition of energy between ions and electrons, and can alter the nonlinear dynamics of the turbulence itself. In this study, we perform a survey of turbulent intervals in the Earth’s magnetosheath as observed by MMS in order to determine how common magnetic reconnection is in the turbulent magnetosheath and how it impacts the small-scale turbulent dynamics. The magnetic correlation length, which dictates the length of the turbulent current sheets, is short enough in most of the examined intervals for reconnection with reduced or absent ion jets to occur. Magnetic reconnection is found to be a common feature within these intervals, with a significant fraction of reconnecting current sheets showing evidence of sub-Alfvénic ion jets and super- Alfvénic electron jets, consistent with electron-only reconnection. Moreover, a subset of the intervals exhibit changes in the behavior of the small-scale magnetic power spectra, which may be related to the reconnecting current sheets. The results of the survey are compared with recent theoretical work on electron-only reconnection in turbulent plasmas.</p>

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