Power spectral analyses of the dipole moment of the earth's magnetic field inferred from ocean sediment cores and archeomagnetic data from time scales of 100 yr to 4 Myr have been carried out. The power spectrum is proportional to 1/f where f is the frequency. These analyses compliment previous work which has established a 1/f^2 spectrum for variations at time scales less than 100 yr. Power spectral analyses of inclination and declination inferred from lake sediments from time scales of 10 yr to 30 kyr have also been performed. The spectra are constant above time scales of 3 kyr, proportional to 1/f^2 from time scales of 500 yr to 3 kyr, and constant again below time scales of 500 yr. The 3 kyr time scale is associated with the decay time of the quadrupole moment. We test the hypothesis that reversals are the result of variations in dipole intensity with a 1/f spectrum which occasionally are large enough to cross the zero intensity value. Synthetic binormal time series with a 1/f power spectrum representing variations in the earth's dipole moment are constructed. Synthetic reversals from these time series exhibit statistics in good agreement with the reversal record. 1/f noise behavior is reproduced with a model of magnetic diffusion in the earth's core driven by dynamo action modeled as a random amplification or destruction of the local magnetic field.
The distribution of inter-occurrence time between seismic events is a quantity of great interest in seismic risk assessment. We evaluate this distribution for different models of earthquakes occurrence and follow two distinct approaches: The non homogeneous Poissonian and the non Poissonian one. In all cases we obtain either a power law or a power law damped by an exponential factor behaviour. This feature of the distribution makes impossible any prediction of earthquakes occurrence. Nevertheless it suggests the interpretation of the earthquake occurrence phenomenon as due to some non-linear d…
Evidence of fast variations in the Earth's core field are seen both in magnetic observatory and satellite records. We present here how they have been identified at the Earth's surface from ground-based observatory records and how their spatio-temporal structure is now characterised by satellite data. It is shown how their properties at the core mantle boundary are extracted through localised and global modelling processes, paying particular attention to their time scales. Finally are listed possible types of waves in the liquid outer core, together with their main properties, that may give ris…
Applying Detrended Fluctuation Analysis (DFA) to the geomagnetic data recorded at three measuring stations in Japan, Rong et al. in 2012 reported that anomalous magnetic field variations were identified well before the occurrence of the disastrous Tohoku $M_w$9.0 earthquake that occurred on 11 March 2011 in Japan exhibiting increased "non-uniform" scaling behavior. Here, we provide an explanation for the appearance of this increase of "non-uniform" scaling on the following grounds: These magnetic field variations are the ones that accompany the electric field variations termed Seismic Electric…
Global warming is affecting our Earth's environment. For example, sea level is rising with thermal expansion of water and fresh water input from the melting of continental ice sheets due to human-induced global warming. However, observing and modeling Earth's surface change has larger uncertainties in the changing rate and the scale and distribution of impacts due to the lack of direct measurements. Nowadays, the Earth observation from space provides a unique opportunity to monitor surface mass transfer and deformations related to climate change, particularly the global positioning system (GPS…
Global climate change, extreme climate events, earthquakes and their accompanying natural disasters pose significant risks to humanity. Yet due to the nonlinear feedbacks, strategic interactions and complex structure of the Earth system, the understanding and in particular the predicting of such disruptive events represent formidable challenges for both scientific and policy communities. During the past years, the emergence and evolution of Earth system science has attracted much attention and produced new concepts and frameworks. Especially, novel statistical physics and complex networks-base…
We consider three questions related to the 2011 Tohoku mega-earthquake: (1) Why was the event size so grossly under-estimated? (2) How should we evaluate the chances of giant earthquakes in subduction zones? and (3) What is the repeat time for magnitude 9 earthquakes off the Tohoku coast? The "maximum earthquake size" is often guessed from the available history of earthquakes, a method known for its significant downward bias. There are two quantitative methods for estimating the maximum magnitude in any region: a statistical analysis of the available earthquake record, and the moment conservat…
Self-similarity may stem from two origins: the process' increments infinite variance and/or process' memory. The $b$-value of the Gutenberg-Richter law comes from the first origin. In the frame of natural time analysis of earthquake data, a fall of the b-value observed before large earthquakes reflects an increase of the order parameter fluctuations upon approaching the critical point (mainshock). The increase of these fluctuations, however, is also influenced from the second origin of self-similarity, i.e., temporal correlations between earthquake magnitudes. This is supported by observations…
We have studied long period, 206 and 412 day, variations in tidal sea level corresponding to various moon phases collected from five observatories in the Northern and Southern hemispheres. Variations in sea level in the Bay of Fundy, on the eastern Canadian seaboard, with periods of variation 206 days, and 412 days, have been discovered and carefully studied by C. Desplanque and D. J. Mossman (2001, 2004). The current manuscript focuses on analyzing a larger volume of observational sea level tide data as well as on rigorous mathematical analysis of tidal force variations in the Sun-Earth-Moon …
We explore in depth the validity of a recently proposed scaling law for earthquake interevent time distributions in the case of the Southern California, using the waveform cross-correlation catalog of Shearer et al. Two statistical tests are used: on the one hand, the standard two-sample Kolmogorov-Smirnov test is in agreement with the scaling of the distributions. On the other hand, the one-sample Kolmogorov-Smirnov statistic complemented with Monte Carlo simulation of the inter-event times, as done by Clauset et al., supports the validity of the gamma distribution as a simple model of the sc…
The possibility of an increasing gravitational constant $G$ and its implication on the Earth's history are discussed. The model is consistent with geophysical and astronomical data. The number of days in early epochs predicted by the model is in agreement with those obtained from fossil corals. The model predicts that the Earth was initially cold and is gradually heating up during its course of evolution. The exact law for the variation of $G$ is still to be obtained from the variation of the Earth's parameters with cosmic expansion.
When applying the Earth's natural pulse electromagnetic fields to geophysical prospecting one should take into account characteristics of their spatial and temporal variations. ENPEMF is known to include both pulses attributed to atmospheric thunderstorms and pulses generated in the lithosphere by mechanic-to-electric energy conversion in rocks. It is evident that the most valuable information on the geophysical structure of a certain area is obviously contained in pulses originated from this area. This article covers a method of recording spatial variations of the Earth's natural pulse electr…
Recent observation studies have revealed that earthquakes are classified into several different categories. Each category might be characterized by the unique statistical feature in the time series, but the present understanding is still limited due to their nonlinear and nonstationary nature. Here we utilize complex network theory to shed new light on the statistical properties of earthquake time series. We investigate two kinds of time series, which are magnitude and inter-event time (IET), for three different categories of earthquakes: regular earthquakes, earthquake swarms, and tectonic tr…
The Late Pleistocene Antarctic temperature variation curve is decomposed into two parts: cyclic and stochastic. These two parts represent different but tightly interconnected processes and also represent two different types of self-organization of the Earth's climate system. The self-organization in the cyclic component is the non-linear auto-oscillation reaction of the Earth's climate system, as a whole, to the input of solar radiation. The self-organization in the stochastic component is a nonlinear critical process, taking energy from and fluctuating around, the cyclic component of the temp…
The mechanically oscillating, due to tidal forces, lithosperic plate activates, because of its high content in quartzite, the generation of a piezoelectric field. Due to the same mechanical oscillation the lithosphere is generally at a state of an oscillating stress load. Therefore, large EQs which occur at the peaks of the stress load must coincide with the peaks of the generated piezoelectric potential. In this work a physical mechanism is postulated that accounts for the latter hypothesis. The postulated model is statistically tested by comparing the time of occurrence of 280 large EQs (Ms>…
Nucleosynthetic Fe isotopic anomalies in meteorites may be used to reconstruct the early dynamical evolution of the solar system and to identify the origin and nature of the material that built planets. Using high-precision iron isotopic data of 23 iron meteorites from nine major chemical groups we show that all iron meteorites show the same fundamental dichotomy between non-carbonaceous (NC) and a carbonaceous (CC) meteorites previously observed for other elements. The Fe isotopic anomalies are predominantly produced by variation in 54Fe, where all CC iron meteorites are characterized by an e…
An Earth-like planetary magnetic field has been widely invoked as a requirement for habitability as it purportedly mitigates the fluxes of ionizing radiation reaching the surface and the escape of neutrals and ions from the atmosphere. Recent paleomagnetic evidence indicates that the nucleation of Earth's inner core, followed perhaps by an increase in geomagnetic field strength, might have occurred close to the Ediacaran period. Motivated by this putative discovery, we explore the ensuing ramifications from the growth or reversals of Earth's dynamo. By reviewing and synthesizing emerging quant…
In statistical seismology, the Epidemic Type Aftershocks Sequence (ETAS) model is a branching process used world-wide to forecast earthquake intensity rates and reproduce many statistical features observed in seismicity catalogs. In this paper, we describe a fractional differential equation that governs the earthquake intensity rate of the pure temporal ETAS model by using the Caputo fractional derivative and we solve it analytically. We highlight that the tools and special functions of fractional calculus simplify the classical methods employed to obtain the intensity rate and let us describe…
The analysis of strong motion recordings in structures is crucial to understand the damaging process during earthquakes. A very precise time-frequency representation, the reassigned smoothed pseudo-Wigner-Ville method, allowed us to follow the variation of the Millikan Library (California) and the Grenoble City Hall building (France) resonance frequencies during earthquakes. Under strong motions, a quick frequency drop, attributed to damage of the soil-structure system, followed by a slower increase is found. However, in the case of weak earthquakes, we show that frequency variations come from…
It has been long stated that there are profound analogies between fracture experiments and earthquakes; however, few works attempt a complete characterization of the parallelisms between these so separate phenomena. We study the Acoustic Emission events produced during the compression of Vycor (SiO2). The Gutenberg-Richter law, the modified Omori's law, and the law of aftershock productivity are found to hold for a minimum of 5 decades, are independent of the compression rate, and keep stationary for all the duration of the experiments. The waiting-time distribution fulfills a unified scaling …
Simultaneous measurements of the small-, intermediate- and large- positive ions and air earth current density made at a coastal station, Maitri at Antarctica during January to February 2005, are reported. Although, small and large positive ion concentrations do not show any systematic diurnal variations, variations in them are almost similar to each other. On the other hand, variations in intermediate positive ion concentrations are independent of variations in the small/large positive ions and exhibit a diurnal variation which is similar to that in atmospheric temperature on fair weather days…
This entry in the Encyclopedia of Complexity and Systems Science, Springer present a summary of some of the concepts and calculational tools that have been developed in attempts to apply statistical physics approaches to seismology. We summarize the leading theoretical physical models of the space-time organization of earthquakes. We present a general discussion and several examples of the new metrics proposed by statistical physicists, underlining their strengths and weaknesses. The entry concludes by briefly outlining future directions. The presentation is organized as follows. I Glossary II…
By using the M>=5 global earthquake data for Jan. 1950 to Dec. 2015, we performed statistical analyses for the parameters magnitude, time, and depth on a yearly scale. The magnitude spectrum, which is the earthquake number accumulated at different magnitudes, had an exponential distribution. For the first time, we report a very significant characteristic of the sinusoidal periodic variation in the spectral index. The cycle of the sine function fitting was 30.98 years. The concept of annual equivalent total magnitude (AETM) of total released energy for each year was introduced and the trend var…
The time dependence of the parameter of the Gutenberg-Richter (GR) magnitude distribution is computed for foreshock sequences of earthquakes, correlated with the main shock, by using the geometric-growth model of earthquake focus, the magnitude distribution of correlated earthquakes and the time-magnitude correlations, derived recently. It is shown that this parameter decreases in time in the foreshock sequence, from the background values down to the main shock. If correlations are present, this time dependence and the time-magnitude correlations provide a tool of monitoring the foreshock seis…
The GPS derived anomalous TEC disturbances before earthquakes were discovered in the last years using global and regional TEC maps, measurements over individual stations as well as measurements along individual GPS satellite passes. For strong mid-latitudinal earthquakes the seismo-ionospheric anomalies look like local TEC enhancements or decreases located in the vicinity of the forthcoming earthquake epicenter In case of strong low-latitudinal earthquakes there are effects related with the modification of the equatorial F2-region anomaly: deepening or filling of the ionospheric electron densi…
Extraction of information in the form of oscillations from noisy data of natural phenomena such as sounds, earthquakes, ionospheric and brain activity, and various emissions from cosmic objects is extremely difficult. As a method for finding periodicity in such challenging data sets, the 2D Hybrid approach, which employs wavelets, is presented. Our technique produces a wavelet transform correlation intensity contour map for two (or one) time series on a period plane defined by two independent period axes. Notably, by spreading peaks across the second dimension, our method improves apparent res…
Glaciations were attributed to variations of the Earths orbit (Milankovitch cycles). But the best ever dated paleoclimatic record (from a speleothem from Devils Hole, Nevada) demonstrated that the end of the last glacial period (termination II) happened 10 000 years before the one suggested by the orbital variations, i.e. the result appeared before the reason. This fact suggests that there is something wrong in the theory. Glaciations and deglaciations drive changes of the sea level. Changes in the speed of Earths rotation during glacial- interglacial transitions produce fracturing of the Eart…
After describing all the contradictions associated with the current Plate Tectonics theory, this paper proposes a model where a single cause can explain all geophysical and geological phenomena. The source of the Earth's activity lies in the difference of the angular velocities of the mantle and of the solid inner core. The friction between both spheres infers heat, which is the cause of the melted iron which constitutes most of the liquid outer core, as well as the source of the global heat flow. The solid inner core angular velocity is supposed to remain steady, while the mantle angular velo…
We use a normal-mode formalism to compute the response of a spherical, self-gravitating anelastic PREM-like Earth model to various excitation sources at the Slichter mode period. The formalism makes use of the theory of the Earth's free oscillations based upon an eigenfunction expansion methodology. We determine the complete response in the form of Green's function obtained from a generalization of Betti's reciprocity theorem. Surficial (surface load, fluid core pressure), internal (earthquakes, explosions) and external (object impact) sources of excitation are investigated to show that the tr…
We study statistical properties of the number of large earthquakes over the past century. We analyze the cumulative distribution of the number of earthquakes with magnitude larger than threshold M in time interval T, and quantify the statistical significance of these results by simulating a large number of synthetic random catalogs. We find that in general, the earthquake record cannot be distinguished from a process that is random in time. This conclusion holds whether aftershocks are removed or not, except at magnitudes below M = 7.3. At long time intervals (T = 2-5 years), we find that stat…
The relationship between the behavior of an ancient geomagnetic field characteristics (paleointensity and frequency of inversions) and cyclic recurrence of endogenic and cosmogeneous processes which are conceivably connected with radial mantle heat transmission and the Earth rotation speed has been studied. It is shown that endogenic processes affect the behavior of the paleointensity and frequency of inversions. Large basalt effusions identified with plumes are accompanied by the changes in paleointensity (by 30-40)% and the frequency of inversions. Characteristic time intervals of paleointen…
While the main causes of the temporal gravity variations observed by the GRACE space mission result from water mass redistributions occurring at the surface of the Earth in response to climatic and anthropogenic forcings (e.g., changes in land hydrology, in ocean mass, in mass of glaciers and ice sheets), solid Earth's mass redistributions are also recorded by these observations. This is the case, in particular, for the Glacial Isostatic Adjustment (GIA) or the viscous response of the mantle to the last deglaciation. However, it is only recently showed that the gravity data also contain the si…
The dynamical ellipticity of a planet expresses the departure of its mass distribution from spherical symmetry. It enters as a parameter in the description of a planet's precession and nutation, as well as other rotational normal modes. In the case of the Earth, uncertainties in this quantity's history produce an uncertainty in the solutions for the past evolution of the Earth-Moon system. Constraining this history has been a target of interdisciplinary efforts as it represents an astro-geodetic parameter whose variation is shaped by geophysical processes, and whose imprints can be found in th…
The polar motion data is analyzed to obtain accurate position of the figure axis referred to the Earth-fixed frame. The variation of the figure axis should be the basic object to which the geophysical events are linked. By the method of rigid dynamics, the relation between the rotational and the figure axes is derived. The polar motion is the motion of the rotational axis on the Earth's surface and therefore the exact position of the figure axis on the surface at each moment is obtained from the polar motion. Since the accuracy of the recent data for the polar motion is very high, the obtained…
The paper is a first attempt for statistical estimation of method for a short time prediction of incoming earthquake in the Balkan and Black Sea region from January to June, 2002. The essence of the discovery is that the geomagnetic local "quake" is a precursor of future earthquake, which time is determined by the tide gravitational potential behavior. A Balkan Black Sea region Earthquake's "When, where" Prediction Network is proposed.
The statistical properties of earthquake aftershocks are studied. The scaling relation for the exponents of the Omori law and the power-law calm time distribution (i.e., the interoccurrence time distribution), which is valid if a sequence of aftershocks is a singular Markovian process, is carefully examined. Data analysis shows significant violation of the scaling relation, implying the non-Markovian nature of aftershocks.
We use 20 years of magnetic field measurements from the Oersted, CHAMP and Swarm satellite missions, supplemented by calibrated platform magnetometer data from the CryoSat2 satellite, to study time variations of the Earth's core field at satellite altitude and at the core-mantle boundary (CMB). From the satellite data we derive composite time series of the core field secular variation (SV) with 4month cadence, at 300 globally distributed Geomagnetic Virtual Observatories (GVO). GVO radial SV series display regional fluctuations with 5-10 years duration and amplitudes reaching 20 nT/yr, most no…
The Late Pleistocene Antarctic temperature variation curve is decomposed into two components: cyclic and high frequency, stochastic. For each of these components, a mathematical model is developed which shows that the cyclic and stochastic temperature variations are distinct, but interconnected, processes with their own self-organization. To model the cyclic component, a system of ordinary differential equations is written which represent an auto-oscillating, self-organized process with constant period. It is also shown that these equations can be used to model more realistic variations in tem…
Large solar proton events (SPEs) affect the solar-terrestrial space environment and become a very important aspect in space weather research. In this work, we statistically investigate 78 solar proton events of 1996-2011 and find that there exists a longitudinally asymmetric distribution of flare sources of the solar proton events observed near 1 AU, namely, with the same longitude separation between magnetic field line footpoint of observer and flare sources, the number of the solar proton events originating from sources located at eastern side of the nominal magnetic footpoint of observer is…
We consider two statistical regularities that were used to explain Omori's law of the aftershock rate decay: the Levy and Inverse Gaussian (IGD) distributions. These distributions are thought to describe stress behavior influenced by various random factors: post-earthquake stress time history is described by a Brownian motion. Both distributions decay to zero for time intervals close to zero. But this feature contradicts the high immediate aftershock level according to Omori's law. We propose that these statistical distributions are influenced by the power-law stress distribution near the eart…
We directly determine the sensitivity and time delay of Earth's surface temperature response to annual solar irradiance variations from 60 years of data. A two-layer energy balance model is developed to interpret the results. Explaining both the resulting low sensitivity and time delay of 1-2 months requires negative feedback.
