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The dynamics of external contributions to the geomagnetic field is investigated by applying time-frequency methods to magnetic observatory data. Fractal models and multiscale analysis enable obtaining maximum quantitative information related to the short-term dynamics of the geomagnetic field activity. The stochastic properties of the horizontal component of the transient external field are determined by searching for scaling laws in the power spectra. The spectrum fits a power law with a scaling exponent beta, a typical characteristic of self-affine time-series. Local variations in the power-law exponent are investigated by applying wavelet analysis to the same time-series. These analyses highlight the self-affine properties of geomagnetic perturbations and their persistence. Moreover, they show that the main phases of sudden storm disturbances are uniquely characterized by a scaling exponent varying between 1 and 3, possibly related to the energy contained in the external field. These new findings suggest the existence of a long-range dependence, the scaling exponent being an efficient indicator of geomagnetic activity and singularity detection. These results show that by using magnetogram regularity to reflect the magnetosphere activity, a theoretical analysis of the external geomagnetic field based on local power-law exponents is possible.
In the eighties, the analysis of satellite altimetry data leads to the major discovery of gravity lineations in the oceans, with wavelengths between 200 and 1400 km. While the existence of the 200 km scale undulations is widely accepted, undulations at scales larger than 400 km are still a matter of debate. In this paper, we revisit the topic of the large-scale geoid undulations over the oceans in the light of the satellite gravity data provided by the GRACE mission, considerably more precise than the altimetry data at wavelengths larger than 400 km. First, we develop a dedicated method of directional Poisson wavelet analysis on the sphere with significance testing, in order to detect and characterize directional structures in geophysical data on the sphere at different spatial scales. This method is particularly well suited for potential field analysis. We validate it on a series of synthetic tests, and then apply it to analyze recent gravity models, as well as a bathymetry data set independent from gravity. Our analysis confirms the existence of gravity undulations at large scale in the oceans, with characteristic scales between 600 and 2000 km. Their direction correlates well with present-day plate motion over the Pacific ocean, where they are particularly clear, and associated with a conjugate direction at 1500 km scale. A major finding is that the 2000 km scale geoid undulations dominate and had never been so clearly observed previously. This is due to the great precision of GRACE data at those wavelengths. Given the large scale of these undulations, they are most likely related to mantle processes. Taking into account observations and models from other geophysical information, as seismological tomography, convection and geochemical models and electrical conductivity in the mantle, we conceive that all these inputs indicate a directional fabric of the mantle flows at depth, reflecting how the history of subduction influences the organization of lower mantle upwellings.
Wavelet modelling of the gravity field by domain decomposition methods: an example over Japan
(2011)
With the advent of satellite gravity, large gravity data sets of unprecedented quality at low and medium resolution become available. For local, high resolution field modelling, they need to be combined with the surface gravity data. Such models are then used for various applications, from the study of the Earth interior to the determination of oceanic currents. Here we show how to realize such a combination in a flexible way using spherical wavelets and applying a domain decomposition approach. This iterative method, based on the Schwarz algorithms, allows to split a large problem into smaller ones, and avoids the calculation of the entire normal system, which may be huge if high resolution is sought over wide areas. A subdomain is defined as the harmonic space spanned by a subset of the wavelet family. Based on the localization properties of the wavelets in space and frequency, we define hierarchical subdomains of wavelets at different scales. On each scale, blocks of subdomains are defined by using a tailored spatial splitting of the area. The data weighting and regularization are iteratively adjusted for the subdomains, which allows to handle heterogeneity in the data quality or the gravity variations. Different levels of approximations of the subdomains normals are also introduced, corresponding to building local averages of the data at different resolution levels.
We first provide the theoretical background on domain decomposition methods. Then, we validate the method with synthetic data, considering two kinds of noise: white noise and coloured noise. We then apply the method to data over Japan, where we combine a satellite-based geopotential model, EIGEN-GL04S, and a local gravity model from a combination of land and marine gravity data and an altimetry-derived marine gravity model. A hybrid spherical harmonics/wavelet model of the geoid is obtained at about 15 km resolution and a corrector grid for the surface model is derived.
Potential fields are classically represented on the sphere using spherical harmonics. However, this decomposition leads to numerical difficulties when data to be modelled are irregularly distributed or cover a regional zone. To overcome this drawback, we develop a new representation of the magnetic and the gravity fields based on wavelet frames. In this paper, we first describe how to build wavelet frames on the sphere. The chosen frames are based on the Poisson multipole wavelets, which are of special interest for geophysical modelling, since their scaling parameter is linked to the multipole depth (Holschneider et al.). The implementation of wavelet frames results from a discretization of the continuous wavelet transform in space and scale. We also build different frames using two kinds of spherical meshes and various scale sequences. We then validate the mathematical method through simple fits of scalar functions on the sphere, named 'scalar models'. Moreover, we propose magnetic and gravity models, referred to as 'vectorial models', taking into account geophysical constraints. We then discuss the representation of the Earth's magnetic and gravity fields from data regularly or irregularly distributed. Comparisons of the obtained wavelet models with the initial spherical harmonic models point out the advantages of wavelet modelling when the used magnetic or gravity data are sparsely distributed or cover just a very local zone
This paper is devoted to the digital processing of multicomponent seismograms using wavelet analysis. The goal of this processing is to identify Rayleigh surface elastic waves and determine their properties. A new method for calculating the ellipticity parameters of a wave in the form of a time-frequency spectrum is proposed, which offers wide possibilities for filtering seismic signals in order to suppress or extract the Rayleigh components. A model of dispersion and dissipation of elliptic waves written in terms of wavelet spectra of complex (two-component) signals is also proposed. The model is used to formulate a nonlinear minimization problem that allows for a high-accuracy calculation of the group and phase velocities and the attenuation factor for a propagating elliptic Rayleigh wave. All methods considered in the paper are illustrated with the use of test signals. (c) 2005 Pleiades Publishing, Inc
Standing stocks are typically easier to measure than process rates such as production. Hence, stocks are often used as indicators of ecosystem functions although the latter are generally more strongly related to rates than to stocks. The regulation of stocks and rates and thus their variability over time may differ, as stocks constitute the net result of production and losses. Based on long-term high frequency measurements in a large, deep lake we explore the variability patterns in primary and bacterial production and relate them to those of the corresponding standing stocks, i.e. chlorophyll concentration, phytoplankton and bacterial biomass. We employ different methods (coefficient of variation, spline fitting and spectral analysis) which complement each other for assessing the variability present in the plankton data, at different temporal scales. In phytoplankton, we found that the overall variability of primary production is dominated by fluctuations at low frequencies, such as the annual, whereas in stocks and chlorophyll in particular, higher frequencies contribute substantially to the overall variance. This suggests that using standing stocks instead of rate measures leads to an under- or overestimation of food shortage for consumers during distinct periods of the year. The range of annual variation in bacterial production is 8 times greater than biomass, showing that the variability of bacterial activity (e.g. oxygen consumption, remineralisation) would be underestimated if biomass is used. The P/B ratios were variable and although clear trends are present in both bacteria and phytoplankton, no systematic relationship between stock and rate measures were found for the two groups. Hence, standing stock and process rate measures exhibit different variability patterns and care is needed when interpreting the mechanisms and implications of the variability encountered.
The magnetosphere-ionosphere-thermosphere (MIT) dynamic system significantly depends on the highly variable solar wind conditions, in particular, on changes of the strength and orientation of the interplanetary magnetic field (IMF). The solar wind and IMF interactions with the magnetosphere drive the MIT system via the magnetospheric field-aligned currents (FACs). The global modeling helps us to understand the physical background of this complex system. With the present study, we test the recently developed high-resolution empirical model of field-aligned currents MFACE (a high-resolution Model of Field-Aligned Currents through Empirical orthogonal functions analysis). These FAC distributions were used as input of the time-dependent, fully self-consistent global Upper Atmosphere Model (UAM) for different seasons and various solar wind and IMF conditions. The modeling results for neutral mass density and thermospheric wind are directly compared with the CHAMP satellite measurements. In addition, we perform comparisons with the global empirical models: the thermospheric wind model (HWM07) and the atmosphere density model (Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Extended 2000). The theoretical model shows a good agreement with the satellite observations and an improved behavior compared with the empirical models at high latitudes. Using the MFACE model as input parameter of the UAM model, we obtain a realistic distribution of the upper atmosphere parameters for the Northern and Southern Hemispheres during stable IMF orientation as well as during dynamic situations. This variant of the UAM can therefore be used for modeling the MIT system and space weather predictions.
We investigate the influence of spatial heterogeneities on various aspects of brittle failure and seismicity in a model of a large strike-slip fault. The model dynamics is governed by realistic boundary conditions consisting of constant velocity motion of regions around the fault, static/kinetic friction laws, creep with depth-dependent coefficients, and 3-D elastic stress transfer. The dynamic rupture is approximated on a continuous time scale using a finite stress propagation velocity ("quasidynamic model''). The model produces a "brittle- ductile'' transition at a depth of about 12.5 km, realistic hypocenter distributions, and other features of seismicity compatible with observations. Previous work suggested that the range of size scales in the distribution of strength-stress heterogeneities acts as a tuning parameter of the dynamics. Here we test this hypothesis by performing a systematic parameter-space study with different forms of heterogeneities. In particular, we analyze spatial heterogeneities that can be tuned by a single parameter in two distributions: ( 1) high stress drop barriers in near- vertical directions and ( 2) spatial heterogeneities with fractal properties and variable fractal dimension. The results indicate that the first form of heterogeneities provides an effective means of tuning the behavior while the second does not. In relatively homogeneous cases, the fault self-organizes to large-scale patches and big events are associated with inward failure of individual patches and sequential failures of different patches. The frequency-size event statistics in such cases are compatible with the characteristic earthquake distribution and large events are quasi-periodic in time. In strongly heterogeneous or near-critical cases, the rupture histories are highly discontinuous and consist of complex migration patterns of slip on the fault. In such cases, the frequency-size and temporal statistics follow approximately power-law relations
The Groningen gas field serves as a natural laboratory for production-induced earthquakes, because no earthquakes were observed before the beginning of gas production. Increasing gas production rates resulted in growing earthquake activity and eventually in the occurrence of the 2012M(w) 3.6 Huizinge earthquake. At least since this event, a detailed seismic hazard and risk assessment including estimation of the maximum earthquake magnitude is considered to be necessary to decide on the future gas production. In this short note, we first apply state-of-the-art methods of mathematical statistics to derive confidence intervals for the maximum possible earthquake magnitude m(max). Second, we calculate the maximum expected magnitude M-T in the time between 2016 and 2024 for three assumed gas-production scenarios. Using broadly accepted physical assumptions and 90% confidence level, we suggest a value of m(max) 4.4, whereas M-T varies between 3.9 and 4.3, depending on the production scenario.
We show how the maximum magnitude within a predefined future time horizon may be estimated from an earthquake catalog within the context of Gutenberg-Richter statistics. The aim is to carry out a rigorous uncertainty assessment, and calculate precise confidence intervals based on an imposed level of confidence a. In detail, we present a model for the estimation of the maximum magnitude to occur in a time interval T-f in the future, given a complete earthquake catalog for a time period T in the past and, if available, paleoseismic events. For this goal, we solely assume that earthquakes follow a stationary Poisson process in time with unknown productivity Lambda and obey the Gutenberg-Richter law in magnitude domain with unknown b-value. The random variables. and b are estimated by means of Bayes theorem with noninformative prior distributions. Results based on synthetic catalogs and on retrospective calculations of historic catalogs from the highly active area of Japan and the low-seismicity, but high-risk region lower Rhine embayment (LRE) in Germany indicate that the estimated magnitudes are close to the true values. Finally, we discuss whether the techniques can be extended to meet the safety requirements for critical facilities such as nuclear power plants. For this aim, the maximum magnitude for all times has to be considered. In agreement with earlier work, we find that this parameter is not a useful quantity from the viewpoint of statistical inference.
Earthquake catalogs are probably the most informative data source about spatiotemporal seismicity evolution. The catalog quality in one of the most active seismogenic zones in the world, Japan, is excellent, although changes in quality arising, for example, from an evolving network are clearly present. Here, we seek the best estimate for the largest expected earthquake in a given future time interval from a combination of historic and instrumental earthquake catalogs. We extend the technique introduced by Zoller et al. (2013) to estimate the maximum magnitude in a time window of length T-f for earthquake catalogs with varying level of completeness. In particular, we consider the case in which two types of catalogs are available: a historic catalog and an instrumental catalog. This leads to competing interests with respect to the estimation of the two parameters from the Gutenberg-Richter law, the b-value and the event rate lambda above a given lower-magnitude threshold (the a-value). The b-value is estimated most precisely from the frequently occurring small earthquakes; however, the tendency of small events to cluster in aftershocks, swarms, etc. violates the assumption of a Poisson process that is used for the estimation of lambda. We suggest addressing conflict by estimating b solely from instrumental seismicity and using large magnitude events from historic catalogs for the earthquake rate estimation. Applying the method to Japan, there is a probability of about 20% that the maximum expected magnitude during any future time interval of length T-f = 30 years is m >= 9.0. Studies of different subregions in Japan indicates high probabilities for M 8 earthquakes along the Tohoku arc and relatively low probabilities in the Tokai, Tonankai, and Nankai region. Finally, for scenarios related to long-time horizons and high-confidence levels, the maximum expected magnitude will be around 10.
We present a new model of the geomagnetic field spanning the last 20 years and called Kalmag. Deriving from the assimilation of CHAMP and Swarm vector field measurements, it separates the different contributions to the observable field through parameterized prior covariance matrices. To make the inverse problem numerically feasible, it has been sequentialized in time through the combination of a Kalman filter and a smoothing algorithm. The model provides reliable estimates of past, present and future mean fields and associated uncertainties. The version presented here is an update of our IGRF candidates; the amount of assimilated data has been doubled and the considered time window has been extended from [2000.5, 2019.74] to [2000.5, 2020.33].
In the present study, we summarize and evaluate the endeavors from recent years to estimate the maximum possible earthquake magnitude m(max) from observed data. In particular, we use basic and physically motivated assumptions to identify best cases and worst cases in terms of lowest and highest degree of uncertainty of m(max). In a general framework, we demonstrate that earthquake data and earthquake proxy data recorded in a fault zone provide almost no information about m(max) unless reliable and homogeneous data of a long time interval, including several earthquakes with magnitude close to m(max), are available. Even if detailed earthquake information from some centuries including historic and paleoearthquakes are given, only very few, namely the largest events, will contribute at all to the estimation of m(max), and this results in unacceptably high uncertainties. As a consequence, estimators of m(max) in a fault zone, which are based solely on earthquake-related information from this region, have to be dismissed.
Both aftershocks and geodetically measured postseismic displacements are important markers of the stress relaxation process following large earthquakes. Postseismic displacements can be related to creep-like relaxation in the vicinity of the coseismic rupture by means of inversion methods. However, the results of slip inversions are typically non-unique and subject to large uncertainties. Therefore, we explore the possibility to improve inversions by mechanical constraints. In particular, we take into account the physical understanding that postseismic deformation is stress-driven, and occurs in the coseismically stressed zone. We do joint inversions for coseismic and postseismic slip in a Bayesian framework in the case of the 2004 M6.0 Parkfield earthquake. We perform a number of inversions with different constraints, and calculate their statistical significance. According to information criteria, the best result is preferably related to a physically reasonable model constrained by the stress-condition (namely postseismic creep is driven by coseismic stress) and the condition that coseismic slip and large aftershocks are disjunct. This model explains 97% of the coseismic displacements and 91% of the postseismic displacements during day 1-5 following the Parkfield event, respectively. It indicates that the major postseismic deformation can be generally explained by a stress relaxation process for the Parkfield case. This result also indicates that the data to constrain the coseismic slip model could be enriched postseismically. For the 2004 Parkfield event, we additionally observe asymmetric relaxation process at the two sides of the fault, which can be explained by material contrast ratio across the fault of similar to 1.15 in seismic velocity.
The motility of adherent eukaryotic cells is driven by the dynamics of the actin cytoskeleton. Despite the common force-generating actin machinery, different cell types often show diverse modes of locomotion that differ in their shape dynamics, speed, and persistence of motion. Recently, experiments in Dictyostelium discoideum have revealed that different motility modes can be induced in this model organism, depending on genetic modifications, developmental conditions, and synthetic changes of intracellular signaling. Here, we report experimental evidence that in a mutated D. discoideum cell line with increased Ras activity, switches between two distinct migratory modes, the amoeboid and fan-shaped type of locomotion, can even spontaneously occur within the same cell. We observed and characterized repeated and reversible switchings between the two modes of locomotion, suggesting that they are distinct behavioral traits that coexist within the same cell. We adapted an established phenomenological motility model that combines a reaction-diffusion system for the intracellular dynamics with a dynamic phase field to account for our experimental findings.
The Smoothing Spline ANOVA (SS-ANOVA) requires a specialized construction of basis and penalty terms in order to incorporate prior knowledge about the data to be fitted. Typically, one resorts to the most general approach using tensor product splines. This implies severe constraints on the correlation structure, i.e. the assumption of isotropy of smoothness can not be incorporated in general. This may increase the variance of the spline fit, especially if only a relatively small set of observations are given. In this article, we propose an alternative method that allows to incorporate prior knowledge without the need to construct specialized bases and penalties, allowing the researcher to choose the spline basis and penalty according to the prior knowledge of the observations rather than choosing them according to the analysis to be done. The two approaches are compared with an artificial example and with analyses of fixation durations during reading.
We present an alarm-based earthquake forecast model that uses the early aftershock statistics (EAST). This model is based on the hypothesis that the time delay before the onset of the power-law aftershock decay rate decreases as the level of stress and the seismogenic potential increase. Here, we estimate this time delay from < t(g)>, the time constant of the Omori-Utsu law. To isolate space-time regions with a relative high level of stress, the single local variable of our forecast model is the E-a value, the ratio between the long-term and short-term estimations of < t(g)>. When and where the E-a value exceeds a given threshold (i.e., the c value is abnormally small), an alarm is issued, and an earthquake is expected to occur during the next time step. Retrospective tests show that the EAST model has better predictive power than a stationary reference model based on smoothed extrapolation of past seismicity. The official prospective test for California started on 1 July 2009 in the testing center of the Collaboratory for the Study of Earthquake Predictability (CSEP). During the first nine months, 44 M >= 4 earthquakes occurred in the testing area. For this time period, the EAST model has better predictive power than the reference model at a 1% level of significance. Because the EAST model has also a better predictive power than several time-varying clustering models tested in CSEP at a 1% level of significance, we suggest that our successful prospective results are not due only to the space-time clustering of aftershocks.
We describe a new, original approach to the modelling of the Earth's magnetic field. The overall objective of this study is to reliably render fast variations of the core field and its secular variation. This method combines a sequential modelling approach, a Kalman filter, and a correlation-based modelling step. Sources that most significantly contribute to the field measured at the surface of the Earth are modelled. Their separation is based on strong prior information on their spatial and temporal behaviours. We obtain a time series of model distributions which display behaviours similar to those of recent models based on more classic approaches, particularly at large temporal and spatial scales. Interesting new features and periodicities are visible in our models at smaller time and spatial scales. An important aspect of our method is to yield reliable error bars for all model parameters. These errors, however, are only as reliable as the description of the different sources and the prior information used are realistic. Finally, we used a slightly different version of our method to produce candidate models for the thirteenth edition of the International Geomagnetic Reference Field.
High-precision observations of the present-day geomagnetic field by ground-based observatories and satellites provide unprecedented conditions for unveiling the dynamics of the Earth’s core. Combining geomagnetic observations with dynamo simulations in a data assimilation (DA) framework allows the reconstruction of past and present states of the internal core dynamics. The essential information that couples the internal state to the observations is provided by the statistical correlations from a numerical dynamo model in the form of a model covariance matrix. Here we test a sequential DA framework, working through a succession of forecast and analysis steps, that extracts the correlations from an ensemble of dynamo models. The primary correlations couple variables of the same azimuthal wave number, reflecting the predominant axial symmetry of the magnetic field. Synthetic tests show that the scheme becomes unstable when confronted with high-precision geomagnetic observations. Our study has identified spurious secondary correlations as the origin of the problem. Keeping only the primary correlations by localizing the covariance matrix with respect to the azimuthal wave number suffices to stabilize the assimilation. While the first analysis step is fundamental in constraining the large-scale interior state, further assimilation steps refine the smaller and more dynamical scales. This refinement turns out to be critical for long-term geomagnetic predictions. Increasing the assimilation steps from one to 18 roughly doubles the prediction horizon for the dipole from about tree to six centuries, and from 30 to about 60 yr for smaller observable scales. This improvement is also reflected on the predictability of surface intensity features such as the South Atlantic Anomaly. Intensity prediction errors are decreased roughly by a half when assimilating long observation sequences.