In this paper, we propose a method of surface waves characterization based on the deformation of the wavelet transform of the analysed signal. An estimate of the phase velocity (the group velocity) ...and the attenuation coefficient is carried out using a model-based approach to determine the propagation operator in the wavelet domain, which depends nonlinearly on a set of unknown parameters. These parameters explicitly define the phase velocity, the group velocity and the attenuation. Under the assumption that the difference between waveforms observed at a couple of stations is solely due to the dispersion characteristics and the intrinsic attenuation of the medium, we then seek to find the set of unknown parameters of this model. Finding the model parameters turns out to be that of an optimization problem, which is solved through the minimization of an appropriately defined cost function. We show that, unlike time–frequency methods that exploit only the square modulus of the transform, we can achieve a complete characterization of surface waves in a dispersive and attenuating medium. Using both synthetic examples and experimental data, we also show that it is in principle possible to separate different modes in both the time domain and the frequency domain.
The aim of this paper is to estimate the Hurst parameter of Fractional Gaussian Noise (FGN) using Bayesian inference. We propose an estimation technique that takes into account the full correlation ...structure of this process. Instead of using the integrated time series and then applying an estimator for its Hurst exponent, we propose to use the noise signal directly. As an application we analyze the time series of the Nile River, where we find a posterior distribution which is compatible with previous findings. In addition, our technique provides natural error bars for the Hurst exponent.
We show that realistic aftershock sequences with space‐time characteristics compatible with observations are generated by a model consisting of brittle fault segments separated by creeping zones. The ...dynamics of the brittle regions is governed by static/kinetic friction, 3D elastic stress transfer and small creep deformation. The creeping parts are characterized by high ongoing creep velocities. These regions store stress during earthquake failures and then release it in the interseismic periods. The resulting postseismic deformation leads to aftershock sequences following the modified Omori law. The ratio of creep coefficients in the brittle and creeping sections determines the duration of the postseismic transients and the exponent p of the modified Omori law.
Borehole logs provide geological information about the rocks crossed by the wells. Several properties of rocks can be interpreted in terms of lithology, type and quantity of the fluid filling the ...pores and fractures. Here, the logs are assumed to be nonhomogeneous Brownian motions (nhBms) which are generalized fractional Brownian motions (fBms) indexed by depth-dependent Hurst parameters H(z). Three techniques, the local wavelet approach (LWA), the average-local wavelet approach (ALWA), and Peltier Algorithm (PA), are suggested to estimate the Hurst functions (or the regularity profiles) from the logs. First, two synthetic sonic logs with different parameters, shaped by the successive random additions (SRA) algorithm, are used to demonstrate the potential of the proposed methods. The obtained Hurst functions are close to the theoretical Hurst functions. Besides, the transitions between the modeled layers are marked by Hurst values discontinuities. It is also shown that PA leads to the best Hurst value estimations. Second, we investigate the multifractional property of sonic logs data recorded at two scientific deep boreholes: the pilot hole VB and the ultra deep main hole HB, drilled for the German Continental Deep Drilling Program (KTB). All the regularity profiles independently obtained for the logs provide a clear correlation with lithology, and from each regularity profile, we derive a similar segmentation in terms of lithological units. The lithological discontinuities (strata' bounds and faults contacts) are located at the local extrema of the Hurst functions. Moreover, the regularity profiles are compared with the KTB estimated porosity logs, showing a significant relation between the local extrema of the Hurst functions and the fluid-filled fractures. The Hurst function may then constitute a tool to characterize underground heterogeneities.
We present a Bayesian method that allows continuous updating the aperiodicity of the recurrence time distribution of large earthquakes based on a catalog with magnitudes above a completeness ...threshold. The approach uses a recently proposed renewal model for seismicity and allows the inclusion of magnitude uncertainties in a straightforward manner. Errors accounting for grouped magnitudes and random errors are studied and discussed. The results indicate that a stable and realistic value of the aperiodicity can be predicted in an early state of seismicity evolution, even though only a small number of large earthquakes has occurred to date. Furthermore, we demonstrate that magnitude uncertainties can drastically influence the results and can therefore not be neglected. We show how to correct for the bias caused by magnitude errors. For the region of Parkfield we find that the aperiodicity, or the coefficient of variation, is clearly higher than in studies which are solely based on the large earthquakes.
We estimate the loading rate in southern California and the change in stress induced by a transient slip event across the San Andreas fault (SAF) system in central California, using a model of static ...fatigue. We analyze temporal properties of aftershocks in order to determine the time delay before the onset of the power law aftershock decay rate. In creep-slip and stick-slip zones, we show that the rate of change of this delay is related to seismic and aseismic deformation across the SAF system. Furthermore, we show that this rate of change is proportional to the deficit of slip rate along the SAF. This new relationship between geodetic and seismological data is in good agreement with predictions from a Limited Power Law model in which the evolution of the duration of a linear aftershock decay rate over short time results from variations in the load of the brittle upper crust.
We propose an equivalence class of nonstationary Gaussian stochastic processes defined in the wavelet domain. These processes are characterized by means of wavelet multipliers and exhibit ...well-defined time-dependent spectral properties. They allow one to generate realizations of any wavelet spectrum. Based on this framework, we study the estimation of continuous wavelet spectra, i.e., we calculate variance and bias of arbitrary estimated continuous wavelet spectra. Finally, we develop an areawise significance test for continuous wavelet spectra to overcome the difficulties of multiple testing; it uses basic properties of continuous wavelet transform to decide whether a pointwise significant result is a real feature of the process or indistinguishable from typical stochastic fluctuations. This test is compared to the conventional one in terms of sensitivity and specificity. A software package for continuous wavelet spectral analysis and synthesis is presented.
Waardenburg syndrome type 4 (WS4), also called Shah-Waardenburg syndrome, is a rare neurocristopathy that results from the absence of melanocytes and intrinsic ganglion cells of the terminal hindgut. ...WS4 is inherited as an autosomal recessive trait attributable to
EDN3 or
EDNRB mutations. It is inherited as an autosomal dominant condition when
SOX10 mutations are involved. We report on three unrelated WS4 patients with growth retardation and an as-yet-unreported neurological phenotype with impairment of both the central and autonomous nervous systems and occasionally neonatal hypotonia and arthrogryposis. Each of the three patients was heterozygous for a
SOX10 truncating mutation (Y313X in two patients and S351X in one patient). The extended spectrum of the WS4 phenotype is relevant to the brain expression of
SOX10 during human embryonic and fetal development. Indeed, the expression of
SOX10 in human embryo was not restricted to neural-crest–derived cells but also involved fetal brain cells, most likely of glial origin. These data emphasize the important role of SOX10 in early development of both neural-crest–derived tissues, namely melanocytes, autonomic and enteric nervous systems, and glial cells of the central nervous system.
We present a strategy for estimating the recurrence times between large earthquakes and associated seismic hazard on a given fault section. The goal of the analysis is to address two fundamental ...problems. (1) The lack of sufficient direct earthquake data and (2) the existence of ‘subgrid’ processes that can not be accounted for in any model. We deal with the first problem by using long simulations (some 10 000 yr) of a physically motivated ‘coarsegrain’ model that reproduces the main statistical properties of seismicity on individual faults. We address the second problem by adding stochasticity to the macroscopic model parameters. A small number N of observational earthquake times (2 ≤ N ≤ 10) can be used to determine the values of model parameters which are most representative for the fault. As an application of the method, we consider a model set-up that produces the characteristic earthquake distribution, and where the stress drops are associated with some uncertainty. Using several model realizations with different values of stress drops, we generate a set of corresponding synthetic earthquake catalogues. The recurrence time distributions in the simulated catalogues are fitted approximately by a gamma distribution. A superposition of appropriately scaled gamma distributions is then used to construct a distribution of recurrence intervals that incorporates the assumed uncertainty of the stress drops. Combining such synthetic data with observed recurrence times between the observational ∼M6 earthquakes on the Parkfield segment of the San Andreas fault, allows us to constrain the distribution of recurrence intervals and to estimate the average stress drop of the events. Based on this procedure, we calculate for the Parkfield region the expected recurrence time distribution, the hazard function, and the mean waiting time to the next ∼M6 earthquake. Using five observational recurrence times from 1857 to 1966, the recurrence time distribution has a maximum at 22.2 yr and decays rapidly for higher intervals. The probability for the post 1966 large event to occur on or before 2004 September 28 is 94 per cent. The average stress drop of ∼M6 Parkfield earthquakes is in the range Δτ = (3.04 ± 0.27) MPa.
Neutral thermospheric wind patterns at high latitudes obtained from cross-track acceleration measurements of the CHAMP satellite above both polar regions are used to deduce statistical neutral wind ...vorticity distributions and were analyzed in their dependence on the Interplanetary Magnetic Field (IMF). The average pattern confirms the large duskside anticyclonic vortex seen in the average wind pattern and reveals a positive (cyclonic) vorticity on the dawnside, which is almost equal in magnitude to the duskside negative one. The IMF dependence of the vorticity pattern resembles the characteristic field-aligned current (FAC) and ionospheric plasma drift pattern known from various statistical studies obtained under the same sorting conditions as, e.g., the EDI Cluster statistical drift pattern. There is evidence for hemispheric differences in the average magnitudes of the statistical patterns both for plasma drift and even more for the neutral wind vorticity. The paper aims at a better understanding of the globally interconnected complex plasma physical and electrodynamic processes of Earth's upper atmosphere by means of first-principle numerical modeling using the Upper Atmosphere Model (UAM). The simulations of, e.g., thermospheric neutral wind and mass density at high latitudes are compared with CHAMP observations for varying IMF conditions. They show an immediate response of the upper atmosphere and its high sensitivity to IMF changes in strength and orientation.
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