Home About us Contact
|
Home About us Contact | ||
|
|
||
Wavelet
Kinds of Wavelet Terms modified by Wavelet Selected AbstractsA Comparative Study of Modal Parameter Identification Based on Wavelet and Hilbert,Huang TransformsCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 1 2006Banfu Yan Special attention is given to some implementation issues, such as the modal separation and end effect in the WT, the optimal parameter selection of the wavelet function, the new stopping criterion for the empirical mode decomposition (EMD) and the end effect in the HHT. The capabilities of these two techniques are compared and assessed by using three examples, namely a numerical simulation for a damped system with two very close modes, an impact test on an experimental model with three well-separated modes, and an ambient vibration test on the Z24-bridge benchmark problem. The results demonstrate that for the system with well-separated modes both methods are applicable when the time,frequency resolutions are sufficiently taken into account, whereas for the system with very close modes, the WT method seems to be more theoretical and effective than HHT from the viewpoint of parameter design. [source] A Wavelet-Based Approach to Identifying Structural Modal Parameters from Seismic Response and Free Vibration DataCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 6 2005C. S. Huang The wavelet transform with orthonormal wavelets is applied to the measured acceleration responses of a structural system, and to reconstruct the discrete equations of motion in various wavelet subspaces. The accuracy of this procedure is numerically confirmed; the effects of mother wavelet functions and noise on the ability to accurately estimate the dynamic characteristics are also investigated. The feasibility of the present procedure to elucidate real structures is demonstrated through processing the measured responses of steel frames in shaking table tests and the free vibration responses of a five-span arch bridge with a total length of 440 m. [source] Hybrid Control of Smart Structures Using a Novel Wavelet-Based AlgorithmCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 1 2005Hongjin Kim A new hybrid control system is presented through judicious combination of a passive supplementary damping system with a semi-active TLCD system. The new model utilizes the advantages of both passive and semi-active control systems, thereby improving the overall performance, reliability, and operability of the control system during normal operations as well as a power or computer failure. The robust wavelet-hybrid feedback least mean square (LMS) control algorithm developed recently by the authors is used to find optimal values of the control parameters. The effectiveness and robustness of the proposed hybrid damper-TLCD system in reducing the vibrations under various seismic excitations are evaluated through numerical simulations performed for an eight-story frame using three different simulated earthquake ground accelerations. It is found that the new model is effective in significantly reducing the response of the structure under various seismic excitations. [source] Wavelet-based simulation of spectrum-compatible aftershock accelerogramsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 11 2008S. Das Abstract In damage-based seismic design it is desirable to account for the ability of aftershocks to cause further damage to an already damaged structure due to the main shock. Availability of recorded or simulated aftershock accelerograms is a critical component in the non-linear time-history analyses required for this purpose, and simulation of realistic accelerograms is therefore going to be the need of the profession for a long time to come. This paper attempts wavelet-based simulation of aftershock accelerograms for two scenarios. In the first scenario, recorded main shock and aftershock accelerograms are available along with the pseudo-spectral acceleration (PSA) spectrum of the anticipated main shock motion, and an accelerogram has been simulated for the anticipated aftershock motion such that it incorporates temporal features of the recorded aftershock accelerogram. In the second scenario, a recorded main shock accelerogram is available along with the PSA spectrum of the anticipated main shock motion and PSA spectrum and strong motion duration of the anticipated aftershock motion. Here, the accelerogram for the anticipated aftershock motion has been simulated assuming that temporal features of the main shock accelerogram are replicated in the aftershock accelerograms at the same site. The proposed algorithms have been illustrated with the help of the main shock and aftershock accelerograms recorded for the 1999 Chi,Chi earthquake. It has been shown that the proposed algorithm for the second scenario leads to useful results even when the main shock and aftershock accelerograms do not share the same temporal features, as long as strong motion duration of the anticipated aftershock motion is properly estimated. Copyright © 2008 John Wiley & Sons, Ltd. [source] Wavelet-based adaptive vector quantization for still-image codingINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 4 2002Wen-Shiung Chen Abstract Wavelet transform coding (WTC) with vector quantization (VQ) has been shown to be efficient in the application of image compression. An adaptive vector quantization coding scheme with the Gold-Washing dynamic codebook-refining mechanism in the wavelet domain, called symmetric wavelet transform-based adaptive vector quantization (SWT-GW-AVQ), is proposed for still-image coding in this article. The experimental results show that the GW codebook-refining mechanism working in the wavelet domain rather than the spatial domain is very efficient, and the SWT-GW-AVQ coding scheme may improve the peak signal-to-noise ratio (PSNR) of the reconstructed images with a lower encoding time. © 2002 Wiley Periodicals, Inc. Int J Imaging Syst Technol 12, 166,174, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10024 [source] Wavelet-based adaptive grid method for the resolution of nonlinear PDEsAICHE JOURNAL, Issue 4 2002Paulo Cruz Theoretical modeling of dynamic processes in chemical engineering often implies the numeric solution of one or more partial differential equations. The complexity of such problems is increased when the solutions exhibit sharp moving fronts. A new numerical method is established, based on interpolating wavelets, that dynamically adapts the collocation grid so that higher resolution is automatically attributed to domain regions where sharp features are present. The effectiveness of the method is demonstrated with some relevant examples in a chemical engineering context. [source] Wavelet-based adaptive robust M-estimator for nonlinear system identificationAICHE JOURNAL, Issue 8 2000D. Wang A wavelet-based robust M-estimation method for the identification of nonlinear systems is proposed. Because it is not based on the assumption that there is the class of error distribution, it takes a flexible, nonparametric approach and has the advantage of directly estimating the error distribution from the data. This M-estimator is optimal over any error distribution in the sense of maximum likelihood estimation. A Monte-Carlo study on a nonlinear chemical engineering example was used to compare the results with various previously utilized methods. [source] Wavelet-based functional mixed modelsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2006Jeffrey S. Morris Summary., Increasingly, scientific studies yield functional data, in which the ideal units of observation are curves and the observed data consist of sets of curves that are sampled on a fine grid. We present new methodology that generalizes the linear mixed model to the functional mixed model framework, with model fitting done by using a Bayesian wavelet-based approach. This method is flexible, allowing functions of arbitrary form and the full range of fixed effects structures and between-curve covariance structures that are available in the mixed model framework. It yields nonparametric estimates of the fixed and random-effects functions as well as the various between-curve and within-curve covariance matrices. The functional fixed effects are adaptively regularized as a result of the non-linear shrinkage prior that is imposed on the fixed effects' wavelet coefficients, and the random-effect functions experience a form of adaptive regularization because of the separately estimated variance components for each wavelet coefficient. Because we have posterior samples for all model quantities, we can perform pointwise or joint Bayesian inference or prediction on the quantities of the model. The adaptiveness of the method makes it especially appropriate for modelling irregular functional data that are characterized by numerous local features like peaks. [source] Wavelet-based estimation of a discriminant functionAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2003Woojin Chang Abstract In this paper, we consider wavelet-based binary linear classifiers. Both consistency results and implementational issues are addressed. We show that under mild assumptions on the design density wavelet discrimination rules are L2 -consistent. The proposed method is illustrated on synthetic data sets in which the ,truth' is known and on an applied discrimination problem from the industrial field. Copyright © 2003 John Wiley & Sons, Ltd. [source] Streaming Surface Reconstruction Using WaveletsCOMPUTER GRAPHICS FORUM, Issue 5 2008J. Manson Abstract We present a streaming method for reconstructing surfaces from large data sets generated by a laser range scanner using wavelets. Wavelets provide a localized, multiresolution representation of functions and this makes them ideal candidates for streaming surface reconstruction algorithms. We show how wavelets can be used to reconstruct the indicator function of a shape from a cloud of points with associated normals. Our method proceeds in several steps. We first compute a low-resolution approximation of the indicator function using an octree followed by a second pass that incrementally adds fine resolution details. The indicator function is then smoothed using a modified octree convolution step and contoured to produce the final surface. Due to the local, multiresolution nature of wavelets, our approach results in an algorithm over 10 times faster than previous methods and can process extremely large data sets in the order of several hundred million points in only an hour. [source] Space-Time Hierarchical Radiosity with Clustering and Higher-Order WaveletsCOMPUTER GRAPHICS FORUM, Issue 2 2004Cyrille Damez Abstract We address in this paper the issue of computing diffuse global illumination solutions for animation sequences. The principal difficulties lie in the computational complexity of global illumination, emphasized by the movement of objects and the large number of frames to compute, as well as the potential for creating temporal discontinuities in the illumination, a particularly noticeable artifact. We demonstrate how space-time hierarchical radiosity, i.e. the application to the time dimension of a hierarchical decomposition algorithm, can be effectively used to obtain smooth animations: first by proposing the integration of spatial clustering in a space-time hierarchy; second, by using a higher-order wavelet basis adapted for the temporal dimension. The resulting algorithm is capable of creating time-dependent radiosity solutions efficiently. [source] Estimation of Frequency-Dependent Strong Motion Duration Via Wavelets and Its Influence on Nonlinear Seismic ResponseCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 4 2008Luis A. Montejo The proposed procedure utilizes the continuous wavelet transform and is based on the decomposition of the earthquake record into a number of component time histories (named "pseudo-details") with frequency content in a selected range. The "significant" strong motion duration of each pseudo-detail is calculated based on the accumulation of the Arias intensity (AI). Finally, the FDSMD of the earthquake record in different frequency ranges is defined as the strong motion duration of the corresponding pseudo-detail scaled by a weight factor that depends on the AI of each pseudo-detail. The efficiency of this new strong motion definition as an intensity measure is evaluated using incremental dynamic analysis (IDA). The results obtained show that the proposed FDSMD influence the peak response of short-period structures with stiffness and strength degradation. [source] Numerical Treatment of Seismic Accelerograms and of Inelastic Seismic Structural Responses Using Harmonic WaveletsCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 4 2007Pol D. Spanos The effectiveness of the harmonic wavelets for capturing the temporal evolution of the frequency content of strong ground motions is demonstrated. In this regard, a detailed study of important earthquake accelerograms is undertaken and smooth joint time-frequency spectra are provided for two near-field and two far-field records; inherent in this analysis is the concept of the mean instantaneous frequency. Furthermore, as a paradigm of usefulness for aseismic structural purposes, a similar analysis is conducted for the response of a 20-story steel frame benchmark building considering one of the four accelerograms scaled by appropriate factors as the excitation to simulate undamaged and severely damaged conditions for the structure. The resulting joint time-frequency representation of the response time histories captures the influence of nonlinearity on the variation of the effective natural frequencies of a structural system during the evolution of a seismic event. In this context, the potential of the harmonic wavelet transform as a detection tool for global structural damage is explored in conjunction with the concept of monitoring the mean instantaneous frequency of records of critical structural responses. [source] Enhancing Neural Network Traffic Incident-Detection Algorithms Using WaveletsCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 4 2001A. Samant Researchers have presented freeway traffic incident-detection algorithms by combining the adaptive learning capability of neural networks with imprecision modeling capability of fuzzy logic. In this article it is shown that the performance of a fuzzy neural network algorithm can be improved through preprocessing of data using a wavelet-based feature-extraction model. In particular, the discrete wavelet transform (DWT) denoising and feature-extraction model proposed by Samant and Adeli (2000) is combined with the fuzzy neural network approach presented by Hsiao et al. (1994). It is shown that substantial improvement can be achieved using the data filtered by DWT. Use of the wavelet theory to denoise the traffic data increases the incident-detection rate, reduces the false-alarm rate and the incident-detection time, and improves the convergence of the neural network training algorithm substantially. [source] Changes in variance and correlation of soil properties with scale and location: analysis using an adapted maximal overlap discrete wavelet transformEUROPEAN JOURNAL OF SOIL SCIENCE, Issue 4 2001R. M. Lark Summary The magnitude of variation in soil properties can change from place to place, and this lack of stationarity can preclude conventional geostatistical and spectral analysis. In contrast, wavelets and their scaling functions, which take non-zero values only over short intervals and are therefore local, enable us to handle such variation. Wavelets can be used to analyse scale-dependence and spatial changes in the correlation of two variables where the linear model of coregionalization is inadmissible. We have adapted wavelet methods to analyse soil properties with non-stationary variation and covariation in fairly small sets of data, such as we can expect in soil survey, and we have applied them to measurements of pH and the contents of clay and calcium carbonate on a 3-km transect in Central England. Places on the transect where significant changes in the variance of the soil properties occur were identified. The scale-dependence of the correlations of soil properties was investigated by calculating wavelet correlations for each spatial scale. We identified where the covariance of the properties appeared to change and then computed the wavelet correlations on each side of the change point and compared them. The correlation of topsoil and subsoil clay content was found to be uniform along the transect at one important scale, although there were significant changes in the variance. In contrast, carbonate content and pH of the topsoil were correlated only in parts of the transect. [source] Noise and background removal in Raman spectra of ancient pigments using wavelet transformJOURNAL OF RAMAN SPECTROSCOPY, Issue 9 2005Pablo Manuel Ramos Abstract The wavelet transform was applied to Raman spectra to remove heteroscedastic noise from ancient pigments such as azurite and ultramarine blue. Wavelets from the Daubechies, Coiflet and Symmlet families were evaluated. Two different thresholding strategies on the detail coefficients were applied; the first is a one-dimensional variance adaptive thresholding and the second is a block threshold denoising. The block thresholding strategy removes the noise and preserves the band shapes best. Background removal during the denoising process was also investigated and the results were very good when the block thresholding strategy was used to suppress background at the optimal level of the denoising process. Copyright © 2005 John Wiley & Sons, Ltd. [source] Littlewood-Paley spline wavelets: a simple and efficient tool for signal and image processing in industrial applicationsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007Eduardo Serrano In this work, we present the Littlewood-Paley Spline Wavelets that are much more effective that the orthonormal discrete wavelets, although it cannot apply the multiresolution scheme. These wavelets carry the advantages of the splines functions what allows their implementation through simple numeric algorithms. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Wavelets in state space modelsAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2003Eliana Zandonade Abstract In this paper, we consider the utilization of wavelets in conjunction with state space models. Specifically, the parameters in the system matrix are expanded in wavelet series and estimated via the Kalman Filter and the EM algorithm. In particular this approach is used for switching models. Two applications are given, one to the problem of detecting the paths of targets using an array of sensors, and the other to a series of daily spreads between two Brazilian bonds. Copyright © 2003 John Wiley & Sons, Ltd. [source] Nondestructive Evaluation of Elastic Properties of Concrete Using Simulation of Surface WavesCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 8 2008Jae Hong Kim In this study, to evaluate information of a surface waveform beyond the simple wave velocity, artificial intelligence engines are employed to estimate simulation parameters, that is, the properties of elastic materials. The developed artificial neural networks are trained with a numerical database having secured its stability. In the process, the appropriate shape of the force,time function for an impact load is assumed so as to avoid Gibbs phenomenon, and the proposed principal wavelet-component analysis accomplishes a feature extraction with a wavelet transformed signal. The results of estimation are validated with experiments focused on concrete materials. [source] A Study on the Effects of Damage Models and Wavelet Bases for Damage Identification and Calibration in BeamsCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 8 2007Vikram Pakrashi A numerical study has been performed in this article addressing these issues for single and multispan beams with an open crack. The first natural modeshapes of single and multispan beams with an open crack have been simulated considering damage models of different levels of complexity and analyzed for different crack depth ratios and crack positions. Gaussian white noise has been synthetically introduced to the simulated modeshape and the effects of varying signal-to-noise ratio have been studied. A wavelet-based damage identification technique has been found to be simple, efficient, and independent of damage models and wavelet basis functions, once certain conditions regarding the modeshape and the wavelet bases are satisfied. The wavelet-based damage calibration is found to be dependent on a number of factors including damage models and the basis function used in the analysis. A curvature-based calibration is more sensitive than a modeshape-based calibration of the extent of damage. [source] Wavelet Transforms for System Identification in Civil EngineeringCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 5 2003T. Kijewski Although challenges did not surface in prior applications concerned with mechanical systems, which are characterized by higher frequency and broader-band signals, the transition to the time-frequency domain for the analysis of civil engineering structures highlighted the need to understand more fully various processing concerns, particularly for the popular Morlet wavelet. In particular, as these systems may possess longer period motions and thus require finer frequency resolutions, the particular impacts of end effects become increasingly apparent. This study discusses these considerations in the context of the wavelet's multi-resolution character and includes guidelines for selection of wavelet central frequencies, highlights their role in complete modal separation, and quantifies their contributions to end-effect errors, which may be minimized through a simple padding scheme. [source] Enhancing Neural Network Traffic Incident-Detection Algorithms Using WaveletsCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 4 2001A. Samant Researchers have presented freeway traffic incident-detection algorithms by combining the adaptive learning capability of neural networks with imprecision modeling capability of fuzzy logic. In this article it is shown that the performance of a fuzzy neural network algorithm can be improved through preprocessing of data using a wavelet-based feature-extraction model. In particular, the discrete wavelet transform (DWT) denoising and feature-extraction model proposed by Samant and Adeli (2000) is combined with the fuzzy neural network approach presented by Hsiao et al. (1994). It is shown that substantial improvement can be achieved using the data filtered by DWT. Use of the wavelet theory to denoise the traffic data increases the incident-detection rate, reduces the false-alarm rate and the incident-detection time, and improves the convergence of the neural network training algorithm substantially. [source] Wavelet-based simulation of spectrum-compatible aftershock accelerogramsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 11 2008S. Das Abstract In damage-based seismic design it is desirable to account for the ability of aftershocks to cause further damage to an already damaged structure due to the main shock. Availability of recorded or simulated aftershock accelerograms is a critical component in the non-linear time-history analyses required for this purpose, and simulation of realistic accelerograms is therefore going to be the need of the profession for a long time to come. This paper attempts wavelet-based simulation of aftershock accelerograms for two scenarios. In the first scenario, recorded main shock and aftershock accelerograms are available along with the pseudo-spectral acceleration (PSA) spectrum of the anticipated main shock motion, and an accelerogram has been simulated for the anticipated aftershock motion such that it incorporates temporal features of the recorded aftershock accelerogram. In the second scenario, a recorded main shock accelerogram is available along with the PSA spectrum of the anticipated main shock motion and PSA spectrum and strong motion duration of the anticipated aftershock motion. Here, the accelerogram for the anticipated aftershock motion has been simulated assuming that temporal features of the main shock accelerogram are replicated in the aftershock accelerograms at the same site. The proposed algorithms have been illustrated with the help of the main shock and aftershock accelerograms recorded for the 1999 Chi,Chi earthquake. It has been shown that the proposed algorithm for the second scenario leads to useful results even when the main shock and aftershock accelerograms do not share the same temporal features, as long as strong motion duration of the anticipated aftershock motion is properly estimated. Copyright © 2008 John Wiley & Sons, Ltd. [source] Estimate of input energy for elasto-plastic SDOF systems during earthquakes based on discrete wavelet coefficientsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 15 2005Jun Iyama Abstract The response of an elasto-plastic single degree of freedom (SDOF) system to ground motion is estimated based on wavelet coefficients calculated by discrete wavelet transform. Wavelet coefficients represent both the time and frequency characteristics of input ground motion, and thus can be considered to be directly related to the dynamic response of a non-linear system. This relationship between the energy input into an elastic SDOF system and wavelet coefficients is derived based on the assumption that wavelets deliver energy to the structure instantaneously and the quantity of energy is constant regardless of yielding. These assumptions are shown to be valid when the natural period of the system is in the predominant period range of the wavelet, the most common scenario for real structures, through dynamic response analysis of a single wavelet. The wavelet-based estimation of elastic and plastic energy transferred by earthquake ground motion is thus shown to be in good agreement with the dynamic response analysis when the natural period is in the predominant range of the input. Copyright © 2005 John Wiley & Sons, Ltd. [source] Signal denoising and baseline correction by discrete wavelet transform for microchip capillary electrophoresisELECTROPHORESIS, Issue 18 2003Bi-Feng Liu Abstract Signal denoising and baseline correction using discrete wavelet transform (DWT) are described for microchip capillary electrophoresis (MCE). DWT was performed on an electropherogram describing a separation of nine tetramethylrohodamine-5-isothiocyanate labeled amino acids, following MCE with laser-induced fluorescence detection, using Daubechies 5 wavelet at a decomposition level of 6. The denoising efficiency was compared with, and proved to be superior to, other commonly used denoising techniques such as Fourier transform, Savitzky-Golay smoothing and moving average, in terms of noise removal and peak preservation by directly visual inspection. Novel strategies for baseline correction were proposed, with a special interest in baseline drift that frequently occurred in chromatographic and electrophoretic separations. [source] Analysing soil variation in two dimensions with the discrete wavelet transformEUROPEAN JOURNAL OF SOIL SCIENCE, Issue 4 2004R. M. Lark Summary Complex spatial variation in soil can be analysed by wavelets into contributions at several scales or resolutions. The first applications were to data recorded at regular intervals in one dimension, i.e. on transects. The theory extends readily to two dimensions, but the application to small sets of gridded data such as one is likely to have from a soil survey requires special adaptation. This paper describes the extension of wavelet theory to two dimensions. The adaptation of the wavelet filters near the limits of a region that was successful in one dimension proved unsuitable in two dimensions. We therefore had to pad the data out symmetrically beyond the limits to minimize edge effects. With the above modifications and Daubechies's wavelet with two vanishing moments the analysis is applied to soil thickness, slope gradient, and direct solar beam radiation at the land surface recorded at 100-m intervals on a 60 × 101 square grid in south-west England. The analysis revealed contributions to the variance at several scales and for different directions and correlations between the variables that were not evident in maps of the original data. In particular, it showed how the thickness of the soil increasingly matches the geological structure with increasing dilation of the wavelet, this relationship being local to the strongly aligned outcrops. The analysis reveals a similar pattern in slope gradient, and a negative correlation with soil thickness, most clearly evident at the coarser scales. The solar beam radiation integrates slope gradient and azimuth, and the analysis emphasizes the relations with topography at the various spatial scales and reveals additional effects of aspect on soil thickness. [source] Combining wavelet-based feature extractions with relevance vector machines for stock index forecastingEXPERT SYSTEMS, Issue 2 2008Shian-Chang Huang Abstract: The relevance vector machine (RVM) is a Bayesian version of the support vector machine, which with a sparse model representation has appeared to be a powerful tool for time-series forecasting. The RVM has demonstrated better performance over other methods such as neural networks or autoregressive integrated moving average based models. This study proposes a hybrid model that combines wavelet-based feature extractions with RVM models to forecast stock indices. The time series of explanatory variables are decomposed using some wavelet bases and the extracted time-scale features serve as inputs of an RVM to perform the non-parametric regression and forecasting. Compared with traditional forecasting models, our proposed method performs best. The root-mean-squared forecasting errors are significantly reduced. [source] Multiscale estimation of GPS velocity fieldsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2009Carl Tape SUMMARY We present a spherical wavelet-based multiscale approach for estimating a spatial velocity field on the sphere from a set of irregularly spaced geodetic displacement observations. Because the adopted spherical wavelets are analytically differentiable, spatial gradient tensor quantities such as dilatation rate, strain rate and rotation rate can be directly computed using the same coefficients. In a series of synthetic and real examples, we illustrate the benefit of the multiscale approach, in particular, the inherent ability of the method to localize a given deformation field in space and scale as well as to detect outliers in the set of observations. This approach has the added benefit of being able to locally match the smallest resolved process to the local spatial density of observations, thereby both maximizing the amount of derived information while also allowing the comparison of derived quantities at the same scale but in different regions. We also consider the vertical component of the velocity field in our synthetic and real examples, showing that in some cases the spatial gradients of the vertical velocity field may constitute a significant part of the deformation. This formulation may be easily applied either regionally or globally and is ideally suited as the spatial parametrization used in any automatic time-dependent geodetic transient detector. [source] Sea surface shape derivation above the seismic streamerGEOPHYSICAL PROSPECTING, Issue 6 2006Robert Laws ABSTRACT The rough sea surface causes perturbations in the seismic data that can be significant for time-lapse studies. The perturbations arise because the reflection response of the non-flat sea perturbs the seismic wavelet. In order to remove these perturbations from the received seismic data, special deconvolution methods can be used, but these methods require, as input, the time varying wave elevation above each hydrophone in the streamer. In addition, the vertical displacement of the streamer itself must also be known at the position of each hydrophone and at all times. This information is not available in conventional seismic acquisition. However, it can be obtained from the hydrophone measurements provided that the hydrophones are recorded individually (not grouped), that the recording bandwidth is extended down to 0.05 Hz and that data are recorded without gaps between the shot records. The sea surface elevation, and also the wave-induced vertical displacement of the streamer, can be determined from the time-varying pressure that the sea waves cause in the hydrophone measurements. When this was done experimentally, using a single sensor seismic streamer without a conventional low cut filter, the wave induced pressure variations were easily detected. The inversion of these experimental data gives results for the sea surface elevation that are consistent with the weather and sea state at the time of acquisition. A high tension approximation allows a simplified solution of the equations that does not demand a knowledge of the streamer tension. However, best results at the tail end of the streamer are obtained using the general equation. [source] Modelling of GPR waves for lossy media obeying a complex power law of frequency for dielectric permittivityGEOPHYSICAL PROSPECTING, Issue 1 2004Maksim Bano ABSTRACT The attenuation of ground-penetrating radar (GPR) energy in the subsurface decreases and shifts the amplitude spectrum of the radar pulse to lower frequencies (absorption) with increasing traveltime and causes also a distortion of wavelet phase (dispersion). The attenuation is often expressed by the quality factor Q. For GPR studies, Q can be estimated from the ratio of the real part to the imaginary part of the dielectric permittivity. We consider a complex power function of frequency for the dielectric permittivity, and show that this dielectric response corresponds to a frequency-independent- Q or simply a constant- Q model. The phase velocity (dispersion relationship) and the absorption coefficient of electromagnetic waves also obey a frequency power law. This approach is easy to use in the frequency domain and the wave propagation can be described by two parameters only, for example Q and the phase velocity at an arbitrary reference frequency. This simplicity makes it practical for any inversion technique. Furthermore, by using the Hilbert transform relating the velocity and the absorption coefficient (which obeys a frequency power law), we find the same dispersion relationship for the phase velocity. Both approaches are valid for a constant value of Q over a restricted frequency-bandwidth, and are applicable in a material that is assumed to have no instantaneous dielectric response. Many GPR profiles acquired in a dry aeolian environment have shown a strong reflectivity inside dunes. Changes in water content are believed to be the origin of this reflectivity. We model the radar reflections from the bottom of a dry aeolian dune using the 1D wavelet modelling method. We discuss the choice of the reference wavelet in this modelling approach. A trial-and-error match of modelled and observed data was performed to estimate the optimum set of parameters characterizing the materials composing the site. Additionally, by combining the complex refractive index method (CRIM) and/or Topp equations for the bulk permittivity (dielectric constant) of moist sandy soils with a frequency power law for the dielectric response, we introduce them into the expression for the reflection coefficient. Using this method, we can estimate the water content and explain its effect on the reflection coefficient and on wavelet modelling. [source] | ||||||||||||||||||||||||||||||||||||||||