F. Glangeaud

Applications of autoregressive models and time–frequency analysis to the study of volcanic tremor and long-period events

Volcanic tremor and long-period (LP) events are characterized by sharp spectral peaks that generally result from resonance effects at the source and which concentrate most of the radiated energy. The understanding of these seismovolcanic phenomena requires good descriptions of the distribution in time and frequency of the different spectral components included in the signals, as well as a separation of the resonance effects from less energetic effects such as excitation and propagation. We address the issue of extracting from individual records information as detailed as possible on the physical processes involved at the source. We introduce and compare several time-frequency analysis methods, and we describe the application of autoregressive modeling and deconvolution methods to the characterization and separation of the main spectral components. We propose a signal analysis approach based on the joint use of a set of complementary methods, and we present applications to several examples of volcanic tremor and LP events. The time-frequency analysis of some of the LP events taken as examples reveals short-duration components at the seismogram onsets with energy concentrated at frequencies either higher or lower than the main resonance frequencies. These seismic phases are probably related to the excitation processes of the volcanic resonators. In several cases, the arrival of the main spectral peak has a delay of a few tenths of a second with respect to the first arrival. The residual signals obtained by deconvolving and eliminating the main spectral components contain information about the excitation, such as duration, delay, or frequency band. The residual signals are short for LP events, and continuous for volcanic tremor. The autoregressive modeling of the sample records gives precise estimations of the frequency and quality factor of the main spectral peaks. The measured parameters cover a wide range of values, which is consistent with the great variety of fluids filling resonating cavities in volcanoes.

Three-component signal recognition using time, time-frequency, and polarization information-application to seismic detection of avalanches

A method for automatic signal recognition, applied to seismic signals classification, is presented. It is based on the fusion of data derived from the analysis of the signal in three domains: time, time-frequency, and polarization. In the time domain, two techniques are used for envelope shape parametrization. In the time-frequency domain, the autoregressive and Capon (ARCAP) time-frequency method is used on a gliding time-window to estimate the spectral components of the signal versus time. For each window, the frequencies are estimated using AR modelization. The power at each frequency and the corresponding filtered signal are estimated using Capons (1969) method. A comparison with Fouriers narrow-bandpass filtering shows that Capons method produces a better filtering. In the polarization domain, two original methods are proposed: one for checking the linear polarization of a signal and one for localizing the linear waves in the time-frequency plane. A system for automatic recognition of seismic signals associated with avalanches is then presented as an application. Signal features are derived from the analysis to sum up the characteristics of the signal in each domain. These features are combined using fuzzy logic and credibility factors, according to rules derived from physical knowledge (generating processes and propagation rules), in order to decide whether a signal comes from an avalanche or not. The global rate of correct recognition is over 90% for that first version of the system.

Separation of seismic waves

This paper presents a multichannel method for enhancing the signal-to-noise ratio, when the noise is purely random. We show that under some assumptions the contribution of each wave may be individualized. The quality of the results is sensitive to the estimation of the interspectral matrix from the initial traces. The proposed method is general: according to the type of document (shot point or CDP gather, stacked seismic section), we indicate how the interspectral matrix is best estimated.

Advanced signal processing tools for dispersive waves

Two field examples are presented, showing the advantages of using multicomponent sensors for surface-wave studies. Multicomponent sensors allow the use of specific signal-processing tools such as the multicomponent singular value decomposition filter and the multicomponent polarization filter, which are both very efficient at separating surface waves from the other waves that comprise a seismic field record. Firstly, some signal-processing tools for studying surface waves are described. The various filters range from classical to advanced techniques. For processing single-component data, the filters are the f–k filter and filters based on singular value decomposition and on spectral matrix decomposition. For processing multicomponent data, the filters are the 4C-singular value decomposition filter and the classical or high-order polarization filter. Secondly, processing sequences that can be applied to the field data are described and the single-component processing sequence and the multicomponent processing sequence are compared. Two field examples are presented. The first data set is a land seismic data recording on 2C sensors. The second data set was obtained from a marine acquisition with OBS (4 components). The results obtained illustrate the advantages of using multicomponent filters. The efficiency of the 4C-SVD filter and the high-order statistic polarization filter is demonstrated.

Study of climatic series by time-frequency analysis

A climatic record given by isotopic composition of ice from Dome C (Antarctica) is studied using evolutive spectral analysis by AR process. Problems which occur when trends and non periodic accidents are present in the signal are examined. Experimental studies show that filtering with a smooth time limited window is better than the use of filters with abrupt cut-off frequencies.

Identification d’ondes UBF dans la magnétosphère en utilisant la matrice interspectrale

AnalyseAprès avoir rappelé les différentes méthodes de mesure de la matrice interspectrale de signaux stationnaires, les auteurs montrent comment l’étude de ses valeurs propres permet de déterminer le nombre de sources indépendantes présentes simultanément.L’application de cette méthode d’identification du nombre de sources à des signaux magnétiques naturels de type pc 1 permet de montrer sur des mesures au sol ou en satellite que ces signaux peuvent présenter à la fois au sol et dans leur propagation magnétosphérique une structure complexe due à la super-position de plusieurs sources indépendantes simultanées.AbstractVarious methods of measurement of the cross spectral matrix of stationary signals are recalled. The study of these matrices enables us to determine the number of independent and simultaneous signal sources.This method of determination of the number of sources is applied to natural magnetic signals of the pc 1 type, recorded on the ground or on satellite. Signals may present, as well on the ground as in the magnetosphere, a complex structure, which is due to the superposition of several independent and simultaneous sources.

Dispersive seismic wave tools in geophysics

Guide mode waves are important tools for geophysical prospecting. These waves are dispersive which means that their group and phase velocities are different and they are functions of frequency. The use of such waves for a geophysical investigation requires a 3 steps process. Firstly, enhancement of signal to noise ratio, secondly an analysis of the dispersion and finally the interpretation of the wave characteristics in terms of physical parameters. The waves are guided either due to the presence of a velocity gradient or by various reflectors. Thus the waves are confined within a specific wave guide. In seismic prospecting such waves are: Rayleigh waves (3 to 50 Hz), and Love waves (2 to 20 Hz) in seismic reflection propection, or Stoneley waves (1 to 5 kHz) in acoustic logging. For example when the impedance of the substrata has a velocity profile without large discontinuities, dispersive waves are present in a shallow water seismic section [Nardin et al 1998]. In presence of sediments. the impedance has a regular variation and dispersion occurs because of the interference of different travel paths for the same wave. Field data comprising Rayleigh, Love, Stoneley waves and shallow water refractiens (SWR) are presented in figures 1 to 4. The Rayleigh wave seismic data have been recorded on an array of 47 two component geophones. (vertical component is presented on figure 1). The Love wave section (figure 2) has been generated using a hammer with the strike action applied horizontally. The Stoneley section (figure 3) shows a 3.25 m offset section (acoustic imaging) recorded in the depth interval of 400-450 m. The acoustic tooI used was a slim-hole SEMM tooI with a monopole source and two pairs of receivers. Shallow water refractiens are presenred in figure 4 after a velocity correction of 1520 m/s over a distance of 5.5 km. First arrival of water guide is plotted as time zero. The signal was recorded by a hydrophone Iying on the sea floor at a depth of 70 m. The seismic source was a 16 liters airgun.

An interactive web platform development for teaching signal processing

Introduction Our bilingual (French-English) platform called e-TSLIS makes signal processing teaching more accessible and interactive by using up-to-date multimedia support (Internet, Web). The main aspects of the e-package presented here were conceived within the work of the Research Group SIN (Signals and Images in Natural environments) of the Signals and Images Laboratory (LIS) at ENSIEG (Ecole Nationale Superieure des Ingenieurs Electriciens de Grenoble) in collaboration with the IFP-School (Ecole Nationale Superieure du Petrole et des Moteurs). E-Learning is defined as training that uses new means to improve teaching: assistance with the organization of personal work time, formal teaching, access to documentary resources, yools for evaluation, and training and simulation (Toxopeus et al., 2003, Hesthammer, 2003). However, technological problems remain: the quality of an e-learning product is called into question when the learner doesn’t benefit from all the necessary tools. For example, in the case of a module using sound animation, if the learner’s computer does not have a sound card then interest in the on-line course will fade. Another issue is the concentration time of the learner, which on average is equal to 20 minutes; it is therefore necessary to be able to structure the e-learning in the form of a cycle of training, which introduces data-processing constraints. E-learning must remain a complementary tool to the traditional course: a 50/50 mix (50% traditional course, 50% on-line) preserves the richness of the exchange between learners and their teachers. Nevertheless, on short duration courses (a few days), we can consider including more on-line than traditional work. A correctly proportioned mixture of remote course and traditional teaching can be presented in the form of a system rich in resources such as CD-ROMs, Internet, teaching models (simulators), etc. Thus, e-learning allows the course to be undertaken in bursts and in a variety of places. Adapting on-line courses to the level of the learner is an important point. Learner build their knowledge by giving instructions to the computer: they test, make errors, and solve problems. Learning while ‘playing’, allows the attention of the learner to be captured for a longer time. Elements of creativity within an e-learning project should not be neglected; the curiosity of the learner must always be stimulated. The open and remote learning can be presented in two forms: synchronous (videoconference, virtual classes, etc) and asynchronous (educational software, personal work, etc) characterized by the following two dimensions: on the one hand the collective versus the individual and on the other hand, presence versus distance. The e-TSLIS program is used by a large audience: researchers, geoscientists, graduate students, and undergraduate students in specialized schools. We need on average three to five years for an e-learning project to give positive results. This implies that the effort of development must be maintained through the medium and long term.

Measurement of phase and group velocities at low frequencies

The dispersive properties of surface waves can be used in a case of exploration technology for weathering calculations. In full waveform acoustic Jogging, the dispersive waves are the Pseudo- Rayleigh waves in fast formations only and the Stoneley modes. The phase velocity of these dispersive waves can be used to evaluate the shear velocity of a formation. The use of dipole tools (Zemanek et al 1991) enables a measurement of the shear velocity in slow formations by studying the dispersion curves of flexural modes (figure 1). The object of this paper is to compare three methods which can be used to evaluate phase and group velocities of dispersive waves. The behavior and the accuracy of the proposed methods are checked on synthetic data. Synthetic data are an acoustic common shot point gather (figure 2).

Use of multidimentional MEM spectral analysis in geophysics

Auto and cross spectral analysis is the basic tool for geophysicist in order to study resonances of the magnetosphere using natural electromagnetic waves recorded in several places. The comparisons of these records must be made by autoregressive (AR) spectral estimators because the signal duration is short. For this application we show that the presentation of AR autospectrum by the position of the poles of the z transform is interesting. We make a direct comparison of the poles position for signal recorded at different places. Finally we present the influence of the choice of the order and discuss the particularities of the two dimensional autoregressive analysis.