Numerical performance of a tensor music algorithm based on HOSVD for a mixture of polarized sources

International audienceIn this paper, we develop an improved tensor MUSIC algorithm adapted to multidimensional data by means of multilinear algebra tools. This approach allows to preserve the multidimensional structure as the signal and the noise subspaces are estimated from the Higher Order Singular Value Decomposition (HOSVD) of the covariance tensor. The proposed algorithm is applied to a polarized source model. By computing the Mean Squared Error (MSE) for different scenarios, the performance of this method is compared to the classical MUSIC algorithm as well as the vector MUSIC algorithm that includes the polarization information. The simulations show that our algorithm outperforms the vector algorithms

Seismo-volcano source localization with triaxial broad-band seismic array

International audienceSeismo-volcano source localization is essential to improve our understanding of eruptive dynamics and of magmatic systems. The lack of clear seismic wave phases prohibits the use of classical location methods. Seismic antennas composed of one-component (1C) seismometers provide a good estimate of the backazimuth of the wavefield. The depth estimation, on the other hand, is difficult or impossible to determine. As in classical seismology, the use of three-component (3C) seismometers is now common in volcano studies. To determine the source location parameters (backazimuth and depth), we extend the 1C seismic antenna approach to 3Cs. This paper discusses a high-resolution location method using a 3C array survey (3CMUSIC algorithm) with data from two seismic antennas installed on an andesitic volcano in Peru (Ubinas volcano). One of the main scientific questions related to the eruptive process of Ubinas volcano is the relationship between the magmatic explosions and long-period (LP) swarms. After introducing the 3C array theory, we evaluate the robustness of the location method on a full wavefield 3-D synthetic data set generated using a digital elevation model of Ubinas volcano and an homogeneous velocity model. Results show that the backazimuth determined using the 3C array has a smaller error than a 1C array. Only the 3C method allows the recovery of the source depths. Finally, we applied the 3C approach to two seismic events recorded in 2009. Crossing the estimated backazimuth and incidence angles, we find sources located 1000 ± 660 m and 3000 ± 730 m below the bottom of the active crater for the explosion and the LP event, respectively. Therefore, extending 1C arrays to 3C arrays in volcano monitoring allows a more accurate determination of the source epicentre and now an estimate for the depth

Tensor decomposition of polarized seismic waves

National audienceIn antenna array processing, tensor decompositions allow to jointly estimate sources and their location. But these rechniques can be used only if data are recorded as a function of at least three diversities, which are usually time, space and space translation. The approach presented therein is based on polarization diversity, a very attractive alternative when the antenna array does not enjoy space invariance. Then we derive Cramér-Rao bounds in this context, by resorting to differentiation conventions for real-complex mixed variables.En traitement d'antenne, les décompositions tensorielles permettent d'estimer conjointement les sources et de les localiser. Pour que ces dernières puissent être utilisées, il faut que les données présentent au moins trois diversités, qui sont habituellement le temps, l'espace, et la translation dans l'espace. L'approche présentée ici est basée sur la diversité de polarisation, une alternative très attractive lorsque l'antenne de jouit pas d'invariance spatiale. Nous dérivons ensuite les bornes de Cramér-Rao dans ce contexte, en nous appuyant sur des conventions de différentiation de variables mixtes réelles et complexes

Angular Resolution Limit for Vector-Sensor Arrays: Detection and Information Theory Approaches

International audienceThe Angular Resolution Limit (ARL) on resolving two closely spaced polarized sources using vector-sensor arrays is considered in this paper. The proposed method is based on the information theory. In particular, the Stein's lemma provides, asymptotically, a link between the probability of false alarm and the relative entropy between two hypothesis of a given statistical binary test. We show that the relative entropy can be approximated by a quadratic function in the ARL. This property allows us to derive and analyze a closed-form expression of the ARL. To illustrate the interest of our approach the ARL, in the sense of the detection theory, is also derived. Finally, we show that the ARL is only sensitive to the norm of the polarization state vector and not to the particular values of the polarization parameters

ANGULAR RESOLUTION LIMIT FOR VECTOR-SENSOR ARRAYS: DETECTION AND INFORMATION THEORY APPROACHES

ABSTRACT The Angular Resolution Limit (ARL) on resolving two closely spaced polarized sources using vector-sensor arrays is considered in this paper. The proposed method is based on the information theory. In particular, the Stein's lemma provides, asymptotically, a link between the probability of false alarm and the relative entropy between two hypothesis of a given statistical binary test. We show that the relative entropy can be approximated by a quadratic function in the ARL. This property allows us to derive and analyze a closed-form expression of the ARL. To illustrate the interest of our approach, the ARL, in the sense of the detection theory, is also derived. Finally, we show that the ARL is only sensitive to the norm of the polarization state vector and not to the particular values of the polarization parameters

Source localization using a sparse representation framework to achieve superresolution

We present a source localization approach using resampling within a sparse representation framework. In particular, the amplitude and phase information of the sparse solution is considered holistically to estimate the direction-of-arrival (DOA), where a resampling technique is developed to determine which information will give a more precise estimation. The simulation results confirm the efficacy of our proposed method. © 2010 The Author(s).published_or_final_versionSpringer Open Choice, 01 Dec 201

Statistical Nested Sensor Array Signal Processing

Source number detection and direction-of-arrival (DOA) estimation are two major applications of sensor arrays. Both applications are often confined to the use of uniform linear arrays (ULAs), which is expensive and difficult to yield wide aperture. Besides, a ULA with N scalar sensors can resolve at most N − 1 sources. On the other hand, a systematic approach was recently proposed to achieve O(N 2 ) degrees of freedom (DOFs) using O(N) sensors based on a nested array, which is obtained by combining two or more ULAs with successively increased spacing. This dissertation will focus on a fundamental study of statistical signal processing of nested arrays. Five important topics are discussed, extending the existing nested-array strategies to more practical scenarios. Novel signal models and algorithms are proposed. First, based on the linear nested array, we consider the problem for wideband Gaussian sources. To employ the nested array to the wideband case, we propose effective strategies to apply nested-array processing to each frequency component, and combine all the spectral information of various frequencies to conduct the detection and estimation. We then consider the practical scenario with distributed sources, which considers the spreading phenomenon of sources. Next, we investigate the self-calibration problem for perturbed nested arrays, for which existing works require certain modeling assumptions, for example, an exactly known array geometry, including the sensor gain and phase. We propose corresponding robust algorithms to estimate both the model errors and the DOAs. The partial Toeplitz structure of the covariance matrix is employed to estimate the gain errors, and the sparse total least squares is used to deal with the phase error issue. We further propose a new class of nested vector-sensor arrays which is capable of significantly increasing the DOFs. This is not a simple extension of the nested scalar-sensor array. Both the signal model and the signal processing strategies are developed in the multidimensional sense. Based on the analytical results, we consider two main applications: electromagnetic (EM) vector sensors and acoustic vector sensors. Last but not least, in order to make full use of the available limited valuable data, we propose a novel strategy, which is inspired by the jackknifing resampling method. Exploiting numerous iterations of subsets of the whole data set, this strategy greatly improves the results of the existing source number detection and DOA estimation methods

Three-Component Seismic Array Analysis in the Discrete Wavelet Domain

The purpose of this PhD thesis was the development of an innovative methodology for the seismic array data analysis, named DWT-MuSiC (Discrete Wavelet Transform -Multiple Signals Classification). DWT-MuSiC is a new proposed method intended to be able to perform near-real time analysis relating to the detection of different seismic wave field and their characterization, starting from raw seismic array data. The innovative point of DWT-MuSiC is that it is thought to combine the resolution of the MuSiC (Multiple Signals Classification) algorithm, methodology used for frequency estimation and source location, proposed by Schmidt (1986), and the potentialities of the discrete wavelet domain analysis. The DWT-MuSiC, in fact other than detecting the presence of different wavefronts, provides both their direction of arrival and apparent speed of advancement, returning even information about the polarization of each identified phases, preserving furthermore spatial and frequency information of the original signals. The synthetic tests performed with the DWT-MuSiC analysis have shown the ability of the algorithm to detect wake signals also in presence of a low signal to noise ratio. The method returned correct output also in those cases where the analysis is performed on multiple seismic phases that overlap in terms of impinging time or/and frequency content of the signals themselves. The comparison between other methodology like the beamforming and MuSiC applied in the Fourier domain, shown how the information returned by the DWT-MuSiC was much more complete. The use of discrete wavelets and the optimization algorithm implemented in the analysis permit moreover to save computational time analyzing only the important data, allowing the recovery of hidden information when more than one wavefronts overlap. The application to real case on data collected at Mount Vesuvius (Italy) and at Krafka caldera (Island) were important to test the applicability of the methodology in different contests

Understanding magmatic processes and seismo-volcano source localization with multicomponent seismic arrays

Dans cette thèse, nous étudions le problème de la localisation de sources sismo-volcanique, à partir des données enregistrées par des réseaux de capteurs composés de nouveaux sismomètres à trois composantes (3C). Nous nous concentrerons sur le volcan Ubinas, l'un des plus actifs au Pérou. Nous développons une nouvelle approche (MUSIC-3C) basée sur la méthode MUSIC permetant de retourner les 3 paramètres utiles (lenteur, azimut et incidence). Pour valider notre méthodologie, nous analysons des sources synthétiques propagées en tenant compte de la topographie du volcan Ubinas. Dans cette expérience, les données synthétiques ont été générées pour plusieurs sources situées à différentes profondeurs sous le cratère Ubinas. Nous utilisons l'algorithme MUSIC-3C pour les relocaliser. Nous traitons également des données réelles provenant d'une expérience de terrain menée sur le volcan Ubinas (Pérou) en 2009 par les équipes de recherche de l'IRD-France (Institut de Recherche pour le Déveleppment), UCD l'Irlande (projet VOLUME) et l'Institut de Géophysique du Pérou (IGP). Nous utilisons l'algorithme MUSIC-3C pour localiser les événements explosifs (type vulcanien), ce qui nous permet d'identifier et d'analyser les processus physiques de ces événements, à la suite de cette analyse, nous avons trouvé deux sources pour chaque explosion situées à 300 m et 1100 m en dessous du fond du cratère actif. Basé sur les mécanismes éruptifs proposés pour d'autres volcans du même type, nous interprétons la position de ces sources ainsi que les limites du conduit éruptif impliqué dans le processus de fragmentation.In this thesis, we study the seismo-volcanic source localization using data recorded by new sensor arrays composed of three-component (3C) seismometers deployed on Ubinas stratovolcano (Peru). We develop a new framework (MUSIC-3C) of source localization method based on the well-known MUSIC algorithm. To investigate the performance of the MUSIC-3C method, we use synthetic datasets designed from eight broadband isotropic seismic sources located beneath the crater floor at different depths. The fundamental scheme of the MUSIC-3C method exploits the fact of the cross-spectral matrix of 3C array data, corresponding to the first seismic signal arrivals, provides of useful vector components (slowness, back-azimuth and incidence angle) from the seismic source. Application of the MUSIC-3C method on synthetic datasets shows the recovery of source positions. Real data used in this study was collected during seismic measurements with two seismic antennas deployed at Ubinas volcano in 2009, whose experiment conduced by volcanic teams of IRD-France (l'Institute de Recherche pour le Déveleppment), Geophysics group University College Dublin Ireland and Geophysical Institute of Peru (IGP). We apply the MUSIC-3C algorithm to investigate wave fields associated with the magmatic activity of Ubinas volcano. These analysis evidence a complex mechanism of vulcanian eruptions in which their seismic sources are found at two separated sources located at depths of 300 m and 1100 m beneath the crater floor. This implies the reproduction of similar mechanisms into the conduit. Based on the eruptive mechanisms proposed for other volcanoes of the same type, we interpret the position of this sources as the limits of the conduit portion that was involved in the fragmentation process.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Beamforming and Direction of Arrival Estimation Based on Vector Sensor Arrays

Array signal processing is a technique linked closely to radar and sonar systems. In communication, the antenna array in these systems is applied to cancel the interference, suppress the background noise and track the target sources based on signals'parameters. Most of existing work ignores the polarisation status of the impinging signals and is mainly focused on their direction parameters. To have a better performance in array processing, polarized signals can be considered in array signal processing and their property can be exploited by employing various electromagnetic vector sensor arrays. In this thesis, firstly, a full quaternion-valued model for polarized array processing is proposed based on the Capon beamformer. This new beamformer uses crossed-dipole array and considers the desired signal as quaternion-valued. Two scenarios are dealt with, where the beamformer works at a normal environment without data model errors or with model errors under the worst-case constraint. After that, an algorithm to solve the joint DOA and polarisation estimation problem is proposed. The algorithm applies the rank reduction method to use two 2-D searches instead of a 4-D search to estimate the joint parameters. Moreover, an analysis is given to introduce the difference using crossed-dipole sensor array and tripole sensor array, which indicates that linear crossed-dipole sensor array has an ambiguity problem in the estimation work and the linear tripole sensor array avoid this problem effectively. At last, we study the problem of DOA estimation for a mixture of single signal transmission (SST) signals and duel signal transmission (DST) signals. Two solutions are proposed: the first is a two-step method to estimate the parameters of SST and DST signals separately; the second one is a unified one-step method to estimate SST and DST signals together, without treating them separately in the estimation process