Vector-Sensor MUSIC for Polarized Seismic Sources Localization
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Vector-Sensor MUSIC for Polarized Seismic Sources Localization Sebastian Miron Laboratoire des Images et des Signaux (LIS), 961 rue de la Houille Blanche, BP 46, 38402 Saint Martin d’H`eres Cedex, France Email: [email protected]
Nicolas Le Bihan Laboratoire des Images et des Signaux (LIS), 961 rue de la Houille Blanche, BP 46, 38402 Saint Martin d’H`eres Cedex, France Email: [email protected]
´ ome ˆ Jer I. Mars Laboratoire des Images et des Signaux (LIS), 961 rue de la Houille Blanche, BP 46, 38402 Saint Martin d’H`eres Cedex, France Email: [email protected] Received 18 December 2003; Revised 7 June 2004 This paper addresses the problem of high-resolution polarized source detection and introduces a new eigenstructure-based algorithm that yields direction of arrival (DOA) and polarization estimates using a vector-sensor (or multicomponent-sensor) array. This method is based on separation of the observation space into signal and noise subspaces using fourth-order tensor decomposition. In geophysics, in particular for reservoir acquisition and monitoring, a set of Nx -multicomponent sensors is laid on the ground with constant distance ∆x between them. Such a data acquisition scheme has intrinsically three modes: time, distance, and components. The proposed method needs multilinear algebra in order to preserve data structure and avoid reorganization. The data is thus stored in tridimensional arrays rather than matrices. Higher-order eigenvalue decomposition (HOEVD) for fourthorder tensors is considered to achieve subspaces estimation and to compute the eigenelements. We propose a tensorial version of the MUSIC algorithm for a vector-sensor array allowing a joint estimation of DOA and signal polarization estimation. Performances of the proposed algorithm are evaluated. Keywords and phrases: vector-sensor array, vector MUSIC, interspectral tensor, higher-order eigenvalue decomposition for 4thorder tensors.
1.
INTRODUCTION
Seismic measurements are used for mapping geological features to discover, locate, and evaluate gas concentrations or oil reservoirs. For this purpose, geophysicists study elastic waves propagating in the earth originating from artificial sources (such as explosions) and recorded on a sensor array (Figure 1). To analyze the recorded data, models of waveforms are used and estimation techniques are applied to find parameters describing the waves such as their direction of arrival (DOA), polarization, power, and so forth. From the estimated parameters, it is possible to obtain information on layer structure, depth, and so forth. [1]. In order to map a field or a reservoir, a sensor array which gives a 2D signal s(tn , xn ) of size Nx × Nt is generally used (tn is the time recording dimension and xn is the distance dimension (array aperture)). After performing a Fourier transform along the time dimension, classical scalar-sensor version of
the MUSIC algorithm can be used in order to estimate the DOAs of sources [2]. Vector sensors are nowadays widely used in seismic acquisiti
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