Antoine Roueff

The San Andreas Fault revisited through seismic‐noise and surface‐wave tomography

[1]xa0We present here surface-wave tomography results for the San Andreas Fault in the Parkfield area, California, USA, that were extracted from microseismic noise in the 0.15 Hz to 0.35 Hz frequency band using passive seismic-correlation techniques. Using directive noise incoming from the Pacific Ocean, passive seismic-noise tomography was performed using three-component sensors from a dense seismic network. A rotation algorithm was applied to the nine-component noise-correlation tensor that optimally forced each station pair to re-align in the noise direction, a necessary condition to extract unbiased travel-times from passive seismic processing. After the rotation was performed, an optimal surface-wave tensor is obtained from which Love waves were extracted for tomography inversion. Dispersion curves were then inverted to obtain a three-dimensional shear-velocity map showing vertical geological structures and a 1.3-km wide low seismic velocity dip, which are in agreement with previous tomography studies in the same area.

Wave separation in ambient seismic noise using intrinsic coherence and polarization filtering

This paper deals with passive ambient seismic noise processing. A new wave separation method is proposed when several polarized waves are recorded by a pair of multicomponent sensors. Although it is well known that the information given by the auto-covariance matrix at one sensor is not sufficient for estimating the mixing matrix, it is shown in this paper that with two multicomponent sensors, the identification of the mixing matrix can be completed. In addition to the mathematical proof and synthetic example, an application to a real geophysical data set is also presented. A previous analysis of these data revealed the presence of surface waves. The application of the proposed algorithm leads to the separation of Rayleigh and Love waves.

Cramer–Rao Lower Bound Analysis of Vegetation Height Estimation With Random Volume Over Ground Model and Polarimetric SAR Interferometry

The random volume over ground model, which is based on a simple description of the electromagnetic wave interaction with a vegetated media, allows one to define techniques to estimate the vegetation height from the polarimetric interferometric synthetic aperture radar observations. We discuss this issue with the Cramer-Rao lower bound (CRLB) which provides a minimal bound of the variance independently of the estimation if it is unbiased. The usefulness of this approach is illustrated on three different examples. The first example deals with the influence of a priori knowledge of some physical parameters. We show that reducing the number of unknown physical parameters does not necessarily improve the CRLB. The second example focus on the efficiency of the Cloude et al. height estimator. On the considered data, this estimator reaches the CRLB when the standard deviation equals approximately one meter. In the third example we optimize the radar baseline.

Vegetation Height Estimation Precision With Compact PolInSAR and Homogeneous Random Volume Over Ground Model

Analyzing the precision of vegetation height estimation with compact (i.e., single transmit instead of dual transmit) polarimetric interferometric synthetic aperture radar (PolInSAR) with the homogeneous random volume over ground model can help justify the use of this type of radar rather than using the full PolInSAR. However, since compact PolInSAR provides less information than full PolInSAR, a loss of precision in the vegetation height estimation is expected, which can depend on the single transmit polarization. The adaptation of the Cramer-Rao bound (CRB) derived for full PolInSAR in our earlier work to compact PolInSAR measurement provides a general methodology to characterize this loss of precision. Indeed, the CRB is a lower bound of the variance of unbiased estimators that does not depend on the choice of a particular estimation method. We illustrate this methodology for P-band measurements with three synthetic examples chosen for their variability of polarimetric responses. For these examples, it is shown that there can exist a large set of transmit polarizations for which the loss of precision described by the CRB is small (smaller than a factor 2) although there also exist transmit polarizations for which the loss can be large (about a factor 100). This loss of precision is compared with the large dependency of the precision to the vegetation height estimation that can be observed with the vegetation height (more than a factor 100 in the precision described by the CRB) when all the other parameters of the vegetation, ground, and radar system are constant.

Separation technique of a mixing of two uncorrelated and perfectly polarized lights with different coherence and polarization properties

The sum of two uncorrelated and totally polarized lights with different coherence and polarization properties usually results in a partially polarized light. It is shown in this paper that the initial totally polarized lights can be recovered from the mixed partially polarized light. The proposed technique is based on coherence analysis and does not require the knowledge of the polarization states or the coherence properties of the initial perfectly polarized beams as long as these properties are different for the two waves. Some practical optical implementations of this technique are discussed on different illustrative applications.

Invariant Contrast Parameters of PolInSAR Homogenous RVoG Model

It has been shown that the Cramer-Rao bound (CRB) can be helpful to characterize vegetation and ground height estimations based on the homogenous random volume over ground (RVoG) model and polarimetric interferometric SAR techniques. However, this model is a function of 20 unknown parameters, which makes the performance analysis a tedious task. We show that the group invariance property of the RVoG model can greatly reduce the complexity of the analysis since the CRB of the vegetation and ground heights only depends on four unknown parameters instead of 20. Furthermore, for the considered situations analyzed in this letter, only three of these four parameters have a nonnegligible influence and can be interpreted as contrast parameters.

Minimum number of modulated Stokes parameters in Young's interference experiment

The contrast parameters associated with the generalized Stokes vector in a Youngs interference experiment are analyzed. It is shown that there are two unitary transformations that can be applied to the electric fields so that a partially polarized light can be described with no more than two non-zero generalized Stokes parameters. Furthermore, general conditions are derived which indicate when totally unpolarized light can be described with only one non-zero generalized Stokes parameter after unitary transformations.

Isotropic bicomponent partially polarized and partially coherent light.

The degree of coherence of scalar light remains constant when the fields are modified by the same random linear transformation, which can be represented by the multiplication by a random complex number. This shows that the coherence properties of scalar light at order two are not modified with the increase of disorder of each field that results from these transformations. We analyze the generalization of this property to partially polarized light. We determine the class of fields that can possess this property for any couple of points in a space-frequency or space-time domain after modification with deterministic Jones transformations. We show that the second-order coherence properties of this class of light can be generated experimentally with two uncorrelated totally polarized sources that have the same scalar coherence properties.

Unsupervised segmentation based on Von Mises circular distributions for orientation estimation in textured images

This paper deals with textured images and more particularly with directional textures. We propose a new parametric technique to estimate the orientation field of textures. It consists in partitioning the image into regions with homogeneous orientations, and then to estimate the orientation inside each of these regions, which allows us to maximize the size of the samples used to estimate the orientation without being corrupted by the presence of frontiers between regions. Once estimated the local - hence noisy - orientations of the texture using small filters (3×3 pixels), image partitioning is based on the minimization of the stochastic complexity (Minimum Description Length principle) of the orientation field. The orientation fluctuations are modeled with Von Mises probability density functions, leading to a fast and unsupervised partitioning algorithm. The accuracy of the orientations estimated with the proposed method is then compared with other approaches on synthetic images. An application to the processing of real images is finally addressed.

Van Cittert-Zernike theorem and symmetry properties of the normalized cross-spectral density matrix.

The van Cittert-Zernike theorem is formulated for the normalized cross-spectral density matrix of fields emitted by spatially incoherent sources. This formulation shows that sources with homogeneous polarization characteristics at second-order lead in the far field to normalized cross-spectral density matrices that possess high-symmetry properties. These symmetry properties are lost with polarization inhomogeneities of the source. These results are illustrated with ring-shaped sources.