Asymptotic results for eigenvector methods

Jeffries, D.J.; Farrier, D.R.

doi:10.1049/ip-f-1.1985.0110

Cited by 51 publications

(15 citation statements)

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“…The second-order moment formulas derived herein are relevant to these applications. As a cross check we show that these formulas reduce to some previous results published in [1][2][3][4] and in [11], under appropriate assumptions.…”

Section: Introductionsupporting

confidence: 66%

“…Inserting (3.4)-(3.6) into (3.1)-(3.3), we get the following well-known formulas (see, for example, [4,5])…”

Section: A Temporally Uncorrelated Datamentioning

confidence: 99%

“…The statistics of the principal eigenvalues 5l k 6 k51 n and their associated eigenvectors 5v k 6 k51 n play a central role in establishing the statistical behavior of a number of temporal or spatial frequency estimation algorithms such as MUSIC, ESPRIT, MIN-NORM, and TAM ( [5,6,12]). These statistics have been obtained, for example, in [1][2][3][4]6,7] under the assumptions that…”

Section: Introductionmentioning

confidence: 99%

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Eigenelement Statistics of Sample Covariance Matrix in the Correlated Data Case

Stoica

Söderström

1997

Digital Signal Processing

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Section: Introductionsupporting

confidence: 66%

“…Inserting (3.4)-(3.6) into (3.1)-(3.3), we get the following well-known formulas (see, for example, [4,5])…”

Section: A Temporally Uncorrelated Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Eigenelement Statistics of Sample Covariance Matrix in the Correlated Data Case

Stoica

Söderström

1997

Digital Signal Processing

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“…MUSIC has received much attention and can provide asymptotically unbiased estimations of signals. The asymptotic properties of MUSIC have been well documented in the literature (e.g., Jeffries and Farrier, 1985;Porat and Friedlander, 1988;Clergeot et al, 1989). Our processing method has the advantage that it does not need NMO corrections of seismic events since it begins by Fourier transforming each seismic waveform into the frequency domain.…”

Section: Introductionmentioning

confidence: 99%

Scattering characteristics in heterogeneous fractured reservoirs from waveform estimation

Feng¹,

Toksöz²

1998

SEG Technical Program Expanded Abstracts 1998

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Offset-dependent characteristics of seismic scattering are useful in the interpretation of fractured reservoirs. Synthetic seismograms generated by a 3-D finite difference modeling are used to study elastic wave propagation and scattering in heterogeneous fraetmed reservoirs. We use two models having different background medium properties and different azimuthal AVO responses and build heterogeneous fracture densit)' realizations through stochastic modeling. Gas-saturated fractured reservoirs and waveforms ill fracture normal and strike directions are considered in this paper. The multiple signal classification (MUSIC) frequency estimator is used in waveform estimation to proYid" frequency domain attributes related to seismic wav" scattering by fractmes. Om l"('sults indicate that the strength of the scattered field increases with increasing fracture scatter density and decreasing correlation length of spatial variations of fracture densit,·. It is also a function of the background medium. The strengt h of the scattering field is stronger in model 1 which has smaller property contrasts in the background medium than model 2. The scattering characteristics for both models are different at the top and the base of the fractured reservoir. Our results show that the scattered field is weak at the top of a fractured reservoir. The first order results are dominated by velocit)' anisotropy of a mean crack density field. However, the base of the fractured reservoir corresponds to a strong scattered field on which fracture heterogeneity has a larger effect. 5-1Shen and Toksiiz

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“…As described in section 2.1, the JAFE algorithm involves three main steps, namely, SVD (singularvalue decomposition) of the data matrix, diagonalization of a set of EVD (eigenvalue decomposition) problems and the transformation of the eigenvalues into signal parameters. The first step, which is equivalent to finding the EVD of the data covariance matrix, is well studied in the literature [7][8][9][10][11], for the case of white Gaussian noise contaminated data model. In our case, however, since some data stacking techniques have been employed, the noise is no more white.…”

Section: A Performance Analysismentioning

confidence: 99%

Analysis of ESPRIT based joint angle-frequency estimation

Lemma

Veen

Deprettere

2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100)

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High-resolution parameter estimation techniques have recently been applied to jointly estimate multiple signal parameters. In this work, we consider the problem of determining the directions and center frequencies of a number of narrow-band sources in a certain frequency band of interest. We present a joint angle-frequency estimation method, based on the multidimensional ESPRIT algorithm. A perturbation error analysis gives bounds on the parameter estimates, and provides optimal values for the temporal and spatial smoothing parameters. The analysis is shown to be consistent with simulation results.

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Asymptotic results for eigenvector methods

Cited by 51 publications

References 1 publication

Eigenelement Statistics of Sample Covariance Matrix in the Correlated Data Case

Eigenelement Statistics of Sample Covariance Matrix in the Correlated Data Case

Scattering characteristics in heterogeneous fractured reservoirs from waveform estimation

Analysis of ESPRIT based joint angle-frequency estimation

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