Experimental identification for inverse problem of a mechanical system with a non-minimum phase based on singular value decomposition

2008 ◽  
Vol 22 (8) ◽  
pp. 1504-1509 ◽  
Author(s):  
Sung-Jong Kim ◽  
Sang-Kwon Lee
Keyword(s):  
Inverse Problem ◽  
Singular Value Decomposition ◽  
Mechanical System ◽  
Singular Value ◽  
Minimum Phase ◽  
Experimental Identification ◽  
Value Decomposition

scholarly journals Singular-value decomposition analysis of source illumination in seismic interferometry by multidimensional deconvolution

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. Q25-Q34 ◽  
Author(s):  
Shohei Minato ◽  
Toshifumi Matsuoka ◽  
Takeshi Tsuji
Keyword(s):  
Inverse Problem ◽  
Numerical Modeling ◽  
Singular Value Decomposition ◽  
Decomposition Analysis ◽  
Incident Field ◽  
Singular Value ◽  
Source Distribution ◽  
Seismic Interferometry ◽  
Source Illumination ◽  
Value Decomposition

We have developed a method to analytically evaluate the relationship between the source-receiver configuration and the retrieved wavefield in seismic interferometry performed by multidimensional deconvolution (MDD). The MDD method retrieves the wavefield with the desired source-receiver configuration from the observed wavefield without source information. We used a singular-value decomposition (SVD) approach to solve the inverse problem of MDD. By introducing SVD into MDD, we obtained quantities that revealed the characteristics of the MDD inverse problem and interpreted the effect of the initial source-receiver configuration for a survey design. We numerically simulated the wavefield with a 2D model and investigated the rank of the incident field matrix of the MDD inverse problem. With a source array of identical length, a sparse and a dense source distribution resulted in an incident field matrix of the same rank and retrieved the same wavefield. Therefore, the optimum source distribution can be determined by analyzing the rank of the incident field matrix of the inverse problem. In addition, the introduction of scatterers into the model improved the source illumination and effectively increased the rank, enabling MDD to retrieve a better wavefield. We found that the ambiguity of the wavefield inferred from the model resolution matrix was a good measure of the amount of illumination of each receiver by the sources. We used the field data recorded at the two boreholes from the surface sources to support our results of the numerical modeling. We evaluated the rank of incident field matrix with the dense and sparse source distribution. We discovered that these two distributions resulted in an incident field matrix of almost the same rank and retrieved almost the same wavefield as the numerical modeling. This is crucial information for designing seismic experiments using the MDD-based approach.

scholarly journals SEISMIC SIGNAL ANALYSIS USING MINIMUM PHASE AND SINGULAR VALUE DECOMPOSITION METHODS. APPLICATION TO GROUNDROLL ATTENUATION

2019 ◽  
Vol 37 (2) ◽  
Author(s):  
Anderson Silva Santos ◽  
Milton José Porsani
Keyword(s):  
Singular Value Decomposition ◽  
Seismic Data ◽  
Seismic Signal ◽  
Singular Value ◽  
Frequency Noise ◽  
Minimum Phase ◽  
Phase Decomposition ◽  
Seismic Section ◽  
Reflectivity Function ◽  
Value Decomposition

ABSTRACT. A challenge in land seismic data processing is the coherent noise groundroll. This noise is related to the propagation of surface waves of the Rayleigh type, this undesired event has as characteristics: low frequencies, high amplitudes and strong dispersion, which masks the events of interest in the stacked seismic section. The seismic data from the Tacutu Basin, besides having a low signal-to-noise ratio, are also strongly contaminated by groundroll noise, which makes it a challenge to obtain stacked seismic section with high resolution of this sedimentary basin. The 1D and 2D frequency filters are widely used for groundroll attenuation, but these methods besides attenuating the noisy also eliminate part of the signal by rejecting part of the frequency band of the seismic signal. Therefore, we are introduce a new filter to groundroll attenuation that uses two powerful tools for decomposition of the seismic signal together, minimum phase decomposition and singular value decomposition. The proposed method aims to estimate the reflectivity function for each seismic trace and then perform a decomposition of this reflectivity function. Since the low frequency noise is confined in the first portion of the decomposed signal it is possible to make a separation between the noise and the signal. The filtering method was included in the 2D seismic processing flow chart of the Tacutu Basin. The results showed that the proposed method was capable of attenuate the groundroll noise and generated at the end a stacked seismic section with a good resolution. Keywords: minimum phase decomposition, singular value decomposition, groundroll attenuation.RESUMO. Um desafio no processamento de dados sísmicos terrestres é o ruído coerente groundroll. Este ruído está relacionado à propagação de ondas de superfície do tipo Rayleigh, este evento indesejado tem como características: baixas frequências, altas amplitudes e forte dispersão, o que mascara os eventos de interesse na seção sísmica empilhada. Os dados sísmicos da Bacia do Tacutu, além de apresentar uma baixa relação sinal-ruído, também estão fortemente contaminados pelo ruído do solo, o que dificulta a obtenção de seções sísmicas empilhadas com alta resolução desta bacia sedimentar. Os filtros de frequência 1D e 2D são amplamente utilizados para a atenuação do groundroll, mas esses métodos além de atenuar o ruído também eliminam parte do sinal rejeitando parte da banda de frequência do sinal sísmico. Portanto, estamos introduzindo um novo filtro para a atenuação de groundroll que usa duas ferramentas poderosas para a decomposição do sinal sísmico, decomposição em fase mínima e decomposição em valor singular. O método proposto tem como objetivo estimar a função de refletividade para cada traço sísmico e então realizar a decomposição dessa função refletividade. Uma vez que o ruído de baixa frequência é confinado na primeira porção do sinal decomposto, é possível fazer uma separação entre o ruído e o sinal. O método de filtragem foi incluído no fluxograma de processamento sísmico 2D da Bacia do Tacutu. Os resultados mostraram que o método proposto foi capaz de atenuar o ruído groundroll e gerar ao final uma seção sísmica empilhada com boa resolução.Palavras-chave: decomposição em fase mínima, decomposição em valores singulares, atenuação do groundroll.  

scholarly journals Singular value decomposition of the velocity‐reflector depth tradeoff, Part 2: High‐resolution analysis of a generic model

Geophysics ◽  
1992 ◽  
Vol 57 (7) ◽  
pp. 933-943 ◽  
Author(s):  
Christof Stork
Keyword(s):  
Inverse Problem ◽  
Singular Value Decomposition ◽  
Circulant Matrix ◽  
Singular Value ◽  
Generic Model ◽  
Lateral Velocity ◽  
Block Circulant Matrix ◽  
Velocity Variations ◽  
Value Decomposition ◽  
Horizontal Wavelength

The symmetries of a block circulant matrix significantly reduce the computational expense of the singular value decomposition (SVD) of the variable velocity inverse problem for a generic reflection seismology model. As a result, the decomposition does not suffer from edge effects or parameterization artifacts that are associated with small model spaces. Using this approach, we study the eigenvector and eigenvalue characteristics for a generic model of a size as large as is used with a variety of iterative inversion techniques (>100 000 parameters). Singular value decomposition of the raypath inverse problem of a discretized generic seismic model having one reflector indicates that the eigenvalue distribution for the inverse problem is nonuniform, with a large concentration near 0 and a gap near 0.4. All but the long horizontal wavelength reflector‐depth variations cannot be uniquely resolved from velocity variations. Lateral velocity variations serve to significantly reduce the ability of seismic data to resolve reflector depth for most of the horizontal wavelength components shorter than twice the cable length. As a result, automatic velocity analysis methods may not be able to resolve reflector variations when the velocity field is allowed to take on an arbitrary structure.

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