On the Optimal Field Sensing in Near-Field Characterization

We deal with the problem of characterizing a source or scatterer from electromagnetic radiated or scattered field measurements. The problem refers to the amplitude and phase measurements which has applications also to interferometric approaches at optical frequencies. From low frequencies (microwaves) to high frequencies or optics, application examples are near-field/far-field transformations, object restoration from measurements within a pupil, near-field THz imaging, optical coherence tomography and ptychography. When analyzing the transmitting-sensing system, we can define “optimal virtual" sensors by using the Singular Value Decomposition (SVD) approach which has been, since long time, recognized as the “optimal” tool to manage linear algebraic problems. The problem however emerges of discretizing the relevant singular functions, thus defining the field sampling. To this end, we have recently developed an approach based on the Singular Value Optimization (SVO) technique. To make the “virtual” sensors physically realizable, in this paper, two approaches are considered: casting the “virtual” field sensors into arrays reaching the same performance of the “virtual” ones; operating a segmentation of the receiver. Concerning the array case, two ways are followed: synthesize the array by a generalized Gaussian quadrature discretizing the linear reception functionals and use elementary sensors according to SVO. We show that SVO is “optimal” in the sense that it leads to the use of elementary, non-uniformly located field sensors having the same performance of the “virtual” sensors and that generalized Gaussian quadrature has essentially the same performance.

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PRINCIPLES OF SINGULAR VALUE DECOMPOSITION FOR RESOLUTION ENHANCEMENT IN NEAR-FIELD OPTICS

Physics, Chemistry and Application of Nanostructures ◽

10.1142/9789814280365_0012 ◽

2009 ◽

Author(s):

M. KARELIN

Keyword(s):

Singular Value Decomposition ◽

Near Field ◽

Resolution Enhancement ◽

Singular Value ◽

Near Field Optics ◽

Value Decomposition

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GROUND ROLL ATTENUATION USING ADAPTIVE SINGULAR VALUE DECOMPOSITION FILTERING IN THE f-k DOMA

Brazilian Journal of Geophysics ◽

10.22564/rbgf.v33i3.939 ◽

2015 ◽

Vol 33 (3) ◽

pp. 421

Author(s):

Danilo S. Cruz ◽

Milton J. Porsani

Keyword(s):

Fourier Transform ◽

Singular Value Decomposition ◽

Signal To Noise Ratio ◽

Singular Value ◽

Coherent Noise ◽

Seismic Line ◽

Low Frequencies ◽

Ground Roll ◽

Window Approach ◽

Value Decomposition

ABSTRACT. The land seismic data often have low signal-to-noise ratio due, among other factors, the presence of ground roll. It is a coherent noise present in seismograms that appears as linear events, with low frequencies and high amplitudes, low velocities and, in most cases, overlapping the reflections and harm both the processing and the interpretation of the data. In this work we present a filtering approach to attenuate the ground roll, which is based on the Singular Value Decomposition (SVD) method applied in the frequency (f-k) domain. Before filtering the data we applied the standard pre-processing procedure to the original seismograms: the static corrections, the spherical divergence and a gain to improving the quality of the seismic records. After application of the 2D Fourier transform, the SVD is applied to a small frequency range using a sliding window approach. The f-k filtered spectrum is obtained with the difference between the original spectrum and the predicted ones and the family of filtered traces is obtained by performing a 2D inverse Fourier transform. The method was applied on a land seismic line of Tacutu Basin locatedin northeastern part of Brazil. The results show that the method is effective for mitigating the ground roll and provides better results when compared to conventionalfiltering method f-k.Keywords: ground roll attenuation, seismic processing, SVD filtering, f-k filtering.RESUMO. Os dados sísmicos terrestres geralmente apresentam baixa razão sinal-ruído devido, entre outros fatores, à presença do ground roll . Trata-se de um ruído dominado por altas amplitudes, baixas frequências, baixas velocidades e de caráter dispersivo, representado no domínio x-t como eventos lineares. Este ruído se sobrepõe às reflexões e prejudica tanto o processamento quanto a interpretação dos dados. Para atenuação do ground roll , utilizamos uma técnica de filtragem adaptativa baseada no método Singular Value Decomposition (SVD) e aplicada no domínio f-k. Como parte do pré-processamento dos dados foram aplicadas a correção estática, a correção de divergência esférica além da aplicação de um ganho com intuito de melhorar a qualidade do registro sísmico. Em seguida, as famílias de ponto de tiro comum foram levadas para o domínio da frequência (f-k), através da transformada dupla de Fourier, e a filtragem SVD foi aplicada na forma de janelas deslizantes confinadas à faixa de frequências dominada pelo ground roll. O espectro f-k filtrado foi obtido tomando a diferença entre o espectro original e o espectro SVD predito com a primeira autoimagem. A família de traços filtrada no domínio x-t é obtida através da transformada inversa dupla de Fourier. O método foi aplicado sobre uma linha sísmica terrestre da Bacia do Tacutu, localizada na parte norte do Brasil. Os resultados mostram que o método proposto é eficaz para atenuar o ground roll e fornece resultados melhores quando comparados ao método convencional de filtragem f-k.Palavras-chave: atenuação do ground roll , processamento sísmico, filtragem SVD, filtragem f-k.

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