• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.113-119
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• 2011

Let T be a bounded linear operator on a complex Hilbert space $\mathcal{H}$. An operator T is called class A operator if ${\left|{T^2}\right|}{\geq}{\left|{T^2}\right|}$ and is called class A(k) operator if $({T^*\left|T\right|^{2k}T})^{\frac{1}{k+1}}{\geq}{\left|T\right|}^2$. In this paper, we show that ${\sigma}$ is continuous when restricted to the set of class A operators and consider the tensor products of class A(k) operators.

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.75-80
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• 2013

Let T be a bounded linear operator on a complex Hilbert space $\mathfrak{H}$. An operator T is called class A operator if ${\mid}T^2{\mid}{\geq}{\mid}T{\mid}^2$ and is called class $A({\kappa})$ operator if $(T^*{\mid}T{\mid}^{2{\kappa}}T)^{\frac{1}{{\kappa}+1}}{\geq}{\mid}T{\mid}^2$ for a positive number ${\kappa}$. In this paper, we show that ${\sigma}$ is continuous when restricted to the set of class $A({\kappa})$ operators.

• The Journal of Engineering Geology
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• v.28 no.3
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• pp.465-473
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• 2018

The application of singular value decomposition (SVD) filtering is examined for attenuation of the ground-roll in land seismic data. Prior to the SVD computation to seek singular values containing the highly correlatable reflection energy, processing steps such as automatic gain control, elevation and refraction statics, NMO correction, and residual statics are performed to enhance the horizontal correlationships and continuities of reflections. Optimal parameters of SVD filtering are effectively chosen with diagnostic display of inverse NMO (INMO) corrected CSP (common shot point) gather. On the field data with dispersion of ground-roll overwhelmed, continuities of reflection events are much improved by SVD filtering than f-k filtering by eliminating the ground-roll with preserving the low-frequency reflections. This is well explained in the average amplitude spectra of the f-k and SVD filtered data. The reflectors including horizontal layer of the reservoir are much clearer on the stack section, with laminated events by SVD filtering and subsequent processing steps of spiking deconvolution and time-variant spectral whitening.

• Geophysics and Geophysical Exploration
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• v.19 no.1
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• pp.11-19
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• 2016

Two representative residual static methods of traveltime decomposition and stack-power maximization are discussed in terms of application to land seismic data. For the model data with synthetic shot/receiver statics (time shift) applied and random noises added, continuities of reflection event are much improved by stack-power maximization method, resulting the derived time-shifts approximately equal to the synthetic statics. Optimal parameters (maximum allowable shift, correlation window, iteration number) for residual statics are effectively chosen with diagnostic displays of CSP (common shot point) stack and CRP (common receiver point) stack as well as CMP gather. In addition to removal of long-wavelength time shift by refraction statics, prior to residual statics, processing steps of f-k filter, predictive deconvolution and time variant spectral whitening are employed to attenuate noises and thereby to minimize the error during the correlation process. The reflectors including horizontal layer of reservoir are more clearly shown in the variable-density section through repicking the velocities after residual statics and inverse NMO correction.