Wave propagation in the viscoacoustic media is physically dispersive and dissipated.Completely excluding the numerical dispersion error from the physical dispersion in the viscoacoustic wave simu-lation is indispensab...Wave propagation in the viscoacoustic media is physically dispersive and dissipated.Completely excluding the numerical dispersion error from the physical dispersion in the viscoacoustic wave simu-lation is indispensable to understanding the intrinsic property of the wave propagation in attenuated media for the petroleum exploration geophysics.In recent years,a viscoacoustic wave equation char-acterized by fractional Laplacian gains wide attention in geophysical community.However,the first-order form of the viscoacoustic wave equation,often solved by the conventional staggered-grid pseu-dospectral method,suffers from the numerical dispersion error in time due to the low-order finite-difference approximation.It is challenging to completely eliminate the error because the viscoacoustic wave equation contains two temporal derivatives,which stem from the time stepping and the amplitude attenuation terms,respectively.To tackle the issue,we derive two exact first-order k-space viscoacoustic formulations that can fully exclude the numerical error from the physical dispersion.For the homoge-neous case,two formulations agree with the viscoacoustic analytical solution very well and have the same efficiency.For the heterogeneous case,our second k-space formulation is more efficient than the first one because the second formulation significantly reduces the number of the wavenumber-space mixed-domain operators,which are the expensive part of the viscoacoustic k-space simulation.Nu-merical cases validate that the two first-order k-space formulations are effective and efficient alternatives to the current staggered-grid pseudospectral formulation for the viscoacoustic wave simulation.展开更多
Planck scale plays a vital role in describing fundamental forces. Space time describes strength of fundamental force. In this paper, Einstein’s general relativity equation has been described in terms of contraction a...Planck scale plays a vital role in describing fundamental forces. Space time describes strength of fundamental force. In this paper, Einstein’s general relativity equation has been described in terms of contraction and expansion forces of space time. According to this, the space time with Planck diameter is a flat space time. This is the only diameter of space time that can be used as signal transformation in special relativity. This space time diameter defines the fundamental force which belongs to that space time. In quantum mechanics, this space time diameter is only the quantum of space which belongs to that particular fundamental force. Einstein’s general relativity equation and Planck parameters of quantum mechanics have been written in terms of equations containing a constant “K”, thus found a new equation for transformation of general relativity space time in to quantum space time. In this process of synchronization, there is a possibility of a new fundamental force between electromagnetic and gravitational forces with Planck length as its space time diameter. It is proposed that dark matter is that fundamental force carrying particle. By grand unification equation with space-time diameter, we found a coupling constant as per standard model “α<sub>s</sub>” for that fundamental force is 1.08 × 10<sup>-23</sup>. Its energy calculated as 113 MeV. A group of experimental scientists reported the energy of dark matter particle as 17 MeV. Thorough review may advance science further.展开更多
The Sensitivity Encoding (SENSE) parallel reconstruction scheme for magnetic resonance imaging (MRI) is implemented with non-cartesian sampled k-space trajectories in this paper. SENSE has the special capability to re...The Sensitivity Encoding (SENSE) parallel reconstruction scheme for magnetic resonance imaging (MRI) is implemented with non-cartesian sampled k-space trajectories in this paper. SENSE has the special capability to reduce the scanning time for MRI experiments while maintaining the image resolution with under-sampling data sets. In this manner, it has become an increasingly popular technique for multiple MRI data acquisition and image reconstruction schemes. The gridding algorithm is also implemented with SENSE due to its ability in evaluating forward and adjoin operator with non-cartesian sampled data. In this paper, the sensitivity map profile, field map information and the spiral k-space data collected from an array of receiver coils are used to reconstruct unaliased images from under-sampled data. The performance of SENSE with real data set identifies the computational issues to be improved for researched.展开更多
文摘Wave propagation in the viscoacoustic media is physically dispersive and dissipated.Completely excluding the numerical dispersion error from the physical dispersion in the viscoacoustic wave simu-lation is indispensable to understanding the intrinsic property of the wave propagation in attenuated media for the petroleum exploration geophysics.In recent years,a viscoacoustic wave equation char-acterized by fractional Laplacian gains wide attention in geophysical community.However,the first-order form of the viscoacoustic wave equation,often solved by the conventional staggered-grid pseu-dospectral method,suffers from the numerical dispersion error in time due to the low-order finite-difference approximation.It is challenging to completely eliminate the error because the viscoacoustic wave equation contains two temporal derivatives,which stem from the time stepping and the amplitude attenuation terms,respectively.To tackle the issue,we derive two exact first-order k-space viscoacoustic formulations that can fully exclude the numerical error from the physical dispersion.For the homoge-neous case,two formulations agree with the viscoacoustic analytical solution very well and have the same efficiency.For the heterogeneous case,our second k-space formulation is more efficient than the first one because the second formulation significantly reduces the number of the wavenumber-space mixed-domain operators,which are the expensive part of the viscoacoustic k-space simulation.Nu-merical cases validate that the two first-order k-space formulations are effective and efficient alternatives to the current staggered-grid pseudospectral formulation for the viscoacoustic wave simulation.
文摘Planck scale plays a vital role in describing fundamental forces. Space time describes strength of fundamental force. In this paper, Einstein’s general relativity equation has been described in terms of contraction and expansion forces of space time. According to this, the space time with Planck diameter is a flat space time. This is the only diameter of space time that can be used as signal transformation in special relativity. This space time diameter defines the fundamental force which belongs to that space time. In quantum mechanics, this space time diameter is only the quantum of space which belongs to that particular fundamental force. Einstein’s general relativity equation and Planck parameters of quantum mechanics have been written in terms of equations containing a constant “K”, thus found a new equation for transformation of general relativity space time in to quantum space time. In this process of synchronization, there is a possibility of a new fundamental force between electromagnetic and gravitational forces with Planck length as its space time diameter. It is proposed that dark matter is that fundamental force carrying particle. By grand unification equation with space-time diameter, we found a coupling constant as per standard model “α<sub>s</sub>” for that fundamental force is 1.08 × 10<sup>-23</sup>. Its energy calculated as 113 MeV. A group of experimental scientists reported the energy of dark matter particle as 17 MeV. Thorough review may advance science further.
文摘The Sensitivity Encoding (SENSE) parallel reconstruction scheme for magnetic resonance imaging (MRI) is implemented with non-cartesian sampled k-space trajectories in this paper. SENSE has the special capability to reduce the scanning time for MRI experiments while maintaining the image resolution with under-sampling data sets. In this manner, it has become an increasingly popular technique for multiple MRI data acquisition and image reconstruction schemes. The gridding algorithm is also implemented with SENSE due to its ability in evaluating forward and adjoin operator with non-cartesian sampled data. In this paper, the sensitivity map profile, field map information and the spiral k-space data collected from an array of receiver coils are used to reconstruct unaliased images from under-sampled data. The performance of SENSE with real data set identifies the computational issues to be improved for researched.