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 Composite Singular Value Decomposition Analysis of Moisture Variations Associated with the Madden–Julian Oscillation: ERA-40 Analysis

2005 ◽  
Vol 18 (20) ◽  
pp. 4329-4335 ◽  
Author(s):  
Bryan C. Weare
Keyword(s):  
Singular Value Decomposition ◽  
Decomposition Analysis ◽  
Longwave Radiation ◽  
Singular Value ◽  
Specific Humidity ◽  
Striking Difference ◽  
Time Lags ◽  
Madden Julian Oscillation ◽  
Singular Value Decomposition Analysis ◽  
Value Decomposition

Abstract The role of moisture variations in the initiation of Madden–Julian oscillation (MJO) variability is reexamined through composite singular value decomposition (CSVD) analyses using the European Centre for Medium-Range Weather Forecasts (ECMWF) 40-yr Re-Analyses (ERA-40) data. The CSVD analyses at various time lags are carried out to discern the complex space–time relationships between convection identified using outgoing longwave radiation and 1000-hPa divergence, 850-hPa specific humidity, and surface evaporation. The most striking difference from the earlier analyses using NCEP–NCAR reanalysis data is that the observed relations between 20–100-day filtered OLR and ∇ · V1000 anomalies are weaker and less significant in the current analyses. On the other hand, both analyses show increasing low-level moisture near and to the east of the developing convection. Thus, both results imply that moisture preconditioning of convective events is not totally driven by boundary layer moisture convergence.

NORMAL MODE ANALYSIS OF A SINGLE-WALLED CARBON NANOTUBE BASED ON MOLECULAR DYNAMIC: A SINGULAR VALUE DECOMPOSITION STUDY

2010 ◽  
Vol 09 (05) ◽  
pp. 471-486 ◽  
Author(s):  
S. NEGI ◽  
S. CHATURVEDI
Keyword(s):  
Carbon Nanotube ◽  
Singular Value Decomposition ◽  
Normal Modes ◽  
Decomposition Analysis ◽  
Singular Value ◽  
Singular Value Decomposition Analysis ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Value Decomposition ◽  
Radial Stretching

The complete set of significant normal modes of a single-walled carbon nanotube has been extracted using singular value decomposition analysis of this molecular dynamics data. The first part of this study focuses on an isolated single-walled carbon nanotube performed with NVE Molecular Dynamic simulations. Singular value decomposition analysis is then done on this data. Normal modes are excited with an initial radial stretching given to all the atomic coordinates. For the case with 5% initial radial stretching given to the carbon nanotube, the two strongest modes involve radial breathing motion combined with a very slow rotational motion of individual rings of the nanotube. There is good agreement between the calculated frequency of radial breathing modes and published experimental measurements, as also the inverse scaling of this frequency with tube diameter. The coupling between these two motions weakens for a smaller initial perturbation. The next eight most significant modes are divided into two classes. The first class is characterized by mz = 0, i.e., axial uniformity and produces azimuthal variation in the radial positions of atoms, with a finite azimuthal mode number. The second class of modes has mθ = 0, with mz = 1 and 2, are with radial uniformity and leads to shifts in the X- and Y-centroid locations of different rings. Mode frequency and the associated spatial distortion are thus obtained for all the above-mentioned modes. Under NPT conditions, similar to laboratory conditions, i.e., at a constant temperature and pressure, mode frequencies change only slightly, but the hierarchy of modes is slightly different. External excitation produced at one of the normal mode frequencies, corresponding to centroid motion with (mθ = 0, mz = 1), shows a significant and steady increase in the amplitude of centroid displacement. Excitation at the second harmonic frequency leads to an initial increase in displacement amplitude, but eventual saturation. These conclusions are important for the application of carbon nanotubes in nanodevices, e.g., as nanomotors.

scholarly journals A study of coupling between viscoelastic parameters using the singular value decomposition analysis

2016 ◽  
pp. 309-317
Author(s):  
Е.С. Ефимова
Keyword(s):  
Singular Value Decomposition ◽  
Original Problem ◽  
Decomposition Analysis ◽  
Singular Value ◽  
Singular Value Decomposition Analysis ◽  
Viscoelastic Parameters ◽  
Standard Linear Solid Model ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Value Decomposition

Исследуется решение обратной задачи сейсмики в линеаризованной постановке для модели вязкоупругой среды. Для описания сред с поглощением используется обобщенная модель стандартного линейного твердого тела, опирающаяся на $\tau$-метод. Если при численном решении неоднородность одного из искомых параметров переходит в изменчивость другого, то такие параметры называются связанными. Связанность параметров является одним из проявлений некорректности изучаемой задачи. Для ее преодоления необходимо привлечение регуляризующей процедуры. В качестве таковой в работе предлагается использовать усечение сингулярного разложения для одновременного определения скорости продольных волн и их поглощения. В качестве параметризации среды рассматривается комбинация параметров Ламе и добротности. The solution of a linearized inverse seismic problem of viscoelasticity is studied. The generalized standard linear solid model and the $\tau$ method are used to describe media with attenuation. If the heterogeneity of one of the sought parameters influence the variability of another one during the process of numerical solution, then such parameters are said to be coupled. Such a coupling is a sign of ill-posedness of the original problem. A regularization is necessary to overcome this difficulty. To accomplish this, we propose the truncation of the singular value decomposition to simultaneously determine the P-velocity and its attenuation. A combination of the Lame parameters and the quality factor are used as the parametrization of the medium under consideration.

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