scholarly journals Improving the use of the randomized singular value decomposition for the inversion of gravity and magnetic data

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. G93-G107
Author(s):  
Saeed Vatankhah ◽  
Shuang Liu ◽  
Rosemary Anne Renaut ◽  
Xiangyun Hu ◽  
Jamaledin Baniamerian
Keyword(s):  
Singular Value Decomposition ◽  
Spectral Properties ◽  
Regularization Parameter ◽  
Gravity Data ◽  
Singular Value ◽  
Magnetic Data ◽  
Gravity And Magnetic ◽  
Magnetic Inversion ◽  
Model Matrix ◽  
Value Decomposition

The focusing inversion of gravity and magnetic potential-field data using the randomized singular value decomposition (RSVD) method is considered. This approach facilitates tackling the computational challenge that arises in the solution of the inversion problem that uses the standard and accurate approximation of the integral equation kernel. We have developed a comprehensive comparison of the developed methodology for the inversion of magnetic and gravity data. The results verify that there is an important difference between the application of the methodology for gravity and magnetic inversion problems. Specifically, RSVD is dependent on the generation of a rank [Formula: see text] approximation to the underlying model matrix, and the results demonstrate that [Formula: see text] needs to be larger, for equivalent problem sizes, for the magnetic problem compared to the gravity problem. Without a relatively large [Formula: see text], the dominant singular values of the magnetic model matrix are not well approximated. We determine that this is due to the spectral properties of the matrix. The comparison also shows us how the use of the power iteration embedded within the randomized algorithm improves the quality of the resulting dominant subspace approximation, especially in magnetic inversion, yielding acceptable approximations for smaller choices of [Formula: see text]. Further, we evaluate how the differences in spectral properties of the magnetic and gravity input matrices also affect the values that are automatically estimated for the regularization parameter. The algorithm is applied and verified for the inversion of magnetic data obtained over a portion of the Wuskwatim Lake region in Manitoba, Canada.

scholarly journals Application of generalized singular value decomposition to ionospheric tomography

2004 ◽  
Vol 22 (10) ◽  
pp. 3437-3444 ◽  
Author(s):  
K. Bhuyan ◽  
S. B. Singh ◽  
P. K. Bhuyan
Keyword(s):  
Singular Value Decomposition ◽  
Regularization Parameter ◽  
Singular Value ◽  
Electron Content ◽  
Generalized Singular Value Decomposition ◽  
Total Electron ◽  
Ionospheric Tomography ◽  
Low Latitude Ionosphere ◽  
A Chain ◽  
Value Decomposition

Abstract. The electron density distribution of the low- and mid-latitude ionosphere has been investigated by the computerized tomography technique using a Generalized Singular Value Decomposition (GSVD) based algorithm. Model ionospheric total electron content (TEC) data obtained from the International Reference Ionosphere 2001 and slant relative TEC data measured at a chain of three stations receiving transit satellite transmissions in Alaska, USA are used in this analysis. The issue of optimum efficiency of the GSVD algorithm in the reconstruction of ionospheric structures is being addressed through simulation of the equatorial ionization anomaly (EIA), in addition to its application to investigate complicated ionospheric density irregularities. Results show that the Generalized Cross Validation approach to find the regularization parameter and the corresponding solution gives a very good reconstructed image of the low-latitude ionosphere and the EIA within it. Provided that some minimum norm is fulfilled, the GSVD solution is found to be least affected by considerations, such as pixel size and number of ray paths. The method has also been used to investigate the behaviour of the mid-latitude ionosphere under magnetically quiet and disturbed conditions.

A fast algorithm for regularized focused 3D inversion of gravity data using randomized singular-value decomposition

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. G25-G34 ◽  
Author(s):  
Saeed Vatankhah ◽  
Rosemary Anne Renaut ◽  
Vahid Ebrahimzadeh Ardestani
Keyword(s):  
Linear System ◽  
Singular Value Decomposition ◽  
Fast Algorithm ◽  
Large Scale ◽  
Gravity Data ◽  
Singular Values ◽  
Singular Value ◽  
System Matrix ◽  
Large Scale System ◽  
Value Decomposition

We develop a fast algorithm for solving the under-determined 3D linear gravity inverse problem based on randomized singular-value decomposition (RSVD). The algorithm combines an iteratively reweighted approach for [Formula: see text]-norm regularization with the RSVD methodology in which the large-scale linear system at each iteration is replaced with a much smaller linear system. Although the optimal choice for the low-rank approximation of the system matrix with [Formula: see text] rows is [Formula: see text], acceptable results are achievable with [Formula: see text]. In contrast to the use of the iterative LSQR algorithm for the solution of linear systems at each iteration, the singular values generated using RSVD yield a good approximation of the dominant singular values of the large-scale system matrix. Thus, the regularization parameter found for the small system at each iteration is dependent on the dominant singular values of the large-scale system matrix and appropriately regularizes the dominant singular space of the large-scale problem. The results achieved are comparable with those obtained using the LSQR algorithm for solving each linear system, but they are obtained at a reduced computational cost. The method has been tested on synthetic models along with real gravity data from the Morro do Engenho complex in central Brazil.

Advanced fusion of geophysical data through combined use of 2D Discrete Wavelet Transform and Multiresolution Singular Value Decomposition applied to GPR-3D and magnetic data

2020 ◽  
Author(s):  
Rui Jorge Oliveira ◽  
Bento Caldeira ◽  
Teresa Teixidó ◽  
José Fernando Borges
Keyword(s):  
Wavelet Transform ◽  
Singular Value Decomposition ◽  
Data Fusion ◽  
Singular Value ◽  
Geophysical Data ◽  
Magnetic Data ◽  
Discrete Wavelet ◽  
Buried Structures ◽  
Combined Use ◽  
Value Decomposition

<p>Despite strong evidences that are visible at the surface that suggests the presence of buried structures, sometimes, both the GPR and magnetic data do not allow to clearly about the presence of these structures. Usually, this lack of perceptibility is due to the physical and chemical conditions of the medium that produces an increasing of background noise and masks the useful information. This causes a decrease in the signal-to-noise ratio of the data, preventing a good assessment about the existence of buried structures at subsurface.</p><p>Nevertheless, we believe that the recorded signal of both methods has the useful part of the signal hidden. Data fusion techniques are widely used in brain tumour detection in medicine by combining data from different clinical exams, both with low perceptibility.</p><p>This work presents an approach that allows using advanced fusion algorithms to combine geophysical data from GPR-3D and magnetics. This creates an enhanced image from both datasets with better quality than the individual images from each method.</p><p>The data fusion approach is performed through the combined use of 2D Discrete Wavelet Transform, Multiresolution Singular Value Decomposition and Image Gradient. This scheme allows us to select the useful information to obtain a higher quality and sharper fused image using the best of input datasets. The geophysical data fusion was successfully tested on three datasets, with different levels of perceptibility: high, intermediate and low.</p><p> </p><p>Acknowledgment: This work is co-funded by the ICT Project (UID/GEO/04683/2019) with the reference POCI-01-0145-FEDER-007690, by the Project SFRH/BSAB/143063/2018 (FCT) and by the INTERREG 2014-2020 Program, through the "Innovación abierta e inteligente en la EUROACE" Project, with the reference 0049_INNOACE_4_E.</p>

Improving TF-IDF with Singular Value Decomposition (SVD) for Feature Extraction on Twitter

2017 ◽  
Author(s):  
Ammar Ismael Kadhim ◽  
Yu-N Cheah ◽  
Inaam Abbas Hieder ◽  
Rawaa Ahmed Ali
Keyword(s):  
Feature Extraction ◽  
Singular Value Decomposition ◽  
Singular Value ◽  
Value Decomposition
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