Derivation of 3D deformation fields for the 2019 Ridgecrest Earthquakes (USA) based on Sentinel-1 TOPS data

2020 ◽  
Author(s):  
Roland Horvath ◽  
Balint Magyar ◽  
Ambrus Kenyeres
Keyword(s):  
Large Scale ◽  
Equation System ◽  
Unit Vector ◽  
Linear Equation System ◽  
Complex Approach ◽  
L2 Norm ◽  
Complete Tree ◽  
The Look ◽  
Value Decomposition ◽  
Along Track

<p>The<!-- Start of main text paraghraphs. --> advances of Sentinel-1 SAR data, like its open access policy and short revisit time, gives an outstanding opportunity to conduct in-situ mapping of large scale deformations. After the requisite calibrations and corrections (radiometric, terrain), geocoding, coregistration and phase unwrapping; the unwrapped phase can be converted to Line-of-site (LOS) displacements. Although it gives a characteristic picture of the investigated phenomena only in one-dimension, but to obtain tree-dimensional (East/North/Up – ENU) deformation, it requires a more complex approach.</p><p>To obtain the complete tree-dimensional displacement field, both ascending and descending LOS displacements shall be retrieved. As well as, the corresponding unit-vector of LOS look-vectors and its parallel, along-track azimuth vector in the direction of the azimuth offsets, from the SAR sensor to all measurements (pixel) in ENU format. This lead to four observations with different incident angles for each measurements, which can be generalized as an over-determined inverse problem. The estimated model vector of the complete tree-dimensional displacement can be obtained, if the Jacobi-matrix can be represented as the look-vectors in ENU basis and the observation vector as LOS deformations acquired from the unwrapped phase of the interferogram. Then the over-determined linear equation system can be solved in the L2 norm via the Gaussian Least Squares (LSQ) approach combined with Singular Value Decomposition (SVD).<!-- OPTIONAL: if reference field exists. --></p><p>Demonstrating the aforementioned, we present the continuation of DInSAR results of the two strike-slip earthquakes between 2019.07.04-06. with foreshock M<sub>W</sub> =6.5 and mainshock M<sub> W</sub> =7.1 in the Eastern Californian Shear Zone near Ridgecrest (US).</p>

scholarly journals Penyelesaian Sistem Persamaan Linier Fully Fuzzy Menggunakan Metode Dekomposisi Nilai Singular (SVD)

2018 ◽  
Vol 4 (2) ◽  
pp. 143-149
Author(s):  
Corry Corazon Marzuki ◽  
Agustian` Agustian` ◽  
Dewi Hariati ◽  
Junitis Afmilda ◽  
Nurul Husna ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Linear Equation ◽  
Fuzzy Numbers ◽  
Equation System ◽  
Singular Value ◽  
Linear Equation System ◽  
Single Solution ◽  
Value Decomposition ◽  
Svd Method ◽  
Linear Equation Systems

Linear equation system can be arranged into the AX = B matrix equation. Constants in linear can also contain fuzzy numbers and all their parameters in fuzzy numbers known as fully fuzzy linear equation systems. singular value decomposition (SVD) is a method that decomposes an A matrix into three components of the USVH. The SVD method can be used to find a solution to the fully fuzzy fully linear equation system that is also an inconsistent fully fuzzy linear equation system. The solution obtained from a fully fuzzy linear equation system that is consistent using SVD is a single solution and many solutions. Whereas, the solution obtained from a fully fuzzy linear equation system that is inconsistent using SVD is the best approach solution.

Solution of large-scale 3D controlled-source electromagnetic modeling problem using efficient iterative solvers

Geophysics ◽  
2021 ◽  
pp. 1-64
Author(s):  
Changkai Qiu ◽  
Changchun Yin ◽  
Yunhe Liu ◽  
Xiuyan Ren ◽  
Hui Chen ◽  
...  
Keyword(s):  
Linear System ◽  
Linear Equation ◽  
Frequency Domain ◽  
Time Domain ◽  
Large Scale ◽  
Equation System ◽  
Iterative Solvers ◽  
Controlled Source ◽  
Linear Equation System ◽  
The Time Domain

With geophysical surveys evolving from traditional 2D to 3D models, the large volume of data adds challenges to inversion, especially when aiming to resolve complex 3D structures. An iterative forward solver for a controlled-source electromagnetic method (CSEM) requires less memory than that for a direct solver; however, it is not easy to iteratively solve an ill-conditioned linear system of equations arising from finite-element discretization of Maxwell’s equations. To solve this problem, we have developed efficient and robust iterative solvers for frequency- and time-domain CSEM modeling problems. For the frequency-domain problem, we first transform the linear system into its equivalent real-number format, and then introduce an optimal block-diagonal preconditioner. Because the condition number of the preconditioned linear equation system has an upper bound of √2, we can achieve fast solution convergence when applying a flexible generalized minimum residual solver. Applying the block preconditioner further results in solving two smaller linear systems with the same coefficient matrix. For the time-domain problem, we first discretize the partial differential equation for the electric field in time using an unconditionally stable backward Euler scheme. We then solve the resulting linear equation system iteratively at each time step. After the spatial discretization in the frequency domain, or space-time discretization in the time domain, we exploit the conjugate-gradient solver with auxiliary-space preconditioners derived from the Hiptmair-Xu decomposition to solve these real linear systems. Finally, we check the efficiency and effectiveness of our iterative methods by simulating complex CSEM models. The most significant advantage of our approach is that the iterative solvers that we adopt have almost the same accuracy and robustness as direct solvers but require much less memory, rendering them more suitable for large-scale 3D CSEM forward modeling and inversion.

scholarly journals Fractional ridge regression: a fast, interpretable reparameterization of ridge regression

GigaScience ◽  
2020 ◽  
Vol 9 (12) ◽  
Author(s):  
Ariel Rokem ◽  
Kendrick Kay
Keyword(s):  
Ridge Regression ◽  
Large Scale ◽  
Imaging Data ◽  
Regularization Technique ◽  
Large Scale Data ◽  
Novel Approach ◽  
Manual Exploration ◽  
L2 Norm ◽  
Software Implementations ◽  
Brain Imaging Data

Abstract Background Ridge regression is a regularization technique that penalizes the L2-norm of the coefficients in linear regression. One of the challenges of using ridge regression is the need to set a hyperparameter (α) that controls the amount of regularization. Cross-validation is typically used to select the best α from a set of candidates. However, efficient and appropriate selection of α can be challenging. This becomes prohibitive when large amounts of data are analyzed. Because the selected α depends on the scale of the data and correlations across predictors, it is also not straightforwardly interpretable. Results The present work addresses these challenges through a novel approach to ridge regression. We propose to reparameterize ridge regression in terms of the ratio γ between the L2-norms of the regularized and unregularized coefficients. We provide an algorithm that efficiently implements this approach, called fractional ridge regression, as well as open-source software implementations in Python and matlab (https://github.com/nrdg/fracridge). We show that the proposed method is fast and scalable for large-scale data problems. In brain imaging data, we demonstrate that this approach delivers results that are straightforward to interpret and compare across models and datasets. Conclusion Fractional ridge regression has several benefits: the solutions obtained for different γ are guaranteed to vary, guarding against wasted calculations; and automatically span the relevant range of regularization, avoiding the need for arduous manual exploration. These properties make fractional ridge regression particularly suitable for analysis of large complex datasets.

scholarly journals A New Hybrid Inversion Method for 2D Nuclear Magnetic Resonance Combining TSVD and Tikhonov Regularization

2021 ◽  
Vol 7 (2) ◽  
pp. 18
Author(s):  
Germana Landi ◽  
Fabiana Zama ◽  
Villiam Bortolotti
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Tikhonov Regularization ◽  
Large Scale ◽  
Regularization Parameter ◽  
High Sensitivity ◽  
Inversion Method ◽  
Nmr Relaxometry ◽  
Value Decomposition ◽  
Nuclear Magnetic

This paper is concerned with the reconstruction of relaxation time distributions in Nuclear Magnetic Resonance (NMR) relaxometry. This is a large-scale and ill-posed inverse problem with many potential applications in biology, medicine, chemistry, and other disciplines. However, the large amount of data and the consequently long inversion times, together with the high sensitivity of the solution to the value of the regularization parameter, still represent a major issue in the applicability of the NMR relaxometry. We present a method for two-dimensional data inversion (2DNMR) which combines Truncated Singular Value Decomposition and Tikhonov regularization in order to accelerate the inversion time and to reduce the sensitivity to the value of the regularization parameter. The Discrete Picard condition is used to jointly select the SVD truncation and Tikhonov regularization parameters. We evaluate the performance of the proposed method on both simulated and real NMR measurements.

PARALLEL COMPUTING OF NUMERICAL SCHEMES AND BIG DATA ANALYTIC FOR SOLVING REAL LIFE APPLICATIONS

2016 ◽  
Vol 78 (8-2) ◽  
Author(s):  
Norma Alias ◽  
Nadia Nofri Yeni Suhari ◽  
Hafizah Farhah Saipan Saipol ◽  
Abdullah Aysh Dahawi ◽  
Masyitah Mohd Saidi ◽  
...  
Keyword(s):  
Big Data ◽  
Parallel Computing ◽  
Parallel Algorithm ◽  
Sparse Matrices ◽  
Real Life ◽  
Poor Performance ◽  
Equation System ◽  
Numerical Schemes ◽  
Linear Equation System ◽  
Data Analytic

This paper proposed the several real life applications for big data analytic using parallel computing software. Some parallel computing software under consideration are Parallel Virtual Machine, MATLAB Distributed Computing Server and Compute Unified Device Architecture to simulate the big data problems. The parallel computing is able to overcome the poor performance at the runtime, speedup and efficiency of programming in sequential computing. The mathematical models for the big data analytic are based on partial differential equations and obtained the large sparse matrices from discretization and development of the linear equation system. Iterative numerical schemes are used to solve the problems. Thus, the process of computational problems are summarized in parallel algorithm. Therefore, the parallel algorithm development is based on domain decomposition of problems and the architecture of difference parallel computing software. The parallel performance evaluations for distributed and shared memory architecture are investigated in terms of speedup, efficiency, effectiveness and temporal performance.

Teaching Materials of Problem-Based Linear Equation System with Two-Variables for Eighth-Grade Students in Junior High School

2021 ◽  
Vol 1 (1) ◽  
pp. 119-123
Author(s):  
Nurhayati Abbas ◽  
Nancy Katili ◽  
Dwi Hardianty Djoyosuroto
Keyword(s):  
High School ◽  
Linear Equation ◽  
Junior High School ◽  
Junior High ◽  
Equation System ◽  
Eighth Grade ◽  
Teaching Material ◽  
Teaching Materials ◽  
Linear Equation System ◽  
Eighth Grade Students

This research is motivated by the lack of mathematics teaching materials that can make students learn on their own. The teaching material can be created by teachers as they are the ones who possess the knowledge about their students’ characteristics. Further, learning materials are a set of materials (information, tools, or texts) that can aid teachers and students to carry out the learning process. The two-variable linear equation system (SPLDV) is one of the mathematics materials taught to eighth-grade students of junior high school; it contains problems related to daily life. However, it is found that this material is still difficult to master by most students. Therefore, it is necessary to develop the SPLDV teaching materials that can help students learn and solve problems as well as be used as examples by teachers in developing other materials. This research aimed to make problem-based SPLDV teaching materials. The research method refers to the Four-D Model by Thiagarajan, Semmel, and Semmel (1974). It consisted of defining, designing, developing, and disseminating. The results showed that problem-based SPLDV teaching materials could be used in learning activities as the students and the teachers had shown their positive responses after going through expert assessments. This study also suggested that the teachers use this teaching material and adopt teaching materials for other similar materials.

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