A computationally efficient tool for assessing the depth resolution in large-scale potential-field inversion

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. A33-A38 ◽  
Author(s):  
Valeria Paoletti ◽  
Per Christian Hansen ◽  
Mads Friis Hansen ◽  
Maurizio Fedi
Keyword(s):  
Potential Field ◽  
Large Scale ◽  
Computing Time ◽  
Depth Resolution ◽  
Source Distribution ◽  
Volcanic Area ◽  
Computationally Efficient ◽  
Large Scale Problems ◽  
Value Decomposition ◽  
Field Inversion

In potential-field inversion, careful management of singular value decomposition components is crucial for obtaining information about the source distribution with respect to depth. In principle, the depth-resolution plot provides a convenient visual tool for this analysis, but its computational complexity has hitherto prevented application to large-scale problems. To analyze depth resolution in such problems, we developed a variant ApproxDRP, which is based on an iterative algorithm and therefore suited for large-scale problems because we avoid matrix factorizations and the associated demands on memory and computing time. We used the ApproxDRP to study retrievable depth resolution in inversion of the gravity field of the Neapolitan Volcanic Area. Our main contribution is the combined use of the Lanczos bidiagonalization algorithm, established in the scientific computing community, and the depth-resolution plot defined in the geoscience community.

Analysis of depth resolution in potential-field inversion

Geophysics ◽  
2005 ◽  
Vol 70 (6) ◽  
pp. A1-A11 ◽  
Author(s):  
Maurizio Fedi ◽  
Per Christian Hansen ◽  
Valeria Paoletti
Keyword(s):  
Potential Field ◽  
Real Data ◽  
Depth Resolution ◽  
Careful Study ◽  
Piecewise Constant ◽  
Data Errors ◽  
Damped Least Squares ◽  
Value Decomposition ◽  
The Given ◽  
Field Inversion

We study the inversion of potential fields and evaluate the degree of depth resolution achievable for a given problem. To this end, we introduce a powerful new tool: the depth-resolution plot (DRP). The DRP allows a theoretical study of how much the depth resolution in a potential-field inversion is influenced by the way the problem is discretized and regularized. The DRP also allows a careful study of the influence of various kinds of ambiguities, such as those from data errors or of a purely algebraic nature. The achievable depth resolution is related to the given discretization, regularization, and data noise level. We compute DRP by means of singular-value decomposition (SVD) or its generalization (GSVD), depending on the particular regularization method chosen. To illustrate the use of the DRP, we assume a source volume of specified depth and horizontal extent in which the solution is piecewise constant within a 3D grid of blocks. We consider various linear regularization terms in a Tikhonov (damped least-squares) formulation, some based on using higher-order derivatives in the objective function. DRPs are illustrated for both synthetic and real data. Our analysis shows that if the algebraic ambiguity is not too large and a suitable smoothing norm is used, some depth resolution can be obtained without resorting to any subjective choice of depth weighting.

Large-Scale Analog Circuit Evolutionary Design Using a Real-Coded Scheme

2012 ◽  
Vol 220-223 ◽  
pp. 2036-2039
Author(s):  
Su Min Jiao ◽  
Cai Hong Wang ◽  
Xue Mei Wang
Keyword(s):  
Analog Circuits ◽  
Large Scale ◽  
Analog Circuit ◽  
Computing Time ◽  
Electronic System ◽  
Small Scale ◽  
Evolutionary Design ◽  
Continuous Space ◽  
Large Scale Problems ◽  
Circuit Representation

Analog circuits are of great importance in electronic system design. Recent evolutionary design results are usually small-scale analog circuits. This paper proposes a real-coded mechanism and uses it in the large-scale analog circuit evolutionary design. The proposed scheme evolves the circuit topology and size to a uniformed continuous space, in which the circuit representation is closed and of causality. Experimental results show that the proposed scheme can work successfully on many analog circuits with different kinds of characteristics. Comparing with other evolutionary methods before, the proposed scheme performs better on large-scale problems of circuit synthesis with higher search efficiency, lower computational complexity, and less computing time.

A Block Matrix Based Precise Integration Algorithm for Solving Non-Homogeneous Dynamic Response

2021 ◽  
Author(s):  
Chao Zhang ◽  
Mingxiang Ling ◽  
Meng Tao
Keyword(s):  
Dynamic Response ◽  
Large Scale ◽  
Computing Time ◽  
Block Matrix ◽  
Computationally Efficient ◽  
Time Step ◽  
Integration Algorithm ◽  
Precise Integration ◽  
High Prediction ◽  
Cycle Oscillation

Abstract This paper puts forward a computationally-efficient parallel precise integration algorithm for solving vibration response subjected to time-variable excitation and nonlinearity, especially for non-homogenous dynamic response solution with large-scale degree of freedom. In detail, both of the nonlinear parts and time-varying inputs of the dynamic system are separated from the original dynamic equations and then simulated by employing a piecewise interpolation function within a computing time-step. A novel closed-form iteration formula is presented in conjunction with the block matrix strategy and modified increment-dimensional precise integration technique. Interestingly, the presented approach is essentially a high-accuracy and parallel algorithm, which exhibits a high prediction accuracy without the limitation of matrix inversion, higher-order derivative, periodicity requirement nor cycle oscillation and instability of high-order interpolation. At last, the feasibility and advantage of the proposed method is verified with two numerical examples.

scholarly journals Golub–Kahan vs. Monte Carlo: a comparison of bidiagonlization and a randomized SVD method for the solution of linear discrete ill-posed problems

2021 ◽  
Author(s):  
Xianglan Bai ◽  
Alessandro Buccini ◽  
Lothar Reichel
Keyword(s):  
Large Scale ◽  
Krylov Subspace ◽  
Computing Time ◽  
Low Rank ◽  
Large Matrix ◽  
Ill Posed ◽  
Randomized Methods ◽  
Value Decomposition ◽  
Svd Method ◽  
Randomized Method

AbstractRandomized methods can be competitive for the solution of problems with a large matrix of low rank. They also have been applied successfully to the solution of large-scale linear discrete ill-posed problems by Tikhonov regularization (Xiang and Zou in Inverse Probl 29:085008, 2013). This entails the computation of an approximation of a partial singular value decomposition of a large matrix A that is of numerical low rank. The present paper compares a randomized method to a Krylov subspace method based on Golub–Kahan bidiagonalization with respect to accuracy and computing time and discusses characteristics of linear discrete ill-posed problems that make them well suited for solution by a randomized method.

A New Numerical Model for Electron-Probe Analysis at High Depth Resolution

1996 ◽  
Vol 54 ◽  
pp. 490-491
Author(s):  
P.-F. Staub ◽  
C. Bonnelle ◽  
F. Vergand ◽  
P. Jonnard
Keyword(s):  
Electron Probe ◽  
Surface Segregation ◽  
Depth Distribution ◽  
Computing Time ◽  
Depth Resolution ◽  
Physical Parameters ◽  
Electron Probe Analysis ◽  
Interface Phases ◽  
Excitation Conditions ◽  
High Depth

Characterizing dimensionally and chemically nanometric structures such as surface segregation or interface phases can be performed efficiently using electron probe (EP) techniques at very low excitation conditions, i.e. using small incident energies (0.5<E0<5 keV) and low incident overvoltages (1<U0<1.7). In such extreme conditions, classical analytical EP models are generally pushed to their validity limits in terms of accuracy and physical consistency, and Monte-Carlo simulations are not convenient solutions as routine tools, because of their cost in computing time. In this context, we have developed an intermediate procedure, called IntriX, in which the ionization depth distributions Φ(ρz) are numerically reconstructed by integration of basic macroscopic physical parameters describing the electron beam/matter interaction, all of them being available under pre-established analytical forms. IntriX’s procedure consists in dividing the ionization depth distribution into three separate contributions:

Cloud-Based Multimedia Content Protection System

2020 ◽  
pp. 164-169
Author(s):  
B. Aparna ◽  
S. Madhavi ◽  
G. Mounika ◽  
P. Avinash ◽  
S. Chakravarthi
Keyword(s):  
Large Scale ◽  
Protection System ◽  
Multimedia Content ◽  
Computationally Efficient ◽  
Content Protection ◽  
Protection Systems ◽  
Multimedia Content Protection ◽  
High Scalability ◽  
Cloud Infrastructures ◽  
Rapid Deployment

We propose a new design for large-scale multimedia content protection systems. Our design leverages cloud infrastructures to provide cost efficiency, rapid deployment, scalability, and elasticity to accommodate varying workloads. The proposed system can be used to protect different multimedia content types, including videos, images, audio clips, songs, and music clips. The system can be deployed on private and/or public clouds. Our system has two novel components: (i) method to create signatures of videos, and (ii) distributed matching engine for multimedia objects. The signature method creates robust and representative signatures of videos that capture the depth signals in these videos and it is computationally efficient to compute and compare as well as it requires small storage. The distributed matching engine achieves high scalability and it is designed to support different multimedia objects. We implemented the proposed system and deployed it on two clouds: Amazon cloud and our private cloud. Our experiments with more than 11,000 videos and 1 million images show the high accuracy and scalability of the proposed system. In addition, we compared our system to the protection system used by YouTube and our results show that the YouTube protection system fails to detect most copies of videos, while our system detects more than 98% of them.

Sign in / Sign up

Export Citation Format

Share Document