Seismic trace interpolation using half‐step prediction filters

Geophysics ◽  
1999 ◽  
Vol 64 (5) ◽  
pp. 1461-1467 ◽  
Author(s):  
Milton J. Porsani
Keyword(s):  
Input Data ◽  
Interpolation Method ◽  
Linear Equations ◽  
Seismic Section ◽  
Linear System Of Equations ◽  
Unit Step ◽  
Systems Of Linear Equations ◽  
Complex Linear ◽  
Marine Seismic ◽  
Prediction Filter

A method to perform seismic trace interpolation known as the Spitz method handles spatially aliased events. The Spitz method uses the unit‐step prediction filter to estimate data spaced at Δx/2. The missing data are obtained by solving a complex linear system of equations whose unknowns are the coefficients at the interpolated location. We attack this problem by introducing a half‐step prediction filter that makes trace interpolation significantly more efficient and easier for implementation. A complex half‐step prediction filter at frequency f/2 is computed in the least‐squares sense to predict odd data components from even ones. At the frequency f, the prediction operator is shrunk and convolved with the input data spaced at Δx to predict data at Δx/2 directly. Instead of solving two systems of linear equations, as proposed by Spitz, only a system for the half‐step prediction filter has to be solved. Numerical examples using a marine seismic common‐midpoint (CMP) gather and a poststack seismic section were used to illustrate the new interpolation method.

A Nonlinear Least-Squares Graphical Tool (‘Gaussfit’) for Educational Purposes

2010 ◽  
Vol 47 (1) ◽  
pp. 11-22 ◽  
Author(s):  
Krešimir Malarić ◽  
Roman Malarić ◽  
Hrvoje Hegeduš
Keyword(s):  
Least Squares ◽  
Input Data ◽  
Least Squares Method ◽  
Linear Equations ◽  
Computer Calculation ◽  
Nonlinear Least Squares ◽  
Undergraduate Level ◽  
Graphical Tool ◽  
Systems Of Linear Equations ◽  
Graphical Presentation

This paper describes a computer program that finds a function which closely approximates experimental data using the least-squares method. The program finds parameters of the function as well as their corresponding uncertainties. It also has a subroutine for graphical presentation of the input data and the function. The program is used for educational purposes at undergraduate level for students who are learning least-squares fitting, how to solve systems of linear equations and about computer calculation errors.

FUZZY CENTRE BASED SOLUTION OF FUZZY COMPLEX LINEAR SYSTEM OF EQUATIONS

2013 ◽  
Vol 21 (04) ◽  
pp. 629-642 ◽  
Author(s):  
DIPTIRANJAN BEHERA ◽  
S. CHAKRAVERTY
Keyword(s):  
Linear Time ◽  
Linear Equations ◽  
Electric Circuit ◽  
System Of Linear Equations ◽  
New Approach ◽  
Linear System Of Equations ◽  
Linear Time Invariant ◽  
Complex Linear ◽  
Time Invariant ◽  
Good Agreement

A new approach to solve Fuzzy Complex System of Linear Equations (FCSLE) based on fuzzy complex centre procedure is presented here. Few theorems related to the investigation are stated and proved. Finally the presented procedure is used to analyze an example problem of linear time invariant electric circuit with complex crisp coefficient and fuzzy complex sources. The results obtained are also compared with the known solutions and are found to be in good agreement.

scholarly journals Software for Solving Fully Fuzzy Linear Systems with Rectangular Matrix

2020 ◽  
Vol 10 (1) ◽  
pp. 129-139
Author(s):  
A.V. Panteleev ◽  
V.S. Saveleva
Keyword(s):  
Linear Systems ◽  
Linear Equations ◽  
Linear System Of Equations ◽  
Software Application ◽  
Rectangular Matrix ◽  
Fuzzy Linear System ◽  
Triangular Numbers ◽  
Systems Of Linear Equations ◽  
The Mean ◽  
Fuzzy Linear Systems

The article discusses the problem of solving a fully fuzzy linear system of equations with a fuzzy rectangular matrix and a fuzzy right-hand side described by fuzzy triangular numbers in a form of deviations from the mean. A solution algorithm based on finding pseudo-solutions of systems of linear equations and corresponding software is formed. Various examples of created software application for arbitrary fuzzy linear systems are given.

Seismic trace interpolation in the F-X domain

Geophysics ◽  
1991 ◽  
Vol 56 (6) ◽  
pp. 785-794 ◽  
Author(s):  
S. Spitz
Keyword(s):  
Interpolation Method ◽  
Random Noise ◽  
A Priori ◽  
Effective Means ◽  
Linear Equations ◽  
Real Data ◽  
Spatial Prediction ◽  
Data Set ◽  
Spatial Interval ◽  
Prediction Filter

Interpolation of seismic traces is an effective means of improving migration when the data set exhibits spatial aliasing. A major difficulty of standard interpolation methods is that they depend on the degree of reliability with which the various geological events can be separated. In this respect, a multichannel interpolation method is described which requires neither a priori knowledge of the directions of lateral coherence of the events, nor estimation of these directions. The method is based on the fact that linear events present in a section made of equally spaced traces may be interpolated exactly, regardless of the original spatial interval, without any attempt to determine their true dips. The predictability of linear events in the f-x domain allows the missing traces to be expressed as the output of a linear system, the input of which consists of the recorded traces. The interpolation operator is obtained by solving a set of linear equations whose coefficients depend only on the spectrum of the spatial prediction filter defined by the recorded traces. Synthetic examples show that this method is insensitive to random noise and that it correctly handles curvatures and lateral amplitude variations. Assessment of the method with a real data set shows that the interpolation yields an improved migrated section.

On Some Properties of Semi-rings

2018 ◽  
pp. 35-50
Author(s):  
A. I. Belousov
Keyword(s):  
Linear Equations ◽  
Oriented Graph ◽  
Theoretical Computer Science ◽  
Alternative Methods ◽  
Main Role ◽  
Cost Matrix ◽  
Sequential Elimination ◽  
The Matrix ◽  
Systems Of Linear Equations ◽  
The Cost

The main objective of this paper is to prove a theorem according to which a method of successive elimination of unknowns in the solution of systems of linear equations in the semi-rings with iteration gives the really smallest solution of the system. The proof is based on the graph interpretation of the system and establishes a relationship between the method of sequential elimination of unknowns and the method for calculating a cost matrix of a labeled oriented graph using the method of sequential calculation of cost matrices following the paths of increasing ranks. Along with that, and in terms of preparing for the proof of the main theorem, we consider the following important properties of the closed semi-rings and semi-rings with iteration.We prove the properties of an infinite sum (a supremum of the sequence in natural ordering of an idempotent semi-ring). In particular, the proof of the continuity of the addition operation is much simpler than in the known issues, which is the basis for the well-known algorithm for solving a linear equation in a semi-ring with iteration.Next, we prove a theorem on the closeness of semi-rings with iteration with respect to solutions of the systems of linear equations. We also give a detailed proof of the theorem of the cost matrix of an oriented graph labeled above a semi-ring as an iteration of the matrix of arc labels.The concept of an automaton over a semi-ring is introduced, which, unlike the usual labeled oriented graph, has a distinguished "final" vertex with a zero out-degree.All of the foregoing provides a basis for the proof of the main theorem, in which the concept of an automaton over a semi-ring plays the main role.The article's results are scientifically and methodologically valuable. The proposed proof of the main theorem allows us to relate two alternative methods for calculating the cost matrix of a labeled oriented graph, and the proposed proofs of already known statements can be useful in presenting the elements of the theory of semi-rings that plays an important role in mathematical studies of students majoring in software technologies and theoretical computer science.

scholarly journals A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhijun Luo ◽  
Lirong Wang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Descent Direction ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Globally Convergent ◽  
Variable Distribution ◽  
Systems Of Linear Equations

A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved.

Mutual Embeddings

2015 ◽  
Vol 15 (01n02) ◽  
pp. 1550001
Author(s):  
ILKER NADI BOZKURT ◽  
HAI HUANG ◽  
BRUCE MAGGS ◽  
ANDRÉA RICHA ◽  
MAVERICK WOO
Keyword(s):  
Iterative Methods ◽  
Lower Bounds ◽  
Linear Equations ◽  
Graph Embedding ◽  
Open Problems ◽  
Linear Arrays ◽  
Systems Of Linear Equations

This paper introduces a type of graph embedding called a mutual embedding. A mutual embedding between two n-node graphs [Formula: see text] and [Formula: see text] is an identification of the vertices of V1 and V2, i.e., a bijection [Formula: see text], together with an embedding of G1 into G2 and an embedding of G2 into G1 where in the embedding of G1 into G2, each node u of G1 is mapped to π(u) in G2 and in the embedding of G2 into G1 each node v of G2 is mapped to [Formula: see text] in G1. The identification of vertices in G1 and G2 constrains the two embeddings so that it is not always possible for both to exhibit small congestion and dilation, even if there are traditional one-way embeddings in both directions with small congestion and dilation. Mutual embeddings arise in the context of finding preconditioners for accelerating the convergence of iterative methods for solving systems of linear equations. We present mutual embeddings between several types of graphs such as linear arrays, cycles, trees, and meshes, prove lower bounds on mutual embeddings between several classes of graphs, and present some open problems related to optimal mutual embeddings.

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