Nonlinear extended images via image-domain interferometry

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. SA105-SA115 ◽  
Author(s):  
Ivan Vasconcelos ◽  
Paul Sava ◽  
Huub Douma
Keyword(s):  
Wave Equation ◽  
Seismic Imaging ◽  
Theory And Practice ◽  
Seismic Interferometry ◽  
Image Domain ◽  
Velocity Inversion ◽  
Nonlinear Imaging ◽  
The One ◽  
Scattered Fields ◽  
And Inversion

Wave-equation, finite-frequency imaging and inversion still face many challenges in addressing the inversion of highly complex velocity models as well as in dealing with nonlinear imaging (e.g., migration of multiples, amplitude-preserving migration). Extended images (EIs) are particularly important for designing image-domain objective functions aimed at addressing standing issues in seismic imaging, such as two-way migration velocity inversion or imaging/inversion using multiples. General one- and two-way representations for scattered wavefields can describe and analyze EIs obtained in wave-equation imaging. We have developed a formulation that explicitly connects the wavefield correlations done in seismic imaging with the theory and practice of seismic interferometry. In light of this connection, we define EIs as locally scattered fields reconstructed by model-dependent, image-domain interferometry. Because they incorporate the same one- and two-way scattering representations usedfor seismic interferometry, the reciprocity-based EIs can in principle account for all possible nonlinear effects in the imaging process, i.e., migration of multiples and amplitude corrections. In this case, the practice of two-way imaging departs considerably from the one-way approach. We have studied the differences between these approaches in the context of nonlinear imaging, analyzing the differences in the wavefield extrapolation steps as well as in imposing the extended imaging conditions. When invoking single-scattering effects and ignoring amplitude effects in generating EIs, the one- and two-way approaches become essentially the same as those used in today’s migration practice, with the straightforward addition of space and time lags in the correlation-based imaging condition. Our formal description of the EIs and the insight that they are scattered fields in the image domain may be useful in further development of imaging and inversion methods in the context of linear, migration-based velocity inversion or in more sophisticated image-domain nonlinear inverse scattering approaches.

A brief comparison of some Kirchhoff integral formulas for migration and inversion

Geophysics ◽  
1991 ◽  
Vol 56 (8) ◽  
pp. 1164-1169 ◽  
Author(s):  
Paul Docherty
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Reflection Coefficients ◽  
Acoustic Wave Equation ◽  
Inversion Formulas ◽  
Kirchhoff Migration ◽  
Integral Formulas ◽  
The One ◽  
And Inversion ◽  
Kirchhoff Integral

Kirchhoff migration has traditionally been viewed as an imaging procedure. Usually, few claims are made regarding the amplitudes in the imaged section. In recent years, a number of inversion formulas, similar in form to those of Kirchhoff migration, have been proposed. A Kirchhoff‐type inversion produces not only an image but also an estimate of velocity variations, or perhaps reflection coefficients. The estimate is obtained from the peak amplitudes in the image. In this paper prestack Kirchhoff migration and inversion formulas for the one‐parameter acoustic wave equation are compared. Following a heuristic approach based on the imaging principle, a migration formula is derived which turns out to be identical to one proposed by Bleistein for inversion. Prestack Kirchhoff migration and inversion are, thus, seen to be the same—both in terms of the image produced and the peak amplitudes of the output.

Wave‐field extrapolation by the linearly transformed wave equation

Geophysics ◽  
1986 ◽  
Vol 51 (8) ◽  
pp. 1538-1551 ◽  
Author(s):  
Zhiming Li
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
High Efficiency ◽  
Seismic Imaging ◽  
Order Approximation ◽  
Finite Difference Methods ◽  
Large Angle ◽  
The One ◽  
First Order Approximation ◽  
Degree Equation

Many approximations to different order of the one‐way scalar wave equation have been suggested in seismic imaging or modeling. Of these approximations, the first‐order approximation, usually called the 15‐degree equation, is most commonly used in industry because of its high efficiency. However, one common constraint of all these approximations is that they cannot handle large‐angle events exactly. Through a linear transformation of the wave equation, the LInearly Transformed Wave EQuation (LITWEQ) is obtainable, without approximation. The LITWEQ has the form of the 15‐degree equation. The solution to the LITWEQ is still a two‐way wave solution. By imposing the boundary condition for upcoming (or downgoing) waves, the LITWEQ can be applied to seismic imaging (or modeling). Implementing the LITWEQ with a finite‐differencing algorithm gives a 180‐degree, or all‐dip, finite‐difference wave‐extrapolation operator, which solves the angle limitation problem of conventional finite‐difference methods.

Heuristic Algorithms for Waste Load Allocation in a River Basin

1989 ◽  
Vol 21 (8-9) ◽  
pp. 1057-1064 ◽  
Author(s):  
Vijay Joshi ◽  
Prasad Modak
Keyword(s):  
Dynamic Programming ◽  
Heuristic Algorithms ◽  
Water Quality Management ◽  
User Preferences ◽  
Theory And Practice ◽  
Waste Load Allocation ◽  
Practical Applications ◽  
Waste Load ◽  
On Line ◽  
The One

Waste load allocation for rivers has been a topic of growing interest. Dynamic programming based algorithms are particularly attractive in this context and are widely reported in the literature. Codes developed for dynamic programming are however complex, require substantial computer resources and importantly do not allow interactions of the user. Further, there is always resistance to utilizing mathematical programming based algorithms for practical applications. There has been therefore always a gap between theory and practice in systems analysis in water quality management. This paper presents various heuristic algorithms to bridge this gap with supporting comparisons with dynamic programming based algorithms. These heuristics make a good use of the insight gained in the system's behaviour through experience, a process akin to the one adopted by field personnel and therefore can readily be understood by a user familiar with the system. Also they allow user preferences in decision making via on-line interaction. Experience has shown that these heuristics are indeed well founded and compare very favourably with the sophisticated dynamic programming algorithms. Two examples have been included which demonstrate such a success of the heuristic algorithms.

scholarly journals On Performance of Sparse Fast Fourier Transform Algorithms Using the Aliasing Filter

Electronics ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 1117
Author(s):  
Bin Li ◽  
Zhikang Jiang ◽  
Jie Chen
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
High Efficiency ◽  
Theory And Practice ◽  
Long Time ◽  
And Performance ◽  
Binary Tree Search ◽  
The One ◽  
Sparse Fast Fourier Transform ◽  
L1 And L2

Computing the sparse fast Fourier transform (sFFT) has emerged as a critical topic for a long time because of its high efficiency and wide practicability. More than twenty different sFFT algorithms compute discrete Fourier transform (DFT) by their unique methods so far. In order to use them properly, the urgent topic of great concern is how to analyze and evaluate the performance of these algorithms in theory and practice. This paper mainly discusses the technology and performance of sFFT algorithms using the aliasing filter. In the first part, the paper introduces the three frameworks: the one-shot framework based on the compressed sensing (CS) solver, the peeling framework based on the bipartite graph and the iterative framework based on the binary tree search. Then, we obtain the conclusion of the performance of six corresponding algorithms: the sFFT-DT1.0, sFFT-DT2.0, sFFT-DT3.0, FFAST, R-FFAST, and DSFFT algorithms in theory. In the second part, we make two categories of experiments for computing the signals of different SNRs, different lengths, and different sparsities by a standard testing platform and record the run time, the percentage of the signal sampled, and the L0, L1, and L2 errors both in the exactly sparse case and the general sparse case. The results of these performance analyses are our guide to optimize these algorithms and use them selectively.

Thermally corrected solutions of the one-dimensional wave equation for the laser-induced ultrasound

2021 ◽  
Vol 130 (2) ◽  
pp. 025104
Author(s):  
Misael Ruiz-Veloz ◽  
Geminiano Martínez-Ponce ◽  
Rafael I. Fernández-Ayala ◽  
Rigoberto Castro-Beltrán ◽  
Luis Polo-Parada ◽  
...  
Keyword(s):  
Wave Equation ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

scholarly journals Practical Quantum Computing

2021 ◽  
Vol 2 (1) ◽  
pp. 1-35
Author(s):  
Adrien Suau ◽  
Gabriel Staffelbach ◽  
Henri Calandra
Keyword(s):  
Wave Equation ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Equation Solving ◽  
Small Quantum ◽  
Quantum Wave ◽  
Variational Algorithms ◽  
The One

In the last few years, several quantum algorithms that try to address the problem of partial differential equation solving have been devised: on the one hand, “direct” quantum algorithms that aim at encoding the solution of the PDE by executing one large quantum circuit; on the other hand, variational algorithms that approximate the solution of the PDE by executing several small quantum circuits and making profit of classical optimisers. In this work, we propose an experimental study of the costs (in terms of gate number and execution time on a idealised hardware created from realistic gate data) associated with one of the “direct” quantum algorithm: the wave equation solver devised in [32]. We show that our implementation of the quantum wave equation solver agrees with the theoretical big-O complexity of the algorithm. We also explain in great detail the implementation steps and discuss some possibilities of improvements. Finally, our implementation proves experimentally that some PDE can be solved on a quantum computer, even if the direct quantum algorithm chosen will require error-corrected quantum chips, which are not believed to be available in the short-term.

A multi-level parallel algorithm for seismic imaging based on one-way wave equation migration

2021 ◽  
Vol 97 ◽  
pp. 344-354
Author(s):  
Alexander Pleshkevich ◽  
Vadim Lisitsa ◽  
Dmitry Vishnevsky ◽  
Vadim Levchenko
Keyword(s):  
Wave Equation ◽  
Parallel Algorithm ◽  
Seismic Imaging ◽  
Multi Level

Notes on Competition and Justum Pretium Theory and Practice in Medieval Italy

2018 ◽  
Vol 63 (3) ◽  
pp. 330-349 ◽  
Author(s):  
Marco Claudio Corradi
Keyword(s):  
European Union ◽  
Cognitive Biases ◽  
Theory And Practice ◽  
Market Mechanisms ◽  
Medieval Italy ◽  
Goods And Services ◽  
Pricing Theory ◽  
Market Variables ◽  
The One ◽  
Capitalist Spirit

Medieval Italian Comuni are often considered as one of the cradles of the modern capitalist spirit. Comuni introduced economic legislation in an attempt to counteract restrictions to competition on the one hand and to control the price of certain goods and services on the other. Price control of basic commodities was often motivated by reasons of public order – such as preventing commoners’ riots. Despite some loose analogies with the modern European Union competition law approach to pricing – namely in the area of excessive pricing – the Italian medieval Comuni pricing theory and practice substantially differed from the modern European Union one. Medieval theory struggled in reconciling market mechanisms with costs analysis and missed the distinction between efficiency and distribution. Moreover, medieval Comuni market variables were substantially divergent from the modern European ones. Despite Comuni being the wealthiest areas in Europe in those days, their consumers had significantly lower buying power, they were affected by different cognitive biases than modern consumers and they were highly segmented from a gender perspective. Medieval producers, that is artisans, did not enjoy the degree of market power that characterizes modern oligopolists. Artisans produced goods for merchants who were the main promoters of trade and economic development. Merchants often succeeded in squeezing artisans’ profits, granting consumers lower prices for manufactured goods, at times also thanks to free trade policies pursued by Comuni administrations.

scholarly journals Horizontal contraction in image domain for velocity inversion

Geophysics ◽  
2015 ◽  
Vol 80 (3) ◽  
pp. R95-R110 ◽  
Author(s):  
Peng Shen ◽  
William W. Symes
Keyword(s):  
Image Domain ◽  
Velocity Inversion

COMMUNICATING EMPIRE: THE HABSBURGS AND THEIR CRITICS, 1700–1919

2009 ◽  
Vol 19 ◽  
pp. 117-138 ◽  
Author(s):  
R. J. W. Evans
Keyword(s):  
Eighteenth Century ◽  
Roman Empire ◽  
Theory And Practice ◽  
Holy Roman Empire ◽  
The Other ◽  
Current Debate ◽  
Free Standing ◽  
Power Base ◽  
The One ◽  
At Home

ABSTRACTIn the vibrant current debate about European empires and their ideologies, one basic dichotomy still tends to be overlooked: that between, on the one hand, the plurality of modern empires of colonisation, commerce and settlement; and, on the other, the traditional claim to single and undividedimperiumso long embodied in the Roman Empire and its successor, the Holy Roman Empire, or (First) Reich. This paper examines the tensions between the two, as manifested in the theory and practice of Habsburg imperial rule. The Habsburgs, emperors of the Reich almost continuously through its last centuries, sought to build their own power-base within and beyond it. The first half of the paper examines how by the eighteenth century their ‘Monarchy’, subsisting alongside the Reich, dealt with the associated legacy of empire. After the dissolution of the Holy Roman Empire in 1806 the Habsburgs could pursue a free-standing Austrian ‘imperialism’, but it rested on an uneasy combination of old and new elements and was correspondingly vulnerable to challenge from abroad and censure at home. The second half of the article charts this aspect of Habsburg government through an age of international imperialism and its contribution to the collapse of the Dual Monarchy in 1918.

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