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1
Content available remote A 3D Fast Radon transform algorithm based on deflecting ellipse model and its application on multiple attenuation
Ma Jitao
Acta Geophysica
|
2024
|
Vol. 72, no. 1
177--193
EN
Three-dimensional seismic exploration has been widely used to produce subsurface images for oil and gas. As one of the most commonly used multiple attenuation methods, 2D Radon transform cannot describe the three-dimensional wave-fields in realistic subsurface conditions. Conventional 3D Radon transform assumes that the properties of the medium are the same, or approximately the same, in all directions. The time slice of seismic data will be a standard ellipse, and its focal points are located at survey lines. However, In the case of complex geology, the medium may have different property in different directions. And the time slice of acquired 3D seismic data becomes a deflected ellipse, and its focal points are no longer located on the survey lines. Conventional 3D Radon transform based on standard ellipse can no longer describe seismic data accurately. A rotating ellipse model parameter is introduced to 3D Radon transform to describe seismic data in complex areas. The three-parameter 3D Radon transform based on rotating ellipse model is derived in detail. However, the operator matrix in the new formula is huge due to the introduced variable, and it cannot be decomposed into small matrices, leading the computation cost to be considerably high. The frequency and curvature are merged into one new parameter to deal with the low computational efficiency problem. The corresponding fast algorithm is also derived. The application of synthetic and real data examples shows that the proposed method can describe complex seismic data more accurately, and the method can attenuate multiples in complex cases much better.
2
Content available remote Thin interbed AVA inversion based on a fast algorithm for refectivity
Yang Zhen, Lu Jun
Acta Geophysica
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2020
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Vol. 68, no. 4
1007--1020
EN
Zoeppritz equations form the theoretical basis of most existing amplitude variation with incident angle (AVA) inversion methods. Assuming that only primary refections exist, that is, the multiples are fully suppressed and the transmission loss and geometric spreading are completely compensated for, Zoeppritz equations can be used to solve for the elastic parameters of strata efectively. However, for thin interbeds, conventional seismic data processing technologies cannot suppress the internal multiples efectively, nor can they compensate for the transmission loss accurately. Therefore, AVA inversion methods based on Zoeppritz equations or their approximations are not applicable to thin interbeds. In this study, we propose a prestack AVA inversion method based on a fast algorithm for refectivity. The fast refectivity method can compute the full-wave responses, including the refection, transmission, mode conversion, and internal multiples, which is benefcial to the seismic inversion of thin interbeds. A further advantage of the fast refectivity method is that the partial derivatives of the refection coefcient with respect to the elastic parameters can be expressed as analytical solutions. Based on the Gauss– Newton method, we construct the objective function and model-updating formula considering sparse constraint, where the Jacobian matrix takes the form of an analytical solution, which can signifcantly accelerate the inversion convergence. We validate our inversion method using numerical examples and feld seismic data. The inversion results demonstrate that the fast refectivity-based inversion method is more efective for thin interbed models in which the wave-propagation efects, such as interval multiples, are difcult to eliminate.
3
Content available remote Fast computation of the SLTF transform
Końca R
Przegląd Elektrotechniczny
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2015
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R. 91, nr 2
40-43
EN
The paper presents computation process of the fast SLTF transform that use matrix-vector algebra. Examples explaining the course of the calculations both analysis and synthesis transform, are also illustrated by the graph-structural models that helps to understand the algorithm principle. Additionally, an improved calculation procedure reducing redundant data redirection was proposed.
PL
W pracy przedstawiono proces obliczania szybkiej transformaty SLTF z wykorzystaniem operacji wektorowo-macierzowych. Przykłady objaśniające przebieg obliczeń zarówno transformaty prostej jak i odwrotnej zilustrowano grafami ułatwiającymi zrozumienie zasady działania algorytmu. Dodatkowo zaproponowano ulepszoną procedurę obliczeniową redukującą nadmiarowe przeadresowania danych.
4
Content available remote An unified approach for developing rationalized algorithms for hypercomplex number multiplication
Cariow A., Cariowa G.
Przegląd Elektrotechniczny
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2015
|
R. 91, nr 2
36-39
EN
In this article we present a common approach for the development of algorithms for calculating products of hypercomplex numbers. The main idea of the proposed approach is based on the representation of hypernumbers multiplying via the matrix-vector products and further creative decomposition of the matrix, leading to the reduction of arithmetical complexity of calculations. The proposed approach allows the construction of sufficiently well algorithms for hypernumbers multiplication with reduced computational complexity. If the schoolbook method requires N2 real multiplications and N(N-1) real additions, the proposed approach allows to develop algorithms, which take only [N(N-1)/2]+2 real multiplications and 3Nlog2N+[N(N-3)+4]/2 real additions.
PL
W artykule zostało przedstawione uogólnione podejście do syntezy algorytmów wyznaczania iloczynów liczb hiperzespolonych. Główna idea proponowanego podejścia polega na reprezentacji operacji mnożenia liczb hiperzespolonych w formie iloczynu wektorowomacierzowego i dalszej możliwości kreatywnej dekompozycji czynnika macierzowego prowadzącej do redukcji złożoności obliczeniowej. Proponowane podejście pozwala zbudować algorytmy wyróżniające się w porównaniu do metody naiwnej zredukowaną złożonością obliczeniową. Jeśli metoda naiwna wymaga wykonania N2 mnożeń oraz N(N-1) dodawań liczb rzeczywistych to proponowane podejście pozwala syntetyzować algorytmy wymagające tylko [N(N-1)/2]+2 mnożeń oraz 3Nlog2N+[N(N-3)+4]/2 dodawań.
5
Content available remote Low complexity algorithm for multiplying octonions
Cariow A., Cariowa G.
Przegląd Elektrotechniczny
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2014
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R. 90, nr 2
109--112
EN
We propose an original algorithmic solution for multiplication of octonions. In previously published algorithms for computing the product of octonions the number of multiplications has been reduced by significantly increasing number of additions and shifts. A dignity of the proposed solutions is to reduce by 25% the number of multiplications needed to calculate the product of octonions compared with naive method. At the same time the number of additions is the same as in the naive way of calculations. During synthesis of the discussed algorithm we use a fact that octonion product may be represented as a matrix-vector product. Such representation provides a possibility to discover repeating elements in the matrix structure and to use specific properties of their mutual placement for reducing the number of real multiplications needed to calculate the octonion product.
PL
W artykule przedstawiono szybki algorytm wyznaczania iloczynu oktonionów. Algorytm ten cechuje się zredukowaną o 25% liczbą operacji mnożenia w porównaniu do algorytmu naiwnego przy zachowaniu takiej samej liczby dodawań liczb rzeczywistych.
6
An algorithm for multiplication of trigintaduonions
Cariow A., Cariowa G.
Journal of Theoretical and Applied Computer Science
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2014
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Vol. 8, nr 1
50--75
EN
In this paper we introduce efficient algorithm for the multiplication of trigintaduonions. The direct multiplication of two trigintaduonions requires 1024 real multiplications and 992 real additions. We show how to compute a trigintaduonion product with 498 real multiplications and 943 real additions. During synthesis of the discussed algorithm we use a fact that trigintaduonion multiplication may be represented by a vector-matrix product. Such representation provides a possibility to discover repeating elements in the matrix structure and to use specific properties of their mutual placement to decrease the number of real multiplications needed to compute the product of two trigintaduonions.
7
Content available remote Bazujący na sygnale wideo algorytm o niskim obliczeniowo koszcie do kontroli bezpieczeństwa osobistego w strefie przemysłowej
Lech P.
Przegląd Elektrotechniczny
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2013
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R. 89, nr 4
335-337
PL
Zapewnienie bezpieczeństwa w strefach przemysłowych jest realizowane w oparciu specjalistyczne systemy eksperckie dedykowane dla konkretnej branży, część z nich działa w oparciu o detekcję zmian w obrazach sekwencji wideo. Prezentowany w pracy szybki algorytm do wykrywania zmian w obrazach, działa w oparciu o metodę Monte Carlo. Badania wykazały dużą szybkość obliczeń wynikającą z redukcji ilości analizowanych danych, odporność na niski poziom zakłóceń oraz wysoką skuteczność wykrywania zmian.
EN
Ensuring safety in the industrial zones is realised on the basis of specialised expert systems, some of them operate on the detection of changes in the image from video sequence. In this paper is presented fast algorithm based on the Monte Carlo method for detecting changes in images. The studies have shown: high-speed calculations resulting from the reduction of the analysed data, resistance to low noise and high efficiency of detection of changes.
8
Content available remote An algorithm for complex-valued vector-matrix multiplication
Cariow A., Cariowa G.
Przegląd Elektrotechniczny
|
2012
|
R. 88, nr 10b
213-216
EN
In this note we present the algorithm for vector-matrix product calculating for vectors and matrices whose elements are complex numbers.
PL
W artykule został przedstawiony zracjonalizowany algorytm wyznaczania iloczynu wektorowo-macierzowego, dla danych będących liczbami zespolonymi. Proponowany algorytm wyróżnia się w stosunku do metody naiwnej zredukowaną złożonością multiplikatywną. Jeśli metoda naiwna wymaga wykonania 4MN mnożeń oraz 2M(2N-1) dodawań liczb rzeczywistych to proponowany algorytm wymaga tylko 3MN mnożeń oraz N+M(5N-1) dodawań.
9
Content available remote A fast algorithm for multiresolution discrete Fourier transform
Andreatto B., Cariow A.
Przegląd Elektrotechniczny
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2012
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R. 88, nr 11a
66-69
EN
The paper presents a fast algorithm for the calculation of a multiresolution discrete Fourier transform. The presented approach is based on the realization of the Fast Fourier Transform for each frequency resolution level. This algorithm allows reducing the number of complex multiplications and additions compared to the method consisting in the multiplication between the input signal expressed as a column vector and the matrix of discrete exponential functions.
PL
W artykule przedstawiono szybki algorytm wyznaczania wielorozdzielczej dyskretnej transformaty Fouriera. Zaprezentowane podejście opiera się na realizacji algorytmu szybkiej transformacji Fouriera na każdym z analizowanych poziomów rozdzielczości częstotliwościowej.
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