Examinando por Materia "Reverse time migrations"

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    Analysis of the stability and dispersion for a Riemannian acoustic wave equation
    (ELSEVIER SCIENCE INC, 2019-01-15) Quiceno, H. R.; Arias, C.; Quiceno, H. R.; Arias, C.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
    The construction of images of the Earth's interior using methods as reverse time migration (RTM) or full wave inversion (FWI) strongly depends on the numerical solution of the wave equation. A mathematical expression of the numerical stability and dispersion for a particular wave equation used must be known in order to avoid unbounded numbers of amplitudes. In case of the acoustic wave equation, the Courant–Friedrich–Lewy (CFL) condition is a necessary but is not a sufficient condition for convergence. Thus, we need to search other types of expression for stability condition. In seismic wave problems, the generalized Riemannian wave equation is used to model their propagation in domains with curved meshes which is suitable for zones with rugged topography. However, only a heuristic version of stability condition was reported in the literature for this equation. We derived an expression for stability condition and numerical dispersion analysis for the Riemannian acoustic wave equation in a two-dimensional medium and analyzed its implications in terms of computational cost. © 2018 Elsevier Inc.
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    Application of the continuous wavelet transform in the extraction of directional data on RTM imaging condition wavefields
    (Ecopetrol, 2018-01-01) Paniagua-Castrillón J.-G.; Quintero-Montoya O.-L.; Universidad EAFIT. Escuela de Ciencias; Modelado Matemático
    Low-frequency artifacts in reverse time migration result from unwanted cross-correlation of the source and receiver wavefields at nonreflecting points along ray-paths. These artifacts can hide important details in migrated models and increase poor interpretation risk. Some methods have been proposed to avoid or reduce the number of these artifacts, preserving reflections, and improving model quality, implementing other strategies such as modification of the wave equation, proposing other imaging conditions, and using image filtering techniques. One of these methods uses wavefield decomposition, correlating components of the wavefields that propagate in opposite directions. We propose a method for extracting directional information from the RTM imaging condition wavefields to obtain characteristics allowing for better, more refined imaging. The method works by separating directional information about the wavefields based on the continuous wavelet transform (CWT), and the analysis of the main changes on the frequency content revealed within the scalogram obtained by a Gaussian wavelet family. Through numerical applications, we demonstrate that this method can effectively remove undesired artifacts in migrated images. In addition, we use the Laguerre-Gauss filtering to improve the results obtained with the proposed method. © 2018 Ecopetrol S.A. All Rights Reserved.