Laguerre-Gauss Filters in Reverse Time Migration Image Reconstruction

Abstract

ABSTRACT. Reverse time migration (RTM) solves the acoustic or elastic wave equation by means of the extrapolation from source and receiver wavefield in time. A migrated image is obtained by applying a criteria known as imaging condition. The cross-correlation between source and receiver wavefields is the commonly used imaging condition. However, this imaging condition produces spatial low-frequency noise, called artifacts, due to the unwanted correlation of the diving, head and backscattered waves. Several techniques have been proposed to reduce the artifacts occurrence. Derivative operators as Laplacian are the most frequently used. In this work, we propose a technique based on a spiral phase filter ranging from 0 to 2π, and a toroidal amplitude bandpass filter, known as Laguerre-Gauss transform. Through numerical experiments we present the application of this particular filter on three synthetic data sets. In addition, we present a comparative spectral study of images obtained by the zero-lag cross-correlation imaging condition, the Laplacian filtering and the Laguerre-Gauss filtering, showing their frequency features. We also present evidences not only with simulated noisy velocity fields but also by comparison with the model velocity field gradients that this method improves the RTM images by reducing the artifacts and notably enhance the reflective events. Keywords: Laguerre-Gauss transform, zero-lag cross-correlation, seismic migration, imaging condition. RESUMO. A migração reversa no tempo (RTM) resolve a equação de onda acústica ou elástica por meio da extrapolação a partir do campo de onda da fonte e do receptor no tempo. Uma imagem migrada é obtida aplicando um critério conhecido como condição de imagem. A correlação cruzada entre campos de onda de fonte e receptor é a condição de imagem comumente usada. No entanto, esta condição de imagem produz ruído espacial de baixa frequência, chamados artefatos, devido à correlação indesejada das ondas de mergulho, cabeça e retrodifusão. Várias técnicas têm sido propostas para reduzir a ocorrência de artefatos. Operadores derivados como Laplaciano são os mais utilizados. Neste trabalho, propomos uma técnica baseada em um filtro de fase espiral que varia de 0 a 2π, e um filtro passabanda de amplitude toroidal, conhecido como transformada de Laguerre-Gauss. Através de experimentos numéricos, apresentamos a aplicação deste filtro particular em três conjuntos de dados sintéticos. Além disso, apresentamos um estudo comparativo espectral de imagens obtidas pela condição de imagem de correlação cruzada atraso zero, a filtragem de Laplaciano e a filtragem Laguerre-Gauss, mostrando suas características de frequência. Apresentamos evidências não somente com campos simulados de velocidade ruidosa, mas também por comparação com os gradientes de campo de velocidade do modelo que este método melhora as imagens RTM, reduzindo os artefatos e aumentando notavelmente os eventos reflexivos. Palavras-chave: Transformação de Laguerre-Gauss, correlação cruzada atraso zero, migração sísmica, condição de imagem.

Application of the continuous wavelet transform in the extraction of directional data on RTM imaging condition wavefields

“…Next, the method is applied to different synthetic datasets to show results by removing lowfrequency spatial artifacts. Finally, results are post-processed using a method proposed by Paniagua, Sierra-Sosa, & Quintero [22] to improve final migrated images.…”

“…Although the results obtained are promising, we apply the postprocessing technique proposed by Paniagua, Sierra-Sosa, & Quintero [22], Paniagua & Quintero [24] and Paniagua & Sierra-Sosa [25] on seismic migrated models obtained by the proposed method which were shown in Figure 8b and Figure 10b).…”

Laguerre-Gauss Preprocessing: Line Profiles as Image Features for Aerial Images Classification

“…This means that the borders will be intensified (in all directions), thus making them easier to detect. In [3] the authors compare LGSF against other common edge enhancing technique (Laplacian filtering) and found it to be superior given that it acts as a bandpass reducing low and high frequency noise, and that it "distributed homogeneously and smoothly the intensity of the magnitude of the Fourier spectrum due to its isotropic feature". The latter statements are an indication that a line profile, along an axis of an image preprocesed with this filter, will result in a coherent curve.…”