Laguerre Gaussian filters in Reverse Time Migration image reconstruction


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 some criteria known as imaging condition. The zero lag cross-correlation between source and receiver wavefields is the commonly used imaging condition. However, this imaging condition produces lowspatial-frequency noise or artifacts, due to the strong contrasts in velocity field (Pestana et al., 2014). Several imaging techniques have been proposed to reduce the artifacts occurrence. Derivative operators as Laplacian are the most frequently used. In this work, we propose the usage of a technique based on a spiral phase filter ranging from 0 to 2, and a toroidal amplitude bandpass filter, known as Laguerre-Gauss transform. Through numerical experiments we present the application of this particular filter on SEG EAGE salt model and Sigsbee 2A model. We also present evidences that this method improves RTM images by reducing the artifacts and notably enhance the reflective events. Introduction Reverse time migration solves the two-way acoustic or elastic wave equation, by the propagation in time domain of the source wavefield in forward direction, and of the receiver wavefield in backward direction. The migrated image is obtained by the cross-correlation between source and receiver wavefields summed over the sources (Claerbout, 1985). The cross-correlation imaging condition produces lowfrequency noise called artifacts due to the superposition between waves (such as head waves, diving waves and backscattered waves) immersed in the source and receiver wavefields and the migrated images amplitude. To reduce the artifacts, several techniques have been proposed. Youn and Zhou (2001) used the Laplacian image reconstruction to process each frame from correlation for an individual shot recorded, Fletcher et al. (2005), added a directional damping term to the nonreflecting wave equation proposed by Baysal et al. (1984) and Yoon and Marfurt (2006) used the Poynting vectors to improve the cross-correlation imaging condition. Kaelin and Guitton (2006) normalized the image of the cross-correlation diving by the source or the receiver illumination, Guitton et al. (2007) used the smooth imaging condition and the least square attenuation method, Costa et al. (2009) combined the obliquity factor weight and illumination compensation in the imaging condition, Whitmore and Crawley (2012) used the inverse scattering theory to attenuate the backscattered waves and Pestana et al. (2014) based on the relation of inversion and imaging, proposed the impedance sensitivity kernel imaging condition combined with Poynting vector. In this paper we propose a method to improve the migrated image and diminish the artifacts occurrence by applying a Laguerre Gauss filter with a spiral phase filter to implement a Radial Hilbert transform to process the cross-correlation images. First, we describe the Cross correlation imaging condition and the Laplacian filtering, which is a simple and popular way to remove the artifacts in RTM images. Second, the proposed method is described. Finally, we compare the images obtained by cross correlation imaging condition, laplacian filtering, and the Laguerre Gauss filtering applied to two synthetic datasets, to present evidences from the effectiveness of our imaging implementation to reduce the low-frequency spatial noise. Cross-correlation imaging condition The zero-lag cross-correlation between the extrapoled source and receiver wavefields is the imaging condition conventionally used in RTM. The cross-correlation imaging condition was proposed originally by Claerbout (1971, 1985) and as defined as follows: Icc(x, z) = ∑ ∑ S(x, z; ti; sj)R(x, z; ti; sj) tmax

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@inproceedings{Paniagua2016LaguerreGF, title={Laguerre Gaussian filters in Reverse Time Migration image reconstruction}, author={J. Paniagua}, year={2016} }