True amplitude imaging by inverse generalized Radon transform based on Gaussian beam decomposition of the acoustic Green's function

Abstract

A B S T R A C TTrue amplitude migration is one of the most important procedures of seismic data processing. As a rule it is based on the decomposition of the velocity model of the medium into a known macrovelocity component and its sharp local perturbations to be determined. Under this decomposition the wavefield can be considered as the superposition of an incident and reflected/scattered waves. The single scattering approximation introduces the linear integral operator that connects the sharp local perturbations of the macrovelocity model with the multishot/multioffset data formed from reflected/scattered waves. We develop the pseudoinverse of this operator using the Gaussian beam based decomposition of acoustic Green's functions. The computation of this pseudoinverse operator is done pointwise by shooting Gaussian beams from the target area towards the acquisition system.The numerical implementation of the pseudoinverse operator was applied to the synthetic data Sigsbee2A. The results obtained demonstrate the high quality of the true amplitude images computed both in the smooth part of the model and under the salt body.

Gaussian beam decomposition for seismic migration

“…Gaussian beams, which are localized solutions of the wave equation, have been used successfully in seismic migration applications (Hill, 1990(Hill, , 2001da Costa et al, 1989;Alkhalifah, 1995;Nowack et al, 2003;Gray, 2005;Popov et al, 2010;Protasov and Tcheverda, 2011). Gaussian beam migration retains the advantages of Kirchhoff migration (such as the ability to handle steep dips) while being able to handle the issue of multipathing, which presents significant difficulties for traditional Kirchhoff implementations (Gray et al, 2002).…”

Fracture Detection via Beam Imaging and Image Spectrum Analysis

“…The beams are computed on the basis of ray tracing from every image point. X par -set of partial reconstruction, see (Protasov and Tcheverda, 2011). This subdomain is a circular sector which is defined by the frequency bandwidth (ω 1 , ω 2 ) of the source function and available range of dip angles (α 1 , α 2 ):…”

“…These weights are computed by tracing a specially chosen Gaussian beams. In order to get image of fractures these beams are taken in a way forming so called selective images (Pozdnyakov and Tcheverda, 2006;Protasov and Tcheverda, 2011). Their geometry provides suppression of regularly reflected waves and, thus, emphasizes the presence of small-scale heterogeneities that give rise to diffracted/scattered waves.…”

Gaussian beam propagation through irregular interfaces

“…Hobro c соавторами предложили метод сглаживания нормали границы [2008], что позволяет выполнять устойчивую трассировку лучей, однако не преодолевает фундаментальных проблем лучевого ме-тода. В [Protasov, Tcheverda, 2011] было предложено и обосновано частотно-зависимое трассирование лучей через нерегулярные границы раздела сред. Этот подход основан на использовании граничных интегралов, где на границе применяется сглаживание в интервале, за-висящем от френелевского объема, который, в свою оче редь, определяется частотой и углом падения луча на границу.…”

“…[Про тасов, Чеверда, 2006;Protasov, Tcheverda, 2011, 2012). Однако Гауссовы пучки -это не только сами лу чи, но и их динамические параметры, которые также необходимо вычислять вдоль лучей.…”