Full-wave directional illumination analysis in the frequency domain

Abstract

Directional illumination analysis based on one-way wave equations has been studied extensively; however, its inherent limitations, e.g., one-way propagation, wide-angle error, and amplitude inaccuracy, can severely hinder its applications for accurate survey design and true-reflection imaging corrections in complex media. We have analyzed the illumination in the frequency domain using full two-way wave propagators considering the extensive computation and huge storage required for time-domain methods, and the fact that the illumination is frequency dependent. This full-wave analysis can provide frequency-dependent full-angle true-amplitude illumination not only for the downgoing waves but also for the upgoing waves, including turning waves and reflected waves. Two methods were considered to decompose the full wavefield into the local angle domain: a direct full-dimensional decomposition and more efficient split-step decomposition composed of three lower-dimensional decompositions.The results of illumination analysis demonstrated the advantages of this method. The two decomposition methods produced similar results.

Angle‐domain imaging of relative impedance perturbation

“…2003, 2004, 2006), and then the two‐way wave equation (Xie and Yang 2008; Yang et al . 2008; Cao and Wu 2009). The spatial distribution of energy is not uniform during the incident waves and the reflected waves propagating in the subsurface complex structures.…”

Reflection multi‐scale envelope inversion

“…In the reflection waveform inversion (RWI), the wavefield is decomposed into different components according to the transmission direction. There are several methods to do wavefield decomposition such as Poynting vector (Yoon and Marfurt 2006), two Fourier transforms (Cao and Wu 2009;Wu and Alkhalifah 2014), and 2D fast Fourier transform (2D FFT) (Liu et al 2011). These methods have advantages in terms of decomposition accuracy or efficiency.…”

Illumination compensation using Poynting vectors, with special treatment for multiples

“…The tantalizing prospect of exploiting the useful information contained in multiples has lead others to propose schemes for imaging with multiples (Malcolm et al, 2009;Fleury, 2013). Cao and Wu (2009) show that internal multiples can provide more even illumination in subsalt areas than singly-scattered primaries. There are also several additional motivations for combining the inclusion of multiples with an illumination compensation method such as the one we propose.…”

“…Several methods employ forms of wavelets (Herrmann et al, 2009;Mao et al, 2010), others exploit the pseudodifferential nature of the illumination compensation operator (Nammour and Symes, 2009;Demanet et al, 2012). Cao and Wu (2009) propose the use of local slant stacks, and Cao (2013) uses a local transformation of point spread functions to obtain the angular information.…”