Toward a wave-equation based true-reflection imaging

Migration can undo wave propagation effects kinematically, but not dynamically due to many factors including geometrical spreading, transmission loss, path absorption, and acquisition aperture effect. True-reflection/amplitude imaging tries to obtain correct image amplitude, i.e. true reflectivity. It has been and remains a challenge. This thesis works on several of the important factors and proposes a local space-angle domain true-reflection imaging scheme using the resolving kernel to compensate all of the above four factors.;For geometrical spreading, I analyze effects of different amplitude correction terms in the asymptotic true-amplitude one-way wave propagator (TAOWP), especially that of the lateral velocity variation. I derive a dual-domain wide-angle screen (or generalized screen) type asymptotic TAOWP and extend it to a Fourier finite-difference type one. I evaluate two implementations of the amplitude correction. I propose a global optimization to improve the amplitude and phase accuracy for wide-angle waves in the TAOWP. Numerical examples demonstrate the above-mentioned points including that the lateral velocity variation has significant effect on the amplitude.;Second, for the local-angle domain (LAD) acquisition aperture correction, I propose an efficient scheme to obtain the LAD image and amplitude correction factor with local wavenumber domain beamlet decomposition. I evaluate two beamlet decomposition methods in terms of accuracy and efficiency. Numerical examples show that this method can produce results very similar to the original one but can be more than twice as fast.;Considering the limitations of one-way propagators based illumination, I propose to analyze the LAD illumination in the frequency domain using full-wave propagators. It can provide frequency-dependent full-angle (both downgoing and upgoing waves) true-amplitude illumination. Therefore it can be used to correct the transmission and absorption loss in the true-reflection imaging, and for accurate survey design. I propose two methods to decompose the full wavefield into the LAD: direct full-dimensional decomposition and more efficient split-step decomposition. I analyze the angle-resolution of the two decompositions analytically and numerically. Numerical examples demonstrate the advantages of the proposed illumination analysis method.;Then I investigate the influence of the one-way propagator geometrical spreading correction and the acquisition aperture correction on the image amplitude. The WKBJ solution for the one-way propagator in smoothly varying v(z) media is reformulated from energy flux conservation and extended to general media with local wavenumber domain methods. I then apply the localized WKBJ solution to migration. Numerical examples demonstrate that the acquisition aperture correction has more significant effect on the image amplitude than the propagator WKBJ compensation.;Finally I propose to use above-discussed flux-transparent one-way and full-wave propagators and the fast implementation of the image amplitude correction to implement an efficient true-reflection imaging scheme based on tomographic deconvolution filtering using the resolving kernel in the scattering tomography for the boundary scattering model. This imaging scheme can compensate the geometrical spreading, transmission loss, absorption loss, and acquisition aperture effects. I also compare the proposed method with least-squares migration: another potential true-reflection imaging scheme. It shows that the proposed method is more flexible and efficient. Preliminary result for the true-reflection image recovery in the boundary model demonstrates the capability of the method. Preliminary result for the volume scattering tomography also demonstrates the capability of the tomographic method.