Implementation of elastic prestack reverse-time migration using an efficient finite-difference scheme

Elastic reverse-time migration (RTM) can reflect the underground elastic information more comprehensively than single-component P-wave migration. One of the most important requirements of elastic RTM is to solve wave equations. The imaging accuracy and efficiency of RTM depends heavily on the algorithms used for solving wave equations. In this paper, we propose an efficient staggered-grid finite-difference (SFD) scheme based on a sampling approximation method with adaptive variable difference operator lengths to implement elastic prestack RTM. Numerical dispersion analysis and wavefield extrapolation results show that the sampling approximation SFD scheme has greater accuracy than the conventional Taylor-series expansion SFD scheme. We also test the elastic RTM algorithm on theoretical models and a field data set, respectively. Experiments presented demonstrate that elastic RTM using the proposed SFD scheme can generate better images than that using the Taylor-series expansion SFD scheme, particularly for PS images. Furthermore, the application of adaptive variable difference operator lengths can effectively improve the computational efficiency of elastic RTM

Seismic reverse-time migration in viscoelastic media

Seismic images are key to exploration seismology. They help identify structures in the subsurface and locate potential reservoirs. However, seismic images suffer from the problem of low resolution caused by the viscoelasticity of the medium. The viscoelasticity of the media is caused by the combination of fractured solid rock and fluids, such as water, oil and gas. This viscoelasticity of the medium causes attenuation of seismic waves, which includes energy absorption and velocity dispersion. These two attenuation effects significantly change the seismic data, and thus the seismic imaging. The aim of this thesis is to deepen the understanding of seismic wave propagation in attenuating media and to further investigate the method for high-resolution seismic imaging. My work, presented in this dissertation, comprises the following three parts. First, the determination of the viscoelastic parameters in the generalised viscoelastic wave equation. The viscoelasticity of subsurface media is succinctly represented in the generalised wave equation by a fractional temporal derivative. This generalised viscoelastic wave equation is characterised by the viscoelastic parameter and the viscoelastic velocity, but these parameters are not well formulated and therefore unfavourable for seismic implementation. The causality and stability of the generalised wave equation are proved by deriving the rate-of-relaxation function. On this basis, the viscoelastic parameter is formulated based on the constant Q model, and the viscoelastic velocity is formulated in terms of the reference velocity and the viscoelastic parameter. These two formulations adequately represent the viscoelastic effect in seismic wave propagation. Second, the development of a fractional spatial derivatives wave equation with a spatial filter. This development aims to effectively and efficiently solve the generalised viscoelastic wave equation with fractional temporal derivative, which is numerically challenging. I have transferred the fractional temporal derivative into fractional spatial derivatives, which can be solved using the pseudo-spectral implementation. However, this method is inaccurate in heterogeneous media. I introduced a spatial filter to correct the simulation error caused by the averaging in this implementation. The numerical test shows that the proposed spatial filter can significantly improve the accuracy of the seismic simulation and maintain high efficiency. Moreover, the proposed wave equation with fractional spatial derivatives is applied to compensate for the attenuation effects in reverse-time migration. This allows the dispersion correction and energy compensation to be performed simultaneously, which improves the resolution of the migration results. Finally, the development of reverse-time migration using biaxial wavefield decomposition to reduce migration artefacts and further improve the resolution of seismic images. In reverse-time migration, the cross-correlation of unphysical waves leads to large artefacts. By decomposing the wavefield both horizontally and vertically, and selecting only the causal waves for cross-correlation, the artefacts are greatly reduced, and the delicate structures can be identified. This decomposition method is also suitable for reverse-time migration with attenuation compensation. The migration results show that the resolution of the final seismic image is significantly improved, compared to conventional reverse-time migration.Open Acces

Converted-wave seismic imaging: Amplitude-balancing source-independent imaging conditions

We have developed crosscorrelational and deconvolutional forms of a source-independent converted-wave imaging condition (SICW-IC) and show the relationship between them using a concept of conversion ratio coefficient, a concept that we developed through reflection, transmission, and conversion coefficients. We applied the SICW-ICs to a two half-space model and the synthetic Marmousi I and II models and show the sensitivity of the SICW-ICs to incorrect wave speed models. We also compare the SICW-ICs and source-dependent elastic reverse time migration. The results of SICW-ICs highlight the improvements in spatial resolution and amplitude balancing with the deconvolutional forms. This is an attractive alternative to active and passive source elastic imaging. Keywords: imaging; converted wave; elastic; illumination; multicomponen

Converted-wave seismic imaging: Amplitude-balancing source-independent imaging conditions

We have developed crosscorrelational and deconvolutional forms of a source-independent converted-wave imaging condition (SICW-IC) and show the relationship between them using a concept of conversion ratio coefficient, a concept that we developed through reflection, transmission, and conversion coefficients. We applied the SICW-ICs to a two half-space model and the synthetic Marmousi I and II models and show the sensitivity of the SICW-ICs to incorrect wave speed models. We also compare the SICW-ICs and source-dependent elastic reverse time migration. The results of SICW-ICs highlight the improvements in spatial resolution and amplitude balancing with the deconvolutional forms. This is an attractive alternative to active and passive source elastic imaging

Converted-wave seismic imaging: Amplitude-balancing source-independent imaging conditions

We have developed crosscorrelational and deconvolutional forms of a source-independent converted-wave imaging condition (SICW-IC) and show the relationship between them using a concept of conversion ratio coefficient, a concept that we developed through reflection, transmission, and conversion coefficients. We applied the SICW-ICs to a two half-space model and the synthetic Marmousi I and II models and show the sensitivity of the SICW-ICs to incorrect wave speed models. We also compare the SICW-ICs and source-dependent elastic reverse time migration. The results of SICW-ICs highlight the improvements in spatial resolution and amplitude balancing with the deconvolutional forms. This is an attractive alternative to active and passive source elastic imaging