Seismic-wave imaging can be seen as a mapping from data space to model space. The objective is to position reflectors and to quantitatively estimate the physical parameters of the medium (such as reflectivity, P-wave velocity, S-wave velocity and density).
From the view of the historical development of seismic wave imaging, there are two ways to reach the goal. The first approach is seismic-wave migration technologies commonly used in the oil industry at present, which includes estimating low-wavenumber macro-velocity (with NMO+DMO velocity analysis, migration velocity analysis or traveltime tomography), positioning the reflectors and qualitatively estimating the reflectivity. However, quantitatively estimating reflectivities (which is called amplitude-preserving imaging or true-amplitude imaging) is currently much more actively pursued by the oil industry and academia. Seismic-wave illumination analysis, migration convolution, least-squares migration, and amplitude analysis of angle gathers are being given increased attention by many authors (, , , , , , ). All of these endeavors aim for clearer imaging and more quantitative reflectivity. The second approach is seismic-wave inversion, which directly and quantitatively estimates the physical contrast parameters of rocks (such as P-wave impedance, S-wave impedance and density).
The advantages of the first approach are that reflectors can be positioned step by step, and that reflectivity estimation can take advantage of many signal/noise enhancement technologies, macro-velocity analysis techniques and migration imaging methods. The procedure can be easily controlled and adjusted, and its calculation cost can be afforded by present computer systems. The geological and lithological knowledge about a survey area can be easily used for adjusting the final imaging results. The disadvantage of this conventional approach is its lack of a unified theoretical framework. Therefore, it is difficult to guarantee the reliability of the quantitative estimation of reflectivities.
The second approach has two subcategories: direct inversion methods (, , ), and iterative inversion methods (, , , , , ). Both have elegant theoretical expressions. However, the inverse problems are inherently ill-posed and the solutions are unstable and nonunique if the observed data set has certain flaws, including frequency band-limitation, aperture limitation, non-Gaussian noise, and/or an unknown source function. An unsuitable modeling algorithm or non-linearity between the observed data and geophysical parameters will also cause problems. In addition, the calculation costs of these methods often exceed the capacities of present computer systems. Until recently, only 2D inversion algorithms can be used in practice. The direct-inversion approach requires an analytical expression, which can be given analytically only in the case of constant background or slow background variance. Otherwise, the approach cannot produce a satisfactory result. Iterative inversion problems deal with either maximum-probability solutions for a Gaussian probability-density function or least-squares solutions of an l2-norm problem. These kinds of inverse problems need huge numbers of iterative modeling calculations.
At present, some trends indicate that standard seismic-wave migration imaging and inversion imaging are merging. The problem at the point of intersection is how to quantitatively estimate the reflectivity. How the shot and receiver configurations affect the imaging resolution and the amplitude of the estimated reflectivity is a question relevant to both imaging approaches.
We think that it is worthwhile to investigate how to generate amplitude-preserving common-image gathers with inversion imaging approaches, while also considering how to include seismic-wave-illumination effects and irregular data sets.
In this research proposal, we review the following topics: (1) expression of data space and model space; (2) relationship between data space and model space; (3) seismic-data preprocessing; (4) seismic-data illumination; (5) migration imaging and inversion imaging as a least-squares inverse problem; (6) amplitude-preserving migration imaging with wavefield extrapolation; (7) migration-velocity analysis or macro-velocity inversion and (8) some other related topics. We try to express the imaging process within the context of inverse theory and give some directions for further research.