Unified seismic-wave imaging - from data space to model space

Under operator, matrix and inverse theory, seismic-wave imaging can be considered a unified process—mapping from data space to model space. The main topics in seismic-wave imaging include (1) seismic-data interpolation, regularization and redatuming, which mainly decrease the imaging noise; (2) seismic-wave illumination analysis, which predicts whether a target reflector can be imaged and evaluates the suitability of an acquisition configuration in the case of rugged topography and severe lateral velocity variations; and (3) seismic-wave migration/inversion imaging algorithms, which give an imaging result with the help of a wave propagator, known a macro-velocity model. The last and most important thing is to build an accurate macro-velocity model. All of the processes can be considered with the conjugate operator/matrix under least-squares theory. In this article, we review the following topics: (1) expression of data space and model space; (2) affiliation between data space and model space; (3) seismic-data preprocessing; (4) seismic-data illumination; (5) migration imaging and inversion imaging as least-squares inverse problems; (6) amplitude-preserving migration imaging with wavefield extrapolation; (7) migration velocity analysis and inversion and (8) some related topics. We express the imaging process with the operator or matrix theory and give some directions for further research. INTRODUCTION 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 (Chavent and Plessix, 1email: [email protected], [email protected] 347 348 Wang and Shan SEP–12