By using OBSs and streamer, we can get seismic data. The next step is seismic data processing, which is in fact the central step for our mission. Among the many steps in seismic data processing, migration is considered as the critical part, which in fact determines the quality of the seismic data processing.

What is migration? Concisely, migration is the step that “moves” seismic data received at the surface receivers to a subsurface image, which is considered to be able to describe the structural information of subsurface. Migration is not the first child of seismic data processing. It was born only after 1930s and emerges rapidly after 1960s and 1970s with the development of digital wave-equation technique. Here I only give some brief description on modern depth migration methods and their comparison. For a more detailed chronology of seismic migration and imaging, please refer to A brief history of seismic migration by J. Bee Bednar on Geophysics Vol. 70, NO. 3, and please refer to An overview of depth imaging in exploration geophysics by John Etgen et al. on Geophysics Vol. 74, No.6, for a detailed description of modern depth imaging methods.

Basically there are two major classes of migration methods, ray-based migration and wave-equation migration. Ray-based migration is based on the high-frequency asymptotic solution of the wave-equation. So from its nature, ray-based migration is in fact wave-equation migration, however in practice, we still differentiate it from wave-equation migration, since they just follow a much different methodology when doing migration. Two main methods are included in ray-based migration, Kirchhoff migration and beam migration. Kirchhoff migration dominates the petroleum industry from 1980s to 1990s, and now is still a living method both in practice and in theoretical research. Kirchhoff migration has its advantages of great flexibility and small computing amount. However, as the Kirchhoff migration is based on ray-tracing, there are deadly limitations in its imaging ability, the most obvious of which is that it uses single arrives along single raypaths to reconstruct the entire wavefield. Beam migration mainly denotes the Gaussian-beam migration, which uses “fat” rays and they can overlap each other. Another important feature of beam migration is that they are not dip-limited. But again, as beam migration is based on rays, in they may fail to image correctly in complex geological areas. Wave-equation migration are based on either acoustic wave equation, which is based on the assumption that our earth is fluid, or elastic wave equation, which is based on the assumption that our earth should be considered to be elastic solid. There are one-way and two-way wave-equation migrations. One-way wave-equation migration (OWEM) applies Green identity, which expresses the wavefield at certain time by the wavefield at earlier time or later time. One-way wave equation downward-propagates the wavefields from zero depth and suffers no upward-propagating wavefields, which justifies “one-way”. By one-way wave equation, based on the separation of two-way wave equation, the source and receiver wavefields are downward extrapolated from shallower depth to deeper depth step by step, and then applying imaging conditions, we can get the migrated image of subsurface. There are mainly four methods to do the downward extrapolation: implicit finite-difference algorithms, which express the single square-root one-way wave equation with infinite fractional series (and truncated to be finite in practice) to numerically implement; stabilized explicit extrapolation methods, which designs numerically Green functions to downward-propagate the one-way wavefield; phase-shift propagation with multireference velocities; dual-space (space-wavenumber) methods, including split-step Fourier (SSF) migration, Fourier finite-difference (FFD) migration, phase-screen and generalized-screen methods, etc.. As its nature is the approximation to two-way wave-equation, OWEM suffers from dip-angle limitation, which means that they are difficult to image steep dips and may give poor reconstructed image in geologically complex areas. On the contrary, two-way wave-equation uses not Green identity but full wavefield to reconstruct the subsurface image. When we refer to two-way wave-equation migration, we often denote the reverse-time migration (RTM). There is no high-frequency assumption and dip-angle limitation in RTM since it uses full wave equation and propagates the wavefield in all directions. For prestack RTM, we implement it by forward-propagating the source wavefield in time and backward-propagate the receiver wavefield in time, and then we get the subsurface image by doing the wavefield crosscorrelation of the source and receiver wavefields. At the emergence of RTM in 1980s, it was almost abandoned because of its high computation cost, both in time consumption and in storage requirements. However in recent years, with the development of computing hardware and algorithms, such as PC cluster, parallel computing technique, GPGPU computing technique, and improvements in computing storage, RTM is gaining the popularity both in practice and theoretical research. In fact, RTM is the most accurate algorithm we can find at present to render a complete and reliable image of subsurface structures. From the beginning acoustic RTM, to recent anisotropic RTM, the RTM is becoming more and more powerful and more and more companies are using RTM as their primary choice.

Full-waveform inversion is another emerging technique for seismic imaging and inversion. But there are many unresolved problems in it. We do not give introduction here.

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