Reverse-time migration (RTM) exhibits great superiority over other imaging algorithms in handling steeply dipping structures and complicated velocity models. However, low-frequency, high-amplitude noises commonly seen in a typical RTM image have been one of the major concerns because they can seriously contaminate the signals in the image if they are not handled properly. We propose a new imaging condition to effectively and efficiently eliminate these specific noises from the image. The method works by first decomposing the source and receiver wavefields to their one-way propagation components, followed by applying a correlation-based imaging condition to the appropriate combinations of the decomposed wavefields. We first give the physical explanation of the principle of such noises in the conventional RTM image. Then we provide the detailed mathematical theory for the new imaging condition. Finally, we propose an efficient scheme for its numerical implementation. It replaces the computationally intensive decomposition with the cost-effective Hilbert transform, which significantly improves the efficiency of the imaging condition. Applications to various synthetic and real data sets demonstrate that this new imaging condition can effectively remove the undesired low-frequency noises in the image.
The field of subsalt imaging has evolved rapidly in the last decade, thanks in part to the availability of low cost massive computing infrastructure, and also to the development of new seismic acquisition techniques that try to mitigate the problems caused by the presence of salt. This paper serves as an introduction to the special Geophysics section on Subsalt Imaging for E&P. The purpose of the special section is to bring together practitioners of subsalt imaging in the wider sense, i.e., not only algorithm developers, but also the interpretation community that utilizes the latest technology to carry out subsalt exploration and development. The purpose of the paper is in many ways pedagogical and historical. We address the question of what subsalt imaging is and discuss the physics of the subsalt imaging problem, especially the illumination issue. After a discussion of the problem, we then give a review of the main algorithms that have been developed and implemented within the last decade, namely Kirchhoff and Beam imaging, one-way wavefield extrapolation methods and the full two-way reverse time migration. This review is not meant to be exhaustive, and is qualitative to make it accessible to a wide audience. For each method and algorithm we highlight the benefits and the weaknesses. We then address the imaging conditions that are a fundamental part of each imaging algorithm. While we dive into more technical detail, the section should still be accessible to a wide audience. Gathers of various sorts are introduced and their usage explained. Model building and velocity update strategies and tools are presented next. Finally, the last section shows a few results from specific algorithms. The latest techniques such as waveform inversion or the “dirty salt” techniques will not be covered, as they will be elaborated upon by other authors in the special section. With the massive effort that the industry has devoted to this field, much remains to be done to give interpreters the accurate detailed images of the subsurface that are needed. In that sense the salt is still winning, although the next decade will most likely change this situation.
In complex areas with large lateral velocity variations, wave-equation-based source plane-wave migration can produce images comparable to those from shot-profile migration, with less computational cost. Image quality can be better than in ray-theory-based Kirchhoff-type methods. This method requires the composition of plane-wave sections from all shot gathers. We provide a general framework to evaluate plane-wave composition in prestack source planewave migration. Our analysis shows that a plane-wave section can be treated as encoded shot gathers. This study provides the theoretical justification for applying plane-wave migration algorithms to sparsely sampled shot gathers with irregularly distributed receivers and limited offset. In addition, we discuss cylindrical-wave migration, which is 3D migration of 2D-constructed plane waves along the inline direction. We mathematically prove the equivalence of shot and plane-wave migration, and their equivalence to cylindrical wave migration in 3D cases when the sail lines are straight. Examples ͑including the Sigsbee 2A model͒ demonstrate the theory.
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