One-way Wavefield Extrapolation Research Articles

Optimized Pseudo-Padé Fourier Migrator in Terms of Propagation Angles

A wide-angle Fourier migrator is proposed to more accurately image complex media with strong lateral velocity contrasts. The broadband wave-equation migrator is developed based on the pseudo-Pade approximation, where the Pade coefficients are independent of spatial coordinates, leading to a pure Fourier transform-based matching solution for one-way wavefield extrapolation. We use genetic algorithms to estimate the constant Pade coefficients more accurately than is feasible with conventional least-squares methods. Because of the global features of pure Fourier migrators, we present an angle-partitioning optimization scheme with dip focusing to improve the performance of the Fourier migrator for super-wide-angle waves and strong velocity contrasts. The wavefield gradient is used to calculate propagation angles during dual-domain wavefield extrapolation. Particular attention is paid to the first-order optimized pseudo-Pade Fourier (OPF1) migrator, which significantly improves the split-step Fourier (SSF) method for strong lateral variations at the cost of one additional Fourier transform in each step. Wavefield extrapolation based on the OPF1 method actually constitutes linear interpolation in the wavenumber domain between two split-step terms. We benchmark the OPF1 migrator with other typical migrators based on the exact dispersion equation. Numerical experiments with impulse responses, the SEG/EAGE salt model and 3D field data demonstrate the excellent performance and efficiency of seismic imaging with the OPF1 migrator.

An improvement in RTM method to image steep dip petroleum bearing structures and its superiority to other methods

In this paper, first the limitations of the ray-based method and the one-way wave-field extrapolation migration (WEM) in imaging steeply dipping structures are discussed by some examples. Then a new method of the reverse time migration (RTM), used in imaging such complex structures is presented. The proposed method uses a new wave-field extrapolator called the Leapfrog-Rapid Expansion Method (L-REM) for wave-field extrapolation. This improved method also includes a new imaging condition based on Poynting vector for wave-field separation and calculating the reflection angles. Afterwards, the results obtained for the application of the new RTM method are compared with those obtained by the harmonic-source method as a delay shot or plane wave RTM. Finally, the efficiency of these imaging methods is tested using the BP 2004 2D seismic dataset. The results obtained indicate the superiority of the presented RTM method in imaging such steep dip structures in comparison with the other imaging procedures.

Subsalt imaging for exploration, production, and development: A review

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.

Wave-equation migration in generalized coordinate systems

Month and year defended: March, 2009 Wave-equation migration using one-way wavefield extrapolation is commonly used to generate images of complex geologic structure from 3D seismic data. Most conventional wave-equation approaches restrict propagation to downward continuation, where wavefields are recursively depth extrapolated on Cartesian meshes. In practice, this approach exhibits limited high-angle accuracy and is restricted to down-going waves, which precludes using some steep-dip and all turning wave …

Seismic imaging using lateral adaptive windows

One-way wavefield extrapolation methods are used routinely in 3D depth migration algorithms for seismic data. Due to their efficient computer implementations, such one-way methods have become increasingly popular and a wide variety of methods have been introduced. In salt provinces, the migration algorithms must be able to handle large velocity contrasts because the velocities in salt are generally much higher than in the surrounding sediments. This can be a challenge for one-way wavefield extrapolation methods. We present a depth migration method using one-way propagators within lateral windows for handling the large velocity contrasts associated with salt-sediment interfaces. Using adaptive windowing, we can handle large perturbations locally in a similar manner as the beamlet propagator, thus limiting the impact of the errors on the global wavefield. We demonstrate the performance of our method by applying it to synthetic data from the 2D SEG/EAGE [Formula: see text] salt model and an offshore real data example.

Plane-wave migration in tilted coordinates

We have developed a plane-wave migration method that efficiently images steeply dipping reflectors using one-way wavefield extrapolation. The recorded surface data are converted to plane-wave source data by slant stacking. The data set corresponding to each plane-wave source is migrated independently in a tilted coordinate system, with the extrapolation direction determined by the initial propagation direction of the plane wave at the surface. Waves illuminating steeply dipping reflectors, such as overturned waves and waves traveling nearly horizontally, are extrapolated accurately in an appropriate tilted coordinate system because the extrapolation direction is close to the propagation directions for these waves. Two-dimensional impulse responses and synthetic data examples demonstrate that plane-wave migration in tilted coordinates generates high-quality images of steeply dipping reflectors, particularly rugose salt tops and steep salt flanks.

Waveform inversion by one-way wavefield extrapolation

One-way Riemannian wavefield extrapolation (RWE) on computational meshes conforming to the direction of turning-wave propagation is an alternative forward-modeling procedure for waveform inversion. Forward-modeling tests demonstrate that the RWE approach may be a sufficiently accurate approximation for calculating the wavefield phases important for early-arrival waveform inversion. Initial results indicate that RWE waveforms are well matched at wide offsets to finite-difference data, and can be used in a waveform inversion scheme to invert synthetic data for moderate 1D velocity perturbations.

3D wavefield extrapolation with optimal separable approximation

An accurate and wide-angle one-way propagator for wavefield extrapolation is an important topic for research on wave-equation prestack depth migration in the presence of large and rapid velocity variations. Based on the optimal separable approximation presented in this paper, the mixed domain algorithm with forward and inverse Fourier transforms is used to construct the 3D one-way wavefield extrapolation operator. This operator separates variables in the wavenumber and spatial domains. The phase shift operation is implemented in the wavenumber domain while the time delay for lateral velocity variation is corrected in the spatial domain. The impulse responses of the one-way wave operator show that the numeric computation is consistent with the theoretical value for each velocity, revealing that the operator constructed with the optimal separable approximation can be applied to lateral velocity variations for the case of small steps. Imaging results of the SEG/EAGE model and field data indicate that the new method can be used to image complex structure.

Riemannian wavefield extrapolation

Riemannian spaces are described by nonorthogonal curvilinear coordinates. We generalize one-way wavefield extrapolation to semiorthogonal Riemannian coordinate systems that include, but are not limited to, ray coordinate systems. We obtain a one-way wavefield extrapolation method that can be used for waves propagating in arbitrary directions, in contrast to downward continuation, which is used for waves propagating mainly in the vertical direction. Ray coordinate systems can be initiated in many different ways; for example, from point sources or from plane waves incident at various angles. Since wavefield propagation happens mostly along the extrapolation direction, we can use inexpensive finite-difference or mixed-domain extrapolators to achieve high angle accuracy. The main applications of our method include imaging of steeply dipping or overturning reflections.

Wavefield extrapolation and amplitude-variation-with-angle migration in highly discontinuous media

SUMMARY Current macromodel-based one-way wavefield extrapolation ignores the practical highly discontinuous character of rock formations. The main effects of this highly discontinuous behaviour on transmitted wavefields are angle-dependent dispersion and amplitude losses. In this paper the angle-dependent dispersion and amplitude losses are quantified by a proposed extended macro model, which is closely related to the current macro model except that two stochastic parameters on the rock formations are added. The stochastic parameters are derived based on the observation of power-law behaviour of subsurface heterogeneity. The resulting replacement medium described by the extended macro model is an anisotropic medium with anelastic losses. Explicit extrapolation operators are used to perform forward and inverse wavefield extrapolation in the inhomogeneous replacement medium, which mimics a true subsurface that is moderately inhomogeneous at the macro scale and highly discontinuous at the subwavelength scale. The stability of the inverse wavefield extrapolation is achieved through controlling the maximum angle of propagation. Also a table-driven true-amplitude pre-stack migration scheme is proposed, which can approximately eliminate the dispersion effects of the fine-layering together with the geometrical spreading effects in imaging the subsurface based on the extended macro model. A number of numerical examples are presented to illustrate the algorithms.

Application of reverse time migration to complex imaging problems

Paul A. Farmer, Ian F. Jones, Hongbo Zhou, Robert I. Bloor, and Mike C. Goodwin explain the revival of interest in reverse time migration with some examples from the North Sea of model building and migrating with the full acoustic two-way wave equation. Standard shot-based one-way wavefield extrapolation (WE) preSDM techniques image the subsurface by downward continuing the source and receiver wave-fields for each shot. The imaging condition is invoked by cross correlating these two wave-fields at each depth level, and then summing the contributions from all shots in the aperture to form the image. One of the assumptions made in using this technique is that the wave-fields travel along the direction of extrapolation only in one direction: downwards for the source wave-field, and upwards for the receiver or scattered wave-field. In practice, each of these wave-fields will generally travel both up and down when the velocity model is complex, when turning (diving) ray-paths are involved, or when multiples are being generated. In addition, approximations in the extrapolation techniques usually limit the dips present in the final image to less than seventy degrees. Steeper dips, and turning rays are usually imaged using Kirchhoff techniques, but these fail to deliver acceptable images once we have a multi-pathing problem. One technique which can address all these issues is migration using the two-way wave equation. Here, we have used an anisotropic reverse time migration (RTM) algorithm to achieve this. RTM properly propagates the wave-field through velocity structures of arbitrary complexity, correctly imaging dips greater than 90 degrees. It even has the potential to image with internal multiples when the boundaries responsible for the multiple are present in the model. Although hitherto considered economically impracticable, recent enhancements to computing capacity, both in terms of CPU speeds and highly efficient hardware infrastructure, have made RTM commercially viable. Following an historical review of the approximations used in migration, we will show anisotropic RTM examples from the North Sea, outlining the potential benefit of model building and migrating with the full acoustic two-way wave equation.