Scott A. Morton

Phase encoding of shot records in prestack migration

Frequency‐domain shot‐record migration can produce higher quality images than Kirchhoff migration but typically at a greater cost. The computing cost of shot‐record migration is the product of the number of shots in the survey and the expense of each individual migration. Many attempts to reduce this cost have focused on the speed of the individual migrations, trying to achieve a better trade‐off between accuracy and speed. Another approach is to reduce the number of migrations. We investigate the simultaneous migration of shot records using frequency‐domain shot‐record migration algorithms. The difficulty with this approach is the production of so‐called crossterms between unrelated shot and receiver wavefields, which generate unwanted artifacts or noise in the final image. To reduce these artifacts and obtain an image comparable in quality to the single‐shot‐per‐migration result, we have introduced a process called phase encoding, which shifts or disperses these crossterms. The process of phase encoding...

An effective imaging condition for reverse-time migration using wavefield decomposition

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 intensiv...

Reverse-time Migration Using One-way Wavefield Imaging Condition

Reverse-time migration has the capability to image all dips including overturned structures. However, the conventional imaging condition produces high-amplitude noises in the image, which often seriously mask the shallow structures. In this paper, we propose a new imaging condition to eliminate these noises which works by decomposing the full wavefields to their one-way components, and applying the imaging condition to the appropriate combinations of the wavefield components. Numerical tests verify that this new imaging condition successfully removes the undesired noises.

Decoupled Wave Equations For P And SV Waves In an Acoustic VTI Media

In this paper, we decouple the P and SV wave components in an acoustic transversely isotropic media with vertical symmetric axis (VTI), and construct an independent pseudo-differential equation for each wave mode. The resulted wave equation for P-wave is unconditionally stable. A scheme based on the optimized separable approximation is proposed for their numerical implementation. We demonstrate the theory with some simple experiments.

Faster shot-record depth migrations using phase encoding

Phase encoding of shot records provides a means of imaging a number of shots within a single migration. This results in a reduction in the required computation for a complete image, a reduction by the number of shots used in each individual migration, trading this increase in speed for additional noise in the resulting image. Some methods for phase encoding have been shown to limit this noise to a tolerable range when combining several shots, enabling speed ups of a factor of a few. In this paper, the authors present a use of phase encoding which allows faster imaging by an order of magnitude or more, with the additional benefit that the individual migrations can be stopped whenever the answer is good enough. This approach may ultimately render 3-D frequency-domain prestack depth migration cost effective.

Differential Semblance Velocity Analysis Via Shot Profile Migration

Shot profile migration provides a convenient framework for implementation of a differential semblance algorithm for estimation of complex, strongly refracting velocity fields. The objective function minimized in this algorithm may measure either focussing of the image in offset or flatness of the image in (scattering) angle. The gradient of this objective is a by-product of a depth marching scheme, an requires a few extra computations beyond those necessary to produce the prestack data volume. A strongly refracting 2D synthetic data example illustrates the excellent image quality obtainable from model-consistent data. Offset and angle variants behave differently, with more rapid convergence for the offset variant, underlining the importance of a mathematically well posed formulation: in 2D, the angle variant is much less well-conditioned than the offset variant.

An optimized wave equation for seismic modeling and reverse time migration

The acoustic wave equation has been widely used for the modeling and reverse time migration of seismic data. Numerical implementation of this equation via finite-difference techniques has established itself as a valuable approach and has long been a favored choice in the industry. To ensure quality results, accurate approximations are required for spatial and time derivatives. Traditionally, they are achieved numerically by using either relatively very fine computation grids or very long finite-difference operators. Otherwise, the numerical error, known as numerical dispersion, is present in the data and contaminates the signals. However, either approach will result in a considerable increase in the computational cost. A simple and computationally low-cost modification to the standard acoustic wave equation is presented to suppress numerical dispersion. This dispersion attenuator is one analogy of the antialiasing operator widely applied in Kirchhoff migration. When the new wave equation is solved numerically using finite-difference schemes, numerical dispersion in the original wave equation is attenuated significantly, leading to a much more accurate finite-difference scheme with little additional computational cost. Numerical tests on both synthetic and field data sets in both two and three dimensions demonstrate that the optimized wave equation dramatically improves the image quality by successfully attenuating dispersive noise. The adaptive application of this new wave equation only increases the computational cost slightly.

An Anti-dispersion Wave Equation For Modeling And Reverse-time Migration

The acoustic wave equation has been widely used for the modeling and reverse-time migration of seismic data. The finite-difference method has long been the favored approach to solve this equation. To ensure quality results, accurate approximations are required for the spatial and time derivatives. This can be achieved numerically by using either very fine computation grids or very long finite-difference operators. Otherwise, the numerical error, called numerical dispersion, will be present in the data and contaminate the signals. However, either approach increases the computation cost dramatically. In this paper, we propose a new approach to address this problem by constructing a new wave equation, which we call the anti-dispersion wave equation. It involves introducing a dispersion attenuation term to the standard wave equation. When it is solved using finite difference, numerical dispersion in the original wave equation is attenuated significantly, leading to a much more accurate finite difference scheme with little additional computation cost.

Automating Prestack Migration Analysis Using Common Focal Point Gathers

CFP technology (Berkhout, 1996a,b) addresses these limitations in a novel way. By breaking the model determination process into two simpler, more easily solved problems, those of operator estimation and macro model estimation, the final solution will typically be more accurate. Moreover, by providing rapid local convergence to the correct travel-time operators, migration analysis can be automated, resulting in reduced manpower requirements and shorter time-to-solution.

Anisotropic model building by integrating welltie and checkshot for Garden Banks of GoM

Summary In order to improve depth positioning and structural accuracy, we b uild an anisotropic velocity model for imaging Northeastern (NE) Garden Banks in the Gulf of Mexico (GoM). We assume vertical transverse isotropy (VTI) and derive Thomsen’s δ by comparing seismic and well data. Both welltie and checkshot data indicate a twolayer δ trend in NE Garden Banks: low δ shallow and high δ deeper. The interface between the two δ zones corresponds to a distinct seismic reflector – the base of a mass transport complex which is also a local maximum in the velocity. Using this two-layer δ model and a scanned Thomsen’s e model, we carry out anisotropic (VTI) imaging. The VTI imaging reduces misties by more than 80% compared to the original isotropic imaging.