Faqi Liu

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...

Toward a unified analysis for source plane-wave migration

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 plane-wave 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 model) demonstrate the theory.

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.

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.

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.

An Anti-dispersion Reverse-time Migration Method With Local Nearly-analytic Operators And Its Application

Finite-difference method, which has been widely used in seismic modeling and reverse-time migration, is one of the most popular numerical methods in exploration geophysics. However, it generally has two issues: large computational cost and numerical dispersion. Recently, a nearly-analytic discrete operator was developed to approximate the partial differential operators. Based on this method, many anti-dispersion schemes have been developed, which are confirmed to be superior to conventional algorithms in suppressing numerical dispersions. In this paper, we apply an Optimal Nearly Analytic Discrete Method (ONADM), one of the many anti-dispersion schemes developed by Yang et al. in 2004, to enhance the accuracy and performance of reverse-time migration. Numerical results show that the ONADM can be used effectively as a new tool for seismic modeling and migration. The ONADM produces little numerical dispersion and requires less computational cost and memory compared with the fourth-order Lax-Wendroff correction (LWC). The reverse time migration results of the 2-D Marmousi and EAGE Salt model show that ONADM can be more than one magnitude faster than the conventional methods while maintaining the same image quality.

Multiple identification in the image domain using map modeling and map migration

Summary In seismic imaging, a fundamental assumption is that reflection data only consist of primaries. If multiples are not fully removed, they can be misinterpreted as primaries. The purpose of this study is to identify the multiples in the image domain by map-migrating the modeled multiples. This can be used as an interpretation tool to avoid picking residual multiples as primary events. In this abstract, we first describe the theory and method of map modeling and map migration and test this algorithm with a simple linear velocity model and a dipping reflection horizon. Then, we apply it to a field data from the Gulf of Mexico. The results show that this algorithm accurately predicts the location of the specified multiples, allowing the identification of the residual multiples in prestack depth migrated images. Finally, we discuss the limitations of this method and the future directions for development.

Phases in One Way Wave Equation Migrations

In this paper, we investigate phases in different one way wave equation based migration algorithms. We found that poststack migrations preserve the characteristics of the input wavelet. However, like Kirchhoff migration, prestack shot and plane wave migration require a phase rotation to match the phase of the image to that of the input data. We use a single impulse response and a flat reflector model to demonstrate our conclusions.