Mingqiu Luo

Acquisition Aperture Correction In Angle-domain And True-amplitude Imaging For Wave Equation Migration

Summary Based on beamlet decomposition of wave field and Green’s function, we formulated an amplitude correction method in angle domain. The formulation relates the local image matr ix (LIM), which bears the footprints of the acquisition apertur e and propagation path effects, and the local scattering mat rix (LSM), which is directly related to the medium propert y. From the formulation, two types of amplitude correction ar e proposed: one is the correction for common reflection-angle image for AVA analysis. The other is the correction fo r total strength image. From the imaging results of the four-laye r model and the SEG/EAGE model, we see significant improvement in amplitude fidelity and image quality.

Beamlet migration using local cosine basis

We have developed the theoretical foundation and technical details of a migration method using a local-cosine-bases (LCB) beamlet propagator. A beamlet propagator for heterogeneous media based on local perturbation theory is derived, and a fast implementation method is constructed. The use of local background velocities and local perturbations results in a two-scale decomposition of beamlet propagators: a background propagator for large-scale structures and a local phase-screen correction for small-scale local perturbations. Because of its locally adaptive nature, the beamlet propagator can handle strong lateral velocity variations with improved accuracy. For high-efficiency migration, we use a table-driven method and apply some techniques of sparse matrix operations. Compared with the Fourier finite-dif-ference and generalized screen propagator methods, the image quality and computational efficiency are similar. In some cases, we see fewer migration artifacts around and inside salt bodies with our method...

3D Beamlet Prestack Depth Migration Using the Local Cosine Basis Propagator

Wave equation based beamlet poststack and prestack depth migration using Local Cosine Basis LCB prop agator is further developed and tested The idea of the method consists of a beamlet propagator and local per turbations for each window of the wave eld decom position using an orthogonal local cosine basis We present a semi analytical beamlet propagator which is easy to be tabulated Combined with phase correction operators the e ciency is greatly improved for prac tical use The numerical experiments in an individ ual beamlet propagation in a homogeneous medium show the beam s localization properties in both space and wavenumber direction Poststack and prestack depth migration applications to the SEG EAGE salt model data demonstrate the great potential of this ap proach

Target oriented full‐wave equation based illumination analysis

We propose a full-wave equation based illumination analysis method with target oriented capability. The fullwave finite-difference propagator is used to extrapolate the source and receiver side wavefields to the subsurface target area. A time-domain local-slowness analysis method is used to decompose the wavefields into local angle domain. The local illumination matrix can be constructed and different types of illumination measurements can be derived. This illumination analysis method does not have angle limitations. Thus this approach can handle structures with their dipping angles beyond 90 degrees and is particularly useful to provide illumination analysis for reverse-time migration.

True amplitude one‐way propagators implemented with localized corrections on beamlets

The transmission coefficient and WKBJ approximation can be adopted for constructing the true amplitude propagators. For vertically inhomogeneous media, the WKBJ approximation or transmission coefficients can be applied on the plane waves at each depth to get the true amplitudes. While for the media with lateral variation, the correction coefficients vary with horizontal locations, and cannot be applied on the global plane waves. However, the beamlet propagators decompose the wavefield into localized beamlets, and the laterally varying WKBJ or transmission correction coefficients can be conducted on a localized basis at each depth. In this paper, the theory for the localized WKBJ and transmission corrections are proposed and implemented with the local cosine basis (LCB) beamlet propagator. Numerical examples of the impulse responses are calculated to demonstrate the feasibility of the local WKBJ and local transmission corrections.

Comparison of illumination analyses using one-way and full-wave propagators

Summary In this paper, we compare one-way wave propagator and full-wave propagator such as finite difference (FD) method i n the evaluation of illumination and acquisition dip response (ADR) maps. For the case of 2D SEG/EAGE salt model, the illumination and ADR maps by the one-way method and the FD method have similar general distributions in space and angle domain. However, some difference exists in absolut e values, especially for the subsalt area. This is due to the strong effects of transmission loss caused by salt boundary scat tering, reflection and defocusing. The difference in wide-angle amplitude behavior is also noticeable. Therefore, in most cases illumination analysis calculated by one-way wave propagators can provide reliable evaluation.

Beamlet migration using local cosine basis with shi fting windows

Summary For beamlet migration methods, the wave fields normally are statically and regularly windowed, and the wave field in e ach window is propagated with beamlet propagators based on local cosine basis (LCB) or Gabor-Daubechies frame (GDF), followed by local perturbations. These methods can provide pretty good imaging results when compared to traditional methods. However, with the LCB beamlet method, some artifacts are present at steeply inclined interface of l arge velocity contracts. The artifacts can be greatly reduc ed by dynamically shifting windows in the LCB beamlet method. The numerical results on 2D and 3D models will show the improvement in the imaging quality.

Illumination amplitude correction with beamlet migration

Subsalt imaging can pose significant imaging challenges for prestack depth migration algorithms. Large local velocity gradients are usually present. Velocity differences between subsalt sediments and salt can exceed 5500 ft/s (1670 m/s). Additionally, the 3D complexity of the salt can introduce rapid spatial variations in subsalt illumination. A methodology that provides a robust and elegant solution to these issues is beamlet migration which involves decomposing source and receiver wavefields into beamlets during the wavefield extrapolation process. Each beamlet has positional information associated with it due to its wavelet transform basis. Also, each beamlet propagates with a local reference velocity in which the local velocity perturbation is small, resulting in accurate wave propagation. Increased accuracy in wavefield propagation permits improved imaging of sediment reflectivity proximate to salt—a critical issue in achieving exploration/development success.

Comparison of different schemes of image amplitude correction in prestack depth migration

We compare different schemes of amplitude correction from the viewpoint of amplitude gain control (AGC) factors with different approximations. Four kinds of amplitude corrections are considered: the traditional vertical AGC, space-domain correction based on total illumination, correction in local scattering angle-domains, and the correction in local dip-angle domain. We analyze the different approximations involved in these schemes and compare their results of amplitude correction for the migrated images of Sigsbee2A model. The advantages of the correction in dip-angle domain can be seen clearly. The image quality of subsalt structures is greatly improved and the image amplitudes along subsalt faults are more balanced. In the meanwhile the noises and migration artifacts become smaller than other schemes.

Application of Beamlet Propagator to Migration Amplitude Correction

Beamlet migration provides robust imaging in the presence of strong velocity contrasts by combining local perturbation theory with wavelet transforms. Source and receiver wavefields are decomposed into beamlets during the wavefield extrapolation. Each beamlet propagates with a local reference velocity in which the local velocity perturbation is small, resulting in accurate and efficient wave propagation. It simultaneously extracts local information in both space and angle. Such information can be further applied to the computation of imaging amplitude corrections using directional illumination in the local angle domain. Synthetic examples show the local angle imaging properties of beamlets and the improved amplitude balance of the depth image after acquisition aperture correction.