Beamlet Propagator Research Articles

Simulative and Experimental Characterization of an Adaptive Astigmatic Membrane Mirror.

Adaptive optical (AO) components play an important role in numerous optical applications, from astronomical telescopes to microscope imaging systems. For most of these AO components, the induced wavefront correction, respectively added optical power, is based on a rotationally symmetric or segmented design of the AO component. In this work, we report on the design, fabrication, and characterization of a micro-electronic-mechanical system (MEMS) adaptive membrane mirror in the shape of a parabolic cylinder. In order to interpret the experimental characterization results correctly and provide a tool for future application development, this is accompanied by the setup of an optical simulation model. The characterization results showed a parabolically deformable membrane mirror with an aperture of 8 × 2 mm2 and an adaptive range for the optical power from 0.3 to 6.1 m−1 (dpt). The optical simulation model, using the Gaussian beamlet propagation method, was successfully validated by laser beam profile measurements taken in the optical characterization setup. This MEMS-based adaptive astigmatic membrane mirror, together with the accompanying simulation model, could be a key component for the rapid development of new optical systems, e.g., adaptive laser line generators.

Preliminary Investigation of Wavefield Depth Extrapolation by Two-Way Wave Equations

Most of the wavefield downward continuation migration approaches are relying on one-way wave equations, which move the seismic energy always in one direction along depth. The one-way downward continuation migrations only use the primaries for imaging and do not treat secondary reflections recorded on the surface correctly. In this paper, we investigate wavefield depth extrapolators based on the full acoustic wave equations, which can propagate wave components to opposite directions. Several two-way wavefield downward continuation propagators are numerically tested in this study. Recursively implementing of the depth extrapolator makes it necessary and important to eliminate the unstable wave modes, that is, evanescent waves. For the laterally varying velocity media, distinction between the propagating and evanescent wave mode is less clear. We demonstrate that the spatially localized two-way beamlet propagator is an effective way to remove the evanescent waves while maintain the propagating mode in laterally inhomogeneous media.

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.

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. We attribute this to the better high-angle accuracy of beamlet propagators in strong-contrast media. Numerical tests using synthetic data sets of the SEG-EAGE 2D salt model, Marmousi model, and Sigsbee 2A model demonstrate its high accuracy and reasonable efficiency. Another special feature of LCB beamlet migration is the availability of information in the local wavenumber domain during migration, which can be used to correct acquisition aperture effect and for other processing. Compared to beamlet migration using the Gabor-Daubechies frame (GDF) propagator, LCB migration is much more efficient because LCB is an orthonormal basis, whereas GDF has redundancy (usually greater than two) in the decomposition.

Target-oriented beamlet migration based on Gabor-Daubechies frame decomposition

We develop beamlet propagation and imaging using Gabor-Daubechies (G-D) frame decomposition based on local perturbation theory and apply it to target-oriented prestack depth migration. The method is formulated with local background velocities and local perturbations in wavefield extrapolation. The localized propagators and phase-correction operators are obtained analytically or semianalytically by one-way operator decomposition and screen approximation in the beamlet and space-beamlet mixed domain. Beamlet wavefields have superior localization properties in both local space and direction (wave-number) over Gaussian beams in the sense that localizations are not limited within short propagation distances in either homogeneous or heterogeneous media. Comparisons of the prestack depth-migrated images for the 2D SEG-EAGE salt model and the Marmousi model indicate that, for seismic-wave propagation and imaging in complex structural environments, the G-D beamlet propagator has higher accuracy and better wide-angle properties than do global propagators. Target-oriented prestack G-D beamlet migration is performed by means of local-angle-domain imaging and controlled superposition of common-dip-angle images based on the local directivity features of the target structures. This considers the spatial and direction localizations of beamlets. As a numerical example, we process the 2D SEG-EAGE salt-model prestack data. The results show that the proposed migration method has considerable advantages in suppressing noise and enhancing structural features. Image quality for subsalt structures, especially for steep faults, is improved through structure-based superposition of common-angle images. This demonstrates the potential and capability of beamlet migration in target-oriented seismic imaging.