Gaussian Beam Imaging Research Articles

Two dimensional elastic dynamically focused beam migration in transversely isotropic (TI) media

The anisotropic ray tracing equations of elastic waves are derived for calculating the central ray's travel time, trajectory, and parameters P and Q. Based on the anisotropic ray tracing algorithm, we proposed a transversely isotropic elastic dynamically focused beam migration for two dimensional media. Based on the two dimensional Kirchhoff-Helmholtz integral of elastic waves, the elastic imaging weight coefficients are used to reduce the crosstalk noise. Then, based on the previous research, we introduced a sign function to eliminate the effect of polarity reversal in qPqSV wave migration. Through model tests, it can be found that the proposed method can process the multicomponent seismic data and image the complex structures for anisotropic media. The optimized dynamic ray tracing algorithm is superior to the conventional one in computational efficiency. Furthermore, the proposed method eliminates the limitations of the Gaussian beam imaging. This method not only does not affect the accuracy of shallow imaging, but also enhances the energy focusing and the amplitude of deep layers. The model tests have shown the accuracy and effectiveness of our proposed method.

Elastic Least-Squares Gaussian Beam Imaging With Point Spread Functions

Elastic least-squares migration (ELSM) has the potential to produce high-resolution images. It can be implemented in either data-domain or image-domain but is much faster in the image domain. A critical step of image-domain ELSM is the calculation of the Hessian. However, it is impractical to directly calculate the Hessian due to its high storage and costs. In this letter, the Hessian is efficiently constructed with elastic point spread functions (PSFs) calculated by a combination of multicomponent Gaussian beam Born modeling (of scattering points with elastic parameters perturbation) and elastic Gaussian beam migration. Based on this, we propose a fast image-domain ELSM method. A hyper-Laplacian priori regularization is used to produce sparse solutions. We evaluate the proposed method with the Marmousi2 model, and the results demonstrate the capability of the method to image complex structures with improved resolution relative to the initial migrated image.

Gaussian beam imaging of fractures near the wellbore using sonic logging tools after removing dispersive borehole waves

The ability to image near-wellbore fractures is critical for wellbore integrity monitoring as well as for energy production and waste disposal. Single-well imaging uses a sonic logging instrument consisting of a source and a receiver array to image geologic structures around a wellbore. We use cross-dipole sources because they can excite waves that can be used to image structures farther away from the wellbore than traditional monopole sources. However, the cross-dipole source also will excite large-amplitude, slowly propagating dispersive waves along the surface of the borehole. These waves will interfere with the formation reflection events. We have adopted a new fracture imaging procedure using sonic data. We first remove the strong amplitude borehole waves using a new nonlinear signal comparison method. We then apply Gaussian beam migration to obtain high-resolution images of the fractures. To verify our method, we first test our method on synthetic data sets modeled using a finite-difference approach. We then validate our method on a field data set collected from a fractured natural gas production well. We are able to obtain high-quality images of the fractures using Gaussian beam migration compared with Kirchhoff migration for the synthetic and field data sets. We also found that a low-frequency source (around 1 kHz) is needed to obtain a sharp image of the fracture because high-frequency wavefields can interact strongly with the fluid-filled borehole.

Nonbulk motion system for simultaneously measuring the refractive index and thickness of a sample using tunable optics and spatial signal processing-based Gaussian beam imaging.

This paper presents a novel approach to simultaneously measuring the thickness and refractive index of a sample. The design uses an electronically controlled tunable lens (ECTL) and a microelectromechanical-system-based digital micromirror device (DMD). The method achieves the desired results by using the DMD to characterize the spatial profile of a Gaussian laser beam at different focal length settings of the ECTL. The ECTL achieves tunable lensing through minimal motion of liquid inside a transparent casing, whereas the DMD contains an array of movable micromirrors, which make it a reflective spatial light modulator. As the proposed system uses an ECTL, a DMD, and other fixed optical components, it measures the thickness and refractive index without requiring any motion of bulk components such as translational and rotational stages. A motion-free system improves measurement repeatability and reliability. Moreover, the measurement of sample thickness and refractive index can be completely automated because the ECTL and DMD are controlled through digital signals. We develop and discuss the theory in detail to explain the measurement methodology of the proposed system and present results from experiments performed to verify the working principle of the method. Refractive index measurement accuracies of 0.22% and 0.2% were achieved for two BK-7 glass samples used, and the thicknesses of the two samples were measured with a 0.1mm accuracy for each sample, corresponding to a 0.39% and 0.78% measurement error, respectively, for the aforementioned samples.

2-D Gaussian beam imaging of multicomponent seismic data in anisotropic media

2-D Gaussian beam imaging of multicomponent seismic data in anisotropic media

Fracture detection by Gaussian beam imaging of seismic data and image spectrum analysis

Localization of fractured areas is of primary interest in the study of oil and gas geology in carbonate environments. Hydrocarbon reservoirs in these environments are embedded within an impenetrable rock matrix but possess a rich system of various microheterogeneities, i.e., cavities, cracks, and fractures. Cavities accumulate oil, but its flow is governed by a system of fractures. A distinctive feature of wave propagation in such media is the excitation of the scattered/diffracted waves by the microheterogeneities. This scattering could be a reliable attribute for characterization of the fine structure of reservoirs, but it has extremely low energy and any standard data processing renders them practically invisible in comparison with images produced by specular reflections. Therefore, any attempts to use these waves for image congestion of microheterogeneities should first have a preliminary separation of the scattering and specular reflections. In this paper, the approach to performing this separation is based on the asymmetric summation. It is implemented by double focusing of Gaussian beams. To do this, the special weights are computed by propagating Gaussian beams from the target area towards the acquisition system separately for sources and receivers. The different mutual positioning of beams in each pair introduces a variety of selective images that are destined to represent some selected singular primitives of the target objects such as fractures, cavities, and edges. In this way, one can construct various wave images of a target reservoir, particularly in scattered/diffracted waves. Additional removal of remnants of specular reflections is done by means of spectral analysis of the scattered/diffracted waves' images to recognize and cancel extended lineaments. Numerical experiments with Sigsbee 2A synthetic seismic data and some typical structures of the Yurubcheno-Tokhomskoye oil field in East Siberia are presented and discussed.

Gaussian beam imaging of walkaway VSP data based on finite differences in time domain

The approach to true amplitude seismic imaging for walkaway vertical seismic profile multicomponent data is presented and discussed. This approach is a migration procedure based on weighted summation of pre-stack data. True amplitude weights are computed with application of Gaussian beams. Gaussian beams are computed in time domain via finite-difference modeling. Numerical experiments with synthetic data generated for realistic salt model are presented and discussed.

Bessel beam spectral-domain high-resolution optical coherence tomography with micro-optic axicon providing extended focusing range

Endoscopic imaging in tubular structures, such as the tracheobronchial tree, could benefit from imaging optics with an extended depth of focus (DOF) to accommodate the varying sizes of tubular structures across patients and along the tree within the same patient. Yet the extended DOF needs to be accomplished without sacrificing resolution while maintaining sufficient sensitivity and speed of imaging. In this Letter, we report on the measured resolution and sensitivity achieved with a custom-made micro-optic axicon lens designed to theoretically achieve an 8 mm DOF. A measured invariant resolution of approximately 8 microm is demonstrated across a 4 mm measured DOF using the micro-optic axicon while achieving an invariant sensitivity of approximately 80 dB with a 25 mW input power. Double-pass Bessel beam spectral-domain optical coherence tomography with an axicon micro-optic lens (i.e., <1 mm in diameter) is, for the first time to our knowledge, demonstrated in a biological sample demonstrating invariant resolution and signal-to-noise ratio across a 4 mm measured DOF, which is compared to Gaussian beam imaging.

Paraxial imaging: Gaussian beams versus paraxial-spherical waves

The features of Gaussian beam imaging are not generally well appreciated. Here we suggest that it is convenient to view a Gaussian beam as a generalization of a paraxial-spherical source with a complex source location. This approach allows one to show that the modification of the geometric optics thin lens equations necessary to adequately describe the imaging of a Gaussian beam is due to the latter being a coherent source of finite extent. An experiment is outlined which highlights the differences between simple geometric and Gaussian beam imaging. Our approach gives students a firm conceptual foundation from which to discuss the concept of spatial coherence in laser beams.