Gaussian Beam Migration Research Articles

A practical data-driven optimization strategy for Gaussian beam migration

Gaussian beam migration (GBM) is an efficient and accurate depth imaging technique, which allows us to resolve steep-dip structures and image multiple arrivals. Similar to Kirchhoff migration, GBM projects reflection events into the subsurface along traveltime isochrons. For data with low folds or signal-to-noise ratio (S/N), it produces migration artifacts, making it difficult for subsequent interpretation and attribute analysis. We have developed a data-driven optimization strategy to solve this problem. First, at the source and beam center locations, we estimate the instantaneous emergence angles of specular rays using semblance analysis for local common-shot and common-receiver gathers. Then, a quality control factor is designed to enhance the imaging results of coherent signals around the specular rays. Synthetic and field data examples demonstrate that our optimization strategy enables us to improve the imaging quality of GBM, especially for sparsely acquired and low-S/N data.

ADCIGs extraction and reflection tomography modeling for elastic wave

Based on the theory of elastic wave, we derive the migration angle formula of P- and S-wave in the Gaussian beam migration and implement the ADCIGs (angle domain common imaging gathers) extraction for Gaussian beam of PP- and PS-wave firstly. Then, we derive the reflection tomography equations for elastic wave velocity analysis. They are used for the tomography velocity modeling base on the Gaussian beam ADCIGs. Making reflection tomography and depth migration into the same velocity modeling process, this method can not only use ADCIGs of elastic wave to update the velocities, but also can apply the migration results of tomography in each iteration as quality control, until the end of whole process in velocity modeling and finally we can get the prestack depth migration results after tomography. Synthetic and field examples validate the correctness and practicability of this method.

Angle-domain common-image gathers from anisotropic Gaussian beam migration and its application to anisotropy-induced imaging errors analysis

An approach for extracting angle-domain common-image gathers (ADCIGs) from anisotropic Gaussian beam prestack depth migration (GB-PSDM) is presented in this paper. The propagation angle is calculated in the process of migration using the real-value traveltime information of Gaussian beam. Based on the above, we further investigate the effects of anisotropy on GB-PSDM, where the corresponding ADCIGs are extracted to assess the quality of migration images. The test results of the VTI syncline model and the TTI thrust sheet model show that anisotropic parameters ε, δ, and tilt angle 𝜃, have a great influence on the accuracy of the migrated image in anisotropic media, and ignoring any one of them will cause obvious imaging errors. The anisotropic GB-PSDM with the true anisotropic parameters can obtain more accurate seismic images of subsurface structures in anisotropic media.

A fast algorithm for prestack Gaussian beam migration adopting the steepest descent approximation

In the past, prestack Gaussian beam migration adopted the steepest descent approximation to reduce the dimension of the integrals and speed up the computation. However, the simplified formula by the steepest descent approximation was still in the frequency domain, and it had to be evaluated at each frequency. To solve this problem, we present a fast algorithm by changing the order of the integrals. The innermost integral is regarded as a two-dimensional continuous function with respect to the real part and the imaginary part of the total traveltime. A lookup table corresponding to the value of the innermost integral is constructed at the sampling points. The value of the innermost integral at one imaging point can be obtained through interpolation in the constructed lookup table. The accuracy and efficiency of the fast algorithm are validated with the Marmousi dataset. The application to the Sigsbee2A dataset shows a good result.

Least-squares Gaussian beam migration

Least-squares Gaussian beam migration

Least-squares Gaussian beam migration

Least-squares migration (LSM) can be effective to mitigate the limitation of finite-seismic acquisition, balance the subsurface illumination, and improve the spatial resolution of the image, but it requires iterations of migration and demigration to obtain the desired subsurface reflectivity model. The computational efficiency and accuracy of migration and demigration operators are crucial for applying the algorithm. We have developed a test of the feasibility of using the Gaussian beam as the wavefield extrapolating operator for the LSM, denoted as least-squares Gaussian beam migration. Our method combines the advantages of the LSM and the efficiency of the Gaussian beam propagator. Our numerical evaluations, including two synthetic data sets and one marine field data set, illustrate that the proposed approach could be used to obtain amplitude-balanced images and to broaden the bandwidth of the migrated images in particular for the low-wavenumber components.

Q-compensated migration by Gaussian beam summation method

Migration by the Gaussian beam summation method (MGBSM) combines the high efficiency and flexibility of Gaussian beam migration with the high accuracy of wave equation reverse-time migration, which can overcome the problems of caustics, handle all arrivals, yield good images of steep flanks, and is readily extendible to target-oriented implementation. The viscoacoustic prestack migration is of practical significance because it considers the viscosity of subsurface media. In this paper, we propose a MGBSM to perform seismic data compensation for frequency dependent absorption and dispersion. First, we derive the expressions for the attenuation equation and analyse the precision of the viscoacoustic Green function based on Gaussian beams. Then, the principle and procedure of compensation is presented. Finally we propose Q-compensated MGBSM. Numerical examples indicate that Q-compensated MGBSM has a higher imaging resolution than acoustic MGBSM when the viscosity of the subsurface is considered.

Common‐shot Fresnel beam migration based on wave‐field approximation in effective vicinity under complex topographic conditions

ABSTRACTGaussian beam migration is a versatile imaging method for geologically complex land areas, which overcomes the limitation of Kirchhoff migration in imaging multiple arrivals and has no steep‐dip limits of one‐way wave‐equation migration. However, its imaging accuracy depends on the geometry of Gaussian beam that is determined by the initial parameter of dynamic ray tracing. As a result, its applications in exploration areas with strong variations in topography and near‐surface velocity are limited. Combined with the concept of Fresnel zone and the theory of wave‐field approximation in effective vicinity, we present a more robust common‐shot Fresnel beam imaging method for complex topographic land areas in this paper. Compared with the conventional Gaussian beam migration for irregular topography, our method improves the beam geometry by limiting its effective half‐width with Fresnel zone radius. Moreover, through a quadratic travel‐time correction and an amplitude correction that is based on the wave‐field approximation in effective vicinity, it gives an accurate method for plane‐wave decomposition at complex topography, which produces good imaging results in both shallow and deep zones. Trials of two typical models and its application in field data demonstrated the validity and robustness of our method.

An amplitude-preserved adaptive focused beam seismic migration method

Gaussian beam migration (GBM) is an effective and robust depth seismic imaging method, which overcomes the disadvantage of Kirchhoff migration in imaging multiple arrivals and has no steep-dip limitation of one-way wave equation migration. However, its imaging quality depends on the initial beam parameters, which can make the beam width increase and wave-front spread with the propagation of the central ray, resulting in poor migration accuracy at depth, especially for exploration areas with complex geological structures. To address this problem, we present an adaptive focused beam method for shot-domain prestack depth migration. Using the information of the input smooth velocity field, we first derive an adaptive focused parameter, which makes a seismic beam focused along the whole central ray to enhance the wave-field construction accuracy in both the shallow and deep regions. Then we introduce this parameter into the GBM, which not only improves imaging quality of deep reflectors but also makes the shallow small-scale geological structures well-defined. As well, using the amplitude-preserved extrapolation operator and deconvolution imaging condition, the concept of amplitude-preserved imaging has been included in our method. Typical numerical examples and the field data processing results demonstrate the validity and adaptability of our method.

Attenuation compensation in multicomponent Gaussian beam prestack depth migration

Gaussian beam prestack depth migration is an accurate imaging method of subsurface media. Prestack depth migration of multicomponent seismic data improves the accuracy of imaging subsurface complex geological structures. Viscoelastic prestack depth migration is of practical significance because it considers the viscosity of the subsurface media. We use Gaussian beam migration to compensate for the attenuation in multicomponent seismic data. First, we use the Gaussian beam method to simulate the wave propagation in a viscoelastic medium and introduce the complex velocity Q-related and exact viscoelastic Zoeppritz equation. Second, we discuss PP- and PS-wave Gaussian beam prestack depth migration algorithms for common-shot gathers to derive expressions for the attenuation and compensation. The algorithms correct the amplitude attenuation and phase distortion caused by Q, and realize multicomponent Gaussian beam prestack depth migration based on the attenuation compensation and account for the effect of inaccurate Q on migration. Numerical modeling suggests that the imaging resolution of viscoelastic Gaussian beam prestack depth migration is high when the viscosity of the subsurface is considered.

Accurate acoustic and elastic beam migration without slant stack for complex topography

Recent trends in seismic exploration have led to the collection of more surveys, often with multi-component recording, in onshore settings where both topography and subsurface targets are complex, leading to challenges for processing methods. Gaussian beam migration (GBM) is an alternative to single-arrival Kirchhoff migration, although there are some issues resulting in unsatisfactory GBM images. For example, static correction will give rise to the distortion of wavefields when near-surface elevation and velocity vary rapidly. Moreover, Green’s function compensated for phase changes from the beam center to receivers is inaccurate when receivers are not placed within some neighborhood of the beam center, that is, GBM is slightly inflexible for irregular acquisition system and complex topography. As a result, the differences of both the near-surface velocity and the surface slope from the beam center to the receivers and the poor spatial sampling of the land data lead to inaccuracy and aliasing of the slant stack, respectively. In order to improve the flexibility and accuracy of GBM, we propose accurate acoustic, PP and polarity-corrected PS beam migration without slant stack for complex topography. The applications of this method to one-component synthetic data from a 2D Canadian Foothills model and a Zhongyuan oilfield fault model, one-component field data and an unseparated multi-component synthetic data demonstrate that the method is effective for structural and relatively amplitude-preserved imaging, but significantly more time-consuming.

True-amplitude vector-acoustic imaging: Application of Gaussian beams

Acoustic Gaussian beam migration is an attractive imaging method because it is flexible with input geometry, efficient, and accurate in imaging multipath arrivals. However, one of the hurdles that this method must overcome in production processing is its extension to use multimeasurement data, as recently allowed by novel acquisition technologies. This is inevitable when the compensation of the ghost effect is best corrected within a true-amplitude imaging process, a necessity for amplitude-variation-with-offset work. For this purpose, I introduced a novel formalism for vector-acoustic imaging, based on Green’s function theory, which can remove the ghost effect and produce amplitudes on reflectors that are proportional to the reflection coefficients. I established a theoretical framework with Gaussian beam representations of Green’s functions, including the weighted beam-stacking approach that reduced the cost of computation. I extended my formulas to use the steep-descent (i.e., stationary phase) approximation. Then, I explained the impact of this approximation on the illumination and the event continuity and sharpness. I also studied the special case of acoustic imaging corresponding to using single-measurement (i.e., pressure) data. I applied the derived formulations to realistic synthetic multisensor data (North Sea) using a research code of Gaussian beam migration. The numerical examples demonstrated that I can improve the illumination of the final images and obtain wide-bandwidth reflectivity maps.

Gabor-frame-based Gaussian packet migration

We present a Gaussian packet migration method based on Gabor frame decomposition and asymptotic propagation of Gaussian packets. A Gaussian packet has both Gaussian-shaped time–frequency localization and space–direction localization. Its evolution can be obtained by ray tracing and dynamic ray tracing. In this paper, we first briefly review the concept of Gaussian packets. After discussing how initial parameters affect the shape of a Gaussian packet, we then propose two Gabor-frame-based Gaussian packet decomposition methods that can sparsely and accurately represent seismic data. One method is the dreamlet–Gaussian packet method. Dreamlets are physical wavelets defined on an observation plane and can represent seismic data efficiently in the local time–frequency space–wavenumber domain. After decomposition, dreamlet coefficients can be easily converted to the corresponding Gaussian packet coefficients. The other method is the Gabor-frame Gaussian beam method. In this method, a local slant stack, which is widely used in Gaussian beam migration, is combined with the Gabor frame decomposition to obtain uniform sampled horizontal slowness for each local frequency. Based on these decomposition methods, we derive a poststack depth migration method through the summation of the backpropagated Gaussian packets and the application of the imaging condition. To demonstrate the Gaussian packet evolution and migration/imaging in complex models, we show several numerical examples. We first use the evolution of a single Gaussian packet in media with different complexities to show the accuracy of Gaussian packet propagation. Then we test the point source responses in smoothed varying velocity models to show the accuracy of Gaussian packet summation. Finally, using poststack synthetic data sets of a four-layer model and the two-dimensional SEG/EAGE model, we demonstrate the validity and accuracy of the migration method. Compared with the more accurate but more time-consuming one-way wave-equation-based migration, such as beamlet migration, the Gaussian packet method proposed in this paper can correctly image the major structures of the complex model, especially in subsalt areas, with much higher efficiency. This shows the application potential of Gaussian packet migration in complicated areas.

Gaussian beam prestack depth migration of converted wave in TI media

Abstract Increasing amounts of multi-component seismic data are being acquired on land and offshore because more complete seismic wavefield information is beneficial for structural imaging, fluid detection, and reservoir monitoring. S-waves are typically influenced more by anisotropy in a medium than are P-waves; as a result, the anisotropy cannot be ignored during the converted PS-wave imaging. Gaussian beam migration, an elegant and efficient depth migration method, is becoming a new topic in the study of PS-wave migration; its accuracy is comparable to that of wave-equation migration, and its flexibility is comparable to that of Kirchhoff migration. In this paper, we introduce an anisotropic Gaussian beam prestack depth migration (GB-PSDM) method for the converted PS-wave, in which the anisotropic media can be a transversely isotropic (TI) medium with a vertical or tilted symmetry axis. We present the PS-wave common shot gathers GB-PSDM imaging condition and derive the ray tracing of P- and SV-waves in two-dimensional TI media. The migration impulse responses of P- and SV-propagation modes in TI media with both vertical and tilted symmetry axes are presented. The results of numerical examples indicate that the method introduced here offers significant improvements in the quality of converted PS-wave imaging compared with an isotropic algorithm.

Seismic imaging of mud volcano boundary in the east of Caspian Sea by common diffraction surface stack method

The problem of seismic imaging in complex structures such as folded faulting areas, salt domes, or mud volcano-bearing areas cannot be properly solved by the conventional seismic processing methods. The reverse time migration, Gaussian beam migration, the extended search strategy in the optimized common reflection surface (CRS) stack, and the partial CRS stack methods are among the new methods introduced for seismic imaging in complex structures. Among them, the CRS stack method is frequently used for seismic imaging. However, besides its great advantage in enhancing the quality of seismic section, it faces with some problem in imaging of complex structures, especially in the existence of conflicting dips. The CRS method transforms pre-processed multi-coverage data into a zero-offset section by summing along stacking surfaces instead of only along a common reflection point trajectory. The extended parameter search strategy in the CRS method and the partial CRS stack method were introduced to solve the problem of conflicting dips in the CRS method. However, some examples showed that these methods could not completely solve the problem of conflicting dips. In this study, a new introduced method is used to completely solve the problem of conflicting dips in complex structures. The new stacking surface is the approximation of diffraction response of a diffraction point. The surface is made by well-known three CRS attributes, where the radius of normal and normal incidence point waves is equals. The third parameter is the emergence angle of the central ray that the stacking surface is built for each angle, thus making an operator volume. Therefore, the operator gathers more energy that might get lost by other stacking surfaces. The new method was applied on a seismic data from a complex geological structure from northeast of Iran. This area contains mud volcano, an indicator for gas reservoir. Mud also absorbs the seismic energy and deteriorates the quality of the seismic section. Therefore, imaging the boundary of the mud volcano is questionable. By applying post-stack time migration on the stacked section obtained by the new method, the advantage of the stacking operator has been evaluated for imaging in complex structures. These advantages were more highlighted in depth migration applied on the new introduced operator volume common diffraction surface (CDS)-stacked section. The results showed that not only the boundary of the mud but also the faults that were completely unclear in previous results were imaged well.

Multiwave velocity analysis based on Gaussian beam prestack depth migration

Prestack depth migration of multicomponent seismic data improves the imaging accuracy of subsurface complex geological structures. An accurate velocity field is critical to accurate imaging. Gaussian beam migration was used to perform multicomponent migration velocity analysis of PP- and PS-waves. First, PP- and PS-wave Gaussian beam prestack depth migration algorithms that operate on common-offset gathers are presented to extract offset-domain common-image gathers of PP- and PS-waves. Second, based on the residual moveout equation, the migration velocity fields of P- and S-waves are updated. Depth matching is used to ensure that the depth of the target layers in the PP- and PS-wave migration profiles are consistent, and high-precision P- and S-wave velocities are obtained. Finally, synthetic and field seismic data suggest that the method can be used effectively in multiwave migration velocity analysis.

Multi-component Gaussian beam prestack depth migration

As the depth migration of multi-component seismic data can obtain better images of the subsurface structures with multi-wave information in seismic records, an effective multi-component Gaussian beam migration method is presented in this paper. Firstly, a detailed numerical analysis on the local slant stack is carried out, which demonstrates that the Gaussian beam migration method has good directionality and computational efficiency through decomposing seismic records into different outgoing directional local plane waves. Then two different Gaussian beam prestack depth migration algorithms are presented, corresponding to the PP- and PS-waves, after a wavefield separation is effected with an affine coordinate system transform. Finally, tests of synthetic and field seismic data show that the method introduced above would be an accurate and efficient prestack depth migration alternative for multi-component seismic data.

Azimuth–opening angle domain imaging in 3D Gaussian beam depth migration

Common-image gathers indexed by opening angle and azimuth at imaging points in 3D situations are the key inputs for amplitude-variation-with-angle and velocity analysis by tomography. The Gaussian beam depth migration, propagating each ray by a Gaussian beam form and summing the contributions from all the individual beams to produce the wavefield, can overcome the multipath problem, image steep reflectors and, even more important, provide a convenient and efficient strategy to extract azimuth?opening angle domain common-image gathers (ADCIGs) in 3D seismic imaging. We present a method for computing azimuth and opening angle at imaging points to output 3D ADCIGs by computing the source and receiver wavefield direction vectors which are restricted in the effective region of the corresponding Gaussian beams. In this paper, the basic principle of Gaussian beam migration (GBM) is briefly introduced; the technology and strategy to yield ADCIGs by GBM are analyzed. Numerical tests and field data application demonstrate that the azimuth?opening angle domain imaging method in 3D Gaussian beam depth migration is effective.

Multiarrival Kirchhoff beam migration

Kirchhoff-type prestack depth migration is the method most popular for outputting offset gathers for velocity-model updating because of its flexibility and efficiency. However, conventional implementations of Kirchhoff migration use only single arrivals. This limits its ability to image complex structures such as subsalt areas. We use the beam methodology to develop a multiarrival Kirchhoff beam migration. The theory and algorithm of our beam migration are analogs to Gaussian beam migration, but we focus on attaining kinematic accuracy and implementation efficiency. The input wavefield of every common offset panel is decomposed into local plane waves at beam centers on the acquisition surface by local slant stacking. Each plane wave contributes a potential single-arrival in Kirchhoff migration. In this way, our method is able to handle multiarrivals caused by model complexity and, therefore, to overcome the limitation of conventional single-arrival Kirchhoff migration. The choice of the width of the beam is critical to the implementation of beam migration. We provide a formula for optimal beam width that achieves both accuracy and efficiency when the velocity model is reasonably smooth. The resulting structural imaging in subsalt and other structurally complex areas is of better quality than that from single-arrival Kirchhoff migration.

Application of Gaussian-Beam Migration to Multiscale Imaging of the Lithosphere beneath the Hi-CLIMB Array in Tibet

Abstract In this study, we apply Gaussian-beam (GB) migration of scattered teleseismic P waves to image the crust and upper mantle beneath Tibet using data from the Hi-CLIMB experiment. We use teleseismic P waves from three groups of earthquakes to the southeast, northeast, and northwest of the Hi-CLIMB array, each within a narrow range of azimuth and distance, to obtain stacked radial receiver functions, which we then use to image the lithosphere by GB migration. We produced images at several different frequency bands in order to constrain the multiscale scattering properties of the lithosphere. For each frequency band, three GB images are generated, each from earthquake sources in a distinct back-azimuth group. The three images are then stacked to form a composite image. The imaged Moho is generally strong and continuous under much of the Lhasa terrane in southern Tibet, corresponding to a well-defined Moho. A major disrupted zone in Moho scattering, extending over 200 km in length, is evident in the vicinity of the Bangong–Nujiang suture, where there is also increased crustal scattering. The disrupted zone marks the diffuse, subsurface join between stable portions of mantle lithosphere under southern and central Tibet, respectively. At the northern end of the profile in the Qiangtang terrane there is an increase in Moho reflectivity but at a shallower depth than under the Lhasa terrane. Comparable length scales of about 200 km between regions with disrupted and smooth-varying Moho suggest that the mechanically strong mantle lithosphere and the crust respond differently to collision, with the upper crust currently undergoing pervasive strain over the entire plateau.