Gaussian beam migration of common-shot records

Geophysics ◽  
2005 ◽  
Vol 70 (4) ◽  
pp. S71-S77 ◽  
Author(s):  
Samuel H. Gray
Keyword(s):  
Gaussian Beam ◽  
Seismic Velocity ◽  
Data Sets ◽  
Model Data ◽  
Near Surface ◽  
Depth Migration ◽  
Migration Method ◽  
Gaussian Beam Migration ◽  
Wavefield Extrapolation ◽  
Natural Way

Gaussian beam migration is a depth migration method whose accuracy rivals that of migration by wavefield extrapolation — so-called “wave-equation migration” — and whose efficiency rivals that of Kirchhoff migration. This migration method can image complicated geologic structures, including very steep dips, in areas where the seismic velocity varies rapidly. However, applications of prestack Gaussian beam migration either have been limited to common-offset common-azimuth data volumes, and thus are inflexible, or suffer from multiarrival inaccuracies in a common-shot implementation. In order to optimize both the flexibility and accuracy of Gaussian beam migration, I present a common-shot implementation that handles multipathing in a natural way. This allows the migration of data sets that can include a variety of azimuths, and it allows a simplified treatment of near-surface issues. Application of this method to model data typical of Canadian Foothills structures and to model data that includes a complicated salt body demonstrates the accuracy and versatility of the migration.

Gaussian beam migration

Geophysics ◽  
1990 ◽  
Vol 55 (11) ◽  
pp. 1416-1428 ◽  
Author(s):  
N. Ross Hill
Keyword(s):  
Gaussian Beam ◽  
Wave Field ◽  
Seismic Source ◽  
Velocity Model ◽  
Downward Continuation ◽  
Gaussian Beams ◽  
Seismic Velocities ◽  
Migration Method ◽  
Gaussian Beam Migration ◽  
Lateral Variations

Just as synthetic seismic data can be created by expressing the wave field radiating from a seismic source as a set of Gaussian beams, recorded data can be downward continued by expressing the recorded wave field as a set of Gaussian beams emerging at the earth’s surface. In both cases, the Gaussian beam description of the seismic‐wave propagation can be advantageous when there are lateral variations in the seismic velocities. Gaussian‐beam downward continuation enables wave‐equation calculation of seismic propagation, while it retains the interpretive raypath description of this propagation. This paper describes a zero‐offset depth migration method that employs Gaussian beam downward continuation of the recorded wave field. The Gaussian‐beam migration method has advantages for imaging complex structures. Like finite‐difference migration, it is especially compatible with lateral variations in velocity, but Gaussian beam migration can image steeply dipping reflectors and will not produce unwanted reflections from structure in the velocity model. Unlike other raypath methods, Gaussian beam migration has guaranteed regular behavior at caustics and shadows. In addition, the method determines the beam spacing that ensures efficient, accurate calculations. The images produced by Gaussian beam migration are usually stable with respect to changes in beam parameters.

Refraction wavefield migration

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. Q27-Q37
Author(s):  
Yang Shen ◽  
Jie Zhang
Keyword(s):  
Signal To Noise Ratio ◽  
Surface Velocity ◽  
Data Set ◽  
Near Surface ◽  
Depth Migration ◽  
Reflection Data ◽  
Imaging Tool ◽  
Imaging Results ◽  
Migration Method ◽  
Single Method

Refraction methods are often applied to model and image near-surface velocity structures. However, near-surface imaging is very challenging, and no single method can resolve all of the land seismic problems across the world. In addition, deep interfaces are difficult to image from land reflection data due to the associated low signal-to-noise ratio. Following previous research, we have developed a refraction wavefield migration method for imaging shallow and deep interfaces via interferometry. Our method includes two steps: converting refractions into virtual reflection gathers and then applying a prestack depth migration method to produce interface images from the virtual reflection gathers. With a regular recording offset of approximately 3 km, this approach produces an image of a shallow interface within the top 1 km. If the recording offset is very long, the refractions may follow a deep path, and the result may reveal a deep interface. We determine several factors that affect the imaging results using synthetics. We also apply the novel method to one data set with regular recording offsets and another with far offsets; both cases produce sharp images, which are further verified by conventional reflection imaging. This method can be applied as a promising imaging tool when handling practical cases involving data with excessively weak or missing reflections but available refractions.

Extended local Rytov Fourier migration method

Geophysics ◽  
1999 ◽  
Vol 64 (5) ◽  
pp. 1535-1545 ◽  
Author(s):  
Lian‐Jie Huang ◽  
Michael C. Fehler ◽  
Peter M. Roberts ◽  
Charles C. Burch
Keyword(s):  
Phase Changes ◽  
Fast Fourier Transform Algorithm ◽  
Scalar Wave ◽  
Depth Migration ◽  
Frequency Space ◽  
Rytov Approximation ◽  
Migration Method ◽  
The Stability ◽  
Wavefield Extrapolation ◽  
Lateral Variations

We develop a novel depth‐migration method termed the extended local Rytov Fourier (ELRF) migration method. It is based on the scalar wave equation and a local application of the Rytov approximation within each extrapolation interval. Wavefields are Fourier transformed back and forth between the frequency‐space and frequency‐wavenumber domains during wavefield extrapolation. The lateral slowness variations are taken into account in the frequency‐space domain. The method is efficient due to the use of a fast Fourier transform algorithm. Under the small angle approximation, the ELRF method leads to the split‐step Fourier (SSF) method that is unconditionally stable. The ELRF method and the extended local Born Fourier (ELBF) method that we previously developed can handle wider propagation angles than the SSF method and account for the phase and amplitude changes due to the lateral variations of slowness, whereas the SSF method only accounts for the phase changes. The stability of the ELRF method is controlled more easily than that of the ELBF method.

2D anisotropic multicomponent Gaussian-beam migration under complex surface conditions

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. S89-S102 ◽  
Author(s):  
Jianguang Han ◽  
Qingtian Lü ◽  
Bingluo Gu ◽  
Jiayong Yan ◽  
Hao Zhang
Keyword(s):  
Gaussian Beam ◽  
Complex Surface ◽  
Dynamic Features ◽  
Surface Conditions ◽  
Depth Migration ◽  
Surface Areas ◽  
Local Plane ◽  
Gaussian Beam Migration ◽  
Wave Migration ◽  
Irregular Topography

Elastic-wave migration in anisotropic media is a vital challenge, particularly for areas with irregular topography. Gaussian-beam migration (GBM) is an accurate and flexible depth migration technique, which is adaptable for imaging complex surface areas. It retains the dynamic features of the wavefield and overcomes the multivalued traveltimes and caustic problems of Kirchhoff migration. We have extended the GBM method to work for 2D anisotropic multicomponent migration under complex surface conditions. We use Gaussian beams to calculate the wavefield from irregular topography, and we use two schemes to derive the down-continued recorded wavefields. One is based on the local slant stack as in classic GBM, in which the PP- and PS-wave seismic records within the local region are directly decomposed into local plane-wave components from irregular topography. The other scheme does not perform the local slant stack. The Green’s function is calculated with a Gaussian beam summation emitted from the receiver point at the irregular surface. Using the crosscorrelation imaging condition and combining with the 2D anisotropic ray-tracing algorithm, we develop two 2D anisotropic multicomponent Gaussian-beam prestack depth migration (GB-PSDM) methods, i.e., using the slant stack and nonslant stack, for irregular topography. Numerical tests demonstrate that our anisotropic multicomponent GB-PSDM can accurately image subsurface structures under complex topography conditions.

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

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. D133-D143
Author(s):  
David Li ◽  
Xiao Tian ◽  
Hao Hu ◽  
Xiao-Ming Tang ◽  
Xinding Fang ◽  
...  
Keyword(s):  
Gaussian Beam ◽  
Field Data ◽  
Gas Production ◽  
Dipole Source ◽  
Data Sets ◽  
Data Set ◽  
Receiver Array ◽  
Gaussian Beam Migration ◽  
Sonic Logging ◽  
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.

Least-squares Gaussian beam migration in viscoacoustic media

Geophysics ◽  
2020 ◽  
Vol 86 (1) ◽  
pp. S17-S28
Author(s):  
Yubo Yue ◽  
Yujin Liu ◽  
Yaonan Li ◽  
Yunyan Shi
Keyword(s):  
Green’S Function ◽  
Least Squares ◽  
Gaussian Beam ◽  
Green's Function ◽  
Seismic Waves ◽  
Image Resolution ◽  
Data Sets ◽  
Phase Dispersion ◽  
Using Data ◽  
Gaussian Beam Migration

Because of amplitude decay and phase dispersion of seismic waves, conventional migrations are insufficient to produce satisfactory images using data observed in highly attenuative geologic environments. We have developed a least-squares Gaussian beam migration method for viscoacoustic data imaging, which can not only compensate for amplitude decay and phase dispersion caused by attenuation, but it can also improve image resolution and amplitude fidelity through linearized least-squares inversion. We represent the viscoacoustic Green’s function by a summation of Gaussian beams, in which an attenuation traveltime is incorporated to simulate or compensate for attenuation effects. Based on the beam representation of the Green’s function, we construct the viscoacoustic Born forward modeling and adjoint migration operators, which can be effectively evaluated by a time-domain approach based on a filter-bank technique. With the constructed operators, we formulate a least-squares migration scheme to iteratively solve for the optimal image. Numerical tests on synthetic and field data sets demonstrate that our method can effectively compensate for the attenuation effects and produce images with higher resolution and more balanced amplitudes than images from acoustic least-squares Gaussian beam migration.

Least-squares Gaussian beam migration

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. S87-S100 ◽  
Author(s):  
Hao Hu ◽  
Yike Liu ◽  
Yingcai Zheng ◽  
Xuejian Liu ◽  
Huiyi Lu
Keyword(s):  
Least Squares ◽  
Gaussian Beam ◽  
Spatial Resolution ◽  
Field Data ◽  
Synthetic Data ◽  
Data Sets ◽  
Data Set ◽  
Seismic Acquisition ◽  
Gaussian Beam Migration ◽  
Least Squares 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.

True-amplitude Gaussian-beam migration

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. S11-S23 ◽  
Author(s):  
Samuel H. Gray ◽  
Norman Bleistein
Keyword(s):  
Wave Equation ◽  
Gaussian Beam ◽  
Opening Angle ◽  
Amplitude Wave ◽  
Amplitude Variation With Offset ◽  
Imaging Condition ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Beam Depth ◽  
Gaussian Beam Migration

Gaussian-beam depth migration and related beam migration methods can image multiple arrivals, so they provide an accurate, flexible alternative to conventional single-arrival Kirchhoff migration. Also, they are not subject to the steep-dip limitations of many (so-called wave-equation) methods that use a one-way wave equation in depth to downward-continue wavefields. Previous presentations of Gaussian-beam migration have emphasized its kinematic imaging capabilities without addressing its amplitude fidelity. We offer two true-amplitude versions of Gaussian-beam migration. The first version combines aspects of the classic derivation of prestack Gaussian-beam migration with recent results on true-amplitude wave-equation migration, yields an expression involving a crosscorrelation imaging condition. To provide amplitude-versus-angle (AVA) information, true-amplitude wave-equation migration requires postmigration mapping from lateral distance (between image location and source location) to subsurface opening angle. However, Gaussian-beam migration does not require postmigration mapping to provide AVA data. Instead, the amplitudes and directions of the Gaussian beams provide information that the migration can use to produce AVA gathers as part of the migration process. The second version of true-amplitude Gaussian-beam migration is an expression involving a deconvolution imaging condition, yielding amplitude-variation-with-offset (AVO) information on migrated shot-domain common-image gathers.

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