Focused gaussian beams for seismic imaging

Nowack, Robert L.

doi:10.1190/1.3059356

Cited by 19 publications

(9 citation statements)

References 15 publications

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“…This extends the work of Nowack [1] in which focusing of Gaussian beams propagated from the source, and receiver surface is used to allow the narrowest portions of the beams to occur at the depth of a specific target structure. The beam fronts at the beam waists are also planar leading to more stable beam summations for imaging.…”

Section: Introductionmentioning

confidence: 82%

“…The application of dynamically focused Gaussian beams has been initially investigated for seismic imaging and is an extension of the focused beam approach of Nowack [1]. The shifting of the beam waists away from the source and receiver aperture adds flexibility to Gaussian beam algorithms allowing for the narrowest portions of the beams to occur at the depth of a specific target structure.…”

Section: Discussionmentioning

confidence: 99%

“…Assuming that the initial beam parameters have been determined from dynamic ray tracing for beam parameters specified at the scattering points, then the algorithm for imaging-focused Gaussian beams from Nowack [1] can be extended to dynamic focusing. For generally nonplanar initial beams at the source or receiver locations launched at some angle to the aperture plane, the quadratic part of the initial beam with respect to the horizontal x coordinate can be written as…”

Section: Gaussian Beam Imaging With Dynamically Focused Beamsmentioning

confidence: 99%

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Dynamically Focused Gaussian Beams for Seismic Imaging

Nowack

2011

International Journal of Geophysics

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An initial study is performed in which dynamically focused Gaussian beams are investigated for seismic imaging. Focused Gaussian beams away from the source and receiver plane allow the narrowest and planar portions of the beams to occur at the depth of a specific target structure. To match the seismic data, quadratic phase corrections are required for the local slant stacks of the surface data. To provide additional control of the imaging process, dynamic focusing is investigated where all subsurface points are specified to have the same planar beam fronts. This gives the effect of using nondiffracting beams, but actually results from the use of multiple focusing depths for each Gaussian beam. However, now different local slant stacks must be performed depending on the position of the subsurface scattering point. To speed up the process, slant stacking of the local data windows is varied to match the focusing depths along individual beams when tracked back into the medium. The approach is tested with a simple model of 5-point scatterers which are then imaged with the data, and then to the imaging of a single dynamically focused beam for one shot gather computed from the Sigsbee2A model.

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Section: Introductionmentioning

confidence: 82%

Section: Discussionmentioning

confidence: 99%

Section: Gaussian Beam Imaging With Dynamically Focused Beamsmentioning

confidence: 99%

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Dynamically Focused Gaussian Beams for Seismic Imaging

Nowack

2011

International Journal of Geophysics

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“…If a purely imaginary number is chosen as the initial value of

M_{n n}^{0}

for a single Gaussian packet, the packet's spatial profile will have zero curvature at the beginning position and spread less. On the other hand, a complex initial value represents a curve front of the packet at the beginning position, and the packet may focus on a certain depth according to the value of

Re (M_{n n}^{0})

during the evolution, which is similar to a focused beam (Nowack ). In this paper, we choose

Re (M_{n n}^{0}) = 0

.…”

Section: Seismic Data Representation Using Gaussian Packetmentioning

confidence: 99%

Gabor‐frame‐based Gaussian packet migration

Geng

Gao

2014

Geophysical Prospecting

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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.

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“…Ever since the basic framework of GBM was presented by Hill (1990Hill ( , 2001, it has been extended to irregular topographic conditions (Gray 2005;Yue et al 2012;Yang et al 2014) and trueamplitude migration (Gray and Bleistein 2009). In addition, many new seismic beam imaging methods have been developed, such as fast beam migration (Gao et al 2006(Gao et al , 2007, focused beam migration (Nowack 2008), and laser beam migration (Xiao et al 2014), which expand the members of the beam migration family. Most of them, however, are based on the GBM framework and use a constant initial beam parameter, which makes a seismic beam focused either at the initial position or at a certain depth.…”

Section: Introductionmentioning

confidence: 99%

An amplitude-preserved adaptive focused beam seismic migration method

et al. 2015

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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 wavefield 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.

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Focused gaussian beams for seismic imaging

Cited by 19 publications

References 15 publications

Dynamically Focused Gaussian Beams for Seismic Imaging

Dynamically Focused Gaussian Beams for Seismic Imaging

Gabor‐frame‐based Gaussian packet migration

An amplitude-preserved adaptive focused beam seismic migration method

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