Skip Nav Destination
Filter
Filter
Filter
Filter
Filter

Search Results for
Traveltime decomposition in practice

Update search

Filter

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

### NARROW

Peer Reviewed

Format

Subjects

Journal

Publisher

Conference Series

Date

Availability

1-20 of 280 Search Results for

#### Traveltime decomposition in practice

**Follow your search**

Access your saved searches in your account

Would you like to receive an alert when new items match your search?

*Close Modal*

Sort by

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017

Paper Number: SEG-2017-17745788

... reflected

**traveltime**inversion (WERTI). The reflection kernel analysis shows that mode**decomposition**can suppress the artifacts**in**gradient calculation. We design a two-step inversion strategy,**in**which PP reflections are firstly used to invert P wave velocity (Vp ), followed by S wave ve- locity (Vs...
Abstract

ABSTRACT Elastic reflection waveform inversion (ERWI) utilize the reflections to update the low and intermediate wavenumbers in the deeper part of model. However, ERWI suffers from the cycle-skipping problem due to the objective function of waveform residual. Since traveltime information relates to the background model more linearly, we use the traveltime residuals as objective function to update background velocity model using wave equation reflected traveltime inversion (WERTI). The reflection kernel analysis shows that mode decomposition can suppress the artifacts in gradient calculation. We design a two-step inversion strategy, in which PP reflections are firstly used to invert P wave velocity (), followed by S wave velocity () inversion with PS reflections. P/S separation of multi-component seismograms and spatial wave mode decomposition can reduce the nonlinearity of inversion effectively by selecting suitable P or S wave subsets for hierarchical inversion. Numerical example of Sigsbee2A model validates the effectiveness of the algorithms and strategies for elastic WERTI (E-WERTI). Presentation Date: Wednesday, September 27, 2017 Start Time: 4:45 PM Location: 361F Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2018 SEG International Exposition and Annual Meeting, October 14–19, 2018

Paper Number: SEG-2018-2989356

... , 10.1190/segam2016-13778747.1 . Resnick , J. R. , 1993 , Seismic data processing for AVO and AVA analysis ,

**in**J.P. Castagna and M.M. Backus , eds ., Offset-dependent reflectivity: Theory and**practice**of AVO analysis : SEG , Investigations**in**Geophysics No. 8 , 175...
Abstract

ABSTRACT Borehole seismic reflection amplitude data have the potential to help characterize subsurface formations. Placing receivers closer to the target enables seismic data collected in such surveys to be of a higher signal-to-noise ratio (S/N) and less distorted by wave propagation effects. Practical application of amplitude analysis for such purpose, however, requires accounting for anisotropy while generating angle gathers. Additionally, geometrical spreading needs to be accurately corrected for without compromising efficiency. This work describes an algorithm developed for such purposes, computing spreading corrections and angles in anisotropic media using traveltime tables calculated with heterogeneous velocity models. The method was applied to synthetic data to demonstrate its effectiveness. Angle gathers generated using the algorithm can help characterize reservoirs with less uncertainty. Presentation Date: Tuesday, October 16, 2018 Start Time: 9:20:00 AM Location: Poster Station 16 Presentation Type: Poster

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015

Paper Number: SEG-2015-5903601

... the gradient is computed based on Born kernels and us- ing a matrix

**decomposition**of the Fre´chet derivative. The**traveltime**sensitivity kernels The sensitivity kernels or the Fre´chet derivatives relate a per- turbation**in**the recorded data to a perturbation**in**the Earth model. The derivation of the...
Abstract

Summary The instantaneous traveltime is able to reduce the non-linearity of full waveform inversion (FWI) that originates from the wrapping of the phase. However, the adjoint state method in this case requires a total of 5 modeling calculations to compute the gradient. Also, considering the larger modeling cost for anisotropic wavefield extrapolation and the necessity to use a line-search algorithm to estimate a step length that depends on the parameters scale, we propose to calculate the gradient based on the instantaneous traveltime sensitivity kernels. We, specifically, use the sensitivity kernels computed using dynamic ray-tracing to build the gradient. The resulting update is computed using a matrix decomposition and accordingly the computational cost is reduced. We consider a simple example where an anomaly is embedded into a constant background medium and we compute the update for the VTI wave equation parameterized using v h , ? and e. Introduction Full waveform inversion (FWI) aims to invert the full recorded data content to recover an accurate Earth model (Virieux and Operto, 2009). Recently, the improvements in seismic data acquisition, with large offsets and broad frequency content, as well as the availability of the advanced computational devices, paved the way for FWI to be more practical (Pratt et al., 1996; Shin and Min, 2006; Choi and Alkhalifah, 2013). In fact, FWI still suffers from the high nonlinearity of the objective function, which may result in convergence to local minima (Virieux and Operto, 2009). Woodward (1992) introduced wave equation tomography as a reduced form of FWI, where the misfit is the difference between a finite-frequency traveltime of the observed and synthetic data. Choi and Alkhalifah (2013) introduced the instantaneous traveltime as an inversion observable based on a derivative operator applied to the wavefield. The derivative operator associated with a variable damping factor is able to unwrap the phase as well as acting as a tomographic inversion and an FWI one with a single objective function (Alkhalifah and Choi, 2014). An additional issue appears when we start to invert for more than one parameter. The ambiguity or trade-off between the different parameters (Plessix and Cao, 2011; Gholami et al., 2013; Alkhalifah and Plessix, 2014; Métivier et al., 2014) affects the accuracy of the inverted model. M´etivier et al. (2014) showed that the Hessian matrix is crucial to correct for the cross-talk and scale difference between the parameter classes. For transversely isotropic media with vertical axis of symmetry (VTI media), Gholami et al. (2013) and Alkhalifah and Plessix (2014) analyzed the trade-off based on the radiation patterns. Djebbi et al. (2015) derived the sensitivity kernels for anisotropy parameter perturbation and analyzed the tradeoff tradeoff along the wave-path. For conventional surface recorded data, where diving waves (transmission) and reflections are available, a parameterization of the wave equation using the horizontal velocity v h , and the anisotropy parameters ? and e shows the least trade-off (Alkhalifah and Plessix, 2014).

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2018 SEG International Exposition and Annual Meeting, October 14–19, 2018

Paper Number: SEG-2018-2992555

... much harder. Conclusion We have derived the misfit sensitivity and

**traveltime**inversion kernels for VTI elastic media for two sets of anisotropic parameters widely used**in****practice**. Data at different offsets have different implications**in**the kernels. For near offsets, misfit sensitivity kernels...
Abstract

ABSTRACT Finite frequency model inversion offers higher accuracy than ray-based inversion. Starting from the sensitivity kernels for general anisotropic elastic media, we derive the explicit formulas for the sensitivity kernels for VTI media for different inversion parameters. Because of the uncertainties of the amplitude inversion, traveltime inversion is a more robust approach. The misfit sensitivity and traveltime inversion kernels in VTI media are given and their properties are discussed. The information contained in the kernels is closely related to the data offset range. The same kernels can also be used for imaging purposes. Using a synthetic example, we show that images based on misfit kernels do not suffer from low frequency noise and polarity reversal issues. Presentation Date: Wednesday, October 17, 2018 Start Time: 9:20:00 AM Location: Poster Station 7 Presentation Type: Poster

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2011 SEG Annual Meeting, September 18–23, 2011

Paper Number: SEG-2011-1608

...- curate estimates of

**traveltimes**, this still requires full (monopole) source coverage, a condition which is rarely met**in****practice**. As a result, we generally recover only estimates of the true GF, which introduces uncertainties to the information recov- ered from these empirical (interferometric) Green s...
Abstract

ABSTRACT In general, Green''s functions obtained with seismic interferometry are only estimates of the true Green''s function, introducing uncertainties to the information recovered from them. However, there are still many cases in which the source-receiver geometries are suitable for seismic interferometry, usually allowing the recovery of kinematic information. Here we show how to use the singular value decomposition to reenforce the accuracy of traveltimes obtained from interferometric Green''s functions. We apply the combination of seismic interferometry and the singular value decomposition to obtain physically accurate inter-event traveltimes for microquake pairs at a geothermal reservoir. With a synthetic example, we show that the P-wave phase and coda-wave energy information are closer to correct with the singular value decomposition than without. These traveltimes could be used for velocity tomography and event location algorithms to obtain more accurate event locations and locally accurate velocity models.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the SEG International Exposition and Annual Meeting, September 15–20, 2019

Paper Number: SEG-2019-3215231

...

**practice**, they are rarely adopted for their large computational costs and wavefield complexity. Accordingly, most anisotropic imaging algorithms are developed under the acoustic approximation (Alkhalifah, 1998, 2000). On the other hand, seismic wave propagation**in**viscoelastic media commonly suffers from...
Abstract

ABSTRACT Considering the anisotropy of velocity and attenuation, we investigate the wavefield simulation of viscoacoustic wave in vertically transverse isotropic (VTI) attenuative media. The equations with decoupled amplitude dissipation and phase dispersion are derived based on the fractional Laplacian operator and acoustic approximation. To suppress the temporal dispersion caused by second-order central finite-difference (FD) discretization, a k (wavenumber)-space operator (KSO) is introduced to the viscoacoustic wave equations. Due to the variable fractional order, a separable low-rank decomposition method (LRDM) is adopted to realize the numerical implementation. Numerical examples illustrate that our proposed scheme can effectively perform the viscoacoustic wavefield simulation with high temporal accuracy in VTI attenuative media. Presentation Date: Tuesday, September 17, 2019 Session Start Time: 8:30 AM Presentation Start Time: 10:10 AM Location: 304A Presentation Type: Oral

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 4–7, 1998

Paper Number: OTC-8759-MS

... depth requires processing algorithms that honor the physics of wave propagation and velocity models that accurately predict the

**traveltimes**of seismic waves. Prestack depth migration algorithms have advanced**in**theory and**in****practice**to the point where they are useful**in**making accurate images of...
Abstract

Abstract Creating accurate images of subsurface structure in depth requires processing algorithms that honor the physics of wavepropagation and velocity models that accurately predict the traveltimes of seismic waves. Prestack depth migration algorithms have advanced in theory and in practice to the point where they are useful in making accurate images of complex subsurface geometries through complex velocity structures. The theory behind velocity estimation techniques has also evolved rapidly in the past few years. Although many of the theoretical issues are resolved, there still exist many practical difficulties in estimating velocity models for prestack depth migration. Some of these issues are human interface issues. Some reflect a deeper problem, that we don't understand how to reconcile traveltime derived velocities with geology. Introduction Seismic data are recorded wavefields, functions of space and time. In the past, processed data were left in time and even interpreted in time. Velocity information was only needed in a qualitative sense. Instead of being a model of the Earth, velocity models were processing parameters, derived from the data and were supposed to represent (loosely) averages of the "true" Earth velocity model. Of course the whole idea behind the seismic experiment is to produce an image of the Earth in depth. But the transformation of seismic data into an image of the Earth in depth was expensive, error prone, and therefore forced to remain qualitative for several reasons. First, seismic data were often collected along 2-D lines; the insufficient spatial density of data made it impossible to resolve details of 3-D complex structure. This often made it impossible to tell if a structural image / velocity model was correct. Second, due to both theoretical and practical reasons, processing technology was not advanced enough to extract quantitative velocity estimates from seismic data or use that velocity information to create accurate images. In the present, 3-D seismic data acquisition is preferred over 2-D acquisition, and seismic processing technology, particularly prestack depth migration, has advanced sufficiently to make quantitatively-accurate images of subsurface structure. Although 3-D prestack depth migration embodies the correct physics to convert seismic wavefields into images of subsurface structure, an accurate velocity model is needed. Now that industry has the ability to make accurate images there is a greater demand on our ability to estimate good seismic velocity models. Velocity Estimation: Another Kind of Seismic Interpretation Seismic data is often visually "pleasing" because it looks like geology. Much of the task of traditional seismic interpretation is carried out by our eyes and brains without effort. We have preconceived notions of how the structural and stratigraphic boundaries in the Earth should look. When we look at seismic data, we are looking at a picture of these boundaries. The picture may be distorted, but in some sense it is a direct image. We get no such direct image of the velocity in the subsurface. The best measure of velocity we get is the traveltime of seismic waves initiated at the surface and reflected from subsurface structure, at best an indirect measure. Furthermore, since we don't actually know the positions of those reflectors, we have less constraint on the travel paths of seismic waves in a reflection experiment than we do in a VSP or cross well experiment.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017

Paper Number: SEG-2017-17779992

... an efficient operator that based on Hilbert transform to improve the resolution of the 3D RTM.

**In**the numerical example, the proposed 3D RTM with wavefield**decomposition**is applied to the two-layer model and SEG/EAGE salt dataset. The results show the effective wavefield**decomposition**operation...
Abstract

ABSTRACT Reverse-time migration (RTM) is an effective technique for complex subsurface imaging with high accuracy and high resolution. It uses two-way wave-equation in wavefield simulation and employs cross-correlation imaging condition. However, the conventional imaging condition generates low-frequency noises and may form false images around the strong velocity gradients or velocity interfaces in the migration velocity model. The wavefiled components that propagate along different directions should be separated and cross-correlated to improve the final images. In this abstract, we use an efficient operator that based on Hilbert transform to improve the resolution of the 3D RTM. In the numerical example, the proposed 3D RTM with wavefield decomposition is applied to the two-layer model and SEG/EAGE salt dataset. The results show the effective wavefield decomposition operation combined with appropriate imaging condition can generate 3D subsurface images with high signal-to-noise ratio. Presentation Date: Tuesday, September 26, 2017 Start Time: 3:55 PM Location: 361A Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010

Paper Number: SEG-2010-1478

... general workflow of the analysis algorithm is to pick a window centered on the interpretation seed along the Z axis and then perform the spectrum

**decomposition****in**the window.**In**the**practice**, the window analysis works best when the interpretation target is almost flat and the signal wavelets travel along...
Abstract

INTRODUCTION Summary Spectral decomposition is a window analysis to characterize the wavelet response of an interpretation target. Spectral analysis can deliver statistically robust results with finer frequency resolution if the analysis window can exclusively sample the signal wavelets while attenuating noise. The general workflow of the analysis algorithm is to pick a window centered on the interpretation seed along the Z axis and then perform the spectrum decomposition in the window. However, the same algorithm will not work properly to sample the signal wavelets when the interpretation targets have strong dips. In order to sample the signal wavelets while attenuating the noise, we developed an algorithm to sample the signal wavelet along the ray path in which the wavelet travels. The ray starts from a point in the picked horizon and follows a path with the minimum travel time, which is computed from the picked horizon as the exploding source. We use a wedge model to compare our algorithm with the traditional method. The result shows that for a wedge dipping at an angle, the measured tuning thickness using a window along the z axis overestimates the true tuning thickness of the dipping bed by a function of the dipping angle. The difference is due to the different wavelets sampled using different methods. Spectral decomposition is a window analysis to characterize the wavelet response of an interpretation target (Partyka et al., 1999). Using a window to exclusively sample the wavelet responsive to the interpretation target, the ideal spectral analysis can deliver statistically robust results with finer frequency resolution. The key to success is to find the window with the right shape and right length to sample the signal wavelets while attenuating the noise. The general workflow of the analysis algorithm is to pick a window centered on the interpretation seed along the Z axis and then perform the spectrum decomposition in the window. In the practice, the window analysis works best when the interpretation target is almost flat and the signal wavelets travel along the Z axis. However, the same algorithm will not work properly to sample the signal wavelets when the interpretation targets have strong dips. For example, a spectral decomposition of the dipping sand wedge in Figure 1 uses the analysis windows along the Z axis (red arrows in Figure 1) and thus samples obliquely signal wavelets (blue wavelets in Figure 1). Also as shown in Figure 1, the bigger the dip angle is and the more the signal wavelets deviate from Z axis. In other words, the traditional analysis window will capture the biased signal wavelets. To fix the bias in sampling, we want to develop an algorithm to sample the signal wavelet along the path in which the wavelet travels, that is, in the direction normal to the sand wedge in the example. Method When the picked horizon is geometrically rugged, the traditional window analysis sliding along the Z axis will capture the biased signal wavelet and other unwanted wavelets from the interpretation target.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2012 SEG Annual Meeting, November 4–9, 2012

Paper Number: SEG-2012-1123

...

**in**Fig- ure 2 represents z0 and which can be automatically or man- ually picked**in****practice**. Each maxmum represents a curve**in**angle-domain CIGs denoted by the blue line**in**Figure 2a. Figure 2: (a). Angel-domain CIGs. (b). Semblance analysis panel. The blue dashed line**in**(a) represents the moveout...
Abstract

SUMMARY The main difficulty with an iterative waveform inversion is that it tends to get stuck in a local minima associated with the waveform misfit function. This is because the waveform misfit function is highly non-linear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. The residual movemout analysis in the angle-domain common image gathers provides a robust estimate of the depth residual which is converted to the reflection traveltime residual for the velocity inversion. We present numerical examples to demonstrate its efficiency in inverting seismic data for complex velocity model.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2013 SEG Annual Meeting, September 22–27, 2013

Paper Number: SEG-2013-1088

...

**traveltimes**while an ideal full waveform inversion uses the complete seismic record, though**in****practice**only a part of the record is used after some preprocessing. FWI provides higher resolution**in**theory but it is less robust than**traveltime**tomography**in****practice**. Frequency-dependent**traveltime**tomography...
Abstract

Summary Traditional ray-theory-based infinite frequency traveltime tomography is likely to be invalid for near-surface studies due to relatively long seismic wavelengths compared with the scale of near-surface velocity heterogeneities (e.g. Gao et al. 2007). As opposed to infinite frequency traveltime tomography (IFTT), we applied a newly developed frequency-dependent traveltime tomography (FDTT) followed by full waveform inversion (FWI) to 2D near-surface compressional wave seismic data. The target of these data is a shallow concrete tunnel with void space inside. The position and dimension of the tunnel are known. This application demonstrates a combined strategy for near-surface seismic data in that FDTT provides a starting model for FWI.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2018 SEG International Exposition and Annual Meeting, October 14–19, 2018

Paper Number: SEG-2018-2995247

... arrivals and the reflection

**traveltimes**simultaneously**in**the velocity inversion. The results of synthetic tests show that the joint MDLT can accurately recover some layered velocity models, with higher stability and accuracy than the first-arrival MDLT. true model raypath deformable layer...
Abstract

Summary Seismic tomography is an important method of subsurface velocity model building. However, it is challenging to determine the geometry of velocity layers in complex areas using only the first-arrivals. We propose a joint multiscale deformable layer tomography (MDLT) to use the first arrivals and the reflection traveltimes simultaneously in the velocity inversion. The results of synthetic tests show that the joint MDLT can accurately recover some layered velocity models, with higher stability and accuracy than the first-arrival MDLT.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2008 SEG Annual Meeting, November 9–14, 2008

Paper Number: SEG-2008-2311

...

**practical**tool for depth imaging, but conventional implementations suffer**in**areas of complicated geology, since only single arrivals are used**in**the implementation.**In**conventional approaches, rays are traced from a surface point to imaging points**in**the subsurface. The**traveltime**table for imaging points...
Abstract

SUMMARY We used the beam methodology to develop multi-arrival Kirchhoff beam migration. Compared to conventional single-arrival Kirchhoff migration, our method is able to handle multi-arrivals caused by model complexity. We provide a formula for optimal beam width that achieves both accuracy and efficiency. The resulting structural imaging in sub-salt areas is of better quality than that from single-arrival Kirchhoff migration. INTRODUCTION Kirchhoff migration is an efficient and practical tool for depth imaging, but conventional implementations suffer in areas of complicated geology, since only single arrivals are used in the implementation. In conventional approaches, rays are traced from a surface point to imaging points in the subsurface. The traveltime table for imaging points is generated by ray tracing, and the input seismic trace is projected to these image points according to the calculated traveltimes. When more than one ray passes an image point, only one ray path may be chosen (either first arrival or most-energetic arrival). In this way, only one seismic arrival is associated with each image point. Therefore, some energy corresponding to other arrivals may be missing or mis-positioned during the imaging process. Multi-arrival traveltimes, from a source (or detector) to an image point, may be used to overcome the problems associated with a single-arrival traveltime (Xu et. al., 2001). However, in general, this approach has issues in a production environment since multi-valued traveltimes are difficult to store and interpolate (Gray et. al., 2002). Beam migration has advantages in handling multi-arrival energy in imaging (Hill, 1990). Here we use the beam methodology to provide multi-arrivals in Kirchhoff migration. In our approach, the input wavefield near a surface point is decomposed into local plane waves by local slant stacking, and each plane wave contributes to one potential single-arrival in Kirchhoff migration. For each plane wave, a central ray is traced from the surface point to imaging points in the subsurface, and the traveltime in a neighborhood along the central ray is calculated. The input seismic plane wave is projected to image points according to the calculated traveltime; since each plane wave corresponds to one arrival, the imaging process uses the energy of all arrivals. In this way, a seismic trace can contribute many times to an image point through all the arrivals, with each arrival being associated with one plane wave. To maintain accuracy and efficiency, each plane wave propagates only within a beam, which is defined by a neighborhood along the central ray. The choice of the width of the beam is critical to the implementation of Kirchhoff beam migration. We choose an optimal beam width using the criterion that the summation of all beams is sufficient to provide minimum coverage of the imaging area. Here, we derived a formula that computes the optimal beam width from ray tracing. METHODOLOGY Plane-wave decomposition The input seismic data can be decomposed into local plane waves at beam centers by using local slant stacking. Data regularization is necessary for such processing. The input data are sorted into common-offset panels, with one trace per bin center in each panel.

Proceedings Papers

Vladimir Bashkardin, Sergey Fomel, Thomas J. Browaeys, Fuchun Gao, Scott A. Morton, Sergey Terentyev, Alexander Vladimirsky

Publisher: Society of Exploration Geophysicists

Paper presented at the 2012 SEG Annual Meeting, November 4–9, 2012

Paper Number: SEG-2012-1537

... SUMMARY Computation of multi-arrival

**traveltimes**for angle-domain Kirchhoff migration is most simply performed by ray tracing from subsurface points. However, the high computational cost of this approach limits its feasibility**in****practice**. Fortunately this ray-tracing procedure can be replaced...
Abstract

SUMMARY Computation of multi-arrival traveltimes for angle-domain Kirchhoff migration is most simply performed by ray tracing from subsurface points. However, the high computational cost of this approach limits its feasibility in practice. Fortunately this ray-tracing procedure can be replaced by the faster computation of escape variables in phase space. In this paper, we provide details of our implementation of an escape-equation solver and address the challenges of the scalability of this method in 3-D. We introduce the "narrow band" concept, which enables solution of large-scale 3-D problems. The resultant algorithm produces accurate traveltimes and provides input for angle-domain imaging.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2009 SEG Annual Meeting, October 25–30, 2009

Paper Number: SEG-2009-4004

... to a synthetic example. Models consist of uniformly gridded cells

**in**three dimensions with a constant velocity for each cell.**Traveltimes**of the model are calculated by applying finite-difference methods of the seismic-ray eikonal equation. The inversion minimizes a functional that includes a least...
Abstract

ABSTRACT This article described a 3D traveltime tomography algorithm using LSQR with regularization and apply it to a synthetic example. Models consist of uniformly gridded cells in three dimensions with a constant velocity for each cell. Traveltimes of the model are calculated by applying finite-difference methods of the seismic-ray eikonal equation. The inversion minimizes a functional that includes a least-square penalty function and horizontal and vertical roughness constraints. The minimization leads to a very large system of linear equations that is solved through LSQR. Normally distributed random numbers are generated and added to the synthetic arrival-times to create noisy synthetic data. The inversion works on these noisy data to produce a 3D model. The velocity anomaly of the inverted model is clearly defined, indicating that the algorithm is valid and effective.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2014 SEG Annual Meeting, October 26–31, 2014

Paper Number: SEG-2014-0590

... Summary

**Decomposition**of interfering wavefields is significant**in**VSP data processing. One of main strategies implementing multicomponent separation is using the difference of polarization directions of P-wave and SV-wave. We develop a wavefield**decomposition**method based on global...
Abstract

Summary Decomposition of interfering wavefields is significant in VSP data processing. One of main strategies implementing multicomponent separation is using the difference of polarization directions of P-wave and SV-wave. We develop a wavefield decomposition method based on global optimization scheme (genetic algorithm). This method includes two steps: first estimate the velocity and propagation angle parameters by inversion, and then calculate downward P-wave, upward P-wave, downward SV-wave and upward SV-wave through solving the corresponding overdetermined equations. The inversion is implemented by the globally optimal algorithm to obtain the global optimal solution. Wavefield separation tests for synthetic and filed VSP data demonstrate that our method is effective, even for equally spaced receivers and inclined well.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2003 SEG Annual Meeting, October 26–31, 2003

Paper Number: SEG-2003-2168

... ? ? ? ?Ll ,0,0 1 ? , where L is half a maximal offset shot-receiver. Let us minimize the objective ? ? ? ? dllablalaJ l 2 0 242 1 ? ?? . (3) From (3) it follows b l aa 7 5 21 . (4) Non-hyperbolic

**traveltime**picking The estimate (4) is the LS one, but**in****practice**, the coefficient standing at 2l is determined...
Abstract

Summary Accurate traveltime picking is a critical issue in terms of the input for the kinematical inversion (Jones, 2003). For the industrial processing, the procedure must also be an automated one to deal with large data volumes. We present a practical approach to the traveltime picking accounting for the fourth-order term in the CMP normal moveout formula. The method can be generalized for traveltime curves of any (even) order. The approach enables to split conventional two-dimensional optimization by the two successive one-dimensional optimization steps using the semblance operator. Once implemented as traveltime analysis software, the method prevents a geophysicist from interpreting two-dimensional spectra at each point of analysis.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010

Paper Number: SEG-2010-3242

...

**practice**is based on the generation of offset gathers first, which are then converted to angle domain. The reason for this is that angle gathers are difficult to gener- ate; while methods for angle gather generation**in**WEM exists, due to the computational expense involved they are employed mostly**in**a...
Abstract

SUMMARY Multidimensional (prestack) migration volumes, encountered typically as angle or offset gathers at each image point, are an essential tool for velocity analysis (and other geophysical analysis). Such gathers are easily obtained from Kirchhoff migration; however, they are challenging to generate in migrations performed using wave based methods. We present a new method of constructing common image angle gathers for oneway wave equation migration, based on the Fourier decomposition of the source and receiver waves at the image point. We show some examples of angle gathers for synthetic datasets. INTRODUCTION In regions with significant geologic complexity, velocity analysis using depth migration (MVA) is superior to methods which operate on prestack data. Migration in general, and depth migration in particular, simplify prestack data by correcting for the effects of offset, reflector dip, and propagation from source to receiver in a heterogeneous medium. When the migration velocity is incorrect, migration will incorrectly position the surface data in depth. Some MVA techniques attempt to flatten Kirchhoff common-offset depth migration gathers by measuring depth error as a function of offset and perturbing the migration velocity accordingly. Kirchhoff offset gathers exhibit artifacts in complex examples, which are not seen in wave equation depth-migrated images, as described in (Stolk and Symes, 2004). Moreover, from a consistency point of view, in a complex region where wave equation methods are used for imaging, it is desirable that the same approach be used for the velocity update. Hence the interest in generating common image point gathers using wave equation methods. Previously published approaches to generate angle gathers from shot record wave equation migration extend zero-time/zero-offset prestack correlation imaging condition (Claerbout, 1985). These approaches correlate upgoing and downgoing wavefields at multiple ”subsurface offsets” (Rickett and Sava, 2002) and/or multiple ”time shifts” (Sava and Fomel, 2006), and then apply a slant stack operation to convert subsurface offset or time shift to incidence angle. This approach suffers from two primary disadvantages: 1) the slant stack may itself introduce spurious artifacts, 2) the correlation imaging condition is expensive, particularly when 3D angle gathers (incidence angle and azimuth angle) are desired. We take an alternate approach to computing 3D angle gathers, which we believe overcomes both of these deficiencies. At each image point, we compute local propagation direction vectors for the upgoing and downgoing wavefields in shot record migration. From these two vectors, we infer the incidence angle, azimuth angle, and dip angle of the corresponding reflection event. A related approach for computing the local direction of the upcoming and downgoing waves was proposed by Yoon and Marfurt in the context of reverse time migration (RTM) (Yoon et al., 2004; Yoon and Marfurt, 2006). Our approach is designed specifically for ”one-way” wave equation migration, or WEM. In this case, unlike RTM, we do not have full access to wavefields as a function of position and depth. As a consequence, while similar from a theoretical perspective, our algorithm to compute angle gathers differs significantly from Yoon and Marfurt’s.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2003 SEG Annual Meeting, October 26–31, 2003

Paper Number: SEG-2003-2004

... basis functions for this vectorial space can be obtained by singular value

**decomposition**(SVD). The new approximation is obtained**in**the form of a**traveltime**series t x , (1)1 1 2 2 3 3( ) ( ) ( ) ( ) c f x c f x c f x ? ? ? ? ? with exponent ? equal to 1 or 2. The functions fi are the basis functions...
Abstract

Summary The traditional hyperbolic traveltime correction is generally inappropriate for flattening reflected events at large offsets. For this, non-hyperbolic traveltime equations may be used. These equations have usually three terms, making the processing more cumbersome and costly. I apply here a new two-term non-hyperbolic traveltime approximation for velocity analysis and moveout correction. Practical aspects and benefits of this approach are illustrated by an application to ground penetrating radar (GPR) field data. Introduction Most high-order traveltime approximations are described by three coefficients: the zero-offset traveltime t 0 , the moveout velocity, and a third parameter.

Proceedings Papers

Vladimir Bashkardin, Sergey Fomel, Thomas J. Browaeys, Fuchun Gao, Paul Williamson, Roman Kazinnik, Scott A. Morton, Sergey Terentyev, Alexander Vladimirsky

Publisher: Society of Exploration Geophysicists

Paper presented at the 2012 SEG Annual Meeting, November 4–9, 2012

Paper Number: SEG-2012-1522

... SUMMARY

**In**complicated geologic environments with multipathing**in****traveltime**fields, Kirchhoff migration can improve imaging results, if the integration is performed**in**the angle domain. Angle-domain migration operates on a**traveltime**table expressed as a function of image points and...
Abstract

SUMMARY In complicated geologic environments with multipathing in traveltime fields, Kirchhoff migration can improve imaging results, if the integration is performed in the angle domain. Angle-domain migration operates on a traveltime table expressed as a function of image points and subsurface angles. For the necessary function to be computed, ray tracing can simply be performed from subsurface locations using different initial take-off angles. Unfortunately, the computational cost of such a bottom-up approach may be prohibitive. However, initial-value ray tracing can be reformulated as escape equations in phase space, which allow for a grid-based solution at a possibly lower cost. In this paper, we derive escape equations for general 2-D and 3-D anisotropic media, derive the reduced phase-space formulation of escape equations, introduce a stable upwind finite-difference discretization, and suggest the use of a hybrid Eulerian-Lagrangian approach for a practical and accurate numerical solution.

Advertisement