Zero-offset sections with a deblurring filter in the time domain

The conventional common-midpoint stack is not equivalent to the zero-offset section due to the existence of velocity uncertainty. To obtain a zero-offset reflection section that preserves most reflections and diffractions, we have developed a velocity-independent workflow for reconstructing a high-quality zero-offset reflection section from prestack data with a deblurring filter. This workflow constructs a migration image volume by prestack time migration using a series of constant-velocity models. A deblurring filter for each constant-velocity model is applied to each time-migration image to get a deblurred image volume. To preserve all events in the image volume, each deblurred image panel is demigrated and then summed over the velocity axis. Compared with the workflow without a deblurring filter, the composite zero-offset reflection section has higher resolution and fewer migration artifacts. We evaluate applications of our method to synthetic and field data to validate its effectiveness.

Download Full-text

Migration velocity analysis based on focusing diffractions generated using the CRS wavefront attributes: Application to real land data

Geophysics ◽

10.1190/geo2020-0696.1 ◽

2021 ◽

pp. 1-50

Author(s):

German Garabito ◽

José Silas dos Santos Silva ◽

Williams Lima

Keyword(s):

Time Domain ◽

Real Data ◽

Normal Incidence ◽

Velocity Model ◽

Migration Velocity ◽

Velocity Analysis ◽

Velocity Models ◽

Time Migration ◽

Migration Velocity Analysis ◽

The Time Domain

In land seismic data processing, the prestack time migration (PSTM) image remains the standard imaging output, but a reliable migrated image of the subsurface depends on the accuracy of the migration velocity model. We have adopted two new algorithms for time-domain migration velocity analysis based on wavefield attributes of the common-reflection-surface (CRS) stack method. These attributes, extracted from multicoverage data, were successfully applied to build the velocity model in the depth domain through tomographic inversion of the normal-incidence-point (NIP) wave. However, there is no practical and reliable method for determining an accurate and geologically consistent time-migration velocity model from these CRS attributes. We introduce an interactive method to determine the migration velocity model in the time domain based on the application of NIP wave attributes and the CRS stacking operator for diffractions, to generate synthetic diffractions on the reflection events of the zero-offset (ZO) CRS stacked section. In the ZO data with diffractions, the poststack time migration (post-STM) is applied with a set of constant velocities, and the migration velocities are then selected through a focusing analysis of the simulated diffractions. We also introduce an algorithm to automatically calculate the migration velocity model from the CRS attributes picked for the main reflection events in the ZO data. We determine the precision of our diffraction focusing velocity analysis and the automatic velocity calculation algorithms using two synthetic models. We also applied them to real 2D land data with low quality and low fold to estimate the time-domain migration velocity model. The velocity models obtained through our methods were validated by applying them in the Kirchhoff PSTM of real data, in which the velocity model from the diffraction focusing analysis provided significant improvements in the quality of the migrated image compared to the legacy image and to the migrated image obtained using the automatically calculated velocity model.

Download Full-text

Viscoacoustic waveform inversion of velocity structures in the time domain

Geophysics ◽

10.1190/geo2013-0030.1 ◽

2014 ◽

Vol 79 (3) ◽

pp. R103-R119 ◽

Cited By ~ 28

Author(s):

Jianyong Bai ◽

David Yingst ◽

Robert Bloor ◽

Jacques Leveille

Keyword(s):

Finite Difference ◽

Time Domain ◽

Field Data ◽

Wave Equations ◽

Finite Difference Methods ◽

Waveform Inversion ◽

Data Set ◽

Velocity Models ◽

Difference Methods ◽

The Time Domain

Because of the conversion of elastic energy into heat, seismic waves are attenuated and dispersed as they propagate. The attenuation effects can reduce the resolution of velocity models obtained from waveform inversion or even cause the inversion to produce incorrect results. Using a viscoacoustic model consisting of a single standard linear solid, we discovered a theoretical framework of viscoacoustic waveform inversion in the time domain for velocity estimation. We derived and found the viscoacoustic wave equations for forward modeling and their adjoint to compensate for the attenuation effects in viscoacoustic waveform inversion. The wave equations were numerically solved by high-order finite-difference methods on centered grids to extrapolate seismic wavefields. The finite-difference methods were implemented satisfying stability conditions, which are also presented. Numerical examples proved that the forward viscoacoustic wave equation can simulate attenuative behaviors very well in amplitude attenuation and phase dispersion. We tested acoustic and viscoacoustic waveform inversions with a modified Marmousi model and a 3D field data set from the deep-water Gulf of Mexico for comparison. The tests with the modified Marmousi model illustrated that the seismic attenuation can have large effects on waveform inversion and that choosing the most suitable inversion method was important to obtain the best inversion results for a specific seismic data volume. The tests with the field data set indicated that the inverted velocity models determined from the acoustic and viscoacoustic inversions were helpful to improve images and offset gathers obtained from migration. Compared to the acoustic inversion, viscoacoustic inversion is a realistic approach for real earth materials because the attenuation effects are compensated.

Download Full-text

Shot-gather time migration of planar reflectors without velocity model

Geophysics ◽

10.1190/1.3549641 ◽

2011 ◽

Vol 76 (2) ◽

pp. S93-S101 ◽

Cited By ~ 10

Author(s):

Andrej Bóna

Keyword(s):

Synthetic Data ◽

Velocity Model ◽

Migration Velocity ◽

Time Migration ◽

Second Derivatives ◽

Migration Method ◽

Prestack Time Migration ◽

Zero Offset ◽

2D And 3D ◽

Homogeneous Media

Standard migration techniques require a velocity model. A new and fast prestack time migration method is presented that does not require a velocity model as an input. The only input is a shot gather, unlike other velocity-independent migrations that also require input of data in other gathers. The output of the presented migration is a time-migrated image and the migration velocity model. The method uses the first and second derivatives of the traveltimes with respect to the location of the receiver. These attributes are estimated by computing the gradient of the amplitude in a shot gather. The assumptions of the approach are a laterally slowly changing velocity and reflectors with small curvatures; the dip of the reflector can be arbitrary. The migration velocity corresponds to the root mean square (rms) velocity for laterally homogeneous media for near offsets. The migration expressions for 2D and 3D cases are derived from a simple geometrical construction considering the image of the source. The strengths and weaknesses of the methods are demonstrated on synthetic data. At last, the applicability of the method is discussed by interpreting the migration velocity in terms of the Taylor expansion of the traveltime around the zero offset.

Download Full-text

A unified approach to 3-D seismic reflection imaging, Part I: Basic concepts

Geophysics ◽

10.1190/1.1444001 ◽

1996 ◽

Vol 61 (3) ◽

pp. 742-758 ◽

Cited By ~ 94

Author(s):

Peter Hubral ◽

Jörg Schleicher ◽

Martin Tygel

Keyword(s):

Time Domain ◽

Seismic Reflection ◽

Velocity Model ◽

Unified Approach ◽

Seismic Record ◽

Kirchhoff Type ◽

Velocity Models ◽

Reflection Imaging ◽

The Time Domain ◽

Image Transformations

Given a 3-D seismic record for an arbitrary measurement configuration and assuming a laterally and vertically inhomogeneous, isotropic macro‐velocity model, a unified approach to amplitude‐preserving seismic reflection imaging is provided. This approach is composed of (1) a weighted Kirchhoff‐type diffraction‐stack integral to transform (migrate) seismic reflection data from the measurement time domain into the model depth domain, and of (2) a weighted Kirchhoff‐type isochrone‐stack integral to transform (demigrate) the migrated seismic image from the depth domain back into the time domain. Both the diffraction‐stack and isochrone‐stack integrals can be applied in sequence (i.e., they can be chained) for different measurement configurations or different velocity models to permit two principally different amplitude‐preserving image transformations. These are (1) the amplitude‐preserving transformation (directly in the time domain) of one 3-D seismic record section into another one pertaining to a different measurement configuration and (2) the transformation (directly in the depth domain) of a 3-D depth‐migrated image into another one for a different (improved) macro‐velocity model. The first transformation is referred to here as a “configuration transform” and the second as a “remigration.” Additional image transformations arise when other parameters, e.g., the ray code of the elementary wave to be imaged, are different in migration and demigration. The diffraction‐ and isochrone‐stack integrals incorporate a fundamental duality that involves the relationship between reflectors and the corresponding reflection‐time surfaces. By analytically chaining these integrals, each of the resulting image transformations can be achieved with only one single weighted stack. In this way, generalized‐Radon‐transform‐type stacking operators can be designed in a straightforward way for many useful image transformations. In this Part I, the common geometrical concepts of the proposed unified approach to seismic imaging are presented in simple pictorial, nonmathematical form. The more thorough, quantitative description is left to Part II.

Download Full-text

Receiver-extension strategy for time-domain full waveform inversion using a relocalization approach

Geophysics ◽

10.1190/geo2020-0922.1 ◽

2021 ◽

pp. 1-85

Author(s):

Ludovic Métivier ◽

Romain Brossier

Keyword(s):

Time Domain ◽

Field Data ◽

Waveform Inversion ◽

Computational Cost ◽

Velocity Model ◽

Full Waveform Inversion ◽

Geological Environment ◽

Extension Method ◽

Velocity Models ◽

Full Waveform

A receiver-extension strategy is presented as an alternative to recently promoted source-extension strategies, in the framework of high resolution seismic imaging by full waveform inversion. This receiver-extension strategy is directly applicable in time-domain full waveform inversion, and unlike source-extension methods it incurs negligible extra computational cost. After connections between difference source-extension strategies are reviewed, the receiver-extension method is introduced and analyzed for single-arrival data. The method results in a misfit function convex with respect to the velocity model in this context. The method is then applied to three exploration scale synthetic case studies representative of different geological environment, based on: the Marmousi model, the BP 2004 salt model, and the Valhall model. In all three cases the receiver-extension strategy makes it possible to start full waveform inversion with crude initial models, and reconstruct meaningful subsurface velocity models. The good performance of the method even considering inaccurate amplitude prediction due to noise, imperfect modeling, and source wavelet estimation, bodes well for field data applications.

Download Full-text

IMAGING BENEATH COMPLEX STRUCTURE: A CASE HISTORY

The APPEA Journal ◽

10.1071/aj80014 ◽

1981 ◽

Vol 21 (1) ◽

pp. 112

Author(s):

K. Lamer ◽

B. Gibson ◽

R. Chambers

Keyword(s):

Velocity Structure ◽

Deep Structure ◽

Complex Structure ◽

Velocity Model ◽

Important Conclusion ◽

Depth Migration ◽

Interval Velocity ◽

Velocity Models ◽

Time Migration ◽

Zero Offset

Migration is recognised as the essential step in converting seismic, data into a representation of the earth's subsurface structure. Ironically, conventional migration often fails where migration is needed most—when the data are recorded over complex structures. Processing field data shot in Central America, and synthetic data derived for that section, demonstrates that time migration actually degrades the image of the deep structure that lies below a complicated overburden.In the Central American example, velocities increase nearly two-fold across an arched and thrust-faulted interface. Wavefront distortion introduced by this feature gives rise to distorted reflections from depth. Even with interval velocity known perfectly, no velocity is proper for time migrating the data here; time migration is the wrong process because it does not honour Snell's Law. Depth migration of the stacked data, on the other hand, produces a reasonable image of the deeper section. The depth migration, however, leaves artifacts that could be attributed to problems that are common in structurally complicated areas: (1) departures of the stacked section from the ideal, a zero-offset section; (2) incorrect specification of velocities; and (3) loss of energy transmitted through the complex zoneFor such an inhomogeneous velocity structure, shortcomings in CDP stacking are directly related to highly non- hyperbolic moveout. As with migration velocity, no proper stacking velocity can be developed for these data, even from the known interval-velocity model. Proper treatment of nonzero-offset reflection data could be accomplished by depth migration before stacking. Simple ray-theoretical correction of the complex moveouts, however, can produce a stack that is similar to the desired zero-offset section.Overall, the choice of velocity model most strongly influences the results of depth migration. Processing the data with a range of plausible velocity models, however, leads to an important conclusion: although the velocities can never be known exactly, depth migration is essential for clarifying structure beneath complex overburden.

Download Full-text

Frequency-domain wave-equation traveltime inversion with a monofrequency component

Geophysics ◽

10.1190/geo2020-0708.1 ◽

2021 ◽

Vol 86 (6) ◽

pp. R913-R926

Author(s):

Jianhua Wang ◽

Jizhong Yang ◽

Liangguo Dong ◽

Yuzhu Liu

Keyword(s):

Wave Equation ◽

Frequency Domain ◽

Time Domain ◽

Computational Cost ◽

Velocity Model ◽

Receiver Side ◽

Data Set ◽

Traveltime Inversion ◽

Velocity Models ◽

The Time Domain

Wave-equation traveltime inversion (WTI) is a useful tool for background velocity model building. It is generally formulated and implemented in the time domain, in which the gradient is calculated by temporally crosscorrelating the source- and receiver-side wavefields. The time-domain source-side snapshots are either stored in memory or are reconstructed through back propagation. The memory requirements and computational cost of WTI are thus prohibitively expensive, especially for 3D applications. To partially alleviate this problem, we provide an implementation of WTI in the frequency domain with a monofrequency component. Because only one frequency is used, it is affordable to directly store the source- and receiver-side wavefields in memory. There is no need for wavefield reconstruction during gradient calculation. In such a way, we have dramatically reduced the memory requirements and computational cost compared with the traditional time-domain WTI realization. For practical implementation, the frequency-domain wavefield is calculated by time-domain finite-difference forward modeling and is transformed to the frequency domain by an on-the-fly discrete Fourier transform. Numerical examples on a simple lateral periodic velocity model and the Marmousi model demonstrate that our method can obtain accurate background velocity models comparable with those from time-domain WTI and frequency-domain WTI with multiple frequencies. A field data set test indicates that our method obtains a background velocity model that well predicts the seismic wave traveltime.

Download Full-text

Accurate and efficient data-assimilated wavefield reconstruction in the time domain

Geophysics ◽

10.1190/geo2019-0535.1 ◽

2020 ◽

Vol 85 (2) ◽

pp. A7-A12 ◽

Cited By ~ 5

Author(s):

Hossein S. Aghamiry ◽

Ali Gholami ◽

Stéphane Operto

Keyword(s):

Wave Equation ◽

Time Domain ◽

Waveform Inversion ◽

Velocity Model ◽

Search Space ◽

Velocity Models ◽

Time Stepping ◽

Efficient Data ◽

The Time Domain ◽

The Right

Wavefield reconstruction inversion (WRI) mitigates cycle skipping in full-waveform inversion by computing wavefields that do not exactly satisfy the wave equation to match data with inaccurate velocity models. We refer to these wavefields as data assimilated wavefields because they are obtained by combining the physics of wave propagation and the observations. Then, the velocity model is updated by minimizing the wave-equation errors, namely, the source residuals. Computing these data-assimilated wavefields in the time domain with explicit time stepping is challenging. This is because the right-hand side of the wave equation to be solved depends on the back-propagated residuals between the data and the unknown wavefields. To bypass this issue, a previously proposed approximation replaces these residuals by those between the data and the exact solution of the wave equation. This approximation is questionable during the early WRI iterations when the wavefields computed with and without data assimilation differ significantly. We have developed a simple backward-forward time-stepping recursion to refine the accuracy of the data-assimilated wavefields. Each iteration requires us to solve one backward and one forward problem, the former being used to update the right side of the latter. An application to the BP salt model indicates that a few iterations are enough to reconstruct data-assimilated wavefields accurately with a crude velocity model. Although this backward-forward recursion leads to increased computational overheads during one WRI iteration, it preserves its capability to extend the search space.

Download Full-text

A comparative study of common-reflection-surface prestack time migration and data regularization: Application in crooked-line data

Geophysics ◽

10.1190/geo2017-0691.1 ◽

2018 ◽

Vol 83 (4) ◽

pp. S355-S364

Author(s):

German Garabito

Keyword(s):

Comparative Study ◽

Time Domain ◽

High Signal ◽

Data Set ◽

Prestack Migration ◽

Time Migration ◽

Data Regularization ◽

Common Reflection Surface ◽

Prestack Time Migration ◽

The Time Domain

To improve the time-domain imaging of poor-quality seismic data, the common-reflection-surface (CRS) stack method was introduced to simulate zero-offset (ZO) stacked sections from a multicoverage data set based on automatic coherence analysis of seismic signals. This method produces improved ZO stacked sections with a high signal-to-noise ratio (S/N) and good continuity of reflection events. However, the stacking results may have some undesirable artifacts that can degrade the poststack migrated image. To overcome these drawbacks, I have developed a prestack data regularization method, based on CRS partial stacks, which produces prestack data with high S/N and enhanced reflection events. The regularized data are usually applied for velocity analysis and conventional prestack migration in the time and depth domains. Recently, the CRS stacking operator has also been applied for developing a new type of prestack beam migration. This new migration combines the classic Kirchhoff migration with the CRS stack method, in which the beam-forming process stacks locally coherent events that are performed using the CRS operator during migration. This work reviews this CRS-based prestack migration method in the time domain and presents a comparative study with the main standard applications of the CRS stack method, such as CRS stacking plus poststack time migration and CRS-based regularization plus prestack time migration (PSTM). To evaluate its effectiveness and reliability, CRS-based PSTM and CRS-based prestack data regularization were applied in a crooked line. The time-migrated image resulting from the regularized data has strong migration artifacts due to the crookedness of the seismic line; in contrast, the CRS-based time migration provides a good-quality image without migration artifacts.

Download Full-text