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

Geophysics ◽  
1996 ◽  
Vol 61 (3) ◽  
pp. 742-758 ◽  
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.

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

Geophysics ◽  
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.

A unified approach to 3-D seismic reflection imaging, Part II: Theory

Geophysics ◽  
1996 ◽  
Vol 61 (3) ◽  
pp. 759-775 ◽  
Author(s):  
Martin Tygel ◽  
Jörg Schleicher ◽  
Peter Hubral
Keyword(s):  
Seismic Reflection ◽  
Seismic Imaging ◽  
Velocity Model ◽  
Image Transformation ◽  
Unified Approach ◽  
Imaging Theory ◽  
Reflection Imaging ◽  
Transformation Problems

Diffraction‐stack and isochrone‐stack integrals are quantitatively described and employed. They constitute an asymptotic transform pair. Both integrals are the key tools of a unified approach to seismic reflection imaging that can be used to solve a multitude of amplitude‐preserving, target‐oriented seismic imaging (or image‐transformation) problems. These include, for instance, the generalizations of the kinematic map‐transformation examples discussed in Part I. All image‐transformation problems can be addressed by applying both stacking integrals in sequence, whereby the macro‐velocity model, the measurement configuration, or the ray‐code of the considered elementary reflections may change from step to step. This leads to weighted (Kirchhoff‐ or generalized‐Radon‐type) summations along certain stacking surfaces (or inplanats) for which true‐amplitude (TA) weights are provided. To demonstrate the value of the proposed imaging theory (which is based on analytically chaining the two stacking integrals and using certain inherent dualities), we examine in detail the amplitude‐preserving configuration transform and remigration for the case of a 3-D laterally inhomogeneous velocity medium.

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

Geophysics ◽  
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.

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

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. A7-A12 ◽  
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.

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

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. S239-S249
Author(s):  
Shihang Feng ◽  
Oz Yilmaz ◽  
Yuqing Chen ◽  
Gerard T. Schuster
Keyword(s):  
Time Domain ◽  
Constant Velocity ◽  
Field Data ◽  
Velocity Model ◽  
Velocity Models ◽  
Time Migration ◽  
Prestack Time Migration ◽  
Zero Offset ◽  
Image Volume ◽  
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.

A Unified approach to seismic reflection imaging

1994 ◽  
Author(s):  
M. Tygel ◽  
P. Hubral ◽  
J. Schleicher
Keyword(s):  
Seismic Reflection ◽  
Unified Approach ◽  
Reflection Imaging

scholarly journals Transmission compensated primary reflection retrieval in the data domain and consequences for imaging

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. Q27-Q36 ◽  
Author(s):  
Lele Zhang ◽  
Jan Thorbecke ◽  
Kees Wapenaar ◽  
Evert Slob
Keyword(s):  
Thin Layer ◽  
Time Domain ◽  
Velocity Model ◽  
Original Data ◽  
Transmission Losses ◽  
Multiple Reflections ◽  
Data Set ◽  
Numerical Examples ◽  
The One ◽  
The Time Domain

We have developed a scheme that retrieves primary reflections in the two-way traveltime domain by filtering the data. The data have their own filter that removes internal multiple reflections, whereas the amplitudes of the retrieved primary reflections are compensated for two-way transmission losses. Application of the filter does not require any model information. It consists of convolutions and correlations of the data with itself. A truncation in the time domain is applied after each convolution or correlation. The retrieved data set can be used as the input to construct a better velocity model than the one that would be obtained by working directly with the original data and to construct an enhanced subsurface image. Two 2D numerical examples indicate the effectiveness of the method. We have studied bandwidth limitations by analyzing the effects of a thin layer. The presence of refracted and scattered waves is a known limitation of the method, and we studied it as well. Our analysis indicates that a thin layer is treated as a more complicated reflector, and internal multiple reflections related to the thin layer are properly removed. We found that the presence of refracted and scattered waves generates artifacts in the retrieved data.

Review of Optimal Solutions to the Robustness Problem in Observer-Based Fault Detection

1993 ◽  
Vol 207 (2) ◽  
pp. 105-112 ◽  
Author(s):  
P M Frank ◽  
B Koppen
Keyword(s):  
Fault Detection ◽  
General Solution ◽  
Frequency Domain ◽  
Time Domain ◽  
Fault Detection And Isolation ◽  
Unknown Input ◽  
Optimal Solutions ◽  
Unified Approach ◽  
Ultimate Objective ◽  
The Time Domain

The paper presents a unified approach and general solution of the robustness problem in fault detection and isolation concepts. The ultimate objective is the design of an unknown input fault-detection observer providing a perfect decoupling between unknown inputs and faults. If this is not possible because certain prerequisites are not fulfilled, two optimal compromises in the time domain and in the frequency domain are described. The basic definitions concerning robustness and unknown input fault detectability are given, and the design techniques for the proposed approaches are outlined. The cross-connections to other methods are discussed and a practical example is given.

An efficient multiscale method for time-domain waveform tomography

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCC59-WCC68 ◽  
Author(s):  
Chaiwoot Boonyasiriwat ◽  
Paul Valasek ◽  
Partha Routh ◽  
Weiping Cao ◽  
Gerard T. Schuster ◽  
...  
Keyword(s):  
Time Domain ◽  
Multiscale Method ◽  
Staggered Grid ◽  
Multiscale Approach ◽  
Efficient Computation ◽  
Computationally Efficient ◽  
Order Accuracy ◽  
Velocity Models ◽  
Waveform Tomography ◽  
The Time Domain

This efficient multiscale method for time-domain waveform tomography incorporates filters that are more efficient than Hamming-window filters. A strategy for choosing optimal frequency bands is proposed to achieve computational efficiency in the time domain. A staggered-grid, explicit finite-difference method with fourth-order accuracy in space and second-order accuracy in time is used for forward modeling and the adjoint calculation. The adjoint method is utilized in inverting for an efficient computation of the gradient directions. In the multiscale approach, multifrequency data and multiple grid sizes are used to overcome somewhat the severe local minima problem of waveform tomography. The method is applied successfully to 1D and 2D heterogeneous models; it can accurately recover low- and high-wavenumber components of the velocity models. The inversion result for the 2D model demonstrates that the multiscale method is computationally efficient and converges faster than a conventional, single-scale method.

Viscoacoustic waveform inversion of velocity structures in the time domain

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. R103-R119 ◽  
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.

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