Seismic wave-equation demigration/migration

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. S111-S119 ◽  
Author(s):  
Hervé Chauris ◽  
Mondher Benjemaa
Keyword(s):  
Wave Equation ◽  
Source Term ◽  
Model Building ◽  
Synthetic Data ◽  
Velocity Model ◽  
Single Scattering ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Velocity Models ◽  
Time Migration

Reverse-time migration is a well-known method based on a single-scattering approximation; it is designed to obtain seismic images in the case of a complex subsurface. It can, however, be a very time-consuming task because the number of computations is directly proportional to the number of processed sources. In the context of velocity model-building, iterative approaches require that one derives a series of migrated sections for different velocity models. We propose to replace the summation over sources by a summation over depth offsets or time delays defined in the subsurface. For that, we have developed a new relationship between two migrated sections obtained for two different velocity models. Starting from one of the two images, we obtain a second section correctly and efficiently. For each time delay, we compute a generalized source term by extending the concept of exploding reflector to nonzero offset. We obtain the final migrated section by solving the same wave equation in the perturbed model with the modified source term. Our work included testing the methodology on 2D synthetic data sets, particularly when the initial and perturbed velocity models differ greatly.

Depth migration by the Gaussian beam summation method

Geophysics ◽  
2010 ◽  
Vol 75 (2) ◽  
pp. S81-S93 ◽  
Author(s):  
Mikhail M. Popov ◽  
Nikolay M. Semtchenok ◽  
Peter M. Popov ◽  
Arie R. Verdel
Keyword(s):  
Wave Equation ◽  
Model Building ◽  
Velocity Structure ◽  
Velocity Model ◽  
Summation Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Depth Migration ◽  
Time Migration ◽  
Ray Methods

Seismic depth migration aims to produce an image of seismic reflection interfaces. Ray methods are suitable for subsurface target-oriented imaging and are less costly compared to two-way wave-equation-based migration, but break down in cases when a complex velocity structure gives rise to the appearance of caustics. Ray methods also have difficulties in correctly handling the different branches of the wavefront that result from wave propagation through a caustic. On the other hand, migration methods based on the two-way wave equation, referred to as reverse-time migration, are known to be capable of dealing with these problems. However, they are very expensive, especially in the 3D case. It can be prohibitive if many iterations are needed, such as for velocity-model building. Our method relies on the calculation of the Green functions for the classical wave equation by per-forming a summation of Gaussian beams for the direct and back-propagated wavefields. The subsurface image is obtained by cal-culating the coherence between the direct and backpropagated wavefields. To a large extent, our method combines the advantages of the high computational speed of ray-based migration with the high accuracy of reverse-time wave-equation migration because it can overcome problems with caustics, handle all arrivals, yield good images of steep flanks, and is readily extendible to target-oriented implementation. We have demonstrated the quality of our method with several state-of-the-art benchmark subsurface models, which have velocity variations up to a high degree of complexity. Our algorithm is especially suited for efficient imaging of selected subsurface subdomains, which is a large advantage particularly for 3D imaging and velocity-model refinement applications such as subsalt velocity-model improvement. Because our method is also capable of providing highly accurate migration results in structurally complex subsurface settings, we have also included the concept of true-amplitude imaging in our migration technique.

Suppressing unwanted internal reflections in prestack reverse-time migration

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. E79-E82 ◽  
Author(s):  
Robin P. Fletcher ◽  
Paul J. Fowler ◽  
Phil Kitchenside ◽  
Uwe Albertin
Keyword(s):  
Wave Equation ◽  
High Velocity ◽  
Synthetic Data ◽  
Velocity Model ◽  
Image Artifacts ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Damping Term ◽  
Time Migration ◽  
Directional Damping

Prestack reverse-time migration, a wave-equation technique using two-way propagation, correctly handles multiarrivals and enables imaging of overturned reflections. However, image artifacts occur when backscattered waves cross-correlate. These artifacts are particularly strong where high-velocity contrasts occur. A method for removing unwanted internal reflections during propagation of both the source and receiver wavefields is presented. This method applies a directional damping term to the wave equation in areas of the velocity model where unwanted reflections occur. Tests on synthetic data show good suppression of image artifacts.

3D angle gathers from reverse time migration

Geophysics ◽  
2011 ◽  
Vol 76 (2) ◽  
pp. S77-S92 ◽  
Author(s):  
Sheng Xu ◽  
Yu Zhang ◽  
Bing Tang
Keyword(s):  
Wave Equation ◽  
Model Building ◽  
Velocity Model ◽  
Azimuth Angle ◽  
Three Dimensions ◽  
Practical Implementation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Reflection Angle

Common-image gathers are an important output of prestack depth migration. They provide information needed for velocity model building and amplitude and phase information for subsurface attribute interpretation. Conventionally, common-image gathers are computed using Kirchhoff migration on common-offset/azimuth data volumes. When geologic structures are complex and strong contrasts exist in the velocity model, the complicated wave behaviors will create migration artifacts in the image gathers. As long as the gather output traces are indexed by any surface attribute, such as source location, receiver location, or surface plane-wave direction, they suffer from the migration artifacts caused by multiple raypaths. These problems have been addressed in a significant amount of work, resulting in common-image gathers computed in the reflection angle domain, whose traces are indexed by the subsurface reflection angle and/or the subsurface azimuth angle. Most of these efforts have concentrated on Kirchhoff and one-way wave-equation migration methods. For reverse time migration, subsurface angle gathers can be produced using the same approach as that used for one-way wave-equation migration. However, these approaches need to be revisited when producing high-quality subsurface angle gathers in three dimensions (reflection angle/azimuth angle), especially for wide-azimuth data. We have developed a method for obtaining 3D subsurface reflection angle/azimuth angle common-image gathers specifically for the amplitude-preserved reverse time migration. The method builds image gathers with a high-dimensional convolution of wavefields in the wavenumber domain. We have found a windowed antileakage Fourier transform method that leads to an efficient and practical implementation. This approach has generated high-resolution angle-domain gathers on synthetic 2.5D data and 3D wide-azimuth real data.

Dirty salt velocity inversion: The road to a clearer subsalt image

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB169-WB174 ◽  
Author(s):  
Shuo Ji ◽  
Tony Huang ◽  
Kang Fu ◽  
Zhengxue Li
Keyword(s):  
Model Building ◽  
Synthetic Data ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Velocity Inversion ◽  
Time Migration ◽  
And Migration ◽  
Subsalt Imaging

For deep-water Gulf of Mexico, accurate salt geometry is critical to subsalt imaging. This requires the definition of both external and internal salt geometries. In recent years, external salt geometry (i.e., boundaries between allochthonous salt and background sediment) has improved a great deal due to advances in acquisition, velocity model building, and migration algorithms. But when it comes to defining internal salt geometry (i.e., intrasalt inclusions or dirty salt), no efficient method has yet been developed. In common industry practices, intrasalt inclusions (and thus their velocity anomalies) are generally ignored during the model building stages. However, as external salt geometries reach higher levels of accuracy, it becomes more important to consider the once-ignored effects of dirty salt. We have developed a reflectivity-based approach for dirty salt velocity inversion. This method takes true-amplitude reverse time migration stack volumes as input, then estimates the dirty salt velocity based on reflectivity under a 1D assumption. Results from a 2D synthetic data set and a real 3D Wide Azimuth data set demonstrated that the reflectivity inversion scheme significantly improves the subsalt image for certain areas. In general, we believe that this method produces a better salt model than the traditional clean salt velocity approach.

Use of RTM full 3D subsurface angle gathers for subsalt velocity update and image optimization: Case study at Shenzi field

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB27-WB39 ◽  
Author(s):  
Zheng-Zheng Zhou ◽  
Michael Howard ◽  
Cheryl Mifflin
Keyword(s):  
Model Building ◽  
Transverse Isotropy ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Edge Diffraction ◽  
Time Migration ◽  
Image Optimization ◽  
Free Generation

Various reverse time migration (RTM) angle gather generation techniques have been developed to address poor subsalt data quality and multiarrival induced problems in gathers from Kirchhoff migration. But these techniques introduce new problems, such as inaccuracies in 2D subsurface angle gathers and edge diffraction artifacts in 3D subsurface angle gathers. The unique rich-azimuth data set acquired over the Shenzi field in the Gulf of Mexico enabled the generally artifact-free generation of 3D subsurface angle gathers. Using this data set, we carried out suprasalt tomography and salt model building steps and then produced 3D angle gathers to update the subsalt velocity. We used tilted transverse isotropy RTM with extended image condition to generate full 3D subsurface offset domain common image gathers, which were subsequently converted to 3D angle gathers. The angle gathers were substacked along the subsurface azimuth axis into azimuth sectors. Residual moveout analysis was carried out, and ray-based tomography was used to update velocities. The updated velocity model resulted in improved imaging of the subsalt section. We also applied residual moveout and selective stacking to 3D angle gathers from the final migration to produce an optimized stack image.

Least-squares reverse time migration in TTI media using a pure qP-wave equation

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. S199-S216
Author(s):  
Xinru Mu ◽  
Jianping Huang ◽  
Jidong Yang ◽  
Xu Guo ◽  
Yundong Guo
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Seismic Imaging ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
The Matrix ◽  
The Stability

Anisotropy is a common phenomenon in subsurface strata and should be considered in seismic imaging and inversion. Seismic imaging in a vertical transversely isotropic (VTI) medium does not take into account the effects of the tilt angles, which can lead to degraded migrated images in areas with strong anisotropy. To correct such waveform distortion, reduce related image artifacts, and improve migration resolution, a tilted transversely isotropic (TTI) least-squares reverse time migration (LSRTM) method is presented. In the LSRTM, a pure qP-wave equation is used and solved with the finite-difference method. We have analyzed the stability condition for the pure qP-wave equation using the matrix method, which is used to ensure the stability of wave propagation in the TTI medium. Based on this wave equation, we derive a corresponding demigration (Born modeling) and adjoint migration operators to implement TTI LSRTM. Numerical tests on the synthetic data show the advantages of TTI LSRTM over VTI RTM and VTI LSRTM when the recorded data contain strong effects caused by large tilt angles. Our numerical experiments illustrate that the sensitivity of the adopted TTI LSRTM to the migration velocity errors is much higher than that to the anisotropic parameters (including epsilon, delta, and tilted angle parameters), and its sensitivity to the epsilon model and tilt angle is higher than that to the delta model.

2.5D reverse-time migration

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. S143-S149 ◽  
Author(s):  
Francisco A. da Silva Neto ◽  
Jessé C. Costa ◽  
Jörg Schleicher ◽  
Amélia Novais
Keyword(s):  
Wave Propagation ◽  
Computing Time ◽  
Synthetic Data ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Translational Invariance ◽  
Time Migration ◽  
Seismic Waveform ◽  
Time Space

Reverse-time migration (RTM) in 2.5D offers an alternative to improve resolution and amplitude when imaging 2D seismic data. Wave propagation in 2.5D assumes translational invariance of the velocity model. Under this assumption, we implement a finite-difference (FD) modeling algorithm in the mixed time-space/wavenumber domain to simulate the velocity and pressure fields for acoustic wave propagation and apply it in RTM. The 2.5D FD algorithm is truly parallel, allowing an efficient implementation in clusters. Storage and computing time requirements are strongly reduced compared to a full 3D FD simulation of the wave propagation. This feature makes 2.5D RTM much more efficient than 3D RTM, while achieving improved modeling of 3D geometrical spreading and phase properties of the seismic waveform in comparison to 2D RTM. Together with an imaging condition that compensates for uneven illumination and/or the obliquity factor, this allows recover of amplitudes proportional to the earth’s reflectivity. Numerical experiments using synthetic data demonstrate the better resolution and improved amplitude recovery of 2.5D RTM relative to 2D RTM.

Reverse time migration of multiples: Reducing migration artifacts using the wavefield decomposition imaging condition

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. S307-S314 ◽  
Author(s):  
Yibo Wang ◽  
Yikang Zheng ◽  
Qingfeng Xue ◽  
Xu Chang ◽  
Tong W. Fei ◽  
...  
Keyword(s):  
Complex Function ◽  
Synthetic Data ◽  
Velocity Model ◽  
High Amplitude ◽  
Frequency Noise ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Time Migration ◽  
Wavefield Decomposition

In the implementation of migration of multiples, reverse time migration (RTM) is superior to other migration algorithms because it can handle steeply dipping structures and offer high-resolution images of the complex subsurface. However, the RTM results using two-way wave equation contain high-amplitude, low-frequency noise and false images generated by improper wave paths in migration velocity model with sharp velocity interfaces or strong velocity gradients. To improve the imaging quality in RTM of multiples, we separate the upgoing and downgoing waves in the propagation of source and receiver wavefields. A complex function involved with the Hilbert transform is used in wavefield decomposition. Our approach is cost effective and avoids the large storage of wavefield snapshots required by the conventional wavefield separation technique. We applied migration of multiples with wavefield decomposition on a simple two-layer model and the Sigsbee 2B synthetic data set. Our results demonstrate that the proposed approach can improve the image generated by migration of multiples significantly.

Salt interpretation enabled by reverse-time migration

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE211-VE216 ◽  
Author(s):  
Jacobus Buur ◽  
Thomas Kühnel
Keyword(s):  
Model Building ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Seismic Line ◽  
Depth Migration ◽  
Time Migration ◽  
Velocity Model Building ◽  
Migration Method

Many production targets in greenfield exploration are found in salt provinces, which have highly complex structures as a result of salt formation over geologic time. Difficult geologic settings, steep dips, and other wave-propagation effects make reverse-time migration (RTM) the migration method of choice, rather than Kirchhoff migration or other (by definition approximate) one-way equation methods. Imaging of the subsurface using any depth-migration algorithm can be done successfully only when the quality of the prior velocity model is sufficient. The (velocity) model-building loop is an iterative procedure for improving the velocity model. This is done by obtaining certain measurements (residual moveout) on image gathers generated during the migration procedure; those measurements then are input into tomographic updating. Commonly RTM is applied around salt bodies, where building the velocity model fails essentially because tomography is ray-trace based. Our idea is to apply RTM directly inside the model-building loop but to do so without using the image gathers. Although the process is costly, we migrate the full frequency content of the data to create a high-quality stack. This enhances the interpretation of top and bottom salt significantly and enables us to include the resulting salt geometry in the velocity model properly. We demonstrate our idea on a 2D West Africa seismic line. After several model-building iterations, the result is a dramatically improved velocity model. With such a good model as input, the final RTM confirms the geometry of the salt bodies and basically the salt interpretation, and yields a compelling image of the subsurface.

scholarly journals 3D high-resolution seismic imaging of the iron-oxide deposits in Ludvika (Sweden) using full-waveform inversion and reverse-time migration

2021 ◽  
Author(s):  
Brij Singh ◽  
Michał Malinowski ◽  
Andrzej Górszczyk ◽  
Alireza Malehmir ◽  
Stefan Buske ◽  
...  
Keyword(s):  
Waveform Inversion ◽  
Velocity Model ◽  
Mine Planning ◽  
Full Waveform Inversion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Depth Imaging ◽  
Velocity Models ◽  
Full Waveform ◽  
Time Migration

Abstract. A sparse 3D seismic survey was acquired over the Blötberget iron-oxide deposits of the Ludvika Mines in south-central Sweden. The main aim of the survey was to delineate the deeper extension of the mineralisation and to better understand its 3D nature and associated fault systems for mine planning purposes. To obtain a high-quality seismic image in depth, we applied time-domain 3D acoustic full-waveform inversion (FWI) to build a high-resolution P-wave velocity model. This model was subsequently used for pre-stack depth imaging with reverse time migration (RTM) to produce the complementary reflectivity section. We developed a data preprocessing workflow and inversion strategy for the successful implementation of FWI in the hardrock environment. We obtained a high-fidelity velocity model using FWI and assessed its robustness. We extensively tested and optimised the parameters associated with the RTM method for subsequent depth imaging using different velocity models: a constant velocity model, a model built using first-arrival traveltime tomography and a velocity model derived by FWI. We compare our RTM results with a priori data available in the area. We conclude that, from all tested velocity models, the FWI velocity model in combination with the subsequent RTM step, provided the most focussed image of the mineralisation and we successfully mapped its 3D geometrical nature. In particular, a major reflector interpreted as a cross-cutting fault, which is restricting the deeper extension of the mineralisation with depth, and several other fault structures which were earlier not imaged were also delineated. We believe that a thorough analysis of the depth images derived with the combined FWIRTM approach that we presented here can provide more details which will help with better estimation of areas with high mineralization, better mine planning and safety measures.

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