Polarization-based wave-equation migration velocity analysis in acoustic media

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. U77-U88 ◽  
Author(s):  
Qunshan Zhang ◽  
George A. McMechan
Keyword(s):  
Wave Equation ◽  
Velocity Ratio ◽  
Empirical Relation ◽  
Synthetic Data ◽  
P Wave ◽  
Reverse Time ◽  
Seismic Reflection Data ◽  
Prestack Migration ◽  
Time Migration ◽  
Acoustic Media

The source extrapolation step in wave-equation prestack reverse-time migration gives wavefield polarization information, which can be used to generate angle-domain common-image gathers (ADCIGs) from seismic reflection data from acoustic media. Concatenation of P-wave polarization segments gives wavefield propagation paths (“wavepaths”), which are similar to the raypaths in ray-based velocity tomography. The ADCIGs provide residual depth moveout (RMO) information, from which a system of linear equations is constructed for tomography to solve for the velocity ratio used for velocity updating. An empirical relation between the RMO data and the velocity ratio updates reduces the amount of computation, and is stabilized by the feedback provided by the iterative loop through prestack migration, to RMO, to velocity update, to prestack migration. Correcting the RMOs to flatten the ADGIGs is the convergence condition. Synthetic data for a layered model with a fault successfully illustrates the method.

3-D prestack migration in anisotropic media

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 79-90 ◽  
Author(s):  
Zhengxin Dong ◽  
George A. McMechan
Keyword(s):  
A Priori ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Anisotropic Media ◽  
P Wave ◽  
Common Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Prestack Migration ◽  
Time Migration

A three‐dimensional (3-D) prestack reverse‐time migration algorithm for common‐source P‐wave data from anisotropic media is developed and illustrated by application to synthetic data. Both extrapolation of the data and computation of the excitation‐time imaging condition are implemented using a second‐order finite‐ difference solution of the 3-D anisotropic scalar‐wave equation. Poorly focused, distorted images are obtained if data from anisotropic media are migrated using isotropic extrapolation; well focused, clear images are obtained using anisotropic extrapolation. A priori estimation of the 3-D anisotropic velocity distribution is required. Zones of anomalous, directionally dependent reflectivity associated with anisotropic fracture zones are detectable in both the 3-D common‐ source data and the corresponding migrated images.

True-amplitude prestack depth migration

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. S155-S166 ◽  
Author(s):  
Feng Deng ◽  
George A. McMechan
Keyword(s):  
Velocity Ratio ◽  
Synthetic Data ◽  
Transmission Losses ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Prestack Migration ◽  
Time Migration ◽  
Geometric Spreading

Most current true-amplitude migrations correct only for geometric spreading. We present a new prestack depth-migration method that uses the framework of reverse-time migration to compensate for geometric spreading, intrinsic [Formula: see text] losses, and transmission losses. Geometric spreading is implicitly compensated by full two-way wave propagation. Intrinsic [Formula: see text] losses are handled by including a [Formula: see text]-dependent term in the wave equation. Transmission losses are compensated based on an estimation of angle-dependent reflectivity using a two-pass recursive reverse-time prestack migration. The image condition used is the ratio of receiver/source wavefield amplitudes. Two-dimensional tests using synthetic data for a dipping-layer model and a salt model show that loss-compensating prestack depth migration can produce reliable angle-dependent reflection coefficients at the target. The reflection coefficient curves are fitted to give least-squares estimates of the velocity ratio at the target. The main new result is a procedure for transmission compensation when extrapolating the receiver wavefield. There are still a number of limitations (e.g., we use only scalar extrapolation for illustration), but these limitations are now better defined.

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.

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.

Accurate simulations of pure quasi-P-waves in complex anisotropic media

Geophysics ◽  
2014 ◽  
Vol 79 (6) ◽  
pp. T341-T348 ◽  
Author(s):  
Sheng Xu ◽  
Hongbo Zhou
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Differential Equations ◽  
Transverse Isotropy ◽  
Anisotropic Media ◽  
Second Order ◽  
P Wave ◽  
Pseudodifferential Equation ◽  
Reverse Time ◽  
Time Migration

Reverse time migration (RTM) in complex anisotropic media requires calculation of the propagation of a single-mode wave, the quasi-P-wave. This was conventionally realized by solving a [Formula: see text] system of second-order partial differential equations. The implementation of this [Formula: see text] system required at least twice the computational resources as compared with the acoustic wave equation. The S-waves, an introduced auxiliary function in this system, were treated as artifacts in the RTM. Furthermore, the [Formula: see text] system suffered numerical stability problems at the places in which abrupt changes of symmetric axis of anisotropy exist, which brings more challenges to real data implementation. On the other hand, the Alkhalifah’s equation, which governs the pure quasi-P-wave propagation, was hard to solve because it was a pseudodifferential equation. We proposed a pure quasi-P-wave equation that can be easily implemented within current imaging framework. Our new equation was obtained by decomposing the original pseudodifferential operator into two numerical solvable operators: a differential operator and a scalar operator. The combination of these two operators yielded an accurate phase of quasi-P-wave propagation. Our solution was S-wave free and numerically stable for very complicated models. Because only one equation was required to resolve numerically, the new proposed scheme was more efficient than those conventional schemes that solve the [Formula: see text] second-order differential equations system. For tilted transverse isotropy (TTI) RTM implementation, the required increase of numerical cost was minimal, and we could expect at least a factor of two of improvement of efficiency. We showed the effectiveness and robustness of our method with numerical examples with simple and very complicated TTI models, the SEG Advanced Modeling (SEAM) model. Further extension of our approach to orthorhombic anisotropy or tilted orthorhombic anisotropy was straightforward.

Elastic least-squares reverse time migration with hybrid l1/l2 misfit function

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. S271-S291 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Peng Yang ◽  
Wencai Xu ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Adjoint Equations ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Wave Image

We have developed the theory and synthetic tests of elastic least-squares reverse time migration (ELSRTM). In this method, a least-squares reverse time migration algorithm is used to image multicomponent seismic data based on the first-order elastic velocity-stress wave equation, in which the linearized elastic modeling equations are used for forward modeling and its adjoint equations are derived based on the adjoint-state method for back propagating the data residuals. Also, we have developed another ELSRTM scheme based on the wavefield separation technique, in which the P-wave image is obtained using P-wave forward and adjoint wavefields and the S-wave image is obtained using P-wave forward and S-wave adjoint wavefields. In this way, the crosstalk artifacts can be minimized to a significant extent. In general, seismic data inevitably contain noise. We apply the hybrid [Formula: see text] misfit function to the ELSRTM algorithm to improve the robustness of our ELSRTM to noise. Numerical tests on synthetic data reveal that our ELSRTM, when compared with elastic reverse time migration, can produce images with higher spatial resolution, more-balanced amplitudes, and fewer artifacts. Moreover, the hybrid [Formula: see text] misfit function makes the ELSRTM more robust than the [Formula: see text] misfit function in the presence of noise.

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.

Acoustic prestack migration of cross‐hole data

Geophysics ◽  
1988 ◽  
Vol 53 (8) ◽  
pp. 1015-1023 ◽  
Author(s):  
Liang‐Zie Hu ◽  
George A. McMechan ◽  
Jerry M. Harris
Keyword(s):  
Synthetic Data ◽  
Field Application ◽  
Scale Model ◽  
Common Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Prestack Migration ◽  
Time Migration ◽  
Time Space ◽  
Low Pass

Subsurface imaging with common‐source cross‐hole data can be achieved using prestack reverse‐time migration. The algorithm consists of extrapolation of the recorded wave field, application of the excitation‐time imaging condition, and postprocessing of the resulting image with a low‐pass wavenumber filter. The wavenumber filter removes the artifact associated with the direct arrival; this artifact is not separable from the scattered data before migration because, in the cross‐hole geometry, they significantly overlap in time, space, and wavenumber. Migration of synthetic data produces the best possible results, but images produced by migration of scale‐model data are not greatly inferior. Apparently, acceptable images can be obtained from a surprisingly few sources, if these sources are located sufficiently far apart to give independent information and the recording aperture is sufficiently wide.

A wavefield-separation-based elastic least-squares reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S279-S297 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Synthetic Data ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
S Waves ◽  
Numerical Tests ◽  
Time Migration

Elastic least-squares reverse time migration (ELSRTM) has the potential to provide improved subsurface reflectivity estimation. Compared with elastic RTM (ERTM), ELSRTM can produce images with higher spatial resolution, more balanced amplitudes, and fewer artifacts. However, the crosstalk between P- and S-waves can significantly degrade the imaging quality of ELSRTM. We have developed an ELSRTM method to suppress the crosstalk artifacts. This method includes three crucial points. The first is that the forward and backward wavefields are extrapolated based on the separated elastic velocity-stress equation of P- and S-waves. The second is that the separated vector P- and S-wave residuals are migrated to form reflectivity images of Lamé constants [Formula: see text] and [Formula: see text] independently. The third is that the reflectivity images of [Formula: see text] and [Formula: see text] are obtained by the vector P-wave wavefields achieved in the backward extrapolation of the separated vector P-wave residuals and the vector S-wave wavefields achieved in the backward extrapolation of the separated vector S-wave residuals, respectively. Numerical tests with synthetic data demonstrate that our ELSRTM method can produce images free of crosstalk artifacts. Compared with ELSRTM based on the coupled wavefields, our ELSRTM method has better convergence and higher accuracy.

A modeling study of preprocessing considerations for reverse-time migration

Geophysics ◽  
2008 ◽  
Vol 73 (6) ◽  
pp. T99-T106 ◽  
Author(s):  
Ian F. Jones
Keyword(s):  
Wave Propagation ◽  
Synthetic Data ◽  
Cost Effective ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Seismic Reflection Data ◽  
Standard Data ◽  
Reflection Data ◽  
Time Migration ◽  
Image Events

Much of the thinking behind conventional geophysical processing assumes that we wanted to image energy that propagates down from the surface of the earth, scatters from a reflector or diffractor, and then propagates back up to the recording surface without being reflected by any other feature. Such travel paths conform to the assumptions of one-way wave propagation, and most contemporary migration schemes are designed to image such data. In addition, the moveout behavior of these primary reflection events in the various prestack domains is well understood, and many of our standard data-preprocessing techniques relied on the assumption that this behavior adequately describes the events we wanted to preserve for imaging. As a corollary, events that do not conform to this prescribed behavior are classified as noise, and many of our standard preprocessing techniqueswere designed to remove them. We assessed the kinematics of moveout behavior of events that arise from two-way wave propagation and the effect of certain preprocessing techniques on those events. This was of interest to us because the recent rapid increase in available cost-effective computing power has enabled industrial implementation of migration algorithms—particularly reverse-time migration—that in principle can image events that reflect more than once on their way from source to receiver. We used 2D synthetic data to show that some conventional data-processing steps—particularly those used in suppression of complex reverberations (“multiples”)—remove nonreverberatory primary events from seismic reflection data. Specifically, they remove events that have repeated or turning reflections in the subsurface (such as double-bounce arrivals) but that otherwise are imageable using reverse-time migration.

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