Common-reflection-point migration velocity analysis of 2D P-wave data from TTI media

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. C65-C79 ◽  
Author(s):  
Ernesto V. Oropeza ◽  
George A. McMechan
Keyword(s):  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Migration Velocity ◽  
P Wave ◽  
Velocity Analysis ◽  
Reflection Point ◽  
Axis Orientation ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Free Data

We have developed a common-reflection-point (CRP)-based kinematic migration velocity analysis for 2D P-wave reflection data to estimate the four transversely isotropic (TI) parameters [Formula: see text], [Formula: see text], and [Formula: see text], and the tilt angle [Formula: see text] of the symmetry axis in a TI medium. In each iteration, the tomographic parameter was updated alternately with prestack anisotropic ray-based migration. Iterations initially used layer stripping to reduce the number of degrees of freedom; after convergence was reached, a couple of more iterations over all parameters and all CRPs ensured global interlayer coupling and parameter interaction. The TI symmetry axis orientation was constrained to be locally perpendicular to the reflectors. The [Formula: see text] dominated the inversion, and so it was weighted less than [Formula: see text] and [Formula: see text] in the parameter updates. Estimates of [Formula: see text] and [Formula: see text] were influenced if the error in [Formula: see text] was [Formula: see text]; estimates of [Formula: see text] were also influenced if the error in [Formula: see text] was [Formula: see text]. Examples included data for a simple model with a homogeneous TI layer whose dips allowed recovery of all anisotropy parameters from noise-free data, and a more realistic model (the BP tilted transversely isotropic (TTI) model) for which only [Formula: see text], [Formula: see text], and [Formula: see text] were recoverable. The adequacy of the traveltimes predicted by the inverted anisotropic models was tested by comparing migrated images and common image gathers, with those produced using the known velocity models.

scholarly journals Joint migration velocity analysis of PP- and PS-waves for VTI media

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. WC123-WC135 ◽  
Author(s):  
Pengfei Cai ◽  
Ilya Tsvankin
Keyword(s):  
Grid Point ◽  
Transversely Isotropic ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Ocean Bottom ◽  
Velocity Models ◽  
The North ◽  
Migration Velocity Analysis ◽  
Vti Media

Combining PP-waves with mode-converted PS reflections in migration velocity analysis (MVA) can help build more accurate VTI (transversely isotropic with a vertical symmetry axis) velocity models. To avoid problems caused by the moveout asymmetry of PS-waves and take advantage of efficient MVA algorithms designed for pure modes, here we generate pure SS-reflections from PP and PS data using the [Formula: see text] method. Then the residual moveout in both PP and SS common-image gathers is minimized during iterative velocity updates. The model is divided into square cells, and the VTI parameters [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] are defined at each grid point. The objective function also includes the differences between the migrated depths of the same reflectors on the PP and SS sections. Synthetic examples confirm that 2D MVA of PP- and PS-waves may be able to resolve all four relevant parameters of VTI media if reflectors with at least two distinct dips are available. The algorithm is also successfully applied to a 2D line from 3D ocean-bottom seismic data acquired at Volve field in the North Sea. After the anisotropic velocity model has been estimated, accurate depth images can be obtained by migrating the recorded PP and PS data.

Migration velocity analysis from locally coherent events in 2‐D laterally heterogeneous media, Part I: Theoretical aspects

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1202-1212 ◽  
Author(s):  
Hervé Chauris ◽  
Mark S. Noble ◽  
Gilles Lambaré ◽  
Pascal Podvin
Keyword(s):  
Cost Function ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Paraxial Ray ◽  
The Cost

We present a new method based on migration velocity analysis (MVA) to estimate 2‐D velocity models from seismic reflection data with no assumption on reflector geometry or the background velocity field. Classical approaches using picking on common image gathers (CIGs) must consider continuous events over the whole panel. This interpretive step may be difficult—particularly for applications on real data sets. We propose to overcome the limiting factor by considering locally coherent events. A locally coherent event can be defined whenever the imaged reflectivity locally shows lateral coherency at some location in the image cube. In the prestack depth‐migrated volume obtained for an a priori velocity model, locally coherent events are picked automatically, without interpretation, and are characterized by their positions and slopes (tangent to the event). Even a single locally coherent event has information on the unknown velocity model, carried by the value of the slope measured in the CIG. The velocity is estimated by minimizing these slopes. We first introduce the cost function and explain its physical meaning. The theoretical developments lead to two equivalent expressions of the cost function: one formulated in the depth‐migrated domain on locally coherent events in CIGs and the other in the time domain. We thus establish direct links between different methods devoted to velocity estimation: migration velocity analysis using locally coherent events and slope tomography. We finally explain how to compute the gradient of the cost function using paraxial ray tracing to update the velocity model. Our method provides smooth, inverted velocity models consistent with Kirchhoff‐type migration schemes and requires neither the introduction of interfaces nor the interpretation of continuous events. As for most automatic velocity analysis methods, careful preprocessing must be applied to remove coherent noise such as multiples.

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.

Migration velocity analysis for TI media in the presence of quadratic lateral velocity variation

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. U87-U96 ◽  
Author(s):  
Mamoru Takanashi ◽  
Ilya Tsvankin
Keyword(s):  
Migration Velocity ◽  
P Wave ◽  
Velocity Variation ◽  
Small Scale ◽  
Velocity Analysis ◽  
Lateral Heterogeneity ◽  
Lateral Velocity ◽  
Symmetry Direction ◽  
Migration Velocity Analysis ◽  
Ti Media

One of the most serious problems in anisotropic velocity analysis is the trade-off between anisotropy and lateral heterogeneity, especially if velocity varies on a scale smaller than the maximum offset. We have developed a P-wave MVA (migration velocity analysis) algorithm for transversely isotropic (TI) models that include layers with small-scale lateral heterogeneity. Each layer is described by constant Thomsen parameters [Formula: see text] and [Formula: see text] and the symmetry-direction velocity [Formula: see text] that varies as a quadratic function of the distance along the layer boundaries. For tilted TI media (TTI), the symmetry axis is taken orthogonal to the reflectors. We analyzed the influence of lateral heterogeneity on image gathers obtained after prestack depth migration and found that quadratic lateral velocity variation in the overburden can significantly distort the moveout of the target reflection. Consequently, medium parameters beneath the heterogeneous layer(s) are estimated with substantial error, even when borehole information (e.g., check shots or sonic logs) is available. Because residual moveout in the image gathers is highly sensitive to lateral heterogeneity in the overburden, our algorithm simultaneously inverts for the interval parameters of all layers. Synthetic tests for models with a gently dipping overburden demonstrate that if the vertical profile of the symmetry-direction velocity [Formula: see text] is known at one location, the algorithm can reconstruct the other relevant parameters of TI models. The proposed approach helps increase the robustness of anisotropic velocity model-building and enhance image quality in the presence of small-scale lateral heterogeneity in the overburden.

Joint PP and PS plane-wave wave-equation migration-velocity analysis

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. R507-R525 ◽  
Author(s):  
Zongcai Feng ◽  
Bowen Guo ◽  
Lianjie Huang
Keyword(s):  
Wave Equation ◽  
Plane Wave ◽  
Wave Velocity ◽  
Migration Velocity ◽  
Relative Depth ◽  
Velocity Analysis ◽  
Analysis Method ◽  
S Wave ◽  
Velocity Models ◽  
Migration Velocity Analysis

Conventional joint PP and PS velocity analysis is based on ray tomography. We develop a joint PP and PS wave-equation migration-velocity-analysis method using plane-wave common-image gathers (CIGs) to produce accurate P- and S-wave velocity models. The objective function of our new method consists of three terms: The first and second terms penalize the moveout residuals computed from PP and PS plane-wave CIGs, respectively, and the third term constrains the nonzero relative depth shifts between the PP and PS migration images. The moveout of plane-wave CIGs is automatically picked using a semblance analysis method, and the relative depth shifts between the PP and PS images are automatically computed using dynamic warping or manually picking the depths of certain primary reflectors. The moveout residuals and the relative depth shifts are transformed into weighted image perturbations, and they are then projected into the velocity models to update the P- and S-wave velocity models using the scalar-wave equations and their linearized forms. Numerical tests with synthetic and multicomponent field data demonstrate that our method can simultaneously invert for accurate P- and S-wave velocity models for elastic migration.

Processing‐induced anisotropy

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1920-1928 ◽  
Author(s):  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Seismic Data ◽  
Symmetry Axis ◽  
Homogeneous Medium ◽  
Transversely Isotropic ◽  
P Wave ◽  
Well Logs ◽  
Velocity Analysis ◽  
Induced Anisotropy ◽  
Vertical Heterogeneity ◽  
Vti Media

Processing of seismic data is often performed under the assumption that the velocity distribution in the subsurface can be approximated by a macromodel composed of isotropic homogeneous layers or blocks. Despite being physically unrealistic, such models are believed to be sufficient for describing the kinematics of reflection arrivals. In this paper, we examine the distortions in normal‐moveout (NMO) velocities caused by the intralayer vertical heterogeneity unaccounted for in velocity analysis. To match P‐wave moveout measurements from a horizontal or a dipping reflector overlaid by a vertically heterogeneous isotropic medium, the effective homogeneous overburden has to be anisotropic. This apparent anisotropy is caused not only by velocity monotonically increasing with depth, but also by random velocity variations similar to those routinely observed in well logs. Assuming that the effective homogeneous medium is transversely isotropic with a vertical symmetry axis (VTI), we express the VTI parameters through the actual depth‐dependent isotropic velocity function. If the reflector is horizontal, combining the NMO and vertical velocities always results in nonnegative values of Thomsen's coefficient δ. For a dipping reflector, the inversion of the P‐wave NMO ellipse yields a nonnegative Alkhalifah‐Tsvankin coefficient η that increases with dip. The values of η obtained by two other methods (2‐D dip‐moveout inversion and nonhyperbolic moveout analysis) are also nonnegative but generally differ from that needed to fit the NMO ellipse. For truly anisotropic (VTI) media, the influence of vertical heterogeneity above the reflector can lead to a bias toward positive δ and η estimates in velocity analysis.

Image gathers of SV-waves in homogeneous and factorized VTI media

Geophysics ◽  
2005 ◽  
Vol 70 (5) ◽  
pp. D55-D64 ◽  
Author(s):  
Ramzy M. Al-Zayer ◽  
Ilya Tsvankin
Keyword(s):  
Shear Wave ◽  
Vertical Velocity ◽  
Migration Velocity ◽  
P Wave ◽  
Model Parameters ◽  
Velocity Analysis ◽  
Wave Data ◽  
Migration Velocity Analysis ◽  
Wave Migration ◽  
Vti Media

Reflection moveout of SV-waves in transversely isotropic media with a vertical symmetry axis (VTI media) can provide valuable information about the model parameters and help to overcome the ambiguities in the inversion of P-wave data. Here, to develop a foundation for shear-wave migration velocity analysis, we study SV-wave image gathers obtained after prestack depth migration. The key issue, addressed using both approximate analytic results and Kirchhoff migration of synthetic data, is whether long-spread SV data can constrain the shear-wave vertical velocity [Formula: see text] and the depth scale of VTI models. For homogeneous media, the residual moveout of horizontal SV events on image gathers is close to hyperbolic and depends just on the NMO velocity [Formula: see text] out to offset-to-depth ratios of about 1.7. Because [Formula: see text] differs from [Formula: see text], flattening moderate-spread gathers of SV-waves does not ensure the correct depth of the migrated events. The residual moveout rapidly becomes nonhyperbolic as the offset-to-depth ratio approaches two, with the migrated depths at long offsets strongly influenced by the SV-wave anisotropy parameter σ. Although the combination of [Formula: see text] and σ is sufficient to constrain the vertical velocity [Formula: see text] and reflector depth, the tradeoff between σ and the Thomsen parameter ε on long-spread gathers causes errors in time-to-depth conversion. The residual moveout of dipping SV events is also controlled by the parameters [Formula: see text], σ, and ε, but in the presence of dip, the contributions of both σ and ε are significant even at small offsets. For factorized v(z) VTI media with a constant SV-wave vertical-velocity gradient [Formula: see text], flattening of horizontal events for a range of depths requires the correct NMO velocity at the surface, the gradient [Formula: see text], and, for long offsets, the parameters σ and ε. On the whole, the nonnegligible uncertainty in the estimation of reflector depth from SV-wave moveout highlights the need to combine P- and SV-wave data in migration velocity analysis for VTI media.

Reflection tomography in the postmigrated domain

Geophysics ◽  
1992 ◽  
Vol 57 (5) ◽  
pp. 680-692 ◽  
Author(s):  
Christof Stork
Keyword(s):  
Migration Velocity ◽  
Inversion Method ◽  
Practical Reasons ◽  
Velocity Analysis ◽  
Reflection Point ◽  
Time Data ◽  
Domain Optimization ◽  
Migration Velocity Analysis ◽  
Work Done ◽  
Reflection Tomography

Reflection tomography is an inversion method that adjusts a velocity and reflector depth model to be consistent with the prestack time data. This tomography approach minimizes the misfit of the data and model in the premigrated domain. Generally, the data are represented by the traveltimes of reflection events, which has made the technique problematic and unpopular. Techniques generally known as “migration velocity analysis” have a similar objective but use the postmigrated domain. For a variety of practical reasons, this postmigrated domain has advantages over the premigrated domain. With slight modifications, the reflection tomography approach can be implemented in the postmigrated domain. In this domain, a model is determined by optimizing the consistency of imaged reflection events on what has been called a common reflection point (CRP) gather. Extending reflection tomography to the postmigrated domain allows much of the knowledge developed for migration velocity analysis to be coupled with that of reflection tomography. As a result, many of the practical techniques developed for migration velocity analysis can be used to improve the robustness and efficiency of reflection tomography. Similarly, much of the reflection tomography work done on analysis and solution of the linear system can be applied to postmigrated domain optimization.

Migration velocity analysis from locally coherent events in 2‐D laterally heterogeneous media, Part II: Applications on synthetic and real data

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1213-1224 ◽  
Author(s):  
Hervé Chauris ◽  
Mark S. Noble ◽  
Gilles Lambaré ◽  
Pascal Podvin
Keyword(s):  
Heterogeneous Media ◽  
Real Data ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Efficient Computation ◽  
Data Set ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Paraxial Ray

We demonstrate a method for estimating 2‐D velocity models from synthetic and real seismic reflection data in the framework of migration velocity analysis (MVA). No assumption is required on the reflector geometry or on the unknown background velocity field, provided that the data only contain primary reflections/diffractions. In the prestack depth‐migrated volume, locations where the reflectivity exhibits local coherency are automatically picked without interpretation in two panels: common image gathers (CIGs) and common offset gathers (COGs). They are characterized by both their positions and two slopes. The velocity is estimated by minimizing all slopes picked in the CIGs. We test the applicability of the method on a real data set, showing the possibility of an efficient inversion using (1) the migration of selected CIGs and COGs, (2) automatic picking on prior uncorrelated locally coherent events, (3) efficient computation of the gradient of the cost function via paraxial ray tracing from the picked events to the surface, and (4) a gradient‐type optimization algorithm for convergence.

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