A robust approach to time-to-depth conversion and interval velocity estimation from time migration in the presence of lateral velocity variations

I appreciate the thoughtful and thorough response given by Tygel et al. They point out that even for a single dipping reflector imaged by a single non‐zero offset raypath, pulse distortion caused by “standard processing” (NM0 correction‐CMP sort‐stack‐time migration) and pulse distortion caused by prestack depth migration are not really the same, because the reflecting point is mispositioned in standard processing. Within a CMP gather, this mispositioning increases with offset, giving rise to “CMP smear.” CMP smear degrades the stack, introducing additional pulse distortion. Where i‐t is significant, and where lateral velocity variations or reflection curvature are large, such as for complex geology, the pulse distortion of standard processing can differ greatly from that of prestack depth migration.

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Improved subsalt images with least-squares reverse time migration

Interpretation ◽

10.1190/int-2016-0203.1 ◽

2017 ◽

Vol 5 (3) ◽

pp. SN25-SN32 ◽

Cited By ~ 4

Author(s):

Ping Wang ◽

Shouting Huang ◽

Ming Wang

Keyword(s):

Least Squares ◽

Field Data ◽

Reverse Time ◽

Reverse Time Migration ◽

Lateral Velocity ◽

Image Domain ◽

Time Migration ◽

Iterative Inversion ◽

Velocity Variations ◽

Subsalt Imaging

Complex overburdens often distort reservoir images in terms of structural positioning, stratigraphic resolution, and amplitude fidelity. One prime example of a complex overburden is in the deepwater Gulf of Mexico, where thick and irregular layers of remobilized (i.e., allochthonous) salt are situated above prospective reservoir intervals. The highly variant salt layers create large lateral velocity variations that distort wave propagation and the illumination of deeper reservoir targets. In subsalt imaging, tools such as reflection tomography, full-waveform inversion, and detailed salt interpretation are needed to derive a high-resolution velocity model that captures the lateral velocity variations. Once a velocity field is obtained, reverse time migration (RTM) can be applied to restore structural positioning of events below and around the salt. However, RTM by nature is unable to fully recover the reflectivity for desired amplitudes and resolution. This shortcoming is well-recognized by the imaging community, and it has propelled the emergence of least-squares RTM (LSRTM) in recent years. We have investigated how current LSRTM methods perform on subsalt images. First, we compared the formulation of data-domain versus image-domain least-squares migration, as well as methods using single-iteration approximation versus iterative inversion. Then, we examined the resulting subsalt images of several LSRTM methods applied on the synthetic and field data. Among our tests, we found that image-domain single-iteration LSRTM methods, including an extension of an approximate inverse Hessian method in the curvelet domain, not only compensated for amplitude loss due to poor illumination caused by complex salt bodies, but it also produced subsalt images with fewer migration artifacts in the field data. In contrast, an iterative inversion method showed its potential for broadening the bandwidth in the subsalt, but it was less effective in reducing migration artifacts and noise. Based on our understanding, we evaluated the current state of LSRTM for subsalt imaging.

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Fast time-to-depth conversion and interval velocity estimation in the case of weak lateral variations

Geophysics ◽

10.1190/geo2017-0338.1 ◽

2018 ◽

Vol 83 (3) ◽

pp. S227-S235 ◽

Cited By ~ 6

Author(s):

Yanadet Sripanich ◽

Sergey Fomel

Keyword(s):

Velocity Model ◽

Velocity Estimation ◽

Fast Time ◽

Lateral Velocity ◽

First Order ◽

Interval Velocity ◽

Order Of Magnitude ◽

Efficient Alternative ◽

Homogeneous Media ◽

Lateral Variations

Time-domain processing has a long history in seismic imaging and has always been a powerful workhorse that is routinely used. It generally leads to an expeditious construction of the subsurface velocity model in time, which can later be expressed in the Cartesian depth coordinates via a subsequent time-to-depth conversion. The conventional practice of such a conversion is done using Dix inversion, which is exact in the case of laterally homogeneous media. For other media with lateral heterogeneity, the time-to-depth conversion involves solving a more complex system of partial differential equations (PDEs). We have developed an efficient alternative for time-to-depth conversion and interval velocity estimation based on the assumption of weak lateral velocity variations. By considering only first-order perturbative effects from lateral variations, the exact system of PDEs required to accomplish the exact conversion reduces to a simpler system that can be solved efficiently in a layer-stripping (downward-stepping) fashion. Numerical synthetic and field data examples show that our method can achieve reasonable accuracy and is significantly more efficient than previously proposed methods with a speedup by an order of magnitude.

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A Robust Approach for Time-to-depth Conversion and Interval Velocity Estimation

London 2013, 75th eage conference en exhibition incorporating SPE Europec ◽

10.3997/2214-4609.20130371 ◽

2013 ◽

Author(s):

S. Li ◽

S. Fomel

Keyword(s):

Velocity Estimation ◽

Robust Approach ◽

Interval Velocity

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2D interval velocity estimation from NMO, DMO, and time-migration velocity spectra

54th EAEG Meeting ◽

10.3997/2214-4609.201410544 ◽

1992 ◽

Author(s):

A. Gonzalez ◽

R. Chambers

Keyword(s):

Migration Velocity ◽

Velocity Estimation ◽

Interval Velocity ◽

Time Migration ◽

Velocity Spectra

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The migration of common midpoint slant stacks

Geophysics ◽

10.1190/1.1441656 ◽

1984 ◽

Vol 49 (3) ◽

pp. 237-249 ◽

Cited By ~ 25

Author(s):

Richard Ottolini ◽

Jon F. Claerbout

Keyword(s):

Seismic Data ◽

Lateral Velocity ◽

Velocity Inversion ◽

Interval Velocity ◽

Reflection Seismic ◽

Straightforward Method ◽

Velocity Surface ◽

Velocity Variations ◽

Migration Equation ◽

Ray Parameter

Reflection seismic data can be imaged by migrating common midpoint slant stacks. The basic method is to assemble slant stack sections from the slant stack of each common midpoint gather at the same ray parameter. Earlier investigators have described migration methods for slant stacked shot profiles or common receiver gathers instead of common midpoint gathers. However, common midpoint slant stacks enjoy the practical advantages of midpoint coordinates. In addition, the migration equation makes no approximation for steep dips, wide offsets, or vertical velocity variations. A theoretical disadvantage is that there is no exact treatment of lateral velocity variations. Slant stack migration is a method of “migration before stack.” It solves the dip selectivity problem of conventional stacking, particularly when horizontal reflectors intersect steep dipping reflectors. The correct handling of all dips also improves lateral resolution in the image. Slant stack migration provides a straightforward method of measuring interval velocity after migration has improved the seismic data. The kinematics (traveltime treatment) of slant stack migration is also accurate for postcritical reflections and refractions. These events transform into a p-τ surface with the additional dimension of midpoint. The slant stack migration equation converts the p-τ surface into a depth‐midpoint velocity surface. As with migration in general, the effects of dip are automatically accounted for during velocity inversion.

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Tomographic velocity analysis and wave-equation depth migration in an overthrust terrain: A case study from the Tuha Basin, China

Interpretation ◽

10.1190/int-2017-0053.1 ◽

2018 ◽

Vol 6 (1) ◽

pp. T1-T13

Author(s):

Bin Lyu ◽

Qin Su ◽

Kurt J. Marfurt

Keyword(s):

Wave Equation ◽

Data Quality ◽

Model Building ◽

Velocity Model ◽

Lateral Velocity ◽

Near Surface ◽

Depth Migration ◽

Time Migration ◽

Head Waves ◽

Velocity Variations

Although the structures associated with overthrust terrains form important targets in many basins, accurately imaging remains challenging. Steep dips and strong lateral velocity variations associated with these complex structures require prestack depth migration instead of simpler time migration. The associated rough topography, coupled with older, more indurated, and thus high-velocity rocks near or outcropping at the surface often lead to seismic data that suffer from severe statics problems, strong head waves, and backscattered energy from the shallow section, giving rise to a low signal-to-noise ratio that increases the difficulties in building an accurate velocity model for subsequent depth migration. We applied a multidomain cascaded noise attenuation workflow to suppress much of the linear noise. Strong lateral velocity variations occur not only at depth but near the surface as well, distorting the reflections and degrading all deeper images. Conventional elevation corrections followed by refraction statics methods fail in these areas due to poor data quality and the absence of a continuous refracting surface. Although a seismically derived tomographic solution provides an improved image, constraining the solution to the near-surface depth-domain interval velocities measured along the surface outcrop data provides further improvement. Although a one-way wave-equation migration algorithm accounts for the strong lateral velocity variations and complicated structures at depth, modifying the algorithm to account for lateral variation in illumination caused by the irregular topography significantly improves the image, preserving the subsurface amplitude variations. We believe that our step-by-step workflow of addressing the data quality, velocity model building, and seismic imaging developed for the Tuha Basin of China can be applied to other overthrust plays in other parts of the world.

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