Interval velocity estimation via NMO-based differential semblance

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. U75-U88 ◽  
Author(s):  
Jintan Li ◽  
William W. Symes
Keyword(s):  
Velocity Model ◽  
Velocity Estimation ◽  
Imaging Method ◽  
Velocity Analysis ◽  
Multiple Reflections ◽  
Coherent Noise ◽  
Interval Velocity ◽  
Velocity Models ◽  
Mean Square Difference ◽  
Rich Data

The differential semblance method of velocity analysis flattens image gathers automatically by updating interval velocity to minimize the mean square difference of neighboring traces. We detail an implementation using hyperbolic normal moveout correction as the imaging method. The algorithm is fully automatic, accommodates arbitrary acquisition geometry, and outputs 1D, 2D, or 3D interval velocity models. This variant of differential semblance velocity analysis is effective within the limits of its imaging methodology: mild lateral heterogeneity and data dominated by primary events. Coherent noise events such as multiple reflections tend to degrade the quality of the velocity model estimated by differential semblance. We show how to combine differential semblance velocity analysis with dip filtering to suppress multiple reflections and thus improve considerably the accuracy of the velocity estimate. We illustrate this possibility using multiple-rich data from a 2D marine survey.

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.

Tomographic velocity estimation with plane‐wave synthesis

Geophysics ◽  
1997 ◽  
Vol 62 (6) ◽  
pp. 1825-1838 ◽  
Author(s):  
Jun Ji
Keyword(s):  
Plane Wave ◽  
Synthetic Data ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Process Measures ◽  
Prestack Migration ◽  
Velocity Models ◽  
Wave Synthesis ◽  
Oriented Plane

In areas with structurally complex geology, tomographic velocity analysis is often required to estimate velocities. In this paper I describe an algorithm for tomographic velocity estimation that uses plane‐wave synthesis imaging as a prestack migration. The classical iterative two‐step process (measures the traveltime errors with the current velocity model and then update the velocity model) is performed as follows. The events are picked in the image space after prestack migration with surface‐oriented plane‐wave synthesis imaging. the traveltime deviations are measured through residual‐moveout (RMO) velocity analysis in common‐surface‐location (CSL) gathers obtained by reflector‐oriented plane‐wave synthesis imaging, and the velocity update is calculated by inverting the traveltime deviations through a conjugate gradient. The results from synthetic data indicate that the tomographic method successfully estimates interval‐velocity models that lead to depth‐migrated images with no residual moveout.

Numeric implementation of wave-equation migration velocity analysis operators

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE145-VE159 ◽  
Author(s):  
Paul Sava ◽  
Ioan Vlad
Keyword(s):  
Wave Equation ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Image Optimization ◽  
Migration Velocity Analysis ◽  
Zero Offset ◽  
Wavefield Extrapolation

Wave-equation migration velocity analysis (MVA) is a technique similar to wave-equation tomography because it is designed to update velocity models using information derived from full seismic wavefields. On the other hand, wave-equation MVA is similar to conventional, traveltime-based MVA because it derives the information used for model updates from properties of migrated images, e.g., focusing and moveout. The main motivation for using wave-equation MVA is derived from its consistency with the corresponding wave-equation migration, which makes this technique robust and capable of handling multipathing characterizing media with large and sharp velocity contrasts. The wave-equation MVA operators are constructed using linearizations of conventional wavefield extrapolation operators, assuming small perturbations relative to the background velocity model. Similar to typical wavefield extrapolation operators, the wave-equation MVA operators can be implemented in the mixed space-wavenumber domain using approximations of differentorders of accuracy. As for wave-equation migration, wave-equation MVA can be formulated in different imaging frameworks, depending on the type of data used and image optimization criteria. Examples of imaging frameworks correspond to zero-offset migration (designed for imaging based on focusing properties of the image), survey-sinking migration (designed for imaging based on moveout analysis using narrow-azimuth data), and shot-record migration (also designed for imaging based on moveout analysis, but using wide-azimuth data). The wave-equation MVA operators formulated for the various imaging frameworks are similar because they share elements derived from linearizations of the single square-root equation. Such operators represent the core of iterative velocity estimation based on diffraction focusing or semblance analysis, and their applicability in practice requires efficient and accurate implementation. This tutorial concentrates strictly on the numeric implementation of those operators and not on their use for iterative migration velocity analysis.

Time-to-depth conversion and velocity estimation by image-wavefront propagation

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. U75-U85 ◽  
Author(s):  
Leandro da S. Sadala Valente ◽  
Henrique B. Santos ◽  
Jessé C. Costa ◽  
Jörg Schleicher
Keyword(s):  
Ray Tracing ◽  
Model Building ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Time Step ◽  
Velocity Anomaly ◽  
Interval Velocity ◽  
Velocity Models ◽  
Wavefront Propagation ◽  
Velocity Model Building

A new strategy for time-to-depth conversion and interval-velocity estimation is based entirely on image-wavefront propagation without the need to follow individual image rays. The procedure has three main features: (1) It computes the velocity field and the traveltime directly, allowing us to dispense with dynamic ray tracing; (2) it requires only the knowledge of the image wavefront at the previous time step; and (3) it inherently smooths the image wavefront, inhibiting the formation of caustics. As a consequence, the method tends to be faster than the usual techniques and does not carry the constraints and limitations inherent to common ray-tracing strategies. Synthetic tests using a Gaussian velocity anomaly as well as the Marmousi velocity model, and two smoothed versions of it show the feasibility of the method. A field-data example demonstrates the use of different numerical procedures. Our results indicate that the present strategy can be used to construct reasonable depth-velocity models that can be used as reliable starting models for velocity-model building in depth migration or for tomographic methods.

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.

High-resolution seismic velocity analysis by sign-based weighted semblance

Geophysics ◽  
2021 ◽  
pp. 1-35
Author(s):  
M. Javad Khoshnavaz
Keyword(s):  
Seismic Velocity ◽  
Resolution Enhancement ◽  
Synthetic Data ◽  
Correlation Coefficients ◽  
Velocity Model ◽  
Seismic Attenuation ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Amplitude Versus Offset ◽  
Amplitude Versus

Building an accurate velocity model plays a vital role in routine seismic imaging workflows. Normal-moveout-based seismic velocity analysis is a popular method to make the velocity models. However, traditional velocity analysis methodologies are not generally capable of handling amplitude variations across moveout curves, specifically polarity reversals caused by amplitude-versus-offset anomalies. I present a normal-moveout-based velocity analysis approach that circumvents this shortcoming by modifying the conventional semblance function to include polarity and amplitude correction terms computed using correlation coefficients of seismic traces in the velocity analysis scanning window with a reference trace. Thus, the proposed workflow is suitable for any class of amplitude-versus-offset effects. The approach is demonstrated to four synthetic data examples of different conditions and a field data consisting a common-midpoint gather. Lateral resolution enhancement using the proposed workflow is evaluated by comparison between the results from the workflow and the results obtained by the application of conventional semblance and three semblance-based velocity analysis algorithms developed to circumvent the challenges associated with amplitude variations across moveout curves, caused by seismic attenuation and class II amplitude-versus-offset anomalies. According to the obtained results, the proposed workflow is superior to all the presented workflows in handling such anomalies.

scholarly journals Seismic velocity estimation: A deep recurrent neural-network approach

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. U21-U29
Author(s):  
Gabriel Fabien-Ouellet ◽  
Rahul Sarkar
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Model Building ◽  
Seismic Velocity ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Interval Velocity ◽  
Velocity Model Building ◽  
3D Velocity Model

Applying deep learning to 3D velocity model building remains a challenge due to the sheer volume of data required to train large-scale artificial neural networks. Moreover, little is known about what types of network architectures are appropriate for such a complex task. To ease the development of a deep-learning approach for seismic velocity estimation, we have evaluated a simplified surrogate problem — the estimation of the root-mean-square (rms) and interval velocity in time from common-midpoint gathers — for 1D layered velocity models. We have developed a deep neural network, whose design was inspired by the information flow found in semblance analysis. The network replaces semblance estimation by a representation built with a deep convolutional neural network, and then it performs velocity estimation automatically with recurrent neural networks. The network is trained with synthetic data to identify primary reflection events, rms velocity, and interval velocity. For a synthetic test set containing 1D layered models, we find that rms and interval velocity are accurately estimated, with an error of less than [Formula: see text] for the rms velocity. We apply the neural network to a real 2D marine survey and obtain accurate rms velocity predictions leading to a coherent stacked section, in addition to an estimation of the interval velocity that reproduces the main structures in the stacked section. Our results provide strong evidence that neural networks can estimate velocity from seismic data and that good performance can be achieved on real data even if the training is based on synthetics. The findings for the 1D problem suggest that deep convolutional encoders and recurrent neural networks are promising components of more complex networks that can perform 2D and 3D velocity model building.

Migration moveout analysis and depth focusing

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Claude F. Lafond ◽  
Alan R. Levander
Keyword(s):  
Heterogeneous Media ◽  
A Priori ◽  
Complex Structure ◽  
Tomographic Reconstruction ◽  
Synthetic Data ◽  
Real Data ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Data Set ◽  
Velocity Models

Prestack depth migration still suffers from the problems associated with building appropriate velocity models. The two main after‐migration, before‐stack velocity analysis techniques currently used, depth focusing and residual moveout correction, have found good use in many applications but have also shown their limitations in the case of very complex structures. To address this issue, we have extended the residual moveout analysis technique to the general case of heterogeneous velocity fields and steep dips, while keeping the algorithm robust enough to be of practical use on real data. Our method is not based on analytic expressions for the moveouts and requires no a priori knowledge of the model, but instead uses geometrical ray tracing in heterogeneous media, layer‐stripping migration, and local wavefront analysis to compute residual velocity corrections. These corrections are back projected into the velocity model along raypaths in a way that is similar to tomographic reconstruction. While this approach is more general than existing migration velocity analysis implementations, it is also much more computer intensive and is best used locally around a particularly complex structure. We demonstrate the technique using synthetic data from a model with strong velocity gradients and then apply it to a marine data set to improve the positioning of a major fault.

Velocity estimation by beam stack

Geophysics ◽  
1992 ◽  
Vol 57 (8) ◽  
pp. 1034-1047 ◽  
Author(s):  
Biondo Biondi
Keyword(s):  
Estimation Method ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Gradient Algorithm ◽  
Stratified Medium ◽  
Detailed Knowledge ◽  
Low Velocity ◽  
Velocity Anomaly ◽  
Interval Velocity ◽  
Lateral Variations

Imaging seismic data requires detailed knowledge of the propagation velocity of compressional waves in the subsurface. In conventional seismic processing, the interval velocity model is usually derived from stacking velocities. Stacking velocities are determined by measuring the coherency of the reflections along hyperbolic moveout trajectories in offset. This conventional method becomes inaccurate in geologically complex areas because the conversion of stacking velocities to interval velocities assumes a horizontally stratified medium and mild lateral variations in velocity. The tomographic velocity estimation proposed in this paper can be applied when there are dipping reflectors and strong lateral variations. The method is based on the measurements of moveouts by beam stacks. A beam stack measures local coherency of reflections along hyperbolic trajectories. Because it is a local operator, the beam stack can provide information on nonhyperbolic moveouts in the data. This information is more reliable than traveltimes of reflections picked directly from the data because many seismic traces are used for computing beam stacks. To estimate interval velocity, I iteratively search for the velocity model that best predicts the events in beam‐stacked data. My estimation method does not require a preliminary picking of the data because it directly maximizes the beam‐stack’s energy at the traveltimes and surface locations predicted by ray tracing. The advantage of this formulation is that detection of the events in the beam‐stacked data can be guided by the imposition of smoothness constraints on the velocity model. The optimization problem of maximizing beam‐stack energy is solved by a gradient algorithm. To compute the derivatives of the objective function with respect to the velocity model, I derive a linear operator that relates perturbations in velocity to the observed changes in the beam‐stack kinematics. The method has been successfully applied to a marine survey for estimating a low‐velocity anomaly. The estimated velocity function correctly predicts the nonhyperbolic moveouts in the data caused by the velocity anomaly.

Wave-equation migration velocity analysis by focusing diffractions and reflections

Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. U19-U27 ◽  
Author(s):  
Paul C. Sava ◽  
Biondo Biondi ◽  
John Etgen
Keyword(s):  
Wave Equation ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Depth Migration ◽  
Interval Velocity ◽  
Migration Velocity Analysis ◽  
Inversion Procedure ◽  
Velocity Information ◽  
Zero Offset

We propose a method for estimating interval velocity using the kinematic information in defocused diffractions and reflections. We extract velocity information from defocused migrated events by analyzing their residual focusing in physical space (depth and midpoint) using prestack residual migration. The results of this residual-focusing analysis are fed to a linearized inversion procedure that produces interval velocity updates. Our inversion procedure uses a wavefield-continuation operator linking perturbations of interval velocities to perturbations of migrated images, based on the principles of wave-equation migration velocity analysis introduced in recent years. We measure the accuracy of the migration velocity using a diffraction-focusing criterion instead of the criterion of flatness of migrated common-image gathers that is commonly used in migration velocity analysis. This new criterion enables us to extract velocity information from events that would be challenging to use with conventional velocity analysis methods; thus, our method is a powerful complement to those conventional techniques. We demonstrate the effectiveness of the proposed methodology using two examples. In the first example, we estimate interval velocity above a rugose salt top interface by using only the information contained in defocused diffracted and reflected events present in zero-offset data. By comparing the results of full prestack depth migration before and after the velocity updating, we confirm that our analysis of the diffracted events improves the velocity model. In the second example, we estimate the migration velocity function for a 2D, zero-offset, ground-penetrating radar data set. Depth migration after the velocity estimation improves the continuity of reflectors while focusing the diffracted energy.

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