Automatic velocity analysis by differential semblance optimization

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1184-1191 ◽  
Author(s):  
W. A. Mulder ◽  
A. P. E. ten Kroode
Keyword(s):  
Seismic Data ◽  
Order Approximation ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Cost Functional ◽  
Adjoint State ◽  
First Order Approximation ◽  
The Time Domain ◽  
The Cost ◽  
Adjoint State Method

We present a method for automatic velocity analysis of seismic data based on differential semblance optimization (DSO). The data are mapped for each offset from the time domain to the depth domain by a Born migration scheme using ray tracing with the efficient wavefront construction method. The DSO cost functional is evaluated by taking differences of the migration images for neighboring offsets. The gradient of this functional with respect to the underlying velocity model is obtained by a first‐order approximation of the adjoint‐state method, leading to an optimal complexity: the cost of evaluating the gradient is about the same as that of evaluating the functional. The method has been applied to a marine line. Multiples turned out to be a problem, but were handled effectively by incorporating a multiple filter inside the DSO cost functional.

Kirchhoff image propagation

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 126-134 ◽  
Author(s):  
Frank Adler
Keyword(s):  
Seismic Data ◽  
Order Approximation ◽  
Computation Time ◽  
Velocity Model ◽  
Image Point ◽  
Computationally Efficient ◽  
Initial Image ◽  
Migration Velocity Analysis ◽  
The Matrix ◽  
First Order Approximation

Seismic imaging processes are, in general, formulated under the assumption of a correct macrovelocity model. However, seismic subsurface images are very sensitive to the accuracy of the macrovelocity model. This paper investigates how the output of Kirchhoff inversion/migration changes for perturbations of a given 3‐D laterally inhomogeneous macrovelocity model. The displacement of a reflector image point from a perturbation of the given velocity model is determined in a first‐order approximation by the corresponding traveltime and slowness perturbations as well as the matrix. of the Beylkin determinant. The required traveltime derivatives can be calculated with ray perturbation theory. Using this result, a new, computationally efficient Kirchhoff inversion/migration technique is developed to predict in parallel a series of subsurface images for perturbations of a given macrovelocity model during a single inversion/migration process applied to the unmigrated seismic data. These images are constructed by superposition of the seismic data at predicted image point locations which lie on surfaces that expand from the initial image point as a function of the velocity perturbation. Because of the analogy to Huygens wavefronts in wave propagation, the technique is called Kirchhoff image propagation. A 2‐D implementation of Kirchhoff image propagation requires about 1.2 times the computation time of a single migration to calculate a set of propagated images. The propagated images provide good approximations to remigrated images and are applied to migration velocity analysis.

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.

2-D continuation operators and their applications

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1846-1858 ◽  
Author(s):  
Claudio Bagaini ◽  
Umberto Spagnolini
Keyword(s):  
Seismic Data ◽  
Real Data ◽  
Integral Form ◽  
Amplitude Distribution ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Seismic Data Processing ◽  
Analysis Method ◽  
Standard Tool ◽  
Zero Offset

Continuation to zero offset [better known as dip moveout (DMO)] is a standard tool for seismic data processing. In this paper, the concept of DMO is extended by introducing a set of operators: the continuation operators. These operators, which are implemented in integral form with a defined amplitude distribution, perform the mapping between common shot or common offset gathers for a given velocity model. The application of the shot continuation operator for dip‐independent velocity analysis allows a direct implementation in the acquisition domain by exploiting the comparison between real data and data continued in the shot domain. Shot and offset continuation allow the restoration of missing shot or missing offset by using a velocity model provided by common shot velocity analysis or another dip‐independent velocity analysis method.

On the topography of the cost functional in linear and nonlinear inverse problems

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. W1-W15 ◽  
Author(s):  
Juan L. Fernández Martínez ◽  
M. Zulima Fernández Muñiz ◽  
Michael J. Tompkins
Keyword(s):  
Inverse Problems ◽  
Null Space ◽  
Order Approximation ◽  
Singular Values ◽  
Physical Models ◽  
Local Data ◽  
Cost Functional ◽  
Nonlinear Inverse Problems ◽  
Linear And Nonlinear ◽  
The Cost

We analyze, through linear algebra, the topography of the cost functional in linear and nonlinear inverse problems with the aim of illuminating general characteristics. To a first-order approximation, the local data misfit function in any inverse problem is valley-shaped and elongated in the directions of the null space of the Jacobian and/or in the directions of the smallest singular values. In nonlinear inverse problems, valleys persist; however, local minima might also coexist in the misfit space and might be related to nonlinear effects ignored by the Gauss-Newton approximation to the Hessian, the regularization term designed to provide convexity to the misfit function, or to noise in the data. Furthermore, noise perturbs the size of the equivalence region making location of solutions easier but finding a global minimum harder (in the case of existence). Understanding the behavior of the cost functional is an important step in the developing techniques to appraise inverse solutions and estimate uncertainties caused by noise, incomplete sampling, regularization, and more fundamentally, simplified physical models.

Analytic solution of ray-tracing equations for a linearly inhomogeneous and elliptically anisotropic velocity model

Geophysics ◽  
2005 ◽  
Vol 70 (5) ◽  
pp. D37-D41 ◽  
Author(s):  
Yves Rogister ◽  
Michael A. Slawinski
Keyword(s):  
Ray Tracing ◽  
Order Approximation ◽  
Anisotropy Parameter ◽  
Field Measurements ◽  
Velocity Model ◽  
Western Canada ◽  
First Order ◽  
Approximation Linear ◽  
The Difference ◽  
First Order Approximation

We study wave propagation in anisotropic inhomogeneous media. Specifically, we formulate and analytically solve the ray-tracing equations for the factorized model with wavefront velocity increasing linearly with depth and depending elliptically on direction. We obtain explicit expressions for traveltime, wavefront (phase) angle, and ray (group) velocity and angle, and study these seismological quantities for a model that successfully describes field measurements in the Western Canada Basin. By considering numerical examples, we also show that the difference between the wavefront and ray velocities depends only slightly on the anisotropy parameter, whereas the difference between the wavefront and ray angles is, in a first-order approximation, linear in the anisotropy parameter.

Oriented prestack time migration using local slopes and predictive painting in the common-source domain for planar reflectors

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. S409-S418 ◽  
Author(s):  
M. Javad Khoshnavaz ◽  
Andrej Bóna ◽  
Aleksander Dzunic ◽  
Kevin Ung ◽  
Milovan Urosevic
Keyword(s):  
Seismic Data ◽  
Imaging Techniques ◽  
Velocity Model ◽  
Higher Order ◽  
Common Source ◽  
Velocity Analysis ◽  
Time Migration ◽  
Prestack Time Migration ◽  
The Common ◽  
Migration Technique

Seismic imaging techniques often require an input velocity model. Velocity analysis is one of the most critical stages in seismic data processing. Standard ways to find the velocity model from seismic data in the time domain are constant velocity stack and semblance velocity analysis that may be time consuming and labor intensive. Oriented/velocity-less imaging using local event slopes is an alternative to the conventional imaging techniques. In some previous oriented techniques, seismic data must be sorted in two different domains, whereas seismic data are not always available in both domains and the use of interpolation is inevitable in such cases. Other methods are developed in terms of the higher order derivatives of traveltime with respect to offset, whereas estimation of the higher order derivatives is difficult to achieve with the required accuracy. We addressed the limitations by developing an oriented local slope based prestack time migration technique in only one domain: the common-source domain. The migration technique is developed for reflectors with small curvature. In the proposed approach, the need for the estimation of higher order derivatives is replaced by a point-to-point mapping of seismic data using the predictive painting technique. The theoretical contents of the proposed technique are tested on a simple synthetic data example and applied to a field data set.

scholarly journals The Seismic Interpretation for (X) Oil Field Depending on 3D Seismic Data of Nearby Oil Field, Southern Iraq

2021 ◽  
Vol 11 (4) ◽  
pp. 36-50
Author(s):  
Wessam Abdul Abbas Alhammod ◽  
Ban Talib Aljizani
Keyword(s):  
Seismic Data ◽  
Velocity Model ◽  
Oil Field ◽  
Seismic Survey ◽  
Rock Properties ◽  
3D Seismic ◽  
Water Contact ◽  
The Time Domain ◽  
Structural Closure ◽  
Southern Iraq

This research focused on using seismic data to review the structure of the (X) Oil Field, located 40 km SW of Basrah, Southern Iraq. The study utilises a 3D seismic survey conducted during 2011-2012, covering the (Y) Oil Field 2 km to the west, and with partial coverage across (X), to map the Top Zubair reflector. Seismic rock properties analysis was conducted on key (X) Oil Field wells and used to tie the Top Zubair reflector on (X) Oil Field. The reflector was mapped within the time domain using DecisionSpace Software, and then converted to depth using a velocity model. The depth structure map was then compared to the original oil water contact (OOWC) across the fields to understand the potential structural closure of the Top Zubair reservoir in both fields.

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