Including Lateral Velocity Variations Into True-Amplitude Wave-Equation Migration

Author(s):  
D. Amazonas ◽  
R. Aleixo ◽  
J. Schleicher ◽  
J. Costa ◽  
A. Novais ◽  
...  
2009 ◽  
Author(s):  
D. Amazonas ◽  
R. Aleixo ◽  
J. Schleicher ◽  
J. Costa ◽  
A. Novais ◽  
...  

2010 ◽  
Author(s):  
Daniela Amazonas ◽  
Rafael Aleixo ◽  
Gabriela Melo ◽  
Jörg Schleicher ◽  
Amélia Novais ◽  
...  

Geophysics ◽  
1982 ◽  
Vol 47 (7) ◽  
pp. 1001-1011 ◽  
Author(s):  
Richard Jay Castle

An algorithm for three‐dimensional wave equation migration in the presence of lateral velocity gradients is developed. The algorithm is based geophysically on the exploding reflector model and mathematically on integral solutions to the scalar wave equation. In addition, the velocity is assumed to vary slowly over a seismic wavelength. The primary application of the algorithm is to stacked sections. However, if the velocity is a function of depth only, the algorithm may be used to migrate and/or image common‐depth‐point gathers.


Geophysics ◽  
1988 ◽  
Vol 53 (10) ◽  
pp. 1311-1322 ◽  
Author(s):  
V. Shtivelman ◽  
A. Canning

Seismic sections are usually datum corrected by static shifting. For small differences in elevation and slow velocity variations between the input datum and the output datum, static shifting is a sufficiently accurate datum correction procedure. However, for significant differences in elevations and a more complicated velocity model, the accuracy of the static solution may prove to be insufficient; and a more exact method should be used. In this paper, we study the limitations of the static method of datum correction and develop simple and effective extrapolation schemes based on the wave equation, schemes which lead to more accurate datum correction. The distortions of seismic events caused by static correction are illustrated by a number of simple examples. To reduce the distortions, we propose a number of extrapolation schemes based on the asymptories of the Kirchhoff integral solution of the 2-D scalar wave equation. Application of the extrapolation algorithms to synthetic data shows that they provide accurate datum corrections even for a nonplanar input datum and vertical and lateral velocity variations. The algorithms have been successfully applied to real data.


2018 ◽  
Vol 6 (1) ◽  
pp. T1-T13
Author(s):  
Bin Lyu ◽  
Qin Su ◽  
Kurt J. Marfurt

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.


Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. S387-S398 ◽  
Author(s):  
Jiachun You ◽  
Ru-Shan Wu ◽  
Xuewei Liu

To meet the requirement of true-amplitude migration and address the shortcomings of the classic one-way wave equations on the dynamic imaging, one-way true-amplitude wave equations were developed. Migration methods, based on the Taylor or other series approximation theory, are introduced to solve the one-way true-amplitude wave equations. This leads to the main weakness of one-way true-amplitude migration for imaging the complex or strong velocity — contrast media — the limited imaging angles. To deal with this issue, we apply a matrix decomposition method to accurately calculate the square-root operator and impose the boundary conditions of the one-way true-amplitude wave equations. Our migration method and the conventional one-way true-amplitude Fourier finite-difference (FFD) migration method are used by us to test and compare the imaging performance. The impulse responses in a strong velocity-contrast model prove that our migration method works for larger imaging angles than the one-way true-amplitude FFD method. The amplitude calculations in a strong-lateral velocity variation media with one reflector and in the Marmousi model demonstrate that our migration method provides better amplitude-preserving performance and offers higher structural imaging quality than the one-way true-amplitude FFD method. We also use field data to indicate the imaging enhancement and the feasibility of our method compared with the one-way true-amplitude FFD method. Our one-way true-amplitude migration method using matrix decomposition fully exploits the features of one-way true-amplitude wave equations with less approximation, and it is capable of producing more accurate amplitude estimations and potentially wider imaging angles.


1988 ◽  
Vol 6 (2) ◽  
pp. 136-150 ◽  
Author(s):  
Glenn P. Thrasher

The western-most region of Taranaki Basin, the Western Platform, has a stratigraphy which permits subdivision into major seismic units. The reflectors separating these units are easily identifiable. Each of the units and reflectors has typical reflection characteristics which are often correlatable with the lithology of the unit. Lateral velocity variations, caused by lateral deposition and compaction variations in prograding sequences, area major problem in developing depth conversion models for this region. Analysis of travel time data from wells shows that velocity variations in both the Oligocene-Miocene and Pliocene-Pleistocene sequences are predictable from the thickness variations of the units (and hence from interval travel times). The imerval velocity variations of the Paleocene-Eocene transgressive sequence are dependent on the overburden history and lithology of the unit.


Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. S199-S209 ◽  
Author(s):  
Flor A. Vivas ◽  
Reynam C. Pestana

One-way wave equation migration is a powerful imaging tool for locating accurately reflectors in complex geologic structures; however, the classical formulation of one-way wave equations does not provide accurate amplitudes for the reflectors. When dynamic information is required after migration, such as studies for amplitude variation with angle or when the correct amplitudes of the reflectors in the zero-offset images are needed, some modifications to the one-way wave equations are required. The new equations, which are called “true-amplitude one-way wave equations,” provide amplitudes that are equivalent to those provided by the leading order of the ray-theoretical approximation through the modification of the transverse Laplacian operator with dependence of lateral velocity variations, the introduction of a new term associated with the amplitudes, and the modification of the source representation. In a smoothly varying vertical medium,the extrapolation of the wavefields with the true-amplitude one-way wave equations simplifies to the product of two separable and commutative factors: one associated with the phase and equal to the phase-shift migration conventional and the other associated with the amplitude. To take advantage of this true-amplitude phase-shift migration, we developed the extension of conventional migration algorithms in a mixed domain, such as phase shift plus interpolation, split step, and Fourier finite difference. Two-dimensional numerical experiments that used a single-shot data set showed that the proposed mixed-domain true-amplitude algorithms combined with a deconvolution-type imaging condition recover the amplitudes of the reflectors better than conventional mixed-domain algorithms. Numerical experiments with multiple-shot Marmousi data showed improvement in the amplitudes of the deepest structures and preservation of higher frequency content in the migrated images.


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