Depth migration from irregular surfaces with depth extrapolation methods

Geophysics ◽  
1991 ◽  
Vol 56 (1) ◽  
pp. 119-122 ◽  
Author(s):  
Moshe Reshef
Keyword(s):  
Wave Equation ◽  
Surface Topography ◽  
Time Shift ◽  
Extrapolation Methods ◽  
Irregular Surfaces ◽  
Depth Migration ◽  
Numerical Problem ◽  
Flat Interface ◽  
Interface Wave ◽  
Computationally Expensive

Nonflat surface topography introduces a numerical problem for migration algorithms that are based on depth extrapolation. Since the numerically efficient migration schemes start at a flat interface, wave‐equation datuming is required (Berryhill, 1979) prior to the migration. The computationally expensive datuming procedure is often replaced by a simple time shift for the elevation to datum correction. For nonvertically traveling energy this correction is inaccurate. Subsequent migration wrongly positions the reflectors in depth.

The zero‐velocity layer: Migration from irregular surfaces

Geophysics ◽  
1992 ◽  
Vol 57 (11) ◽  
pp. 1435-1443 ◽  
Author(s):  
Craig Beasley ◽  
Walt Lynn
Keyword(s):  
Wave Equation ◽  
Seismic Data ◽  
Migration Velocity ◽  
Time Shift ◽  
Irregular Surfaces ◽  
Interval Velocity ◽  
Static Correction ◽  
Zero Velocity ◽  
And Migration ◽  
Velocity Layer

Seismic data acquired in areas with irregular topography are usually corrected to a flat datum before migration. A time‐honored technique for handling elevation changes is to time shift the data before application of migration. This simple time shift, or elevation‐static correction, cannot properly represent wide‐angle or dipping reflections as they would have been recorded at the datum. As a result, when elevation varies significantly, accuracy in event positioning may be compromised for migration and other wave‐equation processes, such as dip moveout processing (DMO). Traditionally, such over‐ and under‐migration artifacts have been dealt with by increasing or decreasing the migration velocity. However, simple adjustment of the migration velocity cannot undo the wave‐field distortions induced in seismic data acquired over varying elevations. More sophisticated and accurate solutions such as wave‐equation datuming are too computationally demanding for routine use. Here, we propose an efficient and accurate technique for doing migration from irregular surfaces using conventional migration algorithms. As in elevation‐static corrections, surface‐recorded data are time‐shifted to a horizontal datum; for our process, we choose to have that datum elevation lie at or above the highest elevation in the survey. After migration, the datum elevation can always be adjusted to any other level by means of a bulk time shift. In the migration step, the velocity is set to zero (or some very small value) in the layer between the surface and the datum; below the original surface, the interval velocity represents the best estimate of the subsurface geology. By adding a zero‐velocity layer, the migration algorithm is applied to the data from the flat datum and no lateral propagation is allowed until a nonzero velocity is encountered at the recording surface. Synthetic and field data examples demonstrate that use of the “zero‐velocity layer” significantly improves imaging accuracy relative to conventional migration from a flat datum. Moreover, the geologically derived migration‐velocity field need not be adjusted to compensate for shortcomings in the datum‐static procedure. The technique can be extended to prestack processes such as DMO, shot‐ and receiver‐gather downward extrapolation, and migration and thus suggests a unified approach to processing data from irregular surfaces.

Q least-squares reverse time migration based on the first-order viscoacoustic quasidifferential equations

Geophysics ◽  
2021 ◽  
pp. 1-65
Author(s):  
Yingming Qu ◽  
Yixin Wang ◽  
Zhenchun Li ◽  
Chang Liu
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Surface Topography ◽  
Density Perturbation ◽  
Second Order ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
First Order ◽  
Time Migration ◽  
Grid Scheme

Seismic wave attenuation caused by subsurface viscoelasticity reduces the quality of migration and the reliability of interpretation. A variety of Q-compensated migration methods have been developed based on the second-order viscoacoustic quasidifferential equations. However, these second-order wave-equation-based methods are difficult to handle with density perturbation and surface topography. In addition, the staggered grid scheme, which has an advantage over the collocated grid scheme because of its reduced numerical dispersion and enhanced stability, works in first-order wave-equation-based methods. We have developed a Q least-squares reverse time migration method based on the first-order viscoacoustic quasidifferential equations by deriving Q-compensated forward-propagated operators, Q-compensated adjoint operators, and Q-attenuated Born modeling operators. Besides, our method using curvilinear grids is available even when the attenuating medium has surface topography and can conduct Q-compensated migration with density perturbation. The results of numerical tests on two synthetic and a field data sets indicate that our method improves the imaging quality with iterations and produces better imaging results with clearer structures, higher signal-to-noise ratio, higher resolution, and more balanced amplitude by correcting the energy loss and phase distortion caused by Q attenuation. It also suppresses the scattering and diffracted noise caused by the surface topography.

Fast acquisition aperture correction in prestack depth migration using beamlet decomposition

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. S67-S74 ◽  
Author(s):  
Jun Cao ◽  
Ru-Shan Wu
Keyword(s):  
Wave Equation ◽  
Correction Factor ◽  
Computing Time ◽  
Computation Time ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Wavenumber Domain ◽  
Amplitude Correction ◽  
Local Wavenumber ◽  
Local Angle

Wave-equation-based acquisition aperture correction in the local angle domain can improve image amplitude significantly in prestack depth migration. However, its original implementation is inefficient because the wavefield decomposition uses the local slant stack (LSS), which is demanding computationally. We propose a faster method to obtain the image and amplitude correction factor in the local angle domain using beamlet decomposition in the local wavenumber domain. For a given frequency, the image matrix in the local wavenumber domain for all shots can be calculated efficiently. We then transform the shot-summed image matrix from the local wavenumber domain to the local angle domain (LAD). The LAD amplitude correction factor can be obtained with a similar strategy. Having a calculated image and correction factor, one can apply similar acquisition aperture corrections to the original LSS-based method. For the new implementation, we compare the accuracy and efficiency of two beamlet decompositions: Gabor-Daubechies frame (GDF) and local exponential frame (LEF). With both decompositions, our method produces results similar to the original LSS-based method. However, our method can be more than twice as fast as LSS and cost only twice the computation time of traditional one-way wave-equation-based migrations. The results from GDF decomposition are superior to those from LEF decomposition in terms of artifacts, although GDF requires a little more computing time.

Modeling and an immersed finite element method for an interface wave equation

2018 ◽  
Vol 76 (7) ◽  
pp. 1625-1638 ◽  
Author(s):  
Jinwei Bai ◽  
Yong Cao ◽  
Xiaoming He ◽  
Hongyan Liu ◽  
Xiaofeng Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equation ◽  
Immersed Finite Element Method ◽  
Immersed Finite Element ◽  
Interface Wave ◽  
Element Method

The case for applying wave equation depth migration in the North Sea

First Break ◽  
2004 ◽  
Vol 22 (8) ◽  
Author(s):  
R. Leggott ◽  
J. Cowley ◽  
R.G. Williams
Keyword(s):  
Wave Equation ◽  
North Sea ◽  
Depth Migration ◽  
The North ◽  
The North Sea

3-D prestack depth migration by wavefield extrapolation methods

2003 ◽  
Vol 2003 (2) ◽  
pp. 1-4
Author(s):  
James Sun ◽  
Carl Notfors ◽  
Zhang Yu ◽  
Gray Sam ◽  
Young Jerry
Keyword(s):  
Extrapolation Methods ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Wavefield Extrapolation

Dsr-Based Wave Equation 3-D Prestack Depth Migration

2003 ◽  
Vol 46 (5) ◽  
pp. 966-977 ◽  
Author(s):  
Jiubing CHENG ◽  
Huazhong WANG ◽  
Zaitian MA
Keyword(s):  
Wave Equation ◽  
Prestack Depth Migration ◽  
Depth Migration

Depth migration by the Gaussian beam summation method

Geophysics ◽  
2010 ◽  
Vol 75 (2) ◽  
pp. S81-S93 ◽  
Author(s):  
Mikhail M. Popov ◽  
Nikolay M. Semtchenok ◽  
Peter M. Popov ◽  
Arie R. Verdel
Keyword(s):  
Wave Equation ◽  
Model Building ◽  
Velocity Structure ◽  
Velocity Model ◽  
Summation Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Depth Migration ◽  
Time Migration ◽  
Ray Methods

Seismic depth migration aims to produce an image of seismic reflection interfaces. Ray methods are suitable for subsurface target-oriented imaging and are less costly compared to two-way wave-equation-based migration, but break down in cases when a complex velocity structure gives rise to the appearance of caustics. Ray methods also have difficulties in correctly handling the different branches of the wavefront that result from wave propagation through a caustic. On the other hand, migration methods based on the two-way wave equation, referred to as reverse-time migration, are known to be capable of dealing with these problems. However, they are very expensive, especially in the 3D case. It can be prohibitive if many iterations are needed, such as for velocity-model building. Our method relies on the calculation of the Green functions for the classical wave equation by per-forming a summation of Gaussian beams for the direct and back-propagated wavefields. The subsurface image is obtained by cal-culating the coherence between the direct and backpropagated wavefields. To a large extent, our method combines the advantages of the high computational speed of ray-based migration with the high accuracy of reverse-time wave-equation migration because it can overcome problems with caustics, handle all arrivals, yield good images of steep flanks, and is readily extendible to target-oriented implementation. We have demonstrated the quality of our method with several state-of-the-art benchmark subsurface models, which have velocity variations up to a high degree of complexity. Our algorithm is especially suited for efficient imaging of selected subsurface subdomains, which is a large advantage particularly for 3D imaging and velocity-model refinement applications such as subsalt velocity-model improvement. Because our method is also capable of providing highly accurate migration results in structurally complex subsurface settings, we have also included the concept of true-amplitude imaging in our migration technique.

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