Efficient one‐pass 3-D time migration

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1833-1845
Author(s):  
Matthew A. Brzostowski ◽  
Fred F. C. Snyder ◽  
Patrick J. Smith
Keyword(s):  
Fourier Transform ◽  
Wave Equation ◽  
Downward Continuation ◽  
Time Dependent ◽  
Single Pass ◽  
Time Migration ◽  
Data Volume ◽  
Lateral Variations ◽  
D Wave

An efficient one‐pass 3-D time migration algorithm is introduced as an alternative to Ristow’s splitting approach. This algorithm extends Black and Leong’s [Formula: see text] approach with a time‐dependent Stolt stretch operation called dilation. Migration using [Formula: see text] dilation consists of a single pass over the 3-D data volume after [Formula: see text] slices are formed with each [Formula: see text] slice downward continued independently. A number of downward continuation algorithms based upon the 3-D wave equation may be used. Dilation accommodates any lateral variations in velocity before the 3-D data volume is decomposed into [Formula: see text] slices via a Fourier transform. An inverse dilation operation is performed after the downward‐continuation operation and after the data volume have been inverse Fourier transformed subsequently along the [Formula: see text] direction. Migration using the [Formula: see text] approach yields a one‐pass 3-D time migration algorithm that is practical and efficient where the medium velocity is smoothly varying.

Fourier prestack migration by equivalent wavenumber

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 197-207 ◽  
Author(s):  
Gary F. Margrave ◽  
John C. Bancroft ◽  
Hugh D. Geiger
Keyword(s):  
Fourier Transform ◽  
Inverse Fourier Transform ◽  
Square Root ◽  
Constant Frequency ◽  
Prestack Migration ◽  
Change Of Variables ◽  
Time Migration ◽  
Data Volume ◽  
And Migration ◽  
Amplitude Preservation

Fourier prestack migration is reformulated through a change of variables, from offset wavenumber to a new equivalent wavenumber, which makes the migration phase shift independent of horizontal wavenumber. After the change of variables, the inverse Fourier transform over horizontal wavenumber can be performed to create unmigrated, but fully horizontally positioned, gathers at each output location. A complete prestack migration then results by imaging each gather independently with a poststack migration algorithm. This equivalent wavenumber migration (EWM) is the Fourier analog of the space‐time domain method of equivalent offset migration (EOM). The latter is a Kirchhoff time‐migration technique which forms common scatterpoint (CSP) gathers for each migrated trace and then images those gathers with a Kirchhoff summation. These CSP gathers are formed by trace mappings at constant time, and migration velocity analysis is easily done after the gathers are formed. Both EWM and EOM are motivated by the algebraic combination of a double square root equation into a single square root. This result defines equivalent wavenumber or offset. EWM is shown to be an exact reformulation of prestack f-k migration. The EWM theory provides explicit Fourier integrals for the formation of CSP gathers from the prestack data volume and the imaging of those gathers to form the final prestack migrated result. The CSP gathers are given by a Fourier mapping, at constant frequency, of the unmigrated spectrum followed by an inverse Fourier transform. The mapping requires angle‐dependent weighting factors for full amplitude preservation. The imaging expression (for each CSP gather) is formally identical to poststack migration with the result retained only at zero equivalent offset. Through a numerical simulation, the impulse responses of EOM and EWM are shown to be kinematically identical. Amplitude scale factors, which are exact in the constant velocity EWM theory, are implemented approximately in variable velocity EOM.

scholarly journals Depth-Extrapolation-Based True-Amplitude Full-Wave-Equation Migration from Topography

2021 ◽  
Vol 11 (7) ◽  
pp. 3010
Author(s):  
Hao Liu ◽  
Xuewei Liu
Keyword(s):  
Wave Equation ◽  
Partial Derivative ◽  
Model Experiment ◽  
Surface Velocity ◽  
Seismic Exploration ◽  
Initial Condition ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Full Wave ◽  
Time Migration

The lack of an initial condition is one of the major challenges in full-wave-equation depth extrapolation. This initial condition is the vertical partial derivative of the surface wavefield and cannot be provided by the conventional seismic acquisition system. The traditional solution is to use the wavefield value of the surface to calculate the vertical partial derivative by assuming that the surface velocity is constant. However, for seismic exploration on land, the surface velocity is often not uniform. To solve this problem, we propose a new method for calculating the vertical partial derivative from the surface wavefield without making any assumptions about the surface conditions. Based on the calculated derivative, we implemented a depth-extrapolation-based full-wave-equation migration from topography using the direct downward continuation. We tested the imaging performance of our proposed method with several experiments. The results of the Marmousi model experiment show that our proposed method is superior to the conventional reverse time migration (RTM) algorithm in terms of imaging accuracy and amplitude-preserving performance at medium and deep depths. In the Canadian Foothills model experiment, we proved that our method can still accurately image complex structures and maintain amplitude under topographic scenario.

An exact non reflecting boundary condition for 2D time-dependent wave equation problems

Wave Motion ◽  
2014 ◽  
Vol 51 (1) ◽  
pp. 168-192 ◽  
Author(s):  
Silvia Falletta ◽  
Giovanni Monegato
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Time Dependent

Gaussian beam migration

Geophysics ◽  
1990 ◽  
Vol 55 (11) ◽  
pp. 1416-1428 ◽  
Author(s):  
N. Ross Hill
Keyword(s):  
Gaussian Beam ◽  
Wave Field ◽  
Seismic Source ◽  
Velocity Model ◽  
Downward Continuation ◽  
Gaussian Beams ◽  
Seismic Velocities ◽  
Migration Method ◽  
Gaussian Beam Migration ◽  
Lateral Variations

Just as synthetic seismic data can be created by expressing the wave field radiating from a seismic source as a set of Gaussian beams, recorded data can be downward continued by expressing the recorded wave field as a set of Gaussian beams emerging at the earth’s surface. In both cases, the Gaussian beam description of the seismic‐wave propagation can be advantageous when there are lateral variations in the seismic velocities. Gaussian‐beam downward continuation enables wave‐equation calculation of seismic propagation, while it retains the interpretive raypath description of this propagation. This paper describes a zero‐offset depth migration method that employs Gaussian beam downward continuation of the recorded wave field. The Gaussian‐beam migration method has advantages for imaging complex structures. Like finite‐difference migration, it is especially compatible with lateral variations in velocity, but Gaussian beam migration can image steeply dipping reflectors and will not produce unwanted reflections from structure in the velocity model. Unlike other raypath methods, Gaussian beam migration has guaranteed regular behavior at caustics and shadows. In addition, the method determines the beam spacing that ensures efficient, accurate calculations. The images produced by Gaussian beam migration are usually stable with respect to changes in beam parameters.

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.

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