Parsimonious 2D prestack Kirchhoff depth migration

Geophysics ◽  
2003 ◽  
Vol 68 (3) ◽  
pp. 1043-1051 ◽  
Author(s):  
Biaolong Hua ◽  
George A. McMechan
Keyword(s):  
Fresnel Zone ◽  
Computation Time ◽  
Structural Features ◽  
Common Source ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Migration Velocity Analysis ◽  
Reflector Surface ◽  
Kirchhoff Depth Migration ◽  
Ray Parameter

The efficiency of prestack Kirchhoff depth migration is much improved by using ray parameter information measured from prestack common‐source and common‐receiver gathers. Ray tracing is performed only back along the emitted and emergent wave directions, and so is much reduced. The position of the intersection of the source and receiver rays is adjusted to satisfy the image time condition. The imaged amplitudes are spread along the local reflector surface only within the first Fresnel zone. There is no need to build traveltime tables before migration because the traveltime calculation is embedded into the migration. To further reduce the computation time, the input data are decimated by applying an amplitude threshold before the estimation of ray parameters, and only peak and trough points on each trace are searched for ray parameters. Numerical results show that the proposed implementation is typically 50–80 times faster than traditional Kirchhoff migration for synthetic 2D prestack data. The migration speed improvement is obtained at the expense of some reduction in migration quality; the optimal compromise is implemented by the choice of migration parameters. The main uses of the algorithm will be to get a fast first look at the main structural features and for iterative migration velocity analysis.

Parsimonious 2‐D poststack Kirchhoff depth migration

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1497-1503 ◽  
Author(s):  
Biao‐Long Hua ◽  
George A. McMechan
Keyword(s):  
Incident Wave ◽  
Input Data ◽  
Fresnel Zone ◽  
Computation Time ◽  
Structural Features ◽  
Seismic Section ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Ray Path ◽  
Kirchhoff Depth Migration

Efficiency of Kirchhoff migration can be much improved by using slope information from the seismic section to estimate the incident wave directions. Ray tracing is performed only back along the incident wave directions and so is much reduced. Unlike in conventional Kirchhoff implementations, there is no need to build traveltime tables, so relatively little memory and input/output use are required. Compression of the input data and restricting the contribution of each time sample to the image to lie within a Fresnel zone of its ray path further reduces the computation time. Synthetic and field data tests show that the new algorithm is about 30 times faster than traditional Kirchhoff migration for 2‐D poststack data. The main structural features may be imaged very quickly at the expense of some details. There is a tradeoff between speed and image quality; the optimal compromise is implemented by the choice of migration parameters.

Prestack 2D parsimonious Kirchhoff depth migration of elastic seismic data

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. S157-S164 ◽  
Author(s):  
Robert Sun ◽  
George A. McMechan
Keyword(s):  
Seismic Data ◽  
Velocity Model ◽  
P Wave ◽  
P Value ◽  
Common Source ◽  
S Wave ◽  
P Values ◽  
Depth Migration ◽  
Reflector Surface ◽  
Kirchhoff Depth Migration

We have extended prestack parsimonious Kirchhoff depth migration for 2D, two-component, reflected elastic seismic data for a P-wave source recorded at the earth’s surface. First, we separated the P-to-P reflected (PP-) waves and P-to-S converted (PS-) waves in an elastic common-source gather into P-wave and S-wave seismograms. Next, we estimated source-ray parameters (source p values) and receiver-ray parameters (receiver p values) for the peaks and troughs above a threshold amplitude in separated P- and S-wavefields. For each PP and PS reflection, we traced (1) a source ray in the P-velocity model in the direction of the emitted ray angle (determined by the source p value) and (2) a receiver ray in the P- or S-velocity model back in the direction of the emergent PP- or PS-wave ray angle (determined by the PP- or PS-wave receiver p value), respectively. The image-point position was adjusted from the intersection of the source and receiver rays to the point where the sum of the source time and receiver-ray time equaled the two-way traveltime. The orientation of the reflector surface was determined to satisfy Snell’s law at the intersection point. The amplitude of a P-wave (or an S-wave) was distributed over the first Fresnel zone along the reflector surface in the P- (or S-) image. Stacking over all P-images of the PP-wave common-source gathers gave the stacked P-image, and stacking over all S-images of the PS-wave common-source gathers gave the stacked S-image. Synthetic examples showed acceptable migration quality; however, the images were less complete than those produced by scalar reverse-time migration (RTM). The computing time for the 2D examples used was about 1/30 of that for scalar RTM of the same data.

3-D prestack Kirchhoff beam migration for depth imaging

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1592-1603 ◽  
Author(s):  
Yonghe Sun ◽  
Fuhao Qin ◽  
Steve Checkles ◽  
Jacques P. Leveille
Keyword(s):  
Distributed Environment ◽  
Small Surface ◽  
Depth Imaging ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Surface Patches ◽  
Image Volume ◽  
Kirchhoff Depth Migration ◽  
Full Volume ◽  
Single Set

A beam implementation is presented for efficient full‐volume 3-D prestack Kirchhoff depth migration of seismic data. Unlike conventional Kirchhoff migration in which the input seismic traces in time are migrated one trace at a time into the 3-D image volume for the earth’s subsurface, the beam migration processes a group of input traces (a supergather) together. The requirement for a supergather is that the source and receiver coordinates of the traces fall into two small surface patches. The patches are small enough that a single set of time maps pertaining to the centers of the patches can be used to migrate all the traces within the supergather by Taylor expansion or interpolation. The migration of a supergather consists of two major steps: stacking the traces into a τ-P beam volume, and mapping the beams into the image volume. Since the beam volume is much smaller than the image volume, the beam migration cost is roughly proportional to the number of input supergathers. The computational speedup of beam migration over conventional Kirchhoff migration is roughly proportional to [Formula: see text], the average number of traces per supergather, resulting a theoretical speedup up to two orders of magnitudes. The beam migration was successfully implemented and has been in production use for several years. A factor of 5–25 speedup has been achieved in our in‐house depth migrations. The implementation made 3-D prestack full‐volume depth imaging feasible in a parallel distributed environment.

2‐D wavepath migration

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1528-1537 ◽  
Author(s):  
H. Sun ◽  
G. T. Schuster
Keyword(s):  
Fresnel Zone ◽  
Complex Structure ◽  
Computation Time ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Kirchhoff Migration ◽  
Time Sample ◽  
Grid Points ◽  
Computationally Intensive ◽  
Single Trace

Prestack Kirchhoff migration (KM) is computationally intensive for iterative velocity analysis. This is partly because each time sample in a trace must be smeared along a quasi‐ellipsoid in the model. As a less costly alternative, we use the stationary phase approximation to the KM integral so that the time sample is smeared along a small Fresnel zone portion of the quasi‐ellipsoid. This is equivalent to smearing the time samples in a trace over a 1.5‐D fat ray (i.e., wavepath), so we call this “wavepath migration” (WM). This compares to standard KM, which smears the energy in a trace along a 3‐D volume of quasi‐concentric ellipsoids. In principle, single trace migration with WM has a computational count of [Formula: see text] compared to KM, which has a computational count of [Formula: see text], where N is the number of grid points along one side of a cubic velocity model. Our results with poststack data show that WM produces an image that in some places contains fewer migration artifacts and is about as well resolved as the KM image. For a 2‐D poststack migration example, the computation time of WM is less than one‐third that of KM. Our results with prestack data show that WM images contain fewer migration artifacts and can define the complex structure more accurately. It is also shown that WM can be significantly faster than KM if a slant stack technique is used in the migration. The drawback with WM is that it is sometimes less robust than KM because of its sensitivity to errors in estimating the incidence angles of the reflections.

Can we image complex structures with first‐arrival traveltime?

Geophysics ◽  
1993 ◽  
Vol 58 (4) ◽  
pp. 564-575 ◽  
Author(s):  
Sébastien Geoltrain ◽  
Jean Brac
Keyword(s):  
Eikonal Equation ◽  
Geological Structure ◽  
Complex Structures ◽  
Complex Velocity ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Finite Differencing ◽  
Explicit Reference ◽  
First Arrival ◽  
Kirchhoff Depth Migration

We experienced difficulties when attempting to perform seismic imaging in complex velocity fields using prestack Kirchhoff depth migration in conjunction with traveltimes computed by finite‐differencing the eikonal equation. The problem arose not because of intrinsic limitations of Kirchhoff migration, but rather from the failure of finite‐differencing to compute traveltimes representative of the energetic part of the wavefield. Further analysis showed that the first arrival is most often associated with a marginally energetic event wherever subsequent arrivals exist. The consequence is that energetic seismic events are imaged with a kinematically incorrect operator and turn out mispositioned at depth. We therefore recommend that first‐arrival traveltime fields, such as those computed by finite‐differencing the eikonal equation, be used in Kirchhoff migration only with great care when the velocity field hosts multiple transmitted arrivals; such a situation is typically met where geological structure creates strong and localized velocity heterogeneities, which partition the incident and reflected wavefields into multiple arrivals; in such an instance, imaging cannot be strictly considered a kinematic process, as it must be performed with explicit reference to the relative amplitudes of multiple arrivals.

Angle‐domain common‐image gathers by wavefield continuation methods

Geophysics ◽  
2003 ◽  
Vol 68 (3) ◽  
pp. 1065-1074 ◽  
Author(s):  
Paul C. Sava ◽  
Sergey Fomel
Keyword(s):  
Continuation Methods ◽  
Depth Migration ◽  
Migration Velocity Analysis ◽  
Wavefield Continuation ◽  
Alternative Approaches ◽  
Radial Trace Transform ◽  
Ray Parameter ◽  
Seismic Images ◽  
Amplitude Versus ◽  
Field Continuation

Migration in the angle domain creates seismic images for different reflection angles. We present a method for computing angle‐domain common‐image gathers from seismic images obtained by depth migration using wave‐field continuation. Our method operates on prestack migrated images and produces the output as a function of the reflection angle, not as a function of offset ray parameter as in other alternative approaches. The method amounts to a radial‐trace transform in the Fourier domain and is equivalent to a slant stack in the space domain. We obtain the angle gathers using a stretch technique that enables us to impose smoothness through regularization. Several examples show that our method is accurate, fast, robust, and easy to implement. The main anticipated applications of our method are in the areas of migration‐velocity analysis and amplitude‐versus‐angle analysis.

Fast model-based migration velocity analysis and reflector shape estimation

Geophysics ◽  
2005 ◽  
Vol 70 (2) ◽  
pp. U9-U17 ◽  
Author(s):  
Weihong Fei ◽  
George A. McMechan
Keyword(s):  
Computation Time ◽  
Migration Velocity ◽  
Velocity Variation ◽  
Velocity Analysis ◽  
Shape Estimation ◽  
Reflection Point ◽  
Data Set ◽  
Depth Migration ◽  
Interval Velocity ◽  
Migration Velocity Analysis

Migration velocity analysis can be made more efficient by preselecting the traces that contribute to a series of common-reflection-point (CRP) gathers and migrating only those traces. The data traces that contribute to a CRP for one reflection point on one layer are defined in a two-step procedure. First, poststack parsimonious Kirchhoff depth migration of zero-offset (or stacked) traces defines approximate reflector positions and orientations. Then, ray tracing from the reflection points for nonzero reflection angles defines the source and receiver locations of the data traces in the CRP gather. These traces are then prestack depth migrated, and the interval velocity model adjustment is obtained by fitting the velocity that maximizes the stack amplitude over the predicted (nonhyperbolic) moveout. A small number (2–3) of iterations converge to a 2D model of layer shape and interval velocity. Further efficiency is obtained by implementing layer stripping. The computation time is greatly reduced by combining parsimonious migration with processing only the salient portions of the whole seismic data set. The algorithm can handle lateral velocity variation within each layer as well as constant velocity. The computation time of the proposed algorithm is of the same order as that of the standard rms velocity scan method, but it does not have the inherent assumptions of the velocity scan method and is faster than current iterative prestack depth migration velocity analysis methods for typical field data.

3D common-reflection-point-based seismic migration velocity analysis

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. S161-S167 ◽  
Author(s):  
Weihong Fei ◽  
George A. McMechan
Keyword(s):  
Synthetic Data ◽  
Computation Time ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Reflection Point ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Migration Velocity Analysis ◽  
Spatial Coordinates

Three-dimensional prestack depth migration and depth residual picking in common-image gathers (CIGs) are the most time-consuming parts of 3D migration velocity analysis. Most migration-based velocity analysis algorithms need spatial coordinates of reflection points and CIG depth residuals at different offsets (or angles) to provide updated velocity information. We propose a new algorithm that can analyze 3D velocity quickly and accurately. Spatial coordinates and orientations of reflection points are provided by a 3D prestack parsimonious depth migration; the migration involves only the time samples picked from the salient reflection events on one 3D common-offset volume. Ray tracing from the reflection points to the surface provides a common-reflection-point (CRP) gather for each reflection point. Predicted (nonhyperbolic) moveouts for local velocity perturbations, based on maximizing the stacked amplitude, give the estimated velocity updates for each CRP gather. Then the velocity update for each voxel in the velocity model is obtained by averaging over all predicted velocity updates for that voxel. Prior model constraints may be used to stabilize velocity updating. Compared with other migration velocity analyses, the traveltime picking is limited to only one common-offset volume (and needs to be done only once); there is no need for intensive 3D prestack depth migration. Hence, the computation time is orders of magnitude less than other migration-based velocity analyses. A 3D synthetic data test shows the algorithm works effectively and efficiently.

Efficient 2.5-D true‐amplitude migration

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 943-950 ◽  
Author(s):  
Joe A. Dellinger ◽  
Samuel H. Gray ◽  
Gary E. Murphy ◽  
John T. Etgen
Keyword(s):  
Seismic Data ◽  
Constant Velocity ◽  
Three Dimensions ◽  
Additional Source ◽  
Standard Methods ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Out Of Plane ◽  
Kirchhoff Method ◽  
Kirchhoff Depth Migration

Kirchhoff depth migration is a widely used algorithm for imaging seismic data in both two and three dimensions. To perform the summation at the heart of the algorithm, standard Kirchhoff migration requires a traveltime map for each source and receiver. True‐amplitude Kirchhoff migration in 2.5-D υ(x, z) media additionally requires maps of amplitudes, out‐of‐plane spreading factors, and takeoff angles; these quantities are necessary for calculating the true‐amplitude weight term in the summation. The increased input/output (I/O) and computational expense of including the true‐amplitude weight term is often not justified by significant improvement in the final muted and stacked image. For this reason, some authors advocate neglecting the weight term in the Kirchhoff summation entirely for most everyday imaging purposes. We demonstrate that for nearly the same expense as ignoring the weight term, a much better solution is possible. We first approximate the true‐amplitude weight term by the weight term for constant‐velocity media; this eliminates the need for additional source and receiver maps. With one small additional approximation, the weight term can then be moved entirely outside the innermost loop of the summation. The resulting Kirchhoff method produces images that are almost as good as for exact true‐amplitude Kirchhoff migration and at almost the same cost as standard methods that do not attempt to preserve amplitudes.

3-D elastic prestack, reverse‐time depth migration

Geophysics ◽  
1994 ◽  
Vol 59 (4) ◽  
pp. 597-609 ◽  
Author(s):  
Wen‐Fong Chang ◽  
George A. McMechan
Keyword(s):  
Finite Differences ◽  
Synthetic Data ◽  
P Wave ◽  
Common Source ◽  
Reverse Time ◽  
Depth Migration ◽  
Full Wave ◽  
Source Data ◽  
Recorded Data ◽  
Time Extrapolation

By combining and extending previous algorithms for 2-D prestack elastic migration and 3-D prestack acoustic migration, a full 3-D elastic prestack depth migration algorithm is developed. Reverse‐time extrapolation of the recorded data is by 3-D elastic finite differences; computation of the image time for each point in the 3-D volume is by 3-D acoustic finite differences. The algorithm operates on three‐component, vector‐wavefield common‐source data and produces three‐component vector reflectivity distributions. Converted P‐to‐S reflections are automatically imaged with the primary P‐wave reflections. There are no dip restrictions as the full wave equation is used. The algorithm is illustrated by application to synthetic data from three models; a flat reflector, a dipping truncated wedge overlying a flat reflector, and the classical French double dome and fault model.

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