Robust and efficient upwind finite‐difference traveltime calculations in three dimensions

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1108-1117 ◽  
Author(s):  
William A. Schneider
Keyword(s):  
Finite Difference ◽  
Seismic Data ◽  
Velocity Model ◽  
Radial Component ◽  
Three Dimensions ◽  
Spherical Coordinate ◽  
Depth Migration ◽  
Slowness Vector ◽  
Kirchhoff Depth Migration ◽  
Upwind Finite Difference

First‐arrival traveltimes in complicated 3-D geologic media may be computed robustly and efficiently using an upwind finite‐difference solution of the 3-D eikonal equation. An important application of this technique is computing traveltimes for imaging seismic data with 3-D prestack Kirchhoff depth migration. The method performs radial extrapolation of the three components of the slowness vector in spherical coordinates. Traveltimes are computed by numerically integrating the radial component of the slowness vector. The original finite‐difference equations are recast into unitless forms that are more stable to numerical errors. A stability condition adaptively determines the radial steps that are used to extrapolate. Computations are done in a rotated spherical coordinate system that places the small arc‐length regions of the spherical grid at the earth’s surface (z = 0 plane). This improves efficiency by placing large grid cells in the central regions of the grid where wavefields are complicated, thereby maximizing the radial steps. Adaptive gridding allows the angular grid spacings to vary with radius. The computation grid is also adaptively truncated so that it does not extend beyond the predefined Cartesian traveltime grid. This grid handling improves efficiency. The method cannot compute traveltimes corresponding to wavefronts that have “turned” so that they propagate in the negative radial direction. Such wavefronts usually represent headwaves and are not needed to image seismic data. An adaptive angular normalization prevents this turning, while allowing lower‐angle wavefront components to accurately propagate. This upwind finite‐difference method is optimal for vector‐parallel supercomputers, such as the CRAY Y-MP. A complicated velocity model that generates turned wavefronts is used to demonstrate the method’s accuracy by comparing with results that were generated by 3-D ray tracing and by an alternate traveltime calculation method. This upwind method has also proven successful in the 3-D prestack Kirchhoff depth migration of field data.

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.

Imaging structures below dipping TI media

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1239-1246 ◽  
Author(s):  
Robert W. Vestrum ◽  
Don C. Lawton ◽  
Ron Schmid
Keyword(s):  
Seismic Data ◽  
Seismic Anisotropy ◽  
Rocky Mountain ◽  
Transversely Isotropic ◽  
Velocity Model ◽  
P Wave ◽  
Depth Imaging ◽  
Depth Migration ◽  
Kirchhoff Depth Migration ◽  
Ti Media

Seismic anisotropy in dipping shales causes imaging and positioning problems for underlying structures. We developed an anisotropic depth‐migration approach for P-wave seismic data in transversely isotropic (TI) media with a tilted axis of symmetry normal to bedding. We added anisotropic and dip parameters to the depth‐imaging velocity model and used prestack depth‐migrated image gathers in a diagnostic manner to refine the anisotropic velocity model. The apparent position of structures below dipping anisotropic overburden changes considerably between isotropic and anisotropic migrations. The ray‐tracing algorithm used in a 2-D prestack Kirchhoff depth migration was modified to calculate traveltimes in the presence of TI media with a tilted symmetry axis. The resulting anisotropic depth‐migration algorithm was applied to physical‐model seismic data and field seismic data from the Canadian Rocky Mountain Thrust and Fold Belt. The anisotropic depth migrations offer significant improvements in positioning and reflector continuity over those obtained using isotropic algorithms.

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.

Prestack Kirchhoff depth migration of shallow seismic data

Geophysics ◽  
1998 ◽  
Vol 63 (4) ◽  
pp. 1241-1247 ◽  
Author(s):  
Linus Pasasa ◽  
Friedemann Wenzel ◽  
Ping Zhao
Keyword(s):  
Waste Disposal ◽  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Disposal Site ◽  
Model Estimation ◽  
Waste Disposal Site ◽  
Depth Migration ◽  
Prestack Migration ◽  
Shallow Seismic ◽  
Kirchhoff Depth Migration

Prestack Kirchhoff depth migration is applied successfully to shallow seismic data from a waste disposal site near Arnstadt in Thuringia, Germany. The motivation behind this study was to locate an underground building buried in a waste disposal. The processing sequence of the prestack migration is simplified significantly as compared to standard common (CMP) data processing. It includes only two parts: (1) velocity‐depth‐model estimation and (2) prestack depth migration. In contrast to conventional CMP stacking, prestack migration does not require a separation of reflections and refractions in the shot data. It still provides an appropriate image. Our data example shows that a superior image can be achieved that would contain not just subtle improvements but a qualitative step forward in resolution and signal‐to‐noise ratio.

Leading-order seismic imaging using curvelets

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. S231-S248 ◽  
Author(s):  
Huub Douma ◽  
Maarten V. de Hoop
Keyword(s):  
Seismic Data ◽  
Order Approximation ◽  
Angular Frequency ◽  
Leading Order ◽  
Numerical Examples ◽  
Depth Migration ◽  
Map Migration ◽  
Kirchhoff Depth Migration ◽  
Homogeneous Media ◽  
Spatial Support

Curvelets are plausible candidates for simultaneous compression of seismic data, their images, and the imaging operator itself. We show that with curvelets, the leading-order approximation (in angular frequency, horizontal wavenumber, and migrated location) to common-offset (CO) Kirchhoff depth migration becomes a simple transformation of coordinates of curvelets in the data, combined with amplitude scaling. This transformation is calculated using map migration, which employs the local slopes from the curvelet decomposition of the data. Because the data can be compressed using curvelets, the transformation needs to be calculated for relatively few curvelets only. Numerical examples for homogeneous media show that using the leading-order approximation only provides a good approximation to CO migration for moderate propagation times. As the traveltime increases and rays diverge beyond the spatial support of a curvelet; however, the leading-order approximation is no longer accurate enough. This shows the need for correction beyond leading order, even for homogeneous media.

Integrated prestack depth migration of vertical seismic profile and surface seismic data from the Rocky Mountain Foothills of southern Alberta, Canada

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 1782-1791 ◽  
Author(s):  
M. Graziella Kirtland Grech ◽  
Don C. Lawton ◽  
Scott Cheadle
Keyword(s):  
Seismic Data ◽  
Rocky Mountain ◽  
Velocity Model ◽  
Seismic Profile ◽  
Vertical Seismic Profile ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Depth Migration ◽  
Southern Alberta ◽  
Vsp Data

We have developed an anisotropic prestack depth migration code that can migrate either vertical seismic profile (VSP) or surface seismic data. We use this migration code in a new method for integrated VSP and surface seismic depth imaging. Instead of splicing the VSP image into the section derived from surface seismic data, we use the same migration algorithm and a single velocity model to migrate both data sets to a common output grid. We then scale and sum the two images to yield one integrated depth‐migrated section. After testing this method on synthetic surface seismic and VSP data, we applied it to field data from a 2D surface seismic line and a multioffset VSP from the Rocky Mountain Foothills of southern Alberta, Canada. Our results show that the resulting integrated image exhibits significant improvement over that obtained from (a) the migration of either data set alone or (b) the conventional splicing approach. The integrated image uses the broader frequency bandwidth of the VSP data to provide higher vertical resolution than the migration of the surface seismic data. The integrated image also shows enhanced structural detail, since no part of the surface seismic section is eliminated, and good event continuity through the use of a single migration–velocity model, obtained by an integrated interpretation of borehole and surface seismic data. This enhanced migrated image enabled us to perform a more robust interpretation with good well ties.

Using orthorhombic depth imaging to image fractures in tight reservoirs of the RDG Field, Barmer Basin, India

2019 ◽  
Vol 38 (4) ◽  
pp. 268-273
Author(s):  
Maheswara Phani ◽  
Sushobhan Dutta ◽  
Kondal Reddy ◽  
Sreedurga Somasundaram
Keyword(s):  
Seismic Data ◽  
Velocity Model ◽  
Substantial Improvement ◽  
Natural Fractures ◽  
Data Set ◽  
Depth Migration ◽  
Velocity Modeling ◽  
Barmer Basin ◽  
Induced Fractures

Raageshwari Deep Gas (RDG) Field is situated in the southern part of the Barmer Basin in Rajasthan, India, at a depth of 3000 m. With both clastic and volcanic lithologies, the main reservoirs are tight, and hydraulic fracturing is required to enhance productivity, especially to improve permeability through interaction of induced fractures with natural fractures. Therefore, optimal development of the RDG Field reservoirs requires characterization of faults and natural fractures. To address this challenge, a wide-azimuth 3D seismic data set over the RDG Field was processed to sharply define faults and capture anisotropy related to open natural fractures. Anisotropy was indicated by the characteristic sinusoidal nature of gather reflection events processed using conventional tilted transverse imaging (TTI); accordingly, we used orthorhombic imaging to correct for these, to quantify fracture-related anisotropy, and to yield a more correct subsurface image. During prestack depth migration (PSDM) processing of the RDG data, TTI and orthorhombic velocity modeling was done with azimuthal sectoring of reflection arrivals. The resultant PSDM data using this velocity model show substantial improvement in image quality and vertical resolution at the reservoir level compared to vintage seismic data. The improved data quality enabled analysis of specialized seismic attributes like curvature and thinned fault likelihood for more reliable characterization of faults and fractures. These attributes delineate the location and distribution of probable fracture networks within the volcanic reservoirs. Interpreted subtle faults, associated with fracture zones, were validated with microseismic, production, and image log data.

3-D prestack Kirchhoff depth migration: From prototype to production in a massively parallel processor environment

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 546-556 ◽  
Author(s):  
Herman Chang ◽  
John P. VanDyke ◽  
Marcelo Solano ◽  
George A. McMechan ◽  
Duryodhan Epili
Keyword(s):  
Model Building ◽  
Velocity Model ◽  
Production Scale ◽  
Data Set ◽  
Depth Migration ◽  
Prestack Migration ◽  
Prototype Development ◽  
Time Migration ◽  
Intel Paragon ◽  
Kirchhoff Depth Migration

Portable, production‐scale 3-D prestack Kirchhoff depth migration software capable of full‐volume imaging has been successfully implemented and applied to a six‐million trace (46.9 Gbyte) marine data set from a salt/subsalt play in the Gulf of Mexico. Velocity model building and updates use an image‐driven strategy and were performed in a Sun Sparc environment. Images obtained by 3-D prestack migration after three velocity iterations are substantially better focused and reveal drilling targets that were not visible in images obtained from conventional 3-D poststack time migration. Amplitudes are well preserved, so anomalies associated with known reservoirs conform to the petrophysical predictions. Prototype development was on an 8-node Intel iPSC860 computer; the production version was run on an 1824-node Intel Paragon computer. The code has been successfully ported to CRAY (T3D) and Unix workstation (PVM) environments.

3D PRE-STACK DEPTH MIGRATION: A TOOL FOR REDUCING EXPLORATION RISK IN THE SWAN GRABEN, TIMOR SEA

2005 ◽  
Vol 45 (1) ◽  
pp. 421
Author(s):  
P. Bocca ◽  
L. Fava ◽  
E. Stolf
Keyword(s):  
Seismic Data ◽  
Integrated Approach ◽  
Velocity Model ◽  
Fault Reactivation ◽  
Depth Image ◽  
Substantial Contribution ◽  
Surface Geometry ◽  
Depth Migration ◽  
Imaging Tool ◽  
Seismic Image

3D pre-stack depth migration (PSDM) reprocessing was conducted in 2003 on a portion of the Onnia 3D seismic cube, located in exploration permit AC/P-21, Timor Sea.The main objective of the reprocessing was to obtain the best seismic depth image and the most realistic structural reconstruction of the sub-surface to mitigate the risk factors associated with trap definition (trap retention and trap efficiency). This represents one of the main challenges for oil exploration in the area.The 3D PSDM methodology was chosen as the most appropriate imaging tool to define the correct sub-surface geometry and fault imaging through the use of an appropriate velocity field. An integrated approach to building the final velocity model was adopted, with a substantial contribution from the regional geological model.Several examples are given to demonstrate that the 3D PSDM reprocessing significantly improved the seismic image and thus the confidence in the interpretation, contributing strongly to the definition of the exploration targets.The interpretation of the new seismic data has resulted in a new structural picture in which higher confidence in seismic imaging has improved fault correlation. This has enabled better structural definition at the Middle Jurassic Plover Formation level that has reduced the complexity of the large Vesta Prospect, in the centre of the Swan Graben to the northwest of East Swan–1. Improved understanding of the fault reactivation mechanism and the structural elements of the trap (trap integrity) were eventually incorporated in the prospect risking.In the Swan Graben 3D PSDM has proved to be a very powerful instrument capable of producing significant impact on the exploration even in an area with a complex geological setting and a fairly poor seismic data quality.

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