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.

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.

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.

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.

Anisotropic parsimonious prestack depth migration

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. S25-S36 ◽  
Author(s):  
Ernesto V. Oropeza ◽  
George A. McMechan
Keyword(s):  
Model Building ◽  
Computing Time ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Velocity Model ◽  
P Wave ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Tti Media ◽  
Map Migration

An efficient Kirchhoff-style prestack depth migration, called “parsimonious” migration, was developed a decade ago for isotropic 2D and 3D media by using measured slownesses to reduce the amount of ray tracing by orders of magnitude. It is conceptually similar to “map” migration, but its implementation has some differences. We have extended this approach to 2D tilted transversely isotropic (TTI) media and illustrated it with synthetic P-wave data. Although the framework of isotropic parsimonious may be retained, the extension to TTI media requires redevelopment of each of the numerical components, calculation of the phase and group velocity for TTI media, development of a new two-point anisotropic ray tracer, and substitution of an initial-angle isotropic shooting ray-trace algorithm for an anisotropic one. The model parameterization consists of Thomsen’s parameters ([Formula: see text], [Formula: see text], [Formula: see text]) and the tilt angle of the symmetry axis of the TI medium. The parsimonious anisotropic migration algorithm is successfully applied to synthetic data from a TTI version of the Marmousi2 model. The quality of the image improves by weighting the impulse response by the calculation of the anisotropic Fresnel radius. The accuracy and speed of this migration makes it useful for anisotropic velocity model building. The elapsed computing time for 101 shots for the Marmousi2 TTI model is 35 s per shot (each with 501 traces) in 32 Opteron cores.

Seismic data processing in vertically inhomogeneous TI media

Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 662-675 ◽  
Author(s):  
Tariq Alkhalifah
Keyword(s):  
Seismic Data ◽  
Transversely Isotropic ◽  
Inhomogeneous Media ◽  
P Wave ◽  
Seismic Data Processing ◽  
Time Migration ◽  
Processing Data ◽  
Two Parameters ◽  
Ti Media ◽  
Ray Parameter

The first and most important step in processing data in transversely isotropic (TI) media for which velocities vary with depth is parameter estimation. The multilayer normal‐moveout (NMO) equation for a dipping reflector provides the basis for extending the TI velocity analysis of Alkhalifah and Tsvankin to vertically inhomogeneous media. This NMO equation is based on a root‐mean‐square (rms) average of interval NMO velocities that correspond to a single ray parameter, that of the dipping event. Therefore, interval NMO velocities [including the normal‐moveout velocity for horizontal events, [Formula: see text]] can be extracted from the stacking velocities using a Dix‐type differentiation procedure. On the other hand, η, which is a key combination of Thomsen's parameters that time‐related processing relies on, is extracted from the interval NMO velocities using a homogeneous inversion within each layer. Time migration, like dip moveout, depends on the same two parameters in vertically inhomogeneous media, namely [Formula: see text] and η, both of which can vary with depth. Therefore, [Formula: see text] and ε estimated using the dip dependency of P‐wave moveout velocity can be used for TI time migration. An application of anisotropic processing to seismic data from offshore Africa demonstrates the importance of considering anisotropy, especially as it pertains to focusing and imaging of dipping events.

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.

Lithospheric architecture of the Ligurian Basin from seismic travel time tomography

2021 ◽  
Author(s):  
Anke Dannowski ◽  
Heidrun Kopp ◽  
Ingo Grevemeyer ◽  
Grazia Caielli ◽  
Roberto de Franco ◽  
...  
Keyword(s):  
Seismic Data ◽  
Velocity Model ◽  
P Wave ◽  
Central Basin ◽  
Uppermost Mantle ◽  
Mantle Boundary ◽  
Oceanic Spreading ◽  
Refraction Seismic ◽  
Back Arc ◽  
Ligurian Basin

<p>The Ligurian Basin is located north-west of Corsica at the transition from the western Alpine orogen to the Apennine system. The Back-arc basin was generated by the southeast retreat of the Apennines-Calabrian subduction zone. The opening took place from late Oligocene to Miocene. While the extension led to extreme continental thinning little is known about the style of back-arc rifting. Today, seismicity indicates the closure of this back-arc basin. In the basin, earthquake clusters occur in the lower crust and uppermost mantle and are related to re-activated, inverted, normal faults created during rifting.</p><p>To shed light on the present day crustal and lithospheric architecture of the Ligurian Basin, active seismic data have been recorded on short period ocean bottom seismometers in the framework of SPP2017 4D-MB, the German component of AlpArray. An amphibious refraction seismic profile was shot across the Ligurian Basin in an E-W direction from the Gulf of Lion to Corsica. The profile comprises 35 OBS and three land stations at Corsica to give a complete image of the continental thinning including the necking zone.</p><p>The majority of the refraction seismic data show mantle phases with offsets up to 70 km. The arrivals of seismic phases were picked and used to generate a 2-D P-wave velocity model. The results show a crust-mantle boundary in the central basin at ~12 km depth below sea surface. The P-wave velocities in the crust reach 6.6 km/s at the base. The uppermost mantle shows velocities >7.8 km/s. The crust-mantle boundary becomes shallower from ~18 km to ~12 km depth within 30 km from Corsica towards the basin centre. The velocity model does not reveal an axial valley as expected for oceanic spreading. Further, it is difficult to interpret the seismic data whether the continental lithosphere was thinned until the mantle was exposed to the seafloor. However, an extremely thinned continental crust indicates a long lasting rifting process that possibly did not initiate oceanic spreading before the opening of the Ligurian Basin stopped. The distribution of earthquakes and their fault plane solutions, projected along our seismic velocity model, is in-line with the counter-clockwise opening of the Ligurian Basin.</p>

Reflection moveout approximations for P-waves in a moderately anisotropic homogeneous tilted transverse isotropy layer

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. C175-C185 ◽  
Author(s):  
Ivan Pšenčík ◽  
Véronique Farra
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
Weak Anisotropy ◽  
P Waves ◽  
3D Space ◽  
Axis Of Symmetry ◽  
Relative Errors ◽  
Symmetry Tests ◽  
Ti Media

We have developed approximate nonhyperbolic P-wave moveout formulas applicable to weakly or moderately anisotropic media of arbitrary anisotropy symmetry and orientation. Instead of the commonly used Taylor expansion of the square of the reflection traveltime in terms of the square of the offset, we expand the square of the reflection traveltime in terms of weak-anisotropy (WA) parameters. No acoustic approximation is used. We specify the formulas designed for anisotropy of arbitrary symmetry for the transversely isotropic (TI) media with the axis of symmetry oriented arbitrarily in the 3D space. Resulting formulas depend on three P-wave WA parameters specifying the TI symmetry and two angles specifying the orientation of the axis of symmetry. Tests of the accuracy of the more accurate of the approximate formulas indicate that maximum relative errors do not exceed 0.3% or 2.5% for weak or moderate P-wave anisotropy, respectively.

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.

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