Estimation of the spatial distribution of fluid permeability from surface and tomographic GPR data and core, with a 2‐D example from the Ferron Sandstone, Utah

Geophysics ◽  
2002 ◽  
Vol 67 (5) ◽  
pp. 1505-1515 ◽  
Author(s):  
William S. Hammon ◽  
Xiaoxian Zeng ◽  
Rucsandra M. Corbeanu ◽  
George A. McMechan
Keyword(s):  
Spatial Distribution ◽  
Fluid Transport ◽  
Velocity Model ◽  
Borehole Data ◽  
Permeability Model ◽  
Depth Migration ◽  
Traveltime Tomography ◽  
Fluid Permeability ◽  
Ground Penetrating ◽  
Kirchhoff Depth Migration

Reservoir analogs provide detailed information that is applicable to fluid transport simulations but that cannot be obtained directly from reservoirs because of inaccessibility. The Ferron Sandstone of east‐central Utah is an analog for fluviodeltaic reservoirs; its excellent outcrop exposures are ideal for detailed study. Ground‐penetrating radar (GPR) data were collected in and between two cored boreholes and are used to build a 2‐D fluid permeability model in four steps. First, an anisotropic GPR propagation velocity model is obtained from traveltime tomography between two boreholes and between each borehole and the earth's surface. Second, the geometry of the sedimentological features is imaged by prestack Kirchhoff depth migration of constant‐offset GPR data acquired along a line between the two holes at the earth's surface. Third, a background permeability is assigned to each layer by interpolating the geometrical average of the measured permeabilities in each sedimentological element. Finally, the spatial distribution of flow baffles and barriers is estimated by calibrating the instantaneous amplitude and frequency of the surface GPR data associated with the mudstone layers in the boreholes via cluster analysis. The result is an integrated model that contains GPR velocity, lithology, and fluid permeability distributions. Low GPR velocities correspond to mudstones with low permeability. The main mudstone layers (potential barriers and/or baffles to fluid flow) do not appear to be continuous between the boreholes, which means that interpretations based on borehole data alone would overestimate element continuity and thereby underestimate effective permeability.

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 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.

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.

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.

Target-oriented interferometric tomography for GPR data

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. J1-J6 ◽  
Author(s):  
Sherif M. Hanafy ◽  
Gerard T. Schuster
Keyword(s):  
Velocity Model ◽  
Estimation Accuracy ◽  
Real Field ◽  
Near Surface ◽  
Interferometric Technique ◽  
Traveltime Tomography ◽  
Transit Times ◽  
The Difference ◽  
Tomography Method ◽  
Ground Penetrating

An interferometric form of Fermat’s principle and traveltime tomography is used to invert ground-penetrating radar (GPR) data for the subsurface velocity distribution. The input data consist of GPR traveltimes of reflections from two buried interfaces, [Formula: see text] (reference) and [Formula: see text] (target), where the data are excited and recorded by GPR antennas at the surface. Fermat’s interferometric principle is then used to redatum the surface transmitters and receivers to interface [Formula: see text] so the associated reflection traveltimes correspond to localized transit times between interfaces [Formula: see text] and [Formula: see text]. The overburden velocity model above interface [Formula: see text] is not required. The result after tomographic inversion is a high-resolution estimate of the velocity between interfaces [Formula: see text] and [Formula: see text] that does not depend on the velocity model above interface [Formula: see text]. A motivation for introducing interferometric traveltime tomography is that typical layer-stripping approaches will see the slowness error increase with depth as the layers are inverted. This suggests that near-surface statics errors are propagated and amplified with depth. In contrast, the interferometric traveltime tomography method largely eliminates statics errors by taking the difference between reflection events that emanate from neighboring layer interfaces. Slowness errors are not amplified with depth. However, the method is sensitive to the estimation accuracy for the geometry of the reference interface. Both synthetic and real field data are used successfully to validate the effectiveness of this interferometric technique.

Mapping prestack depth‐migrated coherent signal and noise events back to the original time gathers using Fermat’s principle

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 934-941 ◽  
Author(s):  
Kurt J. Marfurt ◽  
Bertrand Duquet
Keyword(s):  
Objective Function ◽  
Velocity Model ◽  
Reflection Point ◽  
Coherent Noise ◽  
Depth Migration ◽  
Fermat’S Principle ◽  
Original Time ◽  
Fermat's Principle ◽  
Kirchhoff Depth Migration ◽  
Ray Paths

Because of its computational efficiency, prestack Kirchhoff depth migration is currently the method of choice in both 2-D and 3-D imaging of seismic data. The most algorithmically complex component of the Kirchhoff family of algorithms is the calculation and manipulation of accurate traveltime tables for each source and receiver point. Once calculated, we sum the seismic energy over all possible ray paths, allowing us to accurately image both specular and nonspecular scattered energy. Any seismic events that fall within the velocity passband, including reflected and diffracted signal, mode conversions, multiples, head waves, and aliases of surface waves, are imaged in depth. The transformation of time gathers to depth gathers can be quite complicated and nonintuitive to all but the seasoned imaging expert. In particular, easily recognized head‐wave events on common‐shot gathers are often difficult to differentiate from undermigrated coherent reflections on common‐reflection‐point depth gathers. In contrast, subsalt multiples that have propagated along complex ray paths are often easily recognized on common‐offset depth gathers but are indistinguishable from the distorted primaries on the input common‐shot or common‐midpoint time gathers. In a related area, seismic reflection traveltime tomography is currently the workhorse for 2-D and an active area of research and development for 3-D migration‐driven velocity analysis. The objective function for this “velocity inversion” problem is to either minimize the temporal difference between picked and modeled time picks, or to maximize the similarity between, or flatness of, common‐reflection‐point depth picks. Once picked and associated with the correct reflector, time picks never need to be modified during the velocity‐model updating steps that ultimately lead to a feasible solution. In practice, such time picks are nearly impossible to make in those structurally complex areas that justify the use of prestack depth migration. Instead, we almost always use the second objective function and pick reflector events in depth, where we can use our geologic insight to differentiate between signal and noise and where the difficulty of associating a picked event with the velocity/depth model horizon completely disappears. The major drawback of picking in depth is that these events need to be repicked each time any part of the overlying velocity/depth model has been updated. We show that by applying Fermat’s principle, and by reusing the same traveltime tables used in seismic prestack Kirchhoff depth imaging, we can map interpreted events on the depth gathers to corresponding interpreted events on the original time gathers. This technique, first introduced by J. van Trier in 1990, is considerably more stable and, because we reuse the already computed migration traveltime tables, more economic than two‐point ray‐trace methods. In our first application of coherent noise suppression, we show how we can relate imaging artifacts seen on the depth image to their causative coherent noise on the original time gathers. Once identified, these noise events can be safely suppressed using conventional filtering techniques. In our second application of reflection tomography, we show how we can pick partially focused reflectors in depth, and map them back to time, undoing the effect of the incorrect velocity/depth model used in prestack Kirchhoff depth migration such that the events never need to be repicked during subsequent velocity model updates.

Depth image focusing in traveltime map‐based wide‐angle migration

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1903-1912 ◽  
Author(s):  
Igor B. Morozov ◽  
Alan Levander
Keyword(s):  
Velocity Model ◽  
Depth Image ◽  
Velocity Spectrum ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Arrival Times ◽  
Depth Migration ◽  
Traveltime Tomography ◽  
Interactive Analysis ◽  
The Common

Wide‐aperture, prestack depth migration requires application of challenging and time‐consuming velocity analysis and depth focusing, collectively referred to here as depth focusing. We present an approach to depth focusing using (1) a detailed starting velocity model obtained by a 1‐D transformation of the first‐arrival times, followed iteratively by (2) interactive analysis of the common‐image gathers, (3) computation of coherency attributes of the wavefield in the depth domain, and (4) 2‐D traveltime tomography to update the background velocity model. We employ two interactive method of migration velocities refinement. In the first method (similar to the common‐midpoint velocity spectrum approach), residual velocity updates are picked directly from the common‐image gathers. In another method (analogous to the common velocity stacks), we pick the velocity updates from the areas of maximum coherency in depth sections that are migrated using rescaled traveltime maps. Both types of migration velocity picks, optionally combined with the first arrivals, are inputs for a 2‐D traveltime inversion scheme that uses either the infinite‐frequency or a finite‐bandwidth approximation. This flexible and versatile depth focusing approach is implemented for several prestack depth migration algorithms and illustrated on an application to a real, ultrashallow seismic data set. The technique resolves overburden velocity variations and facilitates reliable high‐resolution reflection imaging of a paleochannel that was the target of the study.

Integrated wide‐angle and near‐vertical subbasalt study using large‐aperture seismic data from the Faeroe—Shetland region

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1340-1348 ◽  
Author(s):  
Juergen Fruehn ◽  
Moritz M. Fliedner ◽  
Robert S. White
Keyword(s):  
Seismic Data ◽  
Velocity Model ◽  
Wide Angle ◽  
Low Velocity ◽  
Depth Migration ◽  
Traveltime Tomography ◽  
Large Aperture ◽  
The North ◽  
Suppression Technique ◽  
Streamer Data

Acquiring large‐aperture seismic data (38 km maximum offset) along a profile crossing the Faeroe—Shetland basin in the North Atlantic enables us to use wide‐angle reflections and refractions, in addition to conventional streamer data (0–6 km), for subbasalt imaging. The wide‐angle results are complemented and confirmed by images obtained from the conventional near‐vertical‐offset range. Traveltime tomography applied to the wide‐angle data shows a low‐velocity layer (3.5–4.5 km/s) underneath southeastward‐thinning lava flows, suggesting a 2.5–3.0‐km‐thick sedimentary layer. The velocity model obtained from traveltime tomography is used to migrate wide‐angle reflections from large offsets that arrive ahead of the water‐wave cone. The migrated image shows base‐basalt and sub—basalt reflections that are locally coincident with the tomographic boundaries. Application of a new multiple suppression technique and controlled stacking of the conventional streamer data produces seismic sections consistent with the wide‐angle results. Prestack depth migration of the near‐vertical offsets shows a continuous base‐basalt reflection and a clearly defined termination of the basalt flows.

scholarly journals The Application of Depth Migration for Processing GPR Data

2018 ◽  
Vol 35 ◽  
pp. 03004
Author(s):  
Dang Hoai Trung ◽  
Nguyen Van Giang ◽  
Nguyen Thanh Van
Keyword(s):  
Significant Role ◽  
Ground Penetrating Radar ◽  
Field Data ◽  
Velocity Model ◽  
Radar Data ◽  
Energy Diagram ◽  
Depth Migration ◽  
Subsurface Structures ◽  
Calculated Velocity ◽  
Ground Penetrating

Migration methods play a significant role in processing ground penetrating radar data. Beside recovering the true image of subsurface structures from the prior designed velocity model and the raw GPR data, the migration algorithm could be an effective tool in bulding real environmental velocity model. In this paper, we have proposed one technique using energy diagram extracted from migrated data as a criterion of looking for the correct velocity. Split Step Fourier migration, a depth migration, is chosen for facing the challenge where the velocity varies laterally and vertically. Some results verified on field data on Vietnam show that migrated sections with calculated velocity from energy diagram have the best quality.

scholarly journals Velocity Analysis Using Separated Diffractions for Lunar Penetrating Radar Obtained by Yutu-2 Rover

2021 ◽  
Vol 13 (7) ◽  
pp. 1387
Author(s):  
Chao Li ◽  
Jinhai Zhang
Keyword(s):  
Dielectric Permittivity ◽  
Lunar Regolith ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Quality Data ◽  
High Quality Data ◽  
Shallow Subsurface ◽  
Subsurface Structures ◽  
Ground Penetrating ◽  
Permittivity Model

The high-frequency channel of lunar penetrating radar (LPR) onboard Yutu-2 rover successfully collected high quality data on the far side of the Moon, which provide a chance for us to detect the shallow subsurface structures and thickness of lunar regolith. However, traditional methods cannot obtain reliable dielectric permittivity model, especially in the presence of high mix between diffractions and reflections, which is essential for understanding and interpreting the composition of lunar subsurface materials. In this paper, we introduce an effective method to construct a reliable velocity model by separating diffractions from reflections and perform focusing analysis using separated diffractions. We first used the plane-wave destruction method to extract weak-energy diffractions interfered by strong reflections, and the LPR data are separated into two parts: diffractions and reflections. Then, we construct a macro-velocity model of lunar subsurface by focusing analysis on separated diffractions. Both the synthetic ground penetrating radar (GPR) and LPR data shows that the migration results of separated reflections have much clearer subsurface structures, compared with the migration results of un-separated data. Our results produce accurate velocity estimation, which is vital for high-precision migration; additionally, the accurate velocity estimation directly provides solid constraints on the dielectric permittivity at different depth.

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