Depth‐focusing analysis using a wavefront‐curvature criterion

Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1148-1156 ◽  
Author(s):  
Scott MacKay ◽  
Ray Abma
Keyword(s):  
Seismic Energy ◽  
Radius Of Curvature ◽  
Large Radius ◽  
Data Set ◽  
Depth Migration ◽  
Amplitude Data ◽  
Zero Radius ◽  
Inverse Radius ◽  
Interpretation Process ◽  
Zero Offset

Depth‐focusing analysis (DFA), a method of refining velocities for prestack depth migration, relies on amplitude buildups at zero offset to determine the extrapolation depths that best focus the migrated data. Unfortunately, seismic energy from dipping interfaces, diffractions, and noise often produce spurious amplitude indications of focusing. To reduce possible ambiguity in the DFA interpretation process, we introduce a new attribute for determining focusing that is relatively independent of amplitude. Our approach is based on estimates of the radius of wavefront curvature. The estimates are derived from normal moveout analysis of nonzero‐offset data saved during migration. By relating steeper moveout to smaller radius of wavefront curvature, focusing is defined by a wavefront curvature of zero radius. Additionally, we show that applying inverse‐radius weights to the amplitude data attenuates nonfocused events due to their large radius of curvature. Using the Marmousi data set, our weighting scheme resulted in reduced spurious focusing and enhanced velocity resolution in DFA.

Three‐dimensional depth imaging with generalized screens: A salt body case study

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1132-1139 ◽  
Author(s):  
Jérôme H. Le Rousseau ◽  
Henry Calandra ◽  
Maarten V. de Hoop
Keyword(s):  
Three Dimensional ◽  
Fourier Method ◽  
Seismic Survey ◽  
Tectonic Deformation ◽  
Data Set ◽  
Depth Imaging ◽  
Depth Migration ◽  
Velocity Models ◽  
The North ◽  
Zero Offset

We illustrate the performance of the generalized screen propagator on real seismic data for 3D zero‐offset and prestack depth imaging. We use TotalFinaElf's L7D data set from the North Sea, a 3D marine seismic survey that contained limited azimuthal coverage. The subsurface shows significant tectonic deformation, including an intrusive salt body in sedimentary sequences. A transformation to common azimuth is applied prior to the 3D prestack depth imaging procedure. We compare the performance of the generalized screen propagator with that of a hybrid phase shift plus interpolation (PSPI)/split‐step Fourier method. Three‐dimensional prestack results confirm the generalized screen method handles multipathing more accurately. Comparisons are also made with Kirchhoff migration results. The results differ mainly in the fine‐scale irregularities of the image and not in the wavefront set of the image. Using synthetic models of similar structure (the SEG/EAGE salt model), we further illustrate the importance of multipathing and multiple scattering. Overall, our results show that our wave‐equation approach produces better images than the Kirchhoff approach to prestack depth migration; we attribute this mainly to a more complete handling of wave diffraction in the generalized screen expansion, which becomes important in strongly heterogeneous and irregular velocity models such as the ones containing salt bodies.

Prestack Gaussian‐beam depth migration

Geophysics ◽  
2001 ◽  
Vol 66 (4) ◽  
pp. 1240-1250 ◽  
Author(s):  
N. Ross Hill
Keyword(s):  
Gaussian Beam ◽  
Velocity Structure ◽  
Saddle Points ◽  
Three Dimensional ◽  
Seismic Energy ◽  
Data Set ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Beam Depth ◽  
Gaussian Beam Migration

Kirchhoff migration is the most popular method of three‐dimensional prestack depth migration because of its flexibility and efficiency. Its effectiveness can become limited, however, when complex velocity structure causes multipathing of seismic energy. An alternative is Gaussian beam migration, which is an extension of Kirchhoff migration that overcomes many of the problems caused by multipathing. Unlike first‐arrival and most‐energetic‐arrival methods, which retain only one traveltime, this alternative method retains most arrivals by the superposition of Gaussian beams. This paper presents a prestack Gaussian beam migration method that operates on common‐offset gathers. The method is efficient because the computation of beam superposition isolates summations that do not depend on the seismic data and evaluates these integrals by considering their saddle points. Gaussian beam migration of the two‐dimensional Marmousi test data set demonstrates the method’s effectiveness for structural imaging in a case where there is multipathing of seismic energy.

Prestack depth migration by symmetric nonstationary phase shift

Geophysics ◽  
2002 ◽  
Vol 67 (2) ◽  
pp. 594-603 ◽  
Author(s):  
Robert J. Ferguson ◽  
Gary F. Margrave
Keyword(s):  
Phase Shift ◽  
Symmetric Operator ◽  
Heterogeneous Media ◽  
Synthetic Data ◽  
Velocity Model ◽  
Computational Effort ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Depth Migration ◽  
Zero Offset

A new depth migration method suitable for heterogeneous media is presented. The well‐known phase shift plus interpolation (PSPI) method and the recently introduced nonstationary phase‐shift (NSPS) method are combined into a single symmetric operator with improved accuracy and stability and with similar computational effort. For prestack depth migration, the symmetric operator is used in a recursive wavefield extrapolation to compute incident and reflected wavefields at any desired depth, and the ratio of the incident and reflected wavefields at a particular depth is used to estimate seismic reflectivity. When the velocity model is made piecewise constant laterally, the symmetric extrapolation operator can be computed efficiently using ordinary phase‐shift extrapolation for a series of reference velocities and appropriate spatial windowing. Migration of the Marmousi synthetic data set by symmetric nonstationary phase shift (SNPS) provides an image that compares favorably with an image of the zero‐offset reflectivity derived from the Marmousi velocity model.

Duplex Spread Blade Method for Cutting Hypoid Gears with Modified Tooth Surface

1998 ◽  
Vol 120 (3) ◽  
pp. 441-447 ◽  
Author(s):  
K. Kawasaki ◽  
H. Tamura
Keyword(s):  
Cutting Edge ◽  
Tooth Surface ◽  
Radius Of Curvature ◽  
Large Radius ◽  
Ring Gear ◽  
Circular Arc ◽  
Hypoid Gears ◽  
Manufacturing Method ◽  
Straight Line

In this paper, a duplex spread blade method for cutting hypoid gears with modified tooth surface is proposed. The duplex spread blade method provides a rapid and economical manufacturing method because both the ring gear and pinion are cut by a spread blade method. In the proposed method, the nongenerated ring gear is manufactured with cutting edge that is altered from the usual straight line to a circular arc with a large radius of curvature and the circular arc cutting edge produces a modified tooth surface. The pinion is generated by a cutter with straight cutting edges as usual. The main procedure of this method is the determination of the cutter specifications and machine settings. The proposed method was validated by gear manufacture.

Résonateur ouvert en géométrie sphérique

1980 ◽  
Vol 58 (1) ◽  
pp. 80-86 ◽  
Author(s):  
Gilles Duret ◽  
Gérard Zepp ◽  
Alain Wick
Keyword(s):  
Radius Of Curvature ◽  
Large Radius ◽  
Open Resonators

Most of the approximate theories of the spherical open resonators are insufficient, except for the very large radius of curvature. It is often necessary to consider other cases. The theory we have developed is applicable for any curvature and aperture of the mirrors. This theory also allows study of multi-dielectric cavities. This method is accurately studied in detail in this paper.

Simulation of a seismic survey with combined surface and in-mine data acquisition for imaging steeply dipping ore veins

2021 ◽  
Author(s):  
Olaf Hellwig ◽  
Stefan Buske
Keyword(s):  
Finite Difference ◽  
Message Passing Interface ◽  
Seismic Survey ◽  
Difference Operators ◽  
Mining District ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Depth Migration ◽  
Difference Grid ◽  
Triangulated Surfaces

<p>The polymetallic, hydrothermal deposit of the Freiberg mining district in the southeastern part of Germany is characterised by ore veins that are framed by Proterozoic orthogneiss. The ore veins consist mainly of quarz, sulfides, carbonates, barite and flourite, which are associated with silver, lead and tin. Today the Freiberg University of Mining and Technology is operating the shafts Reiche Zeche and Alte Elisabeth for research and teaching purposes with altogether 14 km of accessible underground galleries. The mine together with the most prominent geological structures of the central mining district are included in a 3D digital model, which is used in this study to study seismic acquisition geometries that can help to image the shallow as well as the deeper parts of the ore-bearing veins. These veins with dip angles between 40° and 85° are represented by triangulated surfaces in the digital geological model. In order to import these surfaces into our seismic finite-difference simulation code, they have to be converted into bodies with a certain thickness and specific elastic properties in a first step. In a second step, these bodies with their properties have to be discretized on a hexahedral finite-difference grid with dimensions of 1000 m by 1000 m in the horizontal direction and 500 m in the vertical direction. Sources and receiver lines are placed on the surface along roads near the mine. A Ricker wavelet with a central frequency of 50 Hz is used as the source signature at all excitation points. Beside the surface receivers, additional receivers are situated in accessible galleries of the mine at three different depth levels of 100 m, 150 m and 220 m below the surface. Since previous mining activities followed primarily the ore veins, there are only few pilot-headings that cut through longer gneiss sections. Only these positions surrounded by gneiss are suitable for imaging the ore veins. Based on this geometry, a synthetic seismic data set is generated with our explicit finite-difference time-stepping scheme, which solves the acoustic wave equation with second order accurate finite-difference operators in space and time. The scheme is parallelised using a decomposition of the spatial finite-difference grid into subdomains and Message Passing Interface for the exchange of the wavefields between neighbouring subdomains. The resulting synthetic seismic shot gathers are used as input for Kirchhoff prestack depth migration as well as Fresnel volume migration in order to image the ore veins. Only a top mute to remove the direct waves and a time-dependent gain to correct the amplitude decay due to the geometrical spreading are applied to the data before the migration. The combination of surface and in-mine acquisition helps to improve the image of the deeper parts of the dipping ore veins. Considering the limitations for placing receivers in the mine, Fresnel volume migration as a focusing version of Kirchhoff prestack depth migration helps to avoid migration artefacts caused by this sparse and limited acquisition geometry.</p>

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.

Experimental and Computational Investigation of Shaped Film Cooling Holes Designed to Minimize Inlet Separation

2020 ◽  
Author(s):  
Fraser B. Jones ◽  
Dale W. Fox ◽  
David G. Bogard
Keyword(s):  
Film Cooling ◽  
Velocity Ratio ◽  
Tangential Velocity ◽  
Velocity Fields ◽  
Radius Of Curvature ◽  
Large Radius ◽  
Combustion Gases ◽  
Shaped Hole ◽  
Manufacturing Technologies ◽  
Film Cooling Holes

Abstract Film cooling is used to protect turbine components from the extreme temperatures by ejecting coolant through arrays of holes to create an air buffer from the hot combustion gases. Limitations in traditional machining meant film cooling holes universally have sharp inlets which create separation regions at the hole entrance. The present study uses experimental and computational data to show that these inlet separation are a major cause of performance variation in crossflow fed film cooling holes. Three hole designs were experimentally tested by independently varying the coolant velocity ratio (VR) and the coolant channel velocitty ratio (VRc) to isolate the effects of crossflow on hole performance. Leveraging additive manufacturing technologies, the addition of a 0.25D radius fillet to the inlet of a 7-7-7 shaped hole is shown to significantly improve diffuser usage and significantly reduce variation in performance with VRc. A second AM design used a very large radius of curvature inlet to reduce biasing caused by the inlet crossflow. Experiments showed that this “swept” hole design did minimize biasing of coolant flow to one side of the shaped hole and it significantly reduced variations due to varying VRc. RANS simulations at six VR and three VRc conditions were made for each geometry to better understand how the new geometries changed the velocity field within the hole. The sharp and rounded inlets were seen to have very similar tangential velocity fields and jet biasing. Both AM inlets created more uniform, slower velocity fields entering the diffuser. The results of this paper indicate large improvements in film cooling performance can be found by leveraging AM technology.

Refraction wavefield migration

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. Q27-Q37
Author(s):  
Yang Shen ◽  
Jie Zhang
Keyword(s):  
Signal To Noise Ratio ◽  
Surface Velocity ◽  
Data Set ◽  
Near Surface ◽  
Depth Migration ◽  
Reflection Data ◽  
Imaging Tool ◽  
Imaging Results ◽  
Migration Method ◽  
Single Method

Refraction methods are often applied to model and image near-surface velocity structures. However, near-surface imaging is very challenging, and no single method can resolve all of the land seismic problems across the world. In addition, deep interfaces are difficult to image from land reflection data due to the associated low signal-to-noise ratio. Following previous research, we have developed a refraction wavefield migration method for imaging shallow and deep interfaces via interferometry. Our method includes two steps: converting refractions into virtual reflection gathers and then applying a prestack depth migration method to produce interface images from the virtual reflection gathers. With a regular recording offset of approximately 3 km, this approach produces an image of a shallow interface within the top 1 km. If the recording offset is very long, the refractions may follow a deep path, and the result may reveal a deep interface. We determine several factors that affect the imaging results using synthetics. We also apply the novel method to one data set with regular recording offsets and another with far offsets; both cases produce sharp images, which are further verified by conventional reflection imaging. This method can be applied as a promising imaging tool when handling practical cases involving data with excessively weak or missing reflections but available refractions.

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