A constrained parametric inversion for velocity analysis based on CFP technology

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1210-1222 ◽  
Author(s):  
M. M. Nurul Kabir ◽  
D. J. Verschuur
Keyword(s):  
Vertical Velocity ◽  
Velocity Gradient ◽  
Fluid Pressure ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Velocity Variation ◽  
Velocity Analysis ◽  
Parametric Inversion ◽  
Layer Velocity ◽  
Vertical Velocity Gradient

A method of velocity analysis based on the common focusing point (CFP) method is presented. The two important aspects of the method are the use of the CFP domain and the use of a new parameterization—a vertical velocity gradient to describe the lateral velocity variation within a layer. The layer velocity is defined with only two parameters: an average velocity [Formula: see text]and a vertical velocity gradient (β). Layer velocity parameterization using [Formula: see text] and β assumes that the lithology of the layer is constant and that the overburden and fluid pressure increase linearly with depth. This type of parameterization is suitable for areas with gross changes in lithology (clastic‐carbonate‐salt) and for rock in hydrostatic equilibrium. A layer‐based model is required for these areas. The salt dome data example presented belongs to this type of area, so the layer‐based model with the defined parameterization produced a very good subsurface velocity model. The method is based on the principle of equal traveltime between the focusing operator and the corresponding focus point response. The velocity estimation problem is formulated as a constrained parametric inversion process. The method of perturbation is applied where linear assumptions are made; the velocity inversion, however, is a nonlinear problem, and the model parameter updates are computed iteratively using Newton’s method. The velocity model is built by layers in a top‐down approach, which makes the problem quasi‐linear.

Analysis of image gathers in factorized VTI media

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 2016-2025 ◽  
Author(s):  
Debashish Sarkar ◽  
Ilya Tsvankin
Keyword(s):  
Vertical Velocity ◽  
Velocity Gradient ◽  
Migration Velocity ◽  
P Wave ◽  
Velocity Variation ◽  
Velocity Analysis ◽  
Lateral Heterogeneity ◽  
Velocity Models ◽  
Isotropic Media ◽  
Vti Media

Because events in image gathers generated after prestack depth migration are sensitive to the velocity field, they are often used in migration velocity analysis for isotropic media. Here, we present an analytic and numerical study of P‐wave image gathers in transversely isotropic media with a vertical symmetry axis (VTI) and establish the conditions for flattening such events and positioning them at the true reflector depth. Application of the weak‐anisotropy approximation leads to concise expressions for reflections in image gathers from homogeneous and factorized v(z) media in terms of the VTI parameters and the vertical velocity gradient kz. Flattening events in image gathers for any reflector dip requires accurate values of the zero‐dip NMO velocity at the surface [Vnmo (z = 0)], the gradient kz, and the anellipticity coefficient η. For a fixed error in Vnmo and kz, the magnitude of residual moveout of events in image gathers decreases with dip, while the moveout caused by an error in η initially increases for moderate dips but then decreases as dips approach 90°. Flat events in image gathers in VTI media, however, do not guarantee the correct depth scale of the model because reflector depth depends on the vertical migration velocity. For factorized v(x, z) media with a linear velocity variation in both the x‐ and z‐directions, the moveout on image gathers is controlled by Vnmo (x = z = 0), kz, η, and a combination of the horizontal velocity gradient kx and the Thomsen parameter δ (specifically, kx[Formula: see text]). If too large a value of any of these four quantities is used in migration, reflections in the image gathers curve downward (i.e., they are undercorrected; the inferred depth increases with offset), while a negative error results in overcorrection. Lateral heterogeneity tends to increase the sensitivity of moveout of events in image gathers to the parameter η, and errors in η may lead to measurable residual moveout of horizontal events in v(x, z) media even for offset‐to‐depth ratios close to unity. These results provide a basis for extending to VTI media conventional velocity analysis methods operating with image gathers. Although P‐wave traveltimes alone cannot be used to separate anisotropy from lateral heterogeneity (i.e., kx is coupled to δ), moveout of events in image gathers does constrain the vertical gradient kz. Hence, it may be possible to build VTI velocity models in depth by supplementing reflection data with minimal a priori information, such as the vertical velocity at the top of the factorized VTI layer.

Migration velocity analysis from locally coherent events in 2‐D laterally heterogeneous media, Part I: Theoretical aspects

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1202-1212 ◽  
Author(s):  
Hervé Chauris ◽  
Mark S. Noble ◽  
Gilles Lambaré ◽  
Pascal Podvin
Keyword(s):  
Cost Function ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Paraxial Ray ◽  
The Cost

We present a new method based on migration velocity analysis (MVA) to estimate 2‐D velocity models from seismic reflection data with no assumption on reflector geometry or the background velocity field. Classical approaches using picking on common image gathers (CIGs) must consider continuous events over the whole panel. This interpretive step may be difficult—particularly for applications on real data sets. We propose to overcome the limiting factor by considering locally coherent events. A locally coherent event can be defined whenever the imaged reflectivity locally shows lateral coherency at some location in the image cube. In the prestack depth‐migrated volume obtained for an a priori velocity model, locally coherent events are picked automatically, without interpretation, and are characterized by their positions and slopes (tangent to the event). Even a single locally coherent event has information on the unknown velocity model, carried by the value of the slope measured in the CIG. The velocity is estimated by minimizing these slopes. We first introduce the cost function and explain its physical meaning. The theoretical developments lead to two equivalent expressions of the cost function: one formulated in the depth‐migrated domain on locally coherent events in CIGs and the other in the time domain. We thus establish direct links between different methods devoted to velocity estimation: migration velocity analysis using locally coherent events and slope tomography. We finally explain how to compute the gradient of the cost function using paraxial ray tracing to update the velocity model. Our method provides smooth, inverted velocity models consistent with Kirchhoff‐type migration schemes and requires neither the introduction of interfaces nor the interpretation of continuous events. As for most automatic velocity analysis methods, careful preprocessing must be applied to remove coherent noise such as multiples.

Redatuming through a salt canopy and target-oriented salt-flank imaging

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. S63-S71 ◽  
Author(s):  
Rongrong Lu ◽  
Mark Willis ◽  
Xander Campman ◽  
Jonathan Ajo-Franklin ◽  
M. Nafi Toksöz
Keyword(s):  
Velocity Gradient ◽  
Model Building ◽  
Velocity Structure ◽  
Velocity Model ◽  
Seismic Profile ◽  
Velocity Estimation ◽  
Reverse Time ◽  
Estimation Model ◽  
Depth Migration ◽  
Prestack Migration

We describe a new shortcut strategy for imaging the sediments and salt edge around a salt flank through an overburden salt canopy. We tested its performance and capabilities on 2D synthetic acoustic seismic data from a Gulf of Mexico style model. We first redatumed surface shots, using seismic interferometry, from a walkaway vertical seismic profile survey as if the source and receiver pairs had been located in the borehole at the positions of the receivers. This process creates effective downhole shot gathers by completely moving surface shots through the salt canopy, without any knowledge of overburden velocity structure. After redatuming, we can apply multiple passes of prestack migration from the reference datum of the bore-hole. In our example, first-pass migration, using only a simple vertical velocity gradient model, reveals the outline of the salt edge. A second pass of reverse-time, prestack depth migration using full two-way wave equation was performed with an updated velocity model that consisted of the velocity gradient and salt dome. The second-pass migration brings out dipping sediments abutting the salt flank because these reflectors were illuminated by energy that bounced off the salt flank, forming prismatic reflections. In this target-oriented strategy, the computationally fast redatuming process eliminates the need for the traditional complex process of velocity estimation, model building, and iterative depth migration to remove effects of the salt canopy and surrounding overburden. This might allow this strategy to be used in the field in near real time.

scholarly journals The Puffin Field ? a geophysical enigma

1989 ◽  
Vol 20 (2) ◽  
pp. 301
Author(s):  
P.D. Grant
Keyword(s):  
Joint Venture ◽  
Source Area ◽  
Velocity Model ◽  
Minimum Size ◽  
Velocity Variation ◽  
Velocity Analysis ◽  
Low Velocity ◽  
Interval Velocity ◽  
Oil Water

The Puffin Field is located within the Vulcan Sub-basin of the Timor sea, off the Northwest Coast of Australia. It lies within the offshore exploration permit AC/P2, operated by BHP Petroleum and its co-venturers. It is situated on the Ashmore Platform, an old Triassic horst which is normal faulted against the Swan Graben, a major Mesozoic depocentre and the regional source area. Three wells were drilled in the 1970's. Puffin-1 and Puffin-3 encountered oil in "FIT" tests from within the Maastrichtian 100 ft sand, and Puffin-2 flowed over 4000 barrels of oil per day from a slightly younger 4 m sand. On examination of the results of the Puffin wells, it was evident that there were severe velocity anomalies and differing oil water contacts in the Puffin field. The top of the 100 ft reservoir sand is at 2031.4 m subsea in Puffin-1, 2045 m subsea at Puffin-2 and 2074 m subsea at Puffin-3. The two way times to these events were 1392 ms, 1328 ms and 1398 ms respectively. The interpreted oil water contacts in Puffin-1 and Puffin-3 were 2033 and 2077 ms subsea respectively with no contact seen at Puffin-2. In an attempt to resolve these anomalies the AC/P2 joint venture undertook a detailed seismic reprocessing project of the 1980 data with special emphasis on detailed velocity analysis. This 1987 reprocessing effort involved two passes of velocity filtering and velocity analysis at every 600 m. Velocity analyses were picked on a horizon-consistent basis, such that variations in interval velocity for key horizons could be established for later use in depth conversion. Although sceptical in using stacking functions as the input velocities to depth conversion, they were used, as no viable alternative was feasible. Data quality was reliable to the top of the Palaeocene Calcilutite, and six horizons were picked with their respective velocities to this level. Analysis of the data indicated that the two major units exhibiting interval velocity variation were the Pliocene "low velocity layer" and the Eocene carbonates. Using the smoothed stacking velocity down to the Top Palaeocene Calcilutite the three wells tied the depth conversion with an accuracy of 0.5%. Below this horizon two constant interval velocities were used from well data as the quality of the seismic pick were not as reliable. To verify this model BHPP also undertook a "layer-cake" velocity approach which, although confirming the anomalous zones, could not be used laterally away from the three wells, which unfortunately all lay in a straight line. Two wells, Puffin-4 and Parry-1 were drilled in 1988 to test the resultant interpretation. The wells intersected the Top Palaeocene Calcilutite within 1% of prognosis at Puffin-4 and within 2.2% of prognosis at Parry-1, therefore confirming the stacking velocity model used in depth conversion. However, both wells came in deep to prognosis at the deeper, objective level as a result, in the case of Puffin-4, of being on the downthrown side of a small fault, and at Parry-1 due to a thickening of the Paleocene section and seismic mispicking of the Top Palaeocene Calcilutite. Had the mispick at Parry-1 been avoided then the tie would have been less than 1.0%. Both these mis-interpretations were made in the part of the section where the quality of seismic was poorest. These two results suggest that even though the depth conversion to the Top Paleocene Calcilutite is accurate to within 1%, the magnitude of the velocity variation is larger than the magnitude of the independent depth closure. The Puffin Field requires both better quality seismic below the Base Palaeocene Calcilutite, or the means to resolve the lateral extent and possible thickness of a 4 m sand away from Puffin-2. Until such a method of obtaining either better quality seismic to the objective level, or to be able to define the seismic resolution of the differing sand bodies of a minimum size of 4 m, the Puffin Field will remain a Geophysical enigma.

Interval velocity estimation via NMO-based differential semblance

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. U75-U88 ◽  
Author(s):  
Jintan Li ◽  
William W. Symes
Keyword(s):  
Velocity Model ◽  
Velocity Estimation ◽  
Imaging Method ◽  
Velocity Analysis ◽  
Multiple Reflections ◽  
Coherent Noise ◽  
Interval Velocity ◽  
Velocity Models ◽  
Mean Square Difference ◽  
Rich Data

The differential semblance method of velocity analysis flattens image gathers automatically by updating interval velocity to minimize the mean square difference of neighboring traces. We detail an implementation using hyperbolic normal moveout correction as the imaging method. The algorithm is fully automatic, accommodates arbitrary acquisition geometry, and outputs 1D, 2D, or 3D interval velocity models. This variant of differential semblance velocity analysis is effective within the limits of its imaging methodology: mild lateral heterogeneity and data dominated by primary events. Coherent noise events such as multiple reflections tend to degrade the quality of the velocity model estimated by differential semblance. We show how to combine differential semblance velocity analysis with dip filtering to suppress multiple reflections and thus improve considerably the accuracy of the velocity estimate. We illustrate this possibility using multiple-rich data from a 2D marine survey.

scholarly journals Brief Communication: On the influence of vertical velocity profiles on the combined power output of two model wind turbines in yaw

2017 ◽  
Author(s):  
Jannik Schottler ◽  
Agnieszka Hölling ◽  
Joachim Peinke ◽  
Michael Hölling
Keyword(s):  
Wind Turbines ◽  
Vertical Velocity ◽  
Velocity Gradient ◽  
Power Output ◽  
Velocity Profiles ◽  
Total Power ◽  
Misalignment Angle ◽  
Velocity Gradients ◽  
Total Power Output ◽  
Vertical Velocity Gradient

Abstract. The effect of vertical velocity gradients on the total power output of two aligned model wind turbines as a function of yaw misalignment of the upstream turbine is studied experimentally. It is shown that asymmetries of the power output of the downstream turbine and the combined power of both with respect to the upstream turbine's yaw misalignment angle can be linked to the vertical velocity gradient of the inflow.

Accuracy study of velocity estimation in 3-D layered models

Geophysics ◽  
1995 ◽  
Vol 60 (5) ◽  
pp. 1567-1574
Author(s):  
Valery Sorin
Keyword(s):  
Three Dimensional ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Apparent Velocity ◽  
Velocity Anisotropy ◽  
Strike Direction ◽  
Accuracy Study ◽  
Layer Velocity ◽  
Structure Geometry ◽  
Zero Offset

Velocity estimation is examined in 3-D layered structures formed by plane and curved interfaces. The applied technique of coherency inversion tests the layer velocity through the repeating sequence of ray migration/coherency measurement. The reconstructed velocity‐depth model fits zero‐offset reflection times and maximizes semblance on input common midpoint (CMP) gathers. The correctness of layer velocity analysis disregarding the three‐dimensionality of the structures is under consideration. Using the 2-D coherency inversion technique, velocity is correctly determined in the upper layer of the examined structures. Two‐dimensional analysis in the deeper layer gives biased velocity estimates. The errors in the 2-D velocity estimates vary with the profile azimuth and appear in the form of the apparent velocity anisotropy. The inaccuracy of 2-D velocity estimation is analytically considered for the profile oriented along the refractor strike direction. The derived equation relates the velocity error to structure geometry and to the velocity contrast above and below the refractor. Three‐dimensional velocity analysis in the examined structures reveals that the layer velocity resolution is affected by the refractor shape. Below the convex refractor the velocity resolution deteriorates compared with that below the plane.

scholarly journals Fast 3D migration-velocity analysis by wavefield extrapolation using the prestack exploding-reflector model

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB151-WB167 ◽  
Author(s):  
Claudio Guerra ◽  
Biondo Biondi
Keyword(s):  
Initial Conditions ◽  
Model Space ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Image Space ◽  
Velocity Analysis ◽  
The North ◽  
Migration Velocity Analysis ◽  
Wavefield Extrapolation

In areas of complex geology, migration-velocity estimation should use methods that describe the complexity of wavefield propagation, such as focusing and defocusing, multipathing, and frequency-dependent velocity sensitivity. Migration-velocity analysis by wavefield extrapolation has the ability to address these issues because, in contrast to ray-based methods, it uses wavefields as carriers of information. However, its high cost and lack of flexibility with respect to model parametrization and to target-oriented analysis have prevented its routine industrial use. We overcome those limitations by using new types of wavefields as carriers of information: the image-space generalized wavefields. These wavefields are synthesized from a prestack image computed with wavefield-extrapolation methods, using the prestack exploding-reflector model. Cost of migration-velocity analysis (MVA) by wavefield extrapolation is decreased because only a small number of image-space generalized wavefields are necessary to accurately describe the kinematics of velocity errors and because these wavefields can be easily used in a target-oriented way. Flexibility is naturally incorporated because modeling these wavefields has as the initial conditions selected reflectors, which allow use of a horizon-based parametrization of the model space. In a 3D example of the North Sea, we show that using wavefields synthesized by the prestack exploding-reflector model greatly improves efficiency of MVA by wavefield extrapolation, while yielding a final migration-velocity model that is accurate as evidenced by well focused and structurally reasonable reflectors.

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