Accuracy study of velocity estimation in 3-D layered models

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.

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Wave-equation migration velocity analysis by focusing diffractions and reflections

Geophysics ◽

10.1190/1.1925749 ◽

2005 ◽

Vol 70 (3) ◽

pp. U19-U27 ◽

Cited By ~ 87

Author(s):

Paul C. Sava ◽

Biondo Biondi ◽

John Etgen

Keyword(s):

Wave Equation ◽

Migration Velocity ◽

Velocity Estimation ◽

Velocity Analysis ◽

Depth Migration ◽

Interval Velocity ◽

Migration Velocity Analysis ◽

Inversion Procedure ◽

Velocity Information ◽

Zero Offset

We propose a method for estimating interval velocity using the kinematic information in defocused diffractions and reflections. We extract velocity information from defocused migrated events by analyzing their residual focusing in physical space (depth and midpoint) using prestack residual migration. The results of this residual-focusing analysis are fed to a linearized inversion procedure that produces interval velocity updates. Our inversion procedure uses a wavefield-continuation operator linking perturbations of interval velocities to perturbations of migrated images, based on the principles of wave-equation migration velocity analysis introduced in recent years. We measure the accuracy of the migration velocity using a diffraction-focusing criterion instead of the criterion of flatness of migrated common-image gathers that is commonly used in migration velocity analysis. This new criterion enables us to extract velocity information from events that would be challenging to use with conventional velocity analysis methods; thus, our method is a powerful complement to those conventional techniques. We demonstrate the effectiveness of the proposed methodology using two examples. In the first example, we estimate interval velocity above a rugose salt top interface by using only the information contained in defocused diffracted and reflected events present in zero-offset data. By comparing the results of full prestack depth migration before and after the velocity updating, we confirm that our analysis of the diffracted events improves the velocity model. In the second example, we estimate the migration velocity function for a 2D, zero-offset, ground-penetrating radar data set. Depth migration after the velocity estimation improves the continuity of reflectors while focusing the diffracted energy.

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A constrained parametric inversion for velocity analysis based on CFP technology

Geophysics ◽

10.1190/1.1444813 ◽

2000 ◽

Vol 65 (4) ◽

pp. 1210-1222 ◽

Cited By ~ 16

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.

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Velocity analysis based on minimum entropy

Geophysics ◽

10.1190/1.1441629 ◽

1984 ◽

Vol 49 (12) ◽

pp. 2132-2142 ◽

Cited By ~ 24

Author(s):

D. De Vries ◽

A. J. Berkhout

Keyword(s):

Velocity Estimation ◽

Resolving Power ◽

Velocity Analysis ◽

Minimum Entropy ◽

Estimation Techniques ◽

Velocity Error ◽

Seismic Resolution ◽

Velocity Information ◽

Zero Offset

Seismic resolution is determined by the sparsity of reflection events together with the dispersion of the wavelets representing those events. In this paper, minimum entropy (ME) norms are introduced as a measure of spatial resolving power. It is shown that the lateral dispersion of inverted diffractor responses (inverted spatial wavelets) increases with increasing velocity error. Using this property, minimum entropy velocity analysis (MEVA) is proposed to extract velocity information from diffraction energy. MEVA can be successfully applied to zero‐offset (including poststack) data and common‐offset data with a sufficient amount of diffraction energy. In addition, MEVA can be used as an alternative to existing CMP velocity estimation techniques.

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Estimation of azimuthal anisotropy from VSP data using multicomponent S-wave velocity analysis

Geophysics ◽

10.1190/geo2010-0290.1 ◽

2011 ◽

Vol 76 (5) ◽

pp. D1-D9 ◽

Cited By ~ 14

Author(s):

Roman Pevzner ◽

Boris Gurevich ◽

Milovan Urosevic

Keyword(s):

Shear Wave ◽

Transverse Isotropy ◽

Symmetry Plane ◽

Azimuthal Anisotropy ◽

Velocity Analysis ◽

Apparent Velocity ◽

S Wave ◽

North West ◽

Vsp Data ◽

Zero Offset

Observation of azimuthal shear wave anisotropy can be useful for characterization of fractures or stress fields. Shear wave anisotropy is often estimated by measuring splitting of individual shear wave events in vertical seismic profile (VSP) data. However, this method may become unreliable for zero-offset (marine) VSP where the seismogram often contains no strong individual shear events, such as direct downgoing shear wave, but often contains many low-amplitude PS mode converted waves. We have developed a new approach for estimation of the fast and slow shear wave velocities and orientation of polarization planes based on the multicomponent linear traveltime moveout velocity analysis. This technique is applicable to zero-offset VSP data, and should take advantage of the presence of a large number of shear wave events with the same apparent velocity (which, for a horizontally layered medium, should be close to the interval velocity). The approach assumes that the VSP data are acquired in a vertical well drilled in an orthorhombic medium with a horizontal symmetry plane (including horizontal transverse isotropy). The main idea is to estimate the dominant apparent velocity for a given polarization direction by measuring the coherency of the seismic signal of a large number of events as a function of the apparent velocity. The algorithm was tested on marine three-component (3C) VSP acquired in the North West Shelf of Australia, and on land 3C VSP acquired with different sources in the same borehole located in Otway Basin, Victoria. These tests show good agreement between anisotropy parameters (magnitude and orientation) derived from the VSP and cross-dipole sonic log data.

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Numeric implementation of wave-equation migration velocity analysis operators

Geophysics ◽

10.1190/1.2953337 ◽

2008 ◽

Vol 73 (5) ◽

pp. VE145-VE159 ◽

Cited By ~ 37

Author(s):

Paul Sava ◽

Ioan Vlad

Keyword(s):

Wave Equation ◽

Velocity Model ◽

Migration Velocity ◽

Velocity Estimation ◽

Velocity Analysis ◽

Velocity Models ◽

Image Optimization ◽

Migration Velocity Analysis ◽

Zero Offset ◽

Wavefield Extrapolation

Wave-equation migration velocity analysis (MVA) is a technique similar to wave-equation tomography because it is designed to update velocity models using information derived from full seismic wavefields. On the other hand, wave-equation MVA is similar to conventional, traveltime-based MVA because it derives the information used for model updates from properties of migrated images, e.g., focusing and moveout. The main motivation for using wave-equation MVA is derived from its consistency with the corresponding wave-equation migration, which makes this technique robust and capable of handling multipathing characterizing media with large and sharp velocity contrasts. The wave-equation MVA operators are constructed using linearizations of conventional wavefield extrapolation operators, assuming small perturbations relative to the background velocity model. Similar to typical wavefield extrapolation operators, the wave-equation MVA operators can be implemented in the mixed space-wavenumber domain using approximations of differentorders of accuracy. As for wave-equation migration, wave-equation MVA can be formulated in different imaging frameworks, depending on the type of data used and image optimization criteria. Examples of imaging frameworks correspond to zero-offset migration (designed for imaging based on focusing properties of the image), survey-sinking migration (designed for imaging based on moveout analysis using narrow-azimuth data), and shot-record migration (also designed for imaging based on moveout analysis, but using wide-azimuth data). The wave-equation MVA operators formulated for the various imaging frameworks are similar because they share elements derived from linearizations of the single square-root equation. Such operators represent the core of iterative velocity estimation based on diffraction focusing or semblance analysis, and their applicability in practice requires efficient and accurate implementation. This tutorial concentrates strictly on the numeric implementation of those operators and not on their use for iterative migration velocity analysis.

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Ultrasonographic 3D Evaluation in the Diagnosis of Bladder Endometriosis: A Prospective Comparative Diagnostic Accuracy Study

Gynecologic and Obstetric Investigation ◽

10.1159/000516634 ◽

2021 ◽

pp. 1-8

Author(s):

Fabio Barra ◽

Franco Alessandri ◽

Carolina Scala ◽

Simone Ferrero

Keyword(s):

Diagnostic Accuracy ◽

Three Dimensional ◽

3D Ultrasound ◽

Diagnostic Accuracy Study ◽

Extensive Experience ◽

Deep Endometriosis ◽

3D Reconstructions ◽

Analysis Group ◽

Bladder Endometriosis ◽

Accuracy Study

Objective: The use of three-dimensional (3D) transvaginal ultrasonography (TVS) has been investigated for the diagnosis of deep endometriosis (DE). This study aimed to evaluate if 3D reconstructions improve the performance of TVS) in assessing the presence and characteristics of bladder endometriosis (BE). Design: This was a single-center comparative diagnostic accuracy study. Participants/Materials, Setting, Methods: Patients referred to our institution (Piazza della Vittoria 14 Srl, Genova, Italy) with clinical suspicion of DE were included. In case of surgery, women underwent systematic preoperative ultrasonographic imaging; an experienced sonographer performed a conventional TVS; another experienced sonographer, blinded to results of the previous exam, performed TVS, with the addition of 3D modality. The presence and characteristics of BE nodules were described in accord with International DE Analysis group consensus. Ultrasound data were compared with surgical and histological results. Results: Overall, BE was intraoperatively found in 34 out of 194 women who underwent surgery for DE (17.5%; 95% confidence interval: 12.8–23.5%). TVS without and with 3D reconstructions were able to detect endometriotic BE in 82.2% (n = 28/34) and 85.3% (n = 29/34) of the cases (p = 0.125). Both the exams similarly estimated the largest diameter of BE (p = 0.652) and the distance between the endometriotic nodule and the closest ureteral meatus (p = 0.341). However, TVS with 3D reconstructions was more precise in estimating the volume of BE (p = 0.031). In one case (2.9%), TVS without and with 3D reconstructions detected the infiltration of the intramural ureter, which was confirmed at surgery and required laparoscopic ureterovesical reimplantation. Limitations: The extensive experience of the gynecologists performing the ultrasonographic scans, the lack of prestudy power analysis, and the population selected, which may have been influenced by the position of the institution as a referral center specialized in the treatment of severe endometriosis, are limitations of the current study. Conclusion: Our results demonstrated the high accuracy of ultrasound for diagnosing BE. The addition of 3D reconstructions does not improve the performance of TVS in diagnosing the presence and characteristics of BE. However, the volume of BE may be more precisely assessed by 3D ultrasound.

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

Geophysics ◽

10.1190/1.1500382 ◽

2002 ◽

Vol 67 (4) ◽

pp. 1202-1212 ◽

Cited By ~ 72

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.

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Study on the Velocity Analysis Method of Low SNR Seismic Data

Energy and Environment Research ◽

10.5539/eer.v11n1p78 ◽

2021 ◽

Vol 11 (1) ◽

pp. 78

Author(s):

Jianbo He ◽

Zhenyu Wang ◽

Mingdong Zhang

Keyword(s):

Seismic Data ◽

Fresnel Zone ◽

Signal To Noise Ratio ◽

Normal Wave ◽

Curvature Radius ◽

Velocity Spectrum ◽

Velocity Analysis ◽

Signal To Noise ◽

Noise Ratio ◽

Zero Offset

When the signal to noise ratio of seismic data is very low, velocity spectrum focusing will be poor., the velocity model obtained by conventional velocity analysis methods is not accurate enough, which results in inaccurate migration. For the low signal noise ratio (SNR) data, this paper proposes to use partial Common Reflection Surface (CRS) stack to build CRS gathers, making full use of all of the reflection information of the first Fresnel zone, and improves the signal to noise ratio of pre-stack gathers by increasing the number of folds. In consideration of the CRS parameters of the zero-offset rays emitted angle and normal wave front curvature radius are searched on zero offset profile, we use ellipse evolving stacking to improve the zero offset section quality, in order to improve the reliability of CRS parameters. After CRS gathers are obtained, we use principal component analysis (PCA) approach to do velocity analysis, which improves the noise immunity of velocity analysis. Models and actual data results demonstrate the effectiveness of this method.

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A Large Measuring Range Profilometer for Three-Dimensional Surface Topography Measurement

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.364-366.750 ◽

2007 ◽

Vol 364-366 ◽

pp. 750-755 ◽

Cited By ~ 1

Author(s):

Xu Dong Yang ◽

Jia Chun Li ◽

Tie Bang Xie

Keyword(s):

Surface Topography ◽

Three Dimensional ◽

Displacement Sensor ◽

Resistance Force ◽

Sampling Point ◽

Measuring Range ◽

3D Surface Topography ◽

Control Circuits ◽

Industrial Control Computer ◽

Zero Offset

A novel profilometer for three-dimensional (3D) surface topography measurement is presented. The profilometer has large measuring range, high precision and small measuring touch force. It is composed of a two-dimensional (2D) displacement sensor, a 3D platform based on vertical scanning, measuring and control circuits and an industrial control computer. When a workpiece is measured, the vertical undulation of the profile at a sampling point leads to a zero offset of the 2D displacement sensor. According to the zero offset, a piezoelectric actuator and a servo motor drive the vertical scanning platform to move vertically to ensure that the lever returns to its balance position. So the non-linear error caused by the rotation of the lever is very small even if the measuring range is large. When the stylus barges up against a steep wall, the horizontal resistance force results in another zero offset of the 2D displacement sensor. If the zero offset exceeds a quota, the vertical scanning platform descends to make the stylus climb the steep wall successfully. According to the theoretical and experimental analysis, the profilometer can measure roughness, profile of sphere, step, groove and other 3D surfaces with curvature precisely.

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Large‐scale three‐dimensional seismic models and their interpretive significance

Geophysics ◽

10.1190/1.1442933 ◽

1990 ◽

Vol 55 (9) ◽

pp. 1166-1182 ◽

Cited By ~ 21

Author(s):

Irshad R. Mufti

Keyword(s):

Finite Difference ◽

Wave Field ◽

Large Scale ◽

Three Dimensional ◽

Synthetic Data ◽

Real Data ◽

The Real ◽

Need To Evaluate ◽

Zero Offset ◽

Seismic Models

Finite‐difference seismic models are commonly set up in 2-D space. Such models must be excited by a line source which leads to different amplitudes than those in the real data commonly generated from a point source. Moreover, there is no provision for any out‐of‐plane events. These problems can be eliminated by using 3-D finite‐difference models. The fundamental strategy in designing efficient 3-D models is to minimize computational work without sacrificing accuracy. This was accomplished by using a (4,2) differencing operator which ensures the accuracy of much larger operators but requires many fewer numerical operations as well as significantly reduced manipulation of data in the computer memory. Such a choice also simplifies the problem of evaluating the wave field near the subsurface boundaries of the model where large operators cannot be used. We also exploited the fact that, unlike the real data, the synthetic data are free from ambient noise; consequently, one can retain sufficient resolution in the results by optimizing the frequency content of the source signal. Further computational efficiency was achieved by using the concept of the exploding reflector which yields zero‐offset seismic sections without the need to evaluate the wave field for individual shot locations. These considerations opened up the possibility of carrying out a complete synthetic 3-D survey on a supercomputer to investigate the seismic response of a large‐scale structure located in Oklahoma. The analysis of results done on a geophysical workstation provides new insight regarding the role of interference and diffraction in the interpretation of seismic data.

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