Practice and pitfalls in NMO‐based differential semblance velocity analysis

Verm, Richard; Symes, William W.

doi:10.1190/1.2369954

Cited by 7 publications

(9 citation statements)

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“…convolutional model simulation of common‐midpoint (CMP) data (Symes 1993, 1998; Symes and Gockenbach 1995; Li and Symes 2005; Dussaud and Symes 2005; Verm and Symes 2006),…”

Section: Objective Migration Velocity Analysismentioning

confidence: 99%

“…The numerical works cited above suggest in one way or another than not only is the differential semblance objective stable against high‐frequency data perturbation, but it is also essentially monomodal: the only stationary points are physically significant solutions of the waveform inversion problem (and, in particular, velocities kinematically consistent with data). In one special case, this has even been proven with mathematical rigour: for the differential semblance variant for CMP data, based on hyperbolic normal moveout (NMO) (Symes and Gockenbach 1995; Symes 1998; Li and Symes 2005; Verm and Symes 2006; Li and Symes 2007), all stationary points are global minima, up to an error proportional to a dominant wavelength (Symes 1999, 2001). The essential idea of the proof is the relation between the differential semblance objective and fitting of apparent velocities in the data, an approach to velocity estimation also known as stereotomography (Billette and Lambaré 1998).…”

Section: Objective Migration Velocity Analysismentioning

confidence: 99%

“…The differential semblance class (third option from the list above) has many variants, some employing prestack depth migration (i.e., DF [v] * ) rather than (pseudo)inversion to construct the function J A . Differential semblance variants based on surface-oriented extension have used r convolutional model simulation of plane wave data (Symes 1986b(Symes , 1990(Symes , 1991bCarazzone 1991, 1992;Minkoff and Symes 1997), r convolutional model simulation of common-midpoint (CMP) data (Symes 1993(Symes , 1998Symes and Gockenbach 1995;Li and Symes 2005;Dussaud and Symes 2005;Verm and Symes 2006), r two-way wave equation modelling (two-way reverse time migration) (Symes 1991c;Symes and Versteeg 1993;Kern and Symes 1994), r generalized Radon transform simulation of acoustic scattering (Kirchhoff migration) Mulder and ten Kroode 2002;de Hoop, Brandsberg-Dahl and Ursin 2003), and r generalized Radon transform simulation of anisotropic elastic scattering (de Hoop, Foss and Ursin 2005). Variants based on depth-oriented extension have employed r one-way wave equation migration of shot profiles (Shen et al 2005b;Albertin et al 2006), and r one-way wave equation migration via the DSR equation (Shen, Symes and Stolk 2003;Khoury et al 2006).…”

Section: Annihilatorsmentioning

confidence: 99%

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Migration velocity analysis and waveform inversion

Symes

2008

Geophysical Prospecting

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Waveform (output least squares) inversion of seismic reflection data can reconstruct remarkably detailed models of subsurface structure, and take into account essentially any physics of seismic wave propagation that can be modeled. However the waveform inversion objective has many spurious local minima, hence convergence of descent methods (mandatory because of problem size) to useful Earth models requires accurate initial estimates of long-scale velocity structure. Migration velocity analysis, on the other hand, is based on the Born approximation but is capable of correcting substantially erroneous initial velocities. Appropriate choice of objective (differential semblance) turns migration velocity analysis into an optimization problem, for which Newton-like methods exhibit little tendency to stagnate at nonglobal minima. The extended modeling concept links these two apparently unrelated approaches to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized (single scattering, Born) waveform inversion problem. Extended modeling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests that this new approach to nonlinear waveform inversion may combine the global convergence of velocity analysis with the physical fidelity of least squares.

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“…convolutional model simulation of common‐midpoint (CMP) data (Symes 1993, 1998; Symes and Gockenbach 1995; Li and Symes 2005; Dussaud and Symes 2005; Verm and Symes 2006),…”

Section: Objective Migration Velocity Analysismentioning

confidence: 99%

Section: Objective Migration Velocity Analysismentioning

confidence: 99%

Section: Annihilatorsmentioning

confidence: 99%

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Migration velocity analysis and waveform inversion

Symes

2008

Geophysical Prospecting

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448

265

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“…Methods for migration velocity analysis are sensitive to multiples (Mulder and ten Kroode ; Verm and Symes ; Mulder and van Leeuwen ). Multiple suppression is therefore important and should be done thoroughly in some cases.…”

Section: Remarksmentioning

confidence: 99%

Subsurface offset behaviour in velocity analysis with extended reflectivity images

Mulder

2013

Geophysical Prospecting

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A B S T R A C TMigration velocity analysis with the constant-density acoustic wave equation can be accomplished by the focusing of extended migration images, obtained by introducing a subsurface shift in the imaging condition. A reflector in a wrong velocity model will show up as a curve in the extended image. In the correct model, it should collapse to a point. The usual approach to obtain a focused image involves a cost functional that penalizes energy in the extended image at non-zero shift. Its minimization by a gradient-based method should then produce the correct velocity model. Here, asymptotic analysis and numerical examples show that this method may be too sensitive to amplitude peaks at large shifts at the wrong depth and to artefacts. A more robust alternative is proposed that can be interpreted as a generalization of stack power and maximizes the energy at zero-subsurface shift. A real-data example is included.

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“…Previous work has shown that DSVA is quite sensitive to the presence of multiply reflected energy (eg. (Verm and Symes, 2006)). This is hardly surprising, as the method is relies for its theoretical justification (7) with reflecting boundary condition.…”

Section: Real Data Examplesmentioning

confidence: 99%

Automatic velocity analysis via shot profile migration

2008

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Shot profile migration provides a convenient framework for implementation of a differential semblance algorithm for estimation of complex, strongly refracting velocity fields. The objective function minimized in this algorithm may measure either focussing of the image in offset or flatness of the image in (scattering) angle. Velocity estimation based on this measure of data-model consistency uses waveform data directly: it does not require any sort of traveltime picking. We show that the offset variant of differential semblance yields somewhat more reliable migration velocity estimates than does the scattering angle variant, and explain why this is so. We observe that inconsistency with the underlying model (Born scattering about a transparent background) may lead to degraded velocity estimates from differential semblance, and show how to augment the objective function with stack power to enhance ultimate accuracy. A 2D marine survey over a target obscured by the lensing effects of a gas chimney provides an opportunity for direct comparison of differential semblance with reflection tomography. The differential semblance estimate yields a more data-consistent model (flatter angle gathers) than does reflection tomography in this application, resulting in a more interpretable image below the gas cloud.

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Practice and pitfalls in NMO‐based differential semblance velocity analysis

Cited by 7 publications

References 9 publications

Migration velocity analysis and waveform inversion

Migration velocity analysis and waveform inversion

Subsurface offset behaviour in velocity analysis with extended reflectivity images

Automatic velocity analysis via shot profile migration

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