North Sea reservoir description: Benefits of an elastic migration/inversion applied to multicomponent vertical seismic profile data

Beydoun, Wafik; Mendes, Manuela; Blanco, Jacques; Tarantola, Albert

doi:10.1190/1.1442828

Cited by 14 publications

(11 citation statements)

References 2 publications

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“…Although improvements in the inversion results were achieved, the overall patterns of parameter coupling artefacts visible in the inversion results after one iteration remained spatially evident after a single iteration, suggesting that one pass might be sufficient for purposes of interpretation. A similar conclusion was articulated by Beydoun et al (1990) on the basis of a two-iteration isotropic experiment. The decay in residual energy for five iterations is listed in Table 1, where it appears to be approaching an asymptotic value of about 31 per cent.…”

Section: Point-diffractor Testssupporting

confidence: 75%

Migration/inversion for transversely isotropic elastic media

Eaton

Stewart

1994

Geophysical Journal International

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S U M M A R YSeismic migration and inversion are closely related processes for obtaining images of the subsurface. Both techniques attempt to infer petrophysical and structural parameters from seismic data, and both are driven by an underlying mathematical model for wave propagation in the earth. In this sense, migration can be regarded as the first step in' a general linearized-inversion scheme; we adopt this viewpoint here in formulating a joint migration/inversion method for anisotropic elastic media. Our derivation is based on the distorted-wave Born approximation, where approximate Green's functions for the background medium are determined using asymptotic ray theory. We also make use of a stationary-phase correction to account for out-of-plane scattering in a 2-D earth model. The inversion is cast as a discrete, generalized l2 optimization problem, which we regularize using a priori model variances. An approximate solution is obtained in one or more iterations using a quasi-Newton technique. Our implementation is tailored for weakly anisotropic elastic media possessing transversely isotropic (TI) symmetry, and so is well suited for investigations of earth models characterized by a singe set of parallel fractures or periodic thin layering.Several TI model parametrization schemes are evaluated for a vertical-incidence narrow-aperture recording configuration. By applying singular-value decomposition to the approximate Hessian operator used in the inversion, we find that when the symmetry axis of the medium is vertically oriented the condition number is minimized by choosing vertical impedance parameters, density and Thomsen's (1986) anisotropy parameters. Elastic stiffnesses and density may be a better parametrization choice if the symmetry axis is either horizontal or unknown. The small effective rank (2-3) of the Hessian in our narrow-aperture tests implies that migration inversion (without a priori constraints) of surface-reflection data may be inadequate to fully characterize a TI medium, which would require six parameters. However, this result does not in itself justify the use of simpler isotropic inversion schemes, since the principal eigenvectors determined here represent a blend of 'isotropic' and 'anisotropic' information about the earth.A suite of point-diffractor tests shows that individual perturbation amplitudes recovered in the inversion are smaller, but cover a larger region of the image, than those used in the original model, consistent with the band-limited nature of the input signal. Parameter cross-coupling problems affect the inversion results for all parameters, but are more prominent in the inversion images for anisotropy parameters. In our tests, the linearized-inversion results converge to a local minimum after three iterations, and the scatterer distributions in the inversion images are essentially fixed after a single iteration.

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Section: Point-diffractor Testssupporting

confidence: 75%

Migration/inversion for transversely isotropic elastic media

Eaton

Stewart

1994

Geophysical Journal International

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“…The actual relation between short scale parameter fluctuations and bandlimited data is approximately linear when multiply reflected energy is unimportant or has been removed by preprocessing without seriously compromising primary reflection amplitudes. This primaries-only condition can sometimes he met, at least approximately, and linear inversion has actually been used to produce parameter maps of the subsurface, incorporating AVO information (see, e.g., Parsons, 1986;Beydoun et al, 1990;Bourgeois et al, 1989).…”

Section: Introductionmentioning

confidence: 99%

2. A Numerical Study of Linear Viscoacoustic Inversion

Blanch¹,

Symes²,

Versteeg³

1998

Comparison of Seismic Inversion Methods on a Single Real Data Set

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Attenuation and dispersion of the seismic pulse can strongly affect the outcome of amplitude versus offset (AVO) analysis. These anelastic aspects of wave propagation also influence the outcome of linear inversion for short scale fluctuations in elastic parameters, the model based analogue of AVO analysis. The viscoacoustic model provides a framework for illustration of these effects. An efficient time domain viscoacoustic finite difference scheme for synthesis of primaries only plane-wave (1-D model) and line source (2-D model) reflection records is the basis for linear inversion algorithms via iterative minimization of mean square error. This approach to inversion requires computation of the mean square error gradient. The gradient computation becomes feasible through the use of the adjoint state technique, together with a checkpointing scheme due to Griewank. Inversion of synthetic data in the plane-wave domain illustrates the sensitivity to attenuation of even qualitative aspects of inversion. Viscoacoustic 2-D inversion of a small part of the Mobil AVO data illustrates applicability to field data in the offset domain.

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“…Several researchers have applied these methods to ray theoretical solutions of the wave equation (Beydoun et al 1989; Lambare et al 1992). The local nature of the ray approximation makes this approach computationally attractive, and ray‐based techniques have enjoyed considerable application to real reflection data (Beydoun et al 1989; Beydoun et al 1990). Some progress has also been made outside the ray paradigm in terms of application to reflection data (Crase et al 1990).…”

Section: Introductionmentioning

confidence: 99%

Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion

Pratt

Shin

Hicks³

1998

Geophys. J. Int.

1,285

150

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Summary By specifying a discrete matrix formulation for the frequency–space modelling problem for linear partial differential equations (‘FDM’ methods), it is possible to derive a matrix formalism for standard iterative non‐linear inverse methods, such as the gradient (steepest descent) method, the Gauss–Newton method and the full Newton method. We obtain expressions for each of these methods directly from the discrete FDM method, and we refer to this approach as frequency‐domain inversion (FDI). The FDI methods are based on simple notions of matrix algebra, but are nevertheless very general. The FDI methods only require that the original partial differential equations can be expressed as a discrete boundary‐value problem (that is as a matrix problem). Simple algebraic manipulation of the FDI expressions allows us to compute the gradient of the misfit function using only three forward modelling steps (one to compute the residuals, one to backpropagate the residuals, and a final computation to compute a step length). This result is exactly analogous to earlier backpropagation methods derived using methods of functional analysis for continuous problems. Following from the simplicity of this result, we give FDI expressions for the approximate Hessian matrix used in the Gauss–Newton method, and the full Hessian matrix used in the full Newton method. In a new development, we show that the additional term in the exact Hessian, ignored in the Gauss–Newton method, can be efficiently computed using a backpropagation approach similar to that used to compute the gradient vector. The additional term in the Hessian predicts the degradation of linearized inversions due to the presence of first‐order multiples (such as free‐surface multiples in seismic data). Another interpretation is that this term predicts changes in the gradient vector due to second‐order non‐linear effects. In a numerical test, the Gauss–Newton and full Newton methods prove effective in helping to solve the difficult non‐linear problem of extracting a smooth background velocity model from surface seismic‐reflection data.

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North Sea reservoir description: Benefits of an elastic migration/inversion applied to multicomponent vertical seismic profile data

Cited by 14 publications

References 2 publications

Migration/inversion for transversely isotropic elastic media

Migration/inversion for transversely isotropic elastic media

2. A Numerical Study of Linear Viscoacoustic Inversion

Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion

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