Full-waveform inversion FWI is a challenging data-fitting procedure based on full-wavefield modeling to extract quantitative information from seismograms. High-resolution imaging at half the propagated wavelength is expected. Recent advances in high-performance computing and multifold/multicomponent wide-aperture and wide-azimuth acquisitions make 3D acoustic FWI feasible today. Key ingredients of FWI are an efficient forward-modeling engine and a local differential approach, in which the gradient and the Hessian operators are efficiently estimated. Local optimization does not, however, prevent convergence of the misfit function toward local minima because of the limited accuracy of the starting model, the lack of low frequencies, the presence of noise, and the approximate modeling of the wave-physics complexity. Different hierarchical multiscale strategiesaredesignedtomitigatethenonlinearityandill-posedness of FWI by incorporating progressively shorter wavelengths in the parameter space. Synthetic and real-data case studies address reconstructing various parameters, from VP and VS velocities to density, anisotropy, and attenuation. This review attempts to illuminate the state of the art of FWI. Crucial jumps, however, remain necessary to make it as popular as migration techniques. The challenges can be categorized as 1 building accurate starting models with automatic procedures and/or recording low frequencies, 2 defining new minimization criteria to mitigate the sensitivity of FWI to amplitude errors and increasing the robustness of FWI when multiple parameter classes are estimated, and 3 improving computational efficiency by data-compression techniquestomake3DelasticFWIfeasible.

/pdf/an-overview-of-full-waveform-inversion-in-exploration-59sei7fzvh.pdf

An overview of full-waveform inversion in exploration geophysics

Preface 1. The approximation problem and existence of best approximations 2. The uniqueness of best approximations 3. Approximation operators and some approximating functions 4. Polynomial interpolation 5. Divided differences 6. The uniform convergence of polynomial approximations 7. The theory of minimax approximation 8. The exchange algorithm 9. The convergence of the exchange algorithm 10. Rational approximation by the exchange algorithm 11. Least squares approximation 12. Properties of orthogonal polynomials 13. Approximation of periodic functions 14. The theory of best L1 approximation 15. An example of L1 approximation and the discrete case 16. The order of convergence of polynomial approximations 17. The uniform boundedness theorem 18. Interpolation by piecewise polynomials 19. B-splines 20. Convergence properties of spline approximations 21. Knot positions and the calculation of spline approximations 22. The Peano kernel theorem 23. Natural and perfect splines 24. Optimal interpolation Appendices Index.

Approximation theory and methods, by M. J. D. Powell. Pp 339. £25 (hardcover), £8·50 (paperback). 1981. ISBN 0-521-22472-1/29514-9 (Cambridge University Press)

Recent advances in parameter estimation and seismic processing have allowed incorporation of anisotropic models into a wide range of seismic methods. In particular, vertical and tilted transverse isotropy are currently treated as an integral part of velocity fields employed in prestack depth migration algorithms, especially those based on the wave equation. We briefly review the state of the art in modeling, processing, and inversion of seismic data for anisotropic media. Topics include optimal parameterization, body-wave modeling methods, P-wave velocity analysis and imaging, processing in the τ-p domain, anisotropy estimation from vertical-seismic-profiling (VSP) surveys, moveout inversion of wide-azimuth data, amplitude-variation-with-offset (AVO) analysis, processing and applications of shear and mode-converted waves, and fracture characterization. When outlining future trends in anisotropy studies, we emphasize that continued progress in data-acquisition technology is likely to spur transition from t...

Seismic anisotropy in exploration and reservoir characterization: An overview

A method for deriving reservoir lithology and fluid content for a target location (400) from pre-stack seismic reflection data (110). The method uses inversion (200) of pre-stack seismic reflection data for both the target location and a calibration location (110) having known subsurface lithology and fluid content to derive the subsurface lithology and fluid content at the target location (400). The inversion process (200) is preferably a viscoelastic inversion to account for the effects of friction on seismic wave propagation. The results of the inversion process are a set of subsurface elastic parameters for both the target and calibration locations. Relative magnitudes of these subsurface elastic parameters are compared (300), together with the known subsurface lithology and fluid content at the calibration location (146), to derive the subsurface lithology and fluid content at the target location (400).

Method for deriving reservoir lithology and fluid content from pre-stack inversion of seismic data

Seismic reflection profiles across many continental margins have imaged bottom simulating reflectors (BSRs), which have been interpreted as being formed at the base of a methane hydrate stability field. Such reflectors might arise either from an impedance contrast between high-velocity, partially hydrated sediments and water-saturated sediments or from a contrast with partially gas-saturated sediments. These alternatives may be hard to distinguish by conventional amplitude-versus-offset or waveform modeling approaches. Here we investigate the origin of a high amplitude BSR in the accretionary wedge offshore of western Colombia by seismic waveform inversion. The inversion procedure consists of three steps: firstly, determination of root-mean-square velocities and hence estimates of the interval velocities between major reflectors by a global grid search for maximum normalized energy along elliptical trajectories in the intercept time-slowness domain; secondly, determination of accurate interval velocities between these reflectors by a Monte Carlo search for maximum energy; and thirdly, a waveform fit in the frequency-slowness domain, using differential reflectivity seismograms and a conjugate-gradient optimization algorithm to minimize the sample-by-sample waveform misfit between data and synthetic. At two locations, near a structural high, we find a ∼30-m thick low-velocity zone beneath the BSR, with the properties of a partially gas-saturated zone, while at a third location, where the BSR amplitude is lower, we find no evidence for anomalously low velocities. The preferential development of the BSR in structures that would tend to intercept fluid flow or migrating gas and the presence of free gas beneath the BSR indicate a mechanism of BSR formation in which free methane gas migrates upward into the hydrate stability field or is carried there in advecting pore water.

Seismic velocity structure at a gas hydrate reflector, offshore western Colombia, from full waveform inversion

We present a method for determining the elastic parameters of a horizontally stratified medium from its plane-wave reflectivity. The nonlinear inverse problem is iteratively solved by using a generalized least-squares formalism. The proposed method uses the (relatively) fast convergence properties of the conjugate gradient algorithm and achieves computational efficiency through analytical solutions for calculating the reference and perturbational wavefields. The solution method is implemented in the frequency-wave slowness domain and can be readily adapted to various source-receiver configurations.The behavior of the algorithm conforms to the predictions of generalized least-squares inverse the-ory: the inversion scheme yields satisfactory results as long as the correct velocity trends are introduced in the starting model. In practice, the inversion algorithm should be applied first in the precritical region because of the strong nonlinear behavior of postcritical data with respect to velocity perturbations. The suggested inversion strategy consists of first inverting for the density and P-wave velocity (or P-wave impedance) by considering plane waves in the low slowness region (near-normal angles of incidence), then in optimizing for the S-wave velocity by progressively including contributions from the high slowness region (steep angles of incidence). Numerical experiments performed with noise-free synthetic data prove that the proposed inversion method satisfactorally reconstructs the elastic properties of a stratified medium from a limited set of plane-wave components, at a reasonable computing cost.

Francoise Kormendi

Papers

Nonlinear waveform inversion of plane-wave seismograms in stratified elastic media