Analysis of Least-Squares Velocity Inversion

Santosa, Fadil; Symes, William W.; Brown, Raymon L.

doi:10.1190/1.9781560802488

Cited by 54 publications

(29 citation statements)

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“…The nonlinear inverse problem can be solved using iterative gradient techniques, and the first iteration of this process is responsible for imaging the discontinuities of the medium (Tarantola, 1984). Excellent reviews of the least-squares approach have been given by Lines and Treitel (1984), and more recently, by Santosa and Symes (1989).…”

Section: Introductionmentioning

confidence: 99%

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

Körmendi

Dietrich

1991

GEOPHYSICS

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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 leastsquares 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 theory: the inversion scheme yields satisfactory results INTRODUCTION

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Section: Introductionmentioning

confidence: 99%

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

Körmendi

Dietrich

1991

GEOPHYSICS

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“…In fact, the data and their projection for a perturbed model are nearly orthogonal in the high-frequency limit (Santosa & Symes, 1989). This causes very large misfits unless the velocity perturbation is very small, making this approach not optimal for use with gradient-based optimisation methods, as has also been noted by .…”

Section: Separable Least-squaresmentioning

confidence: 96%

Correlation-based seismic velocity inversion

Leeuwen

2010

GEOPHYSICS

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“…This indicates that it should be easier to estimate a sparse set of large discontinuities of c.E x/, which is the goal in imaging, than the rest of the function. There is computational experience on the least squares minimization over c.E x/ in piecewise smooth media, and some convergence studies exist [30,31,34,37]. The problem is difficult because the least squares functional is not convex, and the optimization gets stuck easily in local minima that have nothing to do with the true c.E x/.…”

Section: Challenges Of Imaging In Complex Mediamentioning

confidence: 98%

Imaging in Random Media

Borcea¹

2014

Handbook of Mathematical Methods in Imaging

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We give a self-contained presentation of coherent array imaging in random media, which are mathematical models of media with uncertain small-scale features (inhomogeneities). We describe the challenges of imaging in random media and discuss the coherent interferometric (CINT) imaging approach. It is designed to image with partially coherent waves, so it works at distances that do not exceed a transport mean-free path. The waves are incoherent when they travel longer distances, due to strong cumulative scattering by the inhomogeneities, and coherent imaging becomes impossible. In this article we base the presentation of coherent imaging on a simple geometrical optics model of wave propagation with randomly perturbed travel time. The model captures the canonical form of the second statistical moments of the wave field, which describe the loss of coherence and decorrelation of the waves due to scattering in random media. We use it to give an explicit resolution analysis of CINT which includes the assessment of statistical stability of the images.

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Analysis of Least-Squares Velocity Inversion

Cited by 54 publications

References 0 publications

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

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

Correlation-based seismic velocity inversion

Imaging in Random Media

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