Non-linear optimization for seismic traveltime tomography

Sebudandi, Ch.; Toint, Philippe L.

doi:10.1111/j.1365-246x.1993.tb01502.x

Cited by 7 publications

(4 citation statements)

References 20 publications

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“…This difficulty may arise when the Hessian of f is very ill‐conditioned and can often be overcome by using trust regions (see Conn et al 2000) instead of line‐searches. The former method usually provides more stable and accurate results than the latter (Delbos et al 2001; see also Sebudandi & Toint 1993). In any case, we observe in practice that very few iterations are needed to get convergence, typically of the order of 10.…”

Section: The Seismic Reflection Tomography Problemmentioning

confidence: 99%

Constrained optimization in seismic reflection tomography: a Gauss-Newton augmented Lagrangian approach

Delbos¹,

Gilbert

Glowinski

et al. 2006

Geophysical Journal International

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S U M M A R YSeismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on geological interfaces. From an optimization viewpoint, the problem consists in minimizing a non-linear least-squares function measuring the mismatch between observed traveltimes and those calculated by ray tracing in this model. The introduction of a priori information on the model is crucial to reduce the under-determination. The contribution of this paper is to introduce a technique able to take into account geological a priori information in the reflection tomography problem expressed as inequality constraints in the optimization problem. This technique is based on a Gauss-Newton (GN) sequential quadratic programming approach. At each GN step, a solution to a convex quadratic optimization problem subject to linear constraints is computed thanks to an augmented Lagrangian algorithm. Our choice for this optimization method is motivated and its original aspects are described. First applications on real data sets are presented to illustrate the potential of the approach in practical use of reflection tomography.

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Section: The Seismic Reflection Tomography Problemmentioning

confidence: 99%

Constrained optimization in seismic reflection tomography: a Gauss-Newton augmented Lagrangian approach

Delbos¹,

Gilbert

Glowinski

et al. 2006

Geophysical Journal International

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“…Aki et al 1977; Nolet 1987; Bregman et al . 1989; Sambridge 1990; Sehudandi & Toint 1993; Day et al . 2001; Zelt et al .…”

Section: Introductionmentioning

confidence: 99%

Non-linear traveltime inversion for 3-D seismic tomography in strongly anisotropic media

Zhou¹,

Greenhalgh²

2008

Geophysical Journal International

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SUMMARY We have developed two, new non‐linear traveltime inversion schemes for 3‐D seismic tomography in anisotropic media. They differ from the traditional linearized inversion approach and offer five significant improvements: (1) they are based on an alternative form of the first‐order traveltime perturbation equation, derived so as to simplify the inversion formulae and overcome the quasi shear wave singularity problem; (2) robust 3‐D ray tracing is employed which enables the simultaneous computation of the first‐arrival traveltimes and ray paths for the three body waves (qP, qS1 and qS2) in arbitrary anisotropic media; (3) the Jacobian matrix used in the update is based on an efficient computation for a 3‐D anisotropic model, so that the inversion is applicable to both weakly and strongly anisotropic situations, unlike most previous approaches which assume weak anisotropy; (4) a local‐search, constrained minimization is applied to the non‐linear inversion which makes anisotropic tomographic imaging an iterative procedure; (5) there is an option to invert for the elastic moduli directly or the Thomsen parameters directly in heterogenous, tilted transversely isotropic media, using any source–receiver recording geometry. We have examined the imaging capability of the non‐linear solver with individual body‐wave modes using a 3‐D synthetic anisotropic model incorporating two targets, a ‘high velocity’ and a ‘low velocity’ anomaly, embedded in a titled transversely isotropic medium. The model is illuminated by means of azimuthal VSP and crosshole measurements. The experimental results show that the two non‐linear inversion schemes successfully image the ‘targets’ and yield satisfactory 3‐D tomograms of the elastic moduli and the Thomsen parameters.

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“…The non-linearity of tomographic inversion is as yet not well understood despite considerable research (e.g., SEHUDANDI and TOINT, 1993;BUNKS et al, 1995;REITER and RODI, 1996;VASCO, 1997;CHUNDURU et al, 1997). The mostly linearized schemes that are used in practice are somewhat sensitive to noise, and sometimes may create solutions that are geologically implausible.…”

Section: Introductionmentioning

confidence: 99%

3-D Non-linear Travel-time Tomography: Imaging High Contrast Velocity Anomalies

Bai

Greenhalgh

2005

Pure appl. geophys.

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In this paper we present an approach for 3-D travel-time tomography, which works well in reconstructing high contrast velocity anomalies in both location and strength. It uses a revised 'irregular' approach to the shortest-path method as the ray tracer and a damped minimum norm, and constrained least-squares CG approach as the inversion solver. In ray tracing, the advantages of the revised 'irregular' over the 'regular' approach are that the secondary nodes introduced on the cell surfaces significantly improve accuracy of computed travel times, without dramatically increasing the total number of cells and nodes; the tri-linear velocity function defined across the cell guarantees accurate ray tracing in a high velocity contrast medium; and the capacity to calculate a relatively large 3-D model, due to the fast run speed (at least one order of magnitude over the 'regular' approach) and less number of total nodes. The introduction of 'soft' and 'hard' bounds into the inversion process changes the conditioning and makes the solution meaningful in a physical sense. Thus the artifacts caused by noise and high velocity contrasts are substantially suppressed and the image quality is considerably improved, making the solution realistic with noisy or inconsistent travel-time data. Several numerical tests indicate that we can obtain good quality images even for high velocity contrast anomalies (say more than 20%) in the target region. This means the inversion algorithm is an efficient and effective procedure. Meanwhile, the inversion procedure is not very sensitive to the quality of the travel-time data, which is promising for practical usage.

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Non-linear optimization for seismic traveltime tomography

Cited by 7 publications

References 20 publications

Constrained optimization in seismic reflection tomography: a Gauss-Newton augmented Lagrangian approach

Constrained optimization in seismic reflection tomography: a Gauss-Newton augmented Lagrangian approach

Non-linear traveltime inversion for 3-D seismic tomography in strongly anisotropic media

3-D Non-linear Travel-time Tomography: Imaging High Contrast Velocity Anomalies

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