3-D Refraction Traveltime Tomography Algorithm Based on Adjoint State Techniques

Taillandier, Cédric; Noble, Mark; Calandra, Henri; Chauris, Hervé; Podvin, Pascal

doi:10.3997/2214-4609.20147939

Cited by 4 publications

(2 citation statements)

References 6 publications

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“…. , S with first arrival times u The above approach has been studied numerically in the context of tomography in [11,17,18] using finite difference approximations of the eikonal equation and fast sweeping methods for solving the forward equation and the adjoint equation. The aim of the present work is to present a corresponding numerical analysis.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of an inverse problem for the eikonal equation

2011

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We are concerned with the inverse problem for an eikonal equation of determining the speed function using observations of the arrival time on a fixed surface. This is formulated as an optimisation problem for a quadratic functional with the state equation being the eikonal equation coupled to the so-called Soner boundary condition. The state equation is discretised by a suitable finite difference scheme for which we obtain existence, uniqueness and an error bound. We set up an approximate optimisation problem and show that a subsequence of the discrete mimina converges to a solution of the continuous optimisation problem as the mesh size goes to zero. The derivative of the discrete functional is calculated with the help of an adjoint equation which can be solved efficiently by using fast marching techniques. Finally we describe some numerical results.

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Section: Introductionmentioning

confidence: 99%

Numerical analysis of an inverse problem for the eikonal equation

2011

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“…Among these finite-difference eikonal solvers, the first-order fast marching and the first-order fast sweeping methods have proved to be unconditionally stable. Furthermore, related to the work in [46,47], fast-sweeping-based eikonal solvers have been successfully used in isotropic transmission traveltime tomography in [25], and the resulting method is robust; this method has been further developed in [58,57] for three-dimensional practical data.…”

Section: Introductionmentioning

confidence: 99%

An adaptive phase space method with application to reflection traveltime tomography

et al. 2011

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In this work, an adaptive strategy for the phase space method for traveltime tomography (Chung et al 2007 Inverse Problems 23 309-29) is developed. The method first uses those geodesics/rays that produce smaller mismatch with the measurements and continues on in the spirit of layer stripping without defining the layers explicitly. The adaptive approach improves stability, efficiency and accuracy. We then extend our method to reflection traveltime tomography by incorporating broken geodesics/rays for which a jump condition has to be imposed at the broken point for the geodesic flow. In particular, we show that our method can distinguish non-broken and broken geodesics in the measurement and utilize them accordingly in reflection traveltime tomography. We demonstrate that our method can recover the convex hull (with respect to the underlying metric) of unknown obstacles as well as the metric outside the convex hull.

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Pore pressure prediction using seismic velocity modeling: case study, Sefid-Zakhor gas field in Southern Iran

Bahmaei

Hosseini

2019

J Petrol Explor Prod Technol

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Pore pressure estimation is important for both exploration and drilling projects. During the exploration phase, a prediction of pore pressure can be used to evaluate exploration risk factors including the migration of formation fluids and seal integrity. To optimize drilling decisions and well planning in abnormal pressured areas, it is essential to carry out pore pressure predictions before drilling. Mud weight and fracture gradient are essential parameters to have wellbore stability, prevent blowout, lost circulation, kick, sand production and reservoir damages. Predrill pore pressure accurate prediction allows the appropriate mud weight to be selected and allows the casing program to be optimized, thus enabling safety by preventing wellbore collapse and economic drilling by reducing the cost. The goal of this study is to estimate pore pressure relation with subsurface velocity in the Sefid-Zakhor gas field. Manufactured sonic logs are modified using the check shot interval velocity of Sefid-Zakhor well No. 1. The final acoustic impedance model is converted to the velocity model by removing density. Finally, the velocity model is converted to pore pressure using Bowers (in: IADC/SPE drilling conference proceedings, 1995) relation. The results of the pore pressure model are validated by pore pressure data obtained by the MDT well test tool. Generally, the results show the normal trend for pore pressure in the area, except in the left side of the anticline in the 2D seismic section, because of tectonic uplifting.

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3-D Refraction Traveltime Tomography Algorithm Based on Adjoint State Techniques

Cited by 4 publications

References 6 publications

Numerical analysis of an inverse problem for the eikonal equation

Numerical analysis of an inverse problem for the eikonal equation

An adaptive phase space method with application to reflection traveltime tomography

Pore pressure prediction using seismic velocity modeling: case study, Sefid-Zakhor gas field in Southern Iran

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