Browsing by Author "Fu, Lei"

Now showing 1 - 5 of 5
  • Thumbnail Image
    Item
    A discrepancy-based penalty method for extended waveform inversion
    (Society of Exploration Geophysicists, 2017) Fu, Lei; Symes, William W.; The Rice Inversion Project
    Extended waveform inversion globalizes the convergence of seismic waveform inversion by adding nonphysical degrees of freedom to the model, thus permitting it to fit the data well throughout the inversion process. These extra degrees of freedom must be curtailed at the solution, for example, by penalizing them as part of an optimization formulation. For separable (partly linear) models, a natural objective function combines a mean square data residual and a quadratic regularization term penalizing the nonphysical (linear) degrees of freedom. The linear variables are eliminated in an inner optimization step, leaving a function of the outer (nonlinear) variables to be optimized. This variable projection method is convenient for computation, but it requires that the penalty weight be increased as the estimated model tends to the (physical) solution. We describe an algorithm based on discrepancy, that is, maintaining the data residual at the inner optimum within a prescribed range, to control the penalty weight during the outer optimization. We evaluate this algorithm in the context of constant density acoustic waveform inversion, by recovering background model and perturbation fitting bandlimited waveform data in the Born approximation.
  • Thumbnail Image
    Item
    An adaptive multiscale algorithm for efficient extended waveform inversion
    (Society of Exploration Geophysicists, 2017) Fu, Lei; Symes, William W.; The Rice Inversion Project
    Subsurface-offset extended full-waveform inversion (FWI) may converge to kinematically accurate velocity models without the low-frequency data accuracy required for standard data-domain FWI. However, this robust alternative approach to waveform inversion suffers from a very high computational cost resulting from its use of nonlocal wave physics: The computation of strain from stress involves an integral over the subsurface offset axis, which must be performed at every space-time grid point. We found that a combination of data-fit driven offset limits, grid coarsening, and low-pass data filtering can reduce the cost of extended inversion by one to two orders of magnitude.
  • Thumbnail Image
    Item
    Local events-based fast RTM surface-offset gathers via dip-guided interpolation
    (Springer Nature, 2021) Zhao, Yang; Niu, Feng-Lin; Fu, Lei; Cheng, Cheng; Chen, Jin-Hong; Huo, Shou-Dong
    Reverse Time Migration (RTM) Surface Offset Gathers (SOGs) are demonstrated to deliver more superior residual dip information than ray-based approaches. It appears more powerful in complex geological settings, such as salt areas. Still, the computational cost of constructing RTM SOGs is a big challenge in applying it to 3D field data. To tackle this challenge, we propose a novel method using dips of local events as a guide for RTM gather interpolation. The residual-dip information of the SOGs is created by connecting local events from depth-domain to time-domain via ray tracing. The proposed method is validated by a synthetic experiment and a field example. It mitigates the computational cost by an order of magnitude while producing comparable results as fully computed RTM SOGs.
  • Thumbnail Image
    Item
    Migration velocity analysis and waveform inversion with subsurface offset extension
    (2016-12-01) Fu, Lei; Symes, William W
    Image-domain seismic inversion with subsurface offset extension may converge to kinematically accurate velocity models without the low-frequency data accuracy required for standard data-domain full waveform inversion. However, this robust alternative approach to waveform inversion suffers from very high computational cost, resulting from its use of nonlocal wave physics: the computation of strain from stress involves an integral over the subsurface offset axis, which must be performed at ev- ery space-time grid point. Additionally, under prototypical conditions of acquisition geometry, the existence of artefacts is very likely to deviate the velocity update from its path to the correct velocity. I show here three new approaches that significantly improve both efficiency and robustness of subsurface offset extended waveform in- version and migration velocity analysis (MVA). The global convergence property of the extended waveform inversion is achieved by adaptively determining the penalty weight. It is also shown that a combination of data-fit driven offset limits, grid coarsening, and low-pass data filtering can reduce the cost of extended inversion by one to two orders of magnitude. Lastly, a taper in angle domain depending on acquisition geometry and imaging point is introduced. The application of taper directly on extended image makes migration velocity analysis becomes more robust. I illustrate these new methods in the context of constant density acoustic waveform inversion, by recovering background model and perturbation fitting band-limited waveform data in the Born approximation.
  • Thumbnail Image
    Item
    On the boundaries of special Lagrangian submanifolds
    (1995) Fu, Lei; Harvey, F. Reese
    An n-dimensional submanifold M in ${\bf C}\sp{n} = {\bf R}\sp{2n}$ is called Lagrangian if the restriction of $\omega$ to M is zero, where $\omega = \Sigma{\limits\sb{i}}dz\sb{i}\ \wedge\ d\bar z\sb{i}$. It is called special Lagrangian if the restrictions of $\omega$ and Imdz = Im($dz\sb1 \wedge \cdots \wedge dz\sb{n}$) are zero. Special Lagrangian submanifolds are volume minimizing, and conversely, any minimal Lagrangian submanifold can be transformed to a special Lagrangian submanifold by a unitary transformation. This paper studies the conditions satisfied by the boundaries of special Lagrangian submanifolds. We say an $n-1$ dimensional submanifold N in ${\bf C}\sp{n}$ satisfies the moment condition if $\int\sb{N}\ \phi$ = 0 for any $n-1$ form $\phi$ with $d\phi$ belonging to the differential ideal generated by $\omega$ and Imdz. By Stokes' formula, the boundary of a special Lagrangian submanifold satisfies the moment condition. In fact on ${\bf C}\sp2,$ the converse is also true, that is, a curve is the boundary of a special Lagrangian submanifold if it satisfies the moment condition. However, we show in this paper that for $n\ge3,$ there exist $n-1$ dimensional submanifolds which satisfy the moment condition but do not bound any special Lagrangian submanifolds. Let f be a real valued function defined on some open subset on ${\bf C}\sp{n}$ which contains a special Lagrangian submanifold M. We show that $$\Delta\sb{M}f = d(J(\nabla f)\quad\rfloor\ {\rm Im}dz){\vert}\sb{M},$$where $\Delta\sb{M}$ is the Laplace operator on M and J is the standard complex structure. Using this formula and the maximum principle, we prove that if $d(J(\nabla f)\quad\rfloor$ Imdz) belongs to the differential ideal generated by df, $\omega$ and Imdz, then $f{\vert}\sb{M}$ attains its maximum and minimum on the boundary of M. This result is then used to produce some conditions other than the moment condition which are satisfied by the boundaries of special Lagrangian submanifolds.