Browsing by Author "Terentyev, Igor"

Now showing 1 - 4 of 4
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    A Software Framework for Finite Difference Simulation
    (2009-04) Terentyev, Igor
    This paper describes a software framework for solving time dependent PDEs in simple domains using finite difference (FD) methods. The framework is designed for parallel computations on distributed and shared memory computers, thus allowing for efficient solution of large-scale problems. The framework provides automated data exchange between processors based on stencil information. This automated data exchange allows a user to add FD schemes without knowledge about underlying parallel infrastructure. The framework includes acoustic solver based on staggered second-order in time and various orders in space FD schemes with perfectly matched layer and/or free surface boundary conditions.
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    Mass Lumping for Constant-Density Acoustics
    (2009-04) Symes, William W.; Terentyev, Igor
    Conforming Galerkin discretization of the constant-density acoustic wave equation provides optimal order convergence even in the presence of very rough coefficients, provided that the time dependence of the data (right-hand side) is minimally smooth. Such discretizations avoid the well-known first-order error ("stairstep diffraction") phenomenon produced by standard finite difference methods. On the other hand, Galerkin methods in themselves are inefficient for high frequency wave simulation, due to the implicit nature of the time step system. Mass lumping renders the time step explicit, and provides an avenue for efficient time-stepping of time-dependent problems with conforming finite element spatial discretization. Typical justifications for mass lumping use quadrature error estimates which do not hold for nonsmooth coefficients. In this paper, we show that the mass-lumped semidiscrete system for the constant-density acoustic wave equation with rectangular multilinear elements exhibits optimal order convergence even when the coefficient (bulk modulus) is merely bounded and measurable, provided that the right-hand side possesses some smoothness in time. We illustrate the theory with numerical examples involving discontinuous, non-grid-aligned bulk moduli, in which the coefficient averaging implicit in mass lumping eliminates the stairstep diffraction effect.
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    Nonlinear Waveform Inversion with Surface-Oriented Extended Modeling
    (2017-03) Terentyev, Igor
    This thesis investigates surface-oriented model extension approach to nonlinear full waveform inversion (FWI). Conventional least-squares (LS) approach is capable of reconstructing highly detailed models of subsurface. Resolution requirements of the realistic problems dictate the use of local descent methods to solve the LS optimization problem. However, in the setting of any characteristic seismic problem, LS objective functional has numerous local extrema, rendering descent methods unsuitable when initial estimate is not kinematically accurate. The aim of my work is to improve convexity properties of the objective functional. I use the extended modeling approach, and construct an extended optimization functional incorporating differential semblance condition. An important advantage of surface-oriented extensions is that they do not increase the computational complexity of the forward modeling. This approach blends FWI technique with migration velocity analysis (MVA) capability to recover long scale velocity model, producing optimization problems that combine global convergence properties of the MVA with data fitting approach of FWI. In particular, it takes into account nonlinear physical effects, such as multiple reflections. I employ variable projection approach to solve the extended optimization problem. I validate the method on synthetic models for the constant density acoustics problem.
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    Nonlinear waveform inversion with surface-oriented extended modeling
    (2017-09-25) Terentyev, Igor; Symes, William W
    This thesis investigates surface-oriented model extension approach to nonlinear full waveform inversion (FWI). Conventional least-squares (LS) approach is capable of reconstructing highly detailed models of subsurface. Resolution requirements of the realistic problems dictate the use of local descent methods to solve the LS optimization problem. However, in the setting of any characteristic seismic problem, LS objective functional has numerous local extrema, rendering descent methods unsuitable when initial estimate is not kinematically accurate. The aim of my work is to improve convexity properties of the objective functional. I use the extended modeling approach, and construct an extended optimization functional incorporating differential semblance condition. An important advantage of surface-oriented extensions is that they do not increase the computational complexity of the forward modeling. This approach blends FWI technique with migration velocity analysis (MVA) capability to recover long scale velocity model, producing optimization problems that combine global convergence properties of the MVA with data fitting approach of FWI. In particular, it takes into account nonlinear physical effects, such as multiple reflections. I employ variable projection approach to solve the extended optimization problem. I validate the method on synthetic models for the constant density acoustics problem.