Browsing by Author "Symes, William W"

Now showing 1 - 6 of 6
  • Thumbnail Image
    Item
    Born Waveform Inversion in Shot Coordinate Domain
    (2016-03-11) Huang, Yin; Symes, William W
    The goal of this thesis is to integrate Born waveform inversion, variable projection algorithm and model extension concept to get a method that can improve the long scale background model updates reliably and efficiently from seismic data. Born waveform inversion is a partially linearized version of full waveform inversion based on Born (linearized) modeling, in which the earth model is separated into a smooth long scale background model and an oscillatory short scale reflectivity and both are updated to fit observed trace data. Because kinematic variables (background model) are updated, Born waveform inversion has the same feature as full waveform inversion: very sensitive to initial model when solved by gradient based optimization method (almost the only possible method because of the problem scale). Extended Born waveform inversion allows reflectivity to depend on additional parameters, potentially enlarging the convexity domain by enlarging the searching model space and permitting data fit throughout the inversion process and in turn reducing the sensitivity to initial model. Extended or not, the Born waveform inversion objective function is quadratic in the reflectivity, so that a nested optimization approach is available: minimize over reflectivity in an inner stage, then minimize the background-dependent result in a second, outer stage, which results in a reduced objective function of the background model only (VPE method). This thesis integrates the nested optimization approach into an inversion scheme and analyzes that the accuracy of the solution to the inner optimization is crucial for a robust outer optimization and both model extension and the nested optimization are necessary for a successful Born waveform inversion. And then we propose a flexibly preconditioned least squares migration scheme (FPCG) that significantly improves the convergence of iterative least squares migration and produces high resolution images with balanced amplitude. The proposed scheme also improves the efficiency of the solution to the inner stage of the nested optimization scheme and the accuracy of the gradient, and thus potentially improves the efficiency of the VPE method. However, a theoretical error estimate in the gradient computation of the VPE method is still hard to obtain, and we explain the reason and illustrate with numerical examples.
  • 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
    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.
  • Thumbnail Image
    Item
    OCCA: A Unified Approach to Multi-Threading Languages
    (2014-10-23) Medina, David; Warburton, Timothy; Riviere, Beatrice; Symes, William W
    With the current trend of using co-processors for accelerating computations, we are presented with architectures and corresponding programming languages. The inability to predict lasting languages and architectures has led to the development of distinct languages and standards. This thesis details my work on occa, a unified threading language presented as a portable solution to hardware-accelerated coding that combines aspects of OpenMP, OpenCL, and CUDA. With the similarities between OpenMP, OpenCL and CUDA, I present a macro-based approach on a unified kernel language that currently encompasses OpenMP, OpenCL and CUDA. Along with kernel generation, occa includes an API (application programming interface) which serves as a wrapper on the three multi-threading languages. The back-end on occa dynamically compiles and loads function objects for a flexible run-time environment to use different hardware architectures. Computational results using a spectrum of methods, namely finite difference, spectral element and discontinuous Galerkin methods, utilizing occa are shown to deliver portable high performance on different architectures and platforms. The finite difference method chapter reverse engineers optimized code written in CUDA and used in industry, discusses distinct features available in CUDA and compares occa implementations using different optimization techniques. The spectral element method and discontinuous Galerkin methods are derived from two projects I worked on during my studies: gNek, a distributed high-order spectral element method (SEM) implementation for the incompressible Navier-Stokes equations, and RiDG, equipped with discontinuous Galerkin (DG) to simulate acoustic wave equations under different assumptions in the material anisotropies. The parallel algorithms used to achieve high parallelization for GPU acceleration are discussed in both, gNek and RiDG, together with performance results.
  • Thumbnail Image
    Item
    Representation and Estimation of Seismic Sources via Multipoles
    (2017-04-17) Bencomo, Mario Javier; Symes, William W
    Accurate representation and estimation of seismic sources are essential to the seismic inversion problem. General sources can be approximated by a truncated series of multipoles depending on the source anisotropy. Most research in the joint inversion of source and medium parameters assumes seismic sources can be modeled as isotropic point-sources resulting in an inability to fit the anisotropy observed in data, ultimately impacting the recovery of medium parameters. In this thesis I lay the groundwork for joint source-medium parameter inversion with potentially anisotropic seismic sources via full waveform inversion through three key contributions: a mathematical and computational framework for the modeling and inversion of sources via multipoles, construction and analysis of discretizations of multipole sources on regular grids, and preconditioners based on fractional time derivative/integral operators for the ill-conditioned source estimation subproblem. As an application of my multipole framework, I also study the efficacy of multipoles in modeling the airgun array source, the most common type of active source in marine seismic surveying. Inversion results recovered a dominating isotropic component of the multipole source model that accounted for 84% of the observed radiation pattern. An extra 10% of the observed output pressure field can be explained when incorporating dipole terms in the source representation, thus motivating the use of multipoles to capture source anisotropy.
  • Thumbnail Image
    Item
    Simulation of CO2 sequestration in saline aquifers using discontinuous Galerkin method
    (2014-08-01) Yang, Xin; Riviere, Beatrice M.; Symes, William W; Warburton, Timothy; Verduzco, Rafael
    Carbon dioxide disposal into deep aquifer has been an important venue to trap excess gas emission which causes global warming. In the CO2 sequestration process, CO2 is captured from the point source and injected into the saline aquifer deep enough where CO2 reaches the supercritical state and it has a very high density compared to gaseous state. This process is described by the two-phase two-component model, which involves two nonlinear time dependent advection-diffusion equations. The difficulty lies in the injection phase when the advection terms highly dominate over the diffusion terms. Discontinuous Galerkin (DG) methods, which are famous for the properties of high order accuracy, locality and locally mass conservation, have proved to be promising for advection dominated transport equations. I develop a new fully implicit fully coupled DG method called “partial upwind” method, to discretize the equations. For time discretization, it uses the backward Euler method to allow large time steps. For space discretization, it uses the usual interior penalty DG discretization for the elliptic terms and the upwind for part of the advection terms. The other part of the advection terms are handled specially for stabilization purpose. Numerical simulations show that the new DG method works well for the CO2 sequestration problems in homogenous porous media and has shown great potential in heterogenous porous media. I also compare the new method with the primal interior penalty DG method and show that the new method is superior to the usual DG method for some subsurface fluid flow problems. Though DG methods perform well for the CO2 sequestration problem, they are indeed more costly than traditional numerical methods. The first order finite volume (FV) method, on the other hand, is very efficient. A new coupled finite volume and discontinuous Galerkin method, which uses the accuracy of DG methods on some parts of the domain and the efficiency of FV methods everywhere else to reduce the computational cost, is also studied for the time-dependent advection-diffusion equations. Theoretical and numerical results show that the new coupled method converges and can be both accurate and efficient at the same time for some typical examples. We want to apply the new coupled method to the CO2 sequestration problems in the future.