Curtis C. Ober

Phase encoding of shot records in prestack migration

Frequency‐domain shot‐record migration can produce higher quality images than Kirchhoff migration but typically at a greater cost. The computing cost of shot‐record migration is the product of the number of shots in the survey and the expense of each individual migration. Many attempts to reduce this cost have focused on the speed of the individual migrations, trying to achieve a better trade‐off between accuracy and speed. Another approach is to reduce the number of migrations. We investigate the simultaneous migration of shot records using frequency‐domain shot‐record migration algorithms. The difficulty with this approach is the production of so‐called crossterms between unrelated shot and receiver wavefields, which generate unwanted artifacts or noise in the final image. To reduce these artifacts and obtain an image comparable in quality to the single‐shot‐per‐migration result, we have introduced a process called phase encoding, which shifts or disperses these crossterms. The process of phase encoding...

Faster shot-record depth migrations using phase encoding

Phase encoding of shot records provides a means of imaging a number of shots within a single migration. This results in a reduction in the required computation for a complete image, a reduction by the number of shots used in each individual migration, trading this increase in speed for additional noise in the resulting image. Some methods for phase encoding have been shown to limit this noise to a tolerable range when combining several shots, enabling speed ups of a factor of a few. In this paper, the authors present a use of phase encoding which allows faster imaging by an order of magnitude or more, with the additional benefit that the individual migrations can be stopped whenever the answer is good enough. This approach may ultimately render 3-D frequency-domain prestack depth migration cost effective.

Manufactured Solution for Computational Fluid Dynamics Boundary Condition Verification

Order-of-accuracy verification is necessary to ensure that software correctly solves a given set of equations. One method for verifying the order of accuracy of a code is the method of manufactured solutions. This study documents the development of a manufactured solution that allows verification of not only the Euler, Navier-Stokes, and Reynolds-averaged Navier-Stokes equation sets, but also some of their associated boundary conditions: slip, no-slip (adiabatic and isothermal), and outflow (subsonic, supersonic, and mixed). To demonstrate the usefulness of this manufactured solution, it has been used for order-of-accuracy verification in a compressible computational fluid dynamics code. All of the results shown are on skewed, nonuniform, three-dimensional meshes. The manufactured solution and sequence of meshes are designed to allow asymptotic results to be obtained with reasonable computational cost. In addition to the order of accuracy of the full code for various equation sets and boundary conditions, the order of accuracy of code portions used to calculate solution gradients has been measured as well.

A Manufactured Solution for Verifying CFD Boundary Conditions, Part II

Order-of-accuracy veriflcation is necessary to ensure that software correctly solves a given set of equations. One method for verifying the order of accuracy of a code is the method of manufactured solutions. Part III of this study completes the development of a manufactured solution that allows veriflcation of not only the Euler, Navier-Stokes, and Reynolds-Averaged Navier-Stokes equation sets, but also some of their associated boundary conditions: slip, no-slip (adiabatic and isothermal), and out∞ow (subsonic, supersonic, and mixed). In order to demonstrate the usefulness of this manufactured solution, it has been used for order-of-accuracy veriflcation in a compressible computational ∞uid dynamics code. All of the results shown are on skewed, non-uniform, three-dimensional meshes. Modiflcations have been made to the manufactured solution and sequence of meshes from previous work to allow asymptotic results to be obtained with less computational cost. In addition to the order of accuracy of the full code for various equation sets and boundary conditions, the order of accuracy of code portions used to calculate solution gradients has been measured as well.

SIERRA/Premo-A New General Purpose Compressible Flow Simulation Code

This paper reports on the progress of a new compressible flow simulation code being developed at Sandia National Laboratories. The code called Premo is a CFD module that is part of a much larger multimechanics code framework called SIERRA. The goal of the Premo project is to deliver a general purpose CFD capability for designers and analysts of aerodynamics of flight vehicles. SIERRA provides unstructured mesh data services common to many computational mechanics codes. Utilizing the framework allows for rapid development of physics modules. In addition, the SIERRA framework provides an interface that will make it possible to conduct multiphysics simulations between physics modules to solve such problems as aero-thermal vehicle heating and aero elasticity in the future. Current code capabilities are demonstrated by solving one-, two- and threedimensional flow problems.

Efficient Parallel I/o in sEismic Imaging

Although high performance computers tend to be mea sured by their processor and communication speeds, the bottleneck for many large-scale applications is the I/O performance rather than the computational or communi cation performance. One such application is the process ing of three-dimensional seismic data. Seismic data sets, consisting of recorded pressure waves, can be very large, sometimes more than a terabyte in size. Even if the computations can be performed in core, the time required to read the initial seismic data and velocity model and write images is substantial. In this paper, the authors discuss an approach in handling the massive I/O requirements of seismic processing and show the performance of their imaging code (Salvo) on the Intel Paragon™ computer.

Seismic imaging on massively parallel computers

A key to reducing the risks and costs associated with oil and gas exploration is the fast, accurate imaging of complex geologies, such as salt domes in the Gulf of Mexico and overthrust regions in US onshore regions. Pre-stack depth migration generally yields the most accurate images, and one approach to this is to solve the scalar-wave equation using finite differences. Current industry computational capabilities are insufficient for the application of finite-difference, 3-D, prestack, depth-migration algorithms. High performance computers and state-of-the-art algorithms and software are required to meet this need. As part of an ongoing ACTI project funded by the US Department of Energy, the authors have developed a finite-difference, 3-D prestack, depth-migration code for massively parallel computer systems. The goal of this work is to demonstrate that massively parallel computers (thousands of processors) can be used efficiently for seismic imaging, and that sufficient computing power exists (or soon will exist) to make finite-difference, prestack, depth migration practical for oil and gas exploration.

Intelligent Nonlinear Solvers for Computational Fluid Dynamics

Implicit nonlinear solvers for solving systems of nonlinear PDEs are very powerful. Many compressible flow codes utilize Newton-Krylov (NK) methods and matrix-free NewtonKrylov (MFNK) methods for a range of flow regimes and different flow models such as inviscid, laminar, turbulent and reacting flows. One drawback is that these solvers are complex requiring the specification of many settings. Expertise is necessary to achieve high performance. There is a need to develop ”intelligent nonlinear solvers” that are capable of changing settings dynamically and adapting to evolving solutions and changing solver performance, in order to reduce the burden on the user, and improve overall efficiency and reliability. In this paper we take the first steps in achieving automatic control of nonlinear solvers for compressible flows by combining semi- and fully- implicit solver strategies in ways that utilizes them more efficiently than simply applying one method or another during the entire solution procedure. The understanding gained from this work will lay the groundwork for future development of more autonomous ”intelligent solvers”. Implicit solvers are widely used to in compuational fluid dynamic applications to obtain steady-state solutions to the equations governing fluid flow. Semi-implicit (point-implicit) methods are one of the most common. Semi-implicit methods are relatively easy to implement, have low memory requirements and can march at large time step sizes compared to explicit methods. Semi-implicit iterations are only modestly more expensive than explicit iterations and tend to converge linearly. They are also robust in the sense that they are relatively easy to use. However, convergence ”stalling” can be a problem in certain circumstances. In recent years, Newton-Krylov (NK) methods are becoming more popular. NK methods are less straight forward to use and more expensive per iteration than semi-implicit methods. However, NK methods are very efficient for as the solution is approached in an iterative sense, quadratic convergence rates can be achieved. Very large time steps can be used to advance the solution to steady-state. They are also robust due to the effectiveness of Krylov subspace iterative linear solvers. In both methods, solutions are achieved iteratively by solving a series of nonlinear problems where the system equations are linearized and then solved with an iterative linear solver. Semi-implicit solvers combine the nonlinear and linear loops together, solving a modified linear system less accurately but more cheaply. Typically, semi-implicit solvers are cheaper than NK methods in the beginning when the CFL is small and the linear systems are dominated by a large diagonal inertia term. Later, as the inertia term becomes smaller, the linear problem becomes more difficult to solve and NK methods become more efficient. Therefore, it would make sense to combine these approaches in a single solver stategy.

Unstructured Discontinuous Galerkin For Seismic Inversion

This abstract explores the potential advantages of discontinuous Galerkin (DG) methods for the time-domain inversion of media parameters within the earths interior. In particular, DG methods enable local polynomial refinement to better capture localized geological features within an area of interest while also allowing the use of unstructured meshes that can accurately capture discontinuous material interfaces. This abstract describes our initial findings when using DG methods combined with Runge-Kutta time integration and adjoint-based optimization algorithms for full-waveform inversion. Our initial results suggest that DG methods allow great flexibility in matching the media characteristics (faults, ocean bottom and salt structures) while also providing higher fidelity representations in target regions. Time-domain inversion using discontinuous Galerkin on unstructured meshes and with local polynomial refinement is shown to better capture localized geological features and accurately capture discontinuous-material interfaces. These approaches provide the ability to surgically refine representations in order to improve predicted models for specific geological features. Our future work will entail automated extensions to directly incorporate local refinement and adaptive unstructured meshes within the inversion process.

Practical aspects of prestack depth migration with finite differences

Finite-difference, prestack, depth migrations offers significant improvements over Kirchhoff methods in imaging near or under salt structures. The authors have implemented a finite-difference prestack depth migration algorithm for use on massively parallel computers which is discussed. The image quality of the finite-difference scheme has been investigated and suggested improvements are discussed. In this presentation, the authors discuss an implicit finite difference migration code, called Salvo, that has been developed through an ACTI (Advanced Computational Technology Initiative) joint project. This code is designed to be efficient on a variety of massively parallel computers. It takes advantage of both frequency and spatial parallelism as well as the use of nodes dedicated to data input/output (I/O). Besides giving an overview of the finite-difference algorithm and some of the parallelism techniques used, migration results using both Kirchhoff and finite-difference migration will be presented and compared. The authors start out with a very simple Cartoon model where one can intuitively see the multiple travel paths and some of the potential problems that will be encountered with Kirchhoff migration. More complex synthetic models as well as results from actual seismic data from the Gulf of Mexico will be shown.