Finite difference

About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.

3D finite-difference frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver: A feasibility study

Abstract: We present a finite-difference frequency-domain method for 3D visco-acoustic wave propagation modeling. In the frequency domain, the underlying numerical problem is the resolution of a large sparse system of linear equations whose right-hand side term is the source. This system is solved with a massively parallel direct solver. We first present an optimal 3D finite-difference stencil for frequency-domain modeling. The method is based on a parsimonious staggered-grid method. Differential operators are discretized with second-order accurate staggered-grid stencils on different rotated coordinate systems to mitigate numerical anisotropy. An antilumped mass strategy is implemented to minimize numerical dispersion. The stencil incorporates 27 grid points and spans two grid intervals. Dispersion analysis shows that four grid points per wavelength provide accurate simulations in the 3D domain. To assess the feasibility of the method for frequency-domain full-waveform inversion, we computed simulations in the 3D SEG/EAGE overthrust model for frequencies 5, 7, and 10 Hz. Results confirm the huge memory requirement of the factorization (several hundred Figabytes) but also the CPU efficiency of the resolution phase (few seconds per shot). Heuristic scalability analysis suggests that the memory complexity of the factorization is O(35N(4)) for a N-3 grid. Our method may provide a suitable tool to perform frequency-domain full-waveform inversion using a large distributed-memory platform. Further investigation is still necessary to assess more quantitatively the respective merits and drawbacks of time- and frequency-domain modeling of wave propagation to perform 3D full-waveform inversion.

Random-Walk Simulation of Transport in Heterogeneous Porous Media: Local Mass-Conservation Problem and Implementation Methods

Abstract: The random-walk method for simulating solute transport in porous media is typically based on the assumption that the velocity and velocity-dependent dispersion tensor vary smoothly in space. However, in cases where sharp interfaces separate materials with contrasting hydraulic properties, these quantities may be discontinuous. Normally, velocities are interpolated to arbitrary particle locations when finite difference or finite element methods are used to solve the flow equation. The use of interpolation schemes that preserve discontinuities in velocity at material contacts can result in a random-walk model that does not locally conserve mass unless a correction is applied at these contacts. Test simulations of random-walk particle tracking with and without special treatment of material contacts demonstrate the problem. Techniques for resolving the problem, including interpolation schemes and a reflection principle, are reviewed and tested. Results from simulations of transport in porous media with discontinuities in the dispersion tensor show which methods satisfy continuity. Simulations of transport in two-dimensional heterogeneous porous media demonstrate the potentially significant effect of using a nonconservative model to compute spatial moments and breakthrough of a solute plume.