Acoustic Staggered Grid Modeling in IWAVE

Introduction

Domain-specific simulation such as seismic modeling begs for software re-use via modular design. All applications of this type have the same structure: static fields are initialized, dynamic fields updated, output extracted. A modular approach to code architecture is implicit in this structure, and further specialization leads to even more opportunity for code re-use via modular design.

IWAVE is open source software for finite difference or finite element time-domain simulation on regular rectangular grids, written exclusively in the C/C++. IWAVE is built around a core framework: that is, a collection of separate software packages which together provide essential services upon which applications may be built. These service components completely define the interfaces to which additional code must be written to formulate a complete application. The core framework defines

• parameter-driven job control;
• grid generation and memory allocation in 1D, 2D, and 3D space;
• serial, loop-parallel, and task-parallel execution models, scaling to thousands of threads;
• arbitrary source and receiver locations, and flexible source specification including simultaneous source modeling (random, plane-wave,...)
• standard input and output data formats (SEGY, RSF)
• predefined support for linearized (Born) modeling and adjoint linearized (RTM) modeling, both first and second order;
• uniform interface to optimization and linear algebra for creation of inversion applications via the Rice Vector Library (``RVL'') (Symes et al., 2011; Padula et al., 2009).

Symes (2014) describes the desgn principles underlying the IWAVE core framework, and illustrates the construction of a complete acoustic modeling application using centered finite differences for the second order acoustic constant denstity wave equation.

The primary purpose of this short paper is to illustrate synthetic seismogram generation using another finite difference scheme implemented in IWAVE, the staggered grid approximation to variable-density velocity-pressure acoustodynamics (Virieux, 1984). Exactly the same framework supports this application as was described in Symes (2014); as explained there, only two data structures and six principal functions need be defined to implement this (or any) finite difference method in IWAVE.

The examples illustrate two aspects of finite difference modeling. The IWAVE staggered grid implementation includes a version of PML absorbing boundary conditions (Hu et al., 2007), permitting accurate finite grid approximation of wave propagation in a full- or half-space. The first set of examples demonstrates the effectiveness of these very simple PML conditions. The second set reproduce the examples presented in Symes and Vdovina (2009), and illustrate a fundamental limitation in the use of straightforward finite-difference methods for modeling waves in heterogeneous media.

IWAVE was used in a quality control role in the SEAM Phase I project - see Fehler and Keliher (2011) for an account, including discussion of the many difficulties of large scale numerical simulation of seismograms.

The internal details of IWAVE are not discussed here, except insofar as is necessary to explain the use of the main commands. As mentioned above, Symes (2014) overviews the design of IWAVE and the main features of its internal structure, and defines the elements necessary to compile a new IWAVE application. Symes et al. (2011) briefly describe the IWAVE/RVL mechanisms for coupling modeling with optimization packages to produce inversion applications.

The paper begins with a brief review of the system of partial differential equations solved (approximately) by IWAVE's acoustic application, and the choice of finite difference method. The next section evaluates the effectiveness of the PML absorbing boundary conditions included in the IWAVE staggered grid acoustic application. The following section presents the examples of Symes and Vdovina (2009), along with some additional examples based on the same distribution of mechanical parameters which shed light on the impact of finite difference order on solution accuracy. Instructions follow for recreating these examples, and for using them as starting points for further modeling exercises. The paper ends with a brief discussion of the prospects for improvements in performance and accuracy in FD technology, and the evolutionary advantages flowing from the modular, or object, orientation of IWAVE. Two appendices describe the job parameters used in the examples, and download and install instructions.

Acoustic Staggered Grid Modeling in IWAVE