IWAVE Implementation of Born Simulation

The single-scattering (or Born) approximation is the most fundamental assumption shared by all seismic imaging methods, and plays a crucial role in the nonlinear waveform inversion, an iterative process of linearized inversions. The Born simulator (linearized forward map) shares a computational core with the corresponding simulator (forward map), which has been well implemented in the modeling package IWAVE. This report focuses on implementing the Born simulator based on IWAVE, and reviews the main adaptations we made in IWAVE to accommodate such an implementation in C++. Our goal is to construct a C++ wrapper of IWAVE, which fits into a general framework for inversion. This report is the first of several describing an implementation of such a wrapper. INTRODUCTION A common objective of reflection seismology is to make inferences about physical features (model) of subsurface (e.g., velocity) from data (seismogram) recorded on or near the surface. This inverse problem is often formed as a simulation-driven optimization problem in Hilbert space. Its implementation involves different levels of abstraction: simulation of wave propagation requires a variety of computational types and data structures specific to physical modeling and numerical implementation; Instead, optimization algorithms involve a more abstract layer of mathematical constructs (vectors, functions, gradients, ...) which are independent of physics and its numerical realization. Object-oriented programming offers a way to combine different levels of abstraction (e.g., finite difference grids v.s. vectors in Hilbert space) while keeping them in separate code. A concrete example is the Rice Vector Library (RVL) (Padula et al., 2009). RVL is a collection of C++ classes to express core concepts (vectors, functions,...) of calculus in Hilbert space, and provides standardized interfaces for optimization and linear algebra algorithms. We will use the interfaces provided by RVL to implement this inversion. First of all, we need to construct the modeling code as an RVL operator class (for vector valued functions) with at least methods to compute its value (modeling), first derivative and adjoint derivative (Born and its adjoint modeling). This report is the first of several describing an operator implementation for acoustics based on the modeling package IWAVE (Terentyev, 2009). IWAVE offers many advantages: it provides a parallel framework for solving timedependent partial differential equations, has lots of modeling options already imple-