Approximate vs. exact adjoints in inversion

Sean Crawley

sean@sep.stanford.edu

ABSTRACT

Gradient-based inversion methods employ adjoint operators to find the gradient direction in the objective function. Generally we assume that the exact adjoint is the optimal choice. In this paper I discuss one type of approximate adjoint, called a pull adjoint because of the way it discretizes the output space. For operators which sum and spray data along curved trajectories, such as Kirchoff and moveout operators, pull adjoints more closely approximate an operator in a continuous space. This characteristic is important because we use these operators to emulate the wave equation, which is a continuous and unitary operator. This paper presents a theoretical argument for the use of pull adjoints in some inversions, and presents a simple inversion example where the use of pull adjoints is of benefit.