Eric Milner Colloquium: Computational Methods for Solving Wave Equation Inverse Problem
Date:
Every year, the Eric Milner Graduate Scholarship recipient is invited to present a colloquium lecture.
Information page: https://science.ucalgary.ca/mathematics-statistics/about/history/eric-milner-biography
Abstract: The field of inverse problems has experienced tremendous growth due to the importance of applications, such as biomedical and seismic imaging, that require the practical solution of inverse problems. In particular, in seismic imaging, an inverse problem can be found as the minimization of model parameters from observed data which is an important task in data processing. A number of optimization methods, such as the conjugate gradient and steepest descent methods, are used for the minimization of a function which in this context is the velocity parameter. These methods require Fréchet derivatives of the functions, which are costly by computational means. The adjoint state method, which helps to approximate the gradient of the function, was developed to address this problem. This means extra linear systems should be solved using numerical methods. In this presentation, an outline of my research which includes finite difference methods, adjoint state methods, optimization methods, and also regularization methods, will be presented.