We study in this thesis an inverse problem that originates in geophysics. In this inverse problem, a fault and a slip field have to be determined from an overdetermined Partial Differential Equation (PDE) in half space. We achieve three main goals: first, an existence and uniqueness theorem for this PDE in adequate functional spaces. Second, we show that our overdetermined PDE (which reflects that in practice, geophysicists use a PDE model and have access to boundary measurements) does make it possible to recover the fault and the slip. Third, we show that this recovery is stable, under the assumption that the fault must be planar.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Murdza, Andrew P.

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-051820-191401

Advisor

• Volkov, Darko

Year

• 2020

Date created

• 2020-05-18

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright