Convergence analysis of a coefficient inverse problem for the poroelastic wave system

In this paper, we study the convergence rate of a parameter inverse problem for seven coefficients in the two-dimensional poroelastic wave system. The coefficients in the system are allowed to be discontinuous without high regularity. For solving the inverse problem, we propose a new functional and exploit it by minimizing its regularized version. The differentiability of the mapping from the coefficients to forward solution is proved. The convexity of the functional is also proved, which ensures the uniqueness of the minimization problem in the set of admissible solutions. With a relatively weak source condition, we obtain the convergence rate of the Tikhonov regularized solution. In addition, the stability of the coefficient inverse problem is obtained under different conditions.