Font Size: 

This paper is concerned with the inverse problem for reconstructing of the mass density of rods, directly in the time domain, based on the complete waveform response of one end. Mathematically, the inverse problem can be cast as a partial-differential-equation-constrained optimization problem which is regularized by the time-dependent Tikhonov regularization. Specifically, we seek to minimize a cost functional of the misfit between measured and computed responses. Numerical results are presented to show the accuracy and effectiveness of the proposed scheme in reconstructing sharp profiles of mass density even in the presence of noise in the data.