Characterizing exact energy density distributions for laser-accelerated ion bunches in a medium is challenging due to very high beam intensities and the electro-magnetic pulse (EMP) emitted in the laser-plasma interaction. Ion-bunch energy acoustic tracing (I-BEAT) allows for reconstructing the spatial energy density from the ionoacoustic wave generated upon impact in water. We have extended this approach to tracing ionoacoustic modulations of broad energy distributions (TIMBRE) by introducing thin foils in the water reservoir to shape the acoustic waves at distinct points along the depthdose curve. Here, we present first simulation studies of this new detector and reconstruction approach which provides on-line read-out of the deposited energy with depth within centimeter range behind the ion source of state-of-the-art laser-plasma based accelerators.