A Marchenko equation for acoustic inverse source problems

From acoustics to medical imaging and seismology, one strives to make inferences about the structure of complex media from acoustic wave observations. This study proposes a solution that is derived from the multidimensional Marchenko equation, to learn about the acoustic source distribution inside a volume, given a set of observations outside the volume. Traditionally, this problem has been solved by backpropagation of the recorded signals. However, to achieve accurate results through backpropagation, a detailed model of the medium should be known and observations should be collected along a boundary that completely encloses the volume of excitation. In practice, these requirements are often not fulfilled and artifacts can emerge, especially in the presence of strong contrasts in the medium. On the contrary, the proposed methodology can be applied with a single observation boundary only, without the need of a detailed model. In order to achieve this, additional multi-offset ultrasound reflection data must be acquired at the observation boundary. The methodology is illustrated with one-dimensional synthetics of a photoacoustic imaging experiment. A distribution of simultaneously acting sources is recovered in the presence of sharp density perturbations both below and above the embedded sources, which result in significant scattering that complicates the use of conventional methods.