A Marchenko equation for acoustic inverse source problems

Abstract

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.

Virtual acoustics in inhomogeneous media with single-sided access

“…This expression shows how the recorded data G ( x ′, x , t ), measured at the upper boundary of the medium, are transformed into G ( r , x , t ) and its time-reversal, being the response to a real source at x , observed by a virtual receiver at r anywhere inside the medium. The focusing function F ( x ′, r , t ), required for this transformation, can be derived from the recorded data G ( x ′, x , t ), using the multidimensional Marchenko method 18 – 20 , 32 , 33 . We have implemented a 2D version of the Marchenko method as an iterative process 34 .…”

Green's Theorem in Time-Reversal Acoustics, Back Propagation and Source-Receiver Redatuming: a Tutorial

“…Figure 1 illustrates the principle. In the single-sided homogeneous Green's function representation, the focusing function replaces the complex-conjugated Green's function, as follows (Wapenaar et al, 2016;Van der Neut et al, 2017). The focusing function can be retrieved from reflection data at S 0 using the Marchenko method.…”

Green's theorem in seismic imaging across the scales

“…Unlike the classical representation, which is exact, equation 32holds under the assumption that evanescent waves can be neglected. When S 0 is horizontal and the medium above S 0 is homogeneous (for the Green's function as well as for the focusing function), this representation may be approximated by (Van der Neut et al, 2017)…”