Fundamental solutions of a wave operator in problems of field continuation

In this paper, fundamental solutions of a wave operator in an inhomogeneous medium having the properties of advanced (anti-causal) type are analyzed. These are such functions that act for the future when the field is calculated at the present time. It is shown that the use of this anti-causal property when the wave field is continued from some observation surface allows, in principle, "to look" into the domain containing unknown wave field sources. On the observation surface, the trace of the field and its normal derivative are considered to be known. It is shown that for a certain structure of sources, in particular, for those instantaneously acting in time (Cauchy data), the solution to the inverse problem of reconstructing the sources is given simply by fixing the continued field at the time t = 0.