Quantum seismic imaging: Is it possible?

To get an accurate subsurface image from seismic data we need to build a highly accurate velocity model. In most cases this goal is difficult to achieve due to the ill-poseness of the inverse problem. Numerous tomography schemes are suggested and most of them are based on the common image gather flattening. Another scheme, named "full waveform inversion" is connected to data fitting. There are various reasons why exact velocity knowledge is impossible. A fundamental problem in velocity estimation is related to the erroneous measurements and the stochastic nature of the subsurface velocity. In this case the velocity model should be represented by a probability density function, rather than a unique deterministic value and a single velocity model generally does not exist. In this paper we discuss an alternative way to look at seismic imaging using the quantum mechanics concept and path integral idea. The method computes the image by summing contributions of individual signals propagated along all possible paths between the source and observation points. In fact it samples different paths between the source and receiver instead of relying on only one path derived from Fermat's principle. All random ray or wave trajectories between the source and receiver within this volume are, in principle, taken into account. The focusing mechanism is achieved by a weighting function (probability amplitude), which is designed to emphasize contributions from trajectories close to the stationary one and to suppress contributions from unlikely paths. The presented examples demonstrate principles and feasibility of the new concept. There are many issues still needed to be investigated.