Pitfalls and challenges of seismic imaging

While depth migration and the so-called “full wave-form inversion” play an increasing role in seismic exploration, none of them can be considered as an ultimate tool to infer the interior structure of the Earth. Each of these methods has its own limitations and pitfalls. In the first part of my lecture I will formulate a number of fundamental questions which should be addressed in order to make the field of geophysical inverse problems a mature science, rather than a set of recipes. Usually solutions proposed are based on the criterion of the best fit between calculated and observed data. But it is well understood that by itself, a good fit does not guarantee that an inverted model is correct. The ill-posedness of seismic inverse problems is fundamental and does not depend on a particular type of algorithm or on the approach underlying the algorithms. I will introduce and discuss a way to look at model-independent seismic imaging using the quantum mechanics concept. Today many quantum physicists believe that quantum principles in fact apply on all scales. In Feynman’s path-integral approach a particle does not follow a single trajectory but it follows every possible path in the space-time domain when each of the trajectories has its own amplitude and phase. Thus each trajectory contributes a different phase to the total amplitude of the wave function. Can Feynman’s path integral idea be used for seismic imaging? In analogy to the path integral method we can construct the seismic image by summation over the contributions of elementary signals propagated along a representative sample of possible paths between the source and receiver points. The quantum imaging converges to a standard imaging procedure only in trivial situations of a deterministic and known velocity model. But what happens when the model is unknown, random or estimated with uncertainties, or even worse, the model does not describe adequately the wave propagation process in the real Earth? In my opinion, it happens more often that we think. In this case a single stationary path does not describe adequately ray/wave propagation process and conventional imaging does not produce a correct focused subsurface image. In contrary, quantum imaging using all possible trajectories accounts for multiple stationary paths and takes into account model uncertainties. Small-scale structural details and heterogeneities of the subsurface such as faults, karsts, and fractures are of crucial importance for exploration, production and development of unconventional oil and gas reservoir. Understanding the location and orientation of natural fractures is important for optimal well placement when sweet spotting in unconventional reservoir play. Usually the information on fault and fracture systems is obtained from interpretation, seismic attribute or anisotropy analysis using the effective media. At the same time small scale elements of the subsurface are capable of generating strong scattered/diffracted waves, which are recognized as a main information carrying signals. Although the importance of diffracted waves in seismic has long been recognized it will not be a gross exaggeration to say that for a long time diffractions stay “the abandoned stepchildren of traditional seismic processing and imaging”. Over the last decade there has been an increasing interest to use diffractions as a direct indicator of various reflector discontinuities, faults, karsts, fractures etc. I will present several ways to separate the total wavefield into two components: specular reflections and diffraction. Images of the separated diffractive component of the total wavefield are able to emphasize small but important geologic objects that often are invisible after conventional seismic processing.