Time Reversal - an efficient way of data analysis

Building  knowledge on surrounding world requires information about it. This almost trivial statement gains a much deeper sense in cases when we cannot infer thought information by direct measurements. It  happens quite often, actually too often. In such a case we can still gain (at least partially) thought information from observational data but it requires a more complex approach often referred to as ``inverse approach’’. In this talk I will present the modern inverse  method  called Time Reversal Mirroring (TRM) which provides an efficient way of inferring information from recorded (acoustic/seismic/electromagnetic) waves provided governing  equation is a linear, hyperbolic PDE. From the physical point of view the method is based on two basic symmetries of underlying equation(s): time reversal and source-receiver reciprocity. They allow to construct an extremely  efficient  numerical algorithm for  analysis of omplex time series data in searching for ``hidden’’ information about waves source and/or medium properties. My talk will begin with basic introduction mathematical principle upon which the TRM method is build up. Next I will give a short overview of  idea of ``inverse problems’’ and how TRM fits to this framework.  Finally, I will discuss the particular applications of TRM method, namely the source location task.  

In the second part of the talk, to relax you after boring description of dealing with real data I will present a few movies of  numerical simulations of breaking solid materials – something we know from our everyday experience.  The context of this part is a never ending discussion starting yet in Greek times if the world is continuous or discrete.