THE FIRST WAVE EQUATION MIGRATION RTM WITH DATA CONSISTING OF PRIMARIES AND INTERNAL MULTIPLES: THEORY AND 1D EXAMPLES

摘要

Reverse time migration (RTM) is the cutting-edge imaging method used in seismic exploration. In earlier RTM publications, density was often chosen and used to balance a medium with velocity variation, such that the acoustic impedance - the product of velocity and density - stays constant. Thus, normal incidence reflections from sharp boundaries are avoided. In order to be more complete, consistent, realistic, and predictive, general velocity and density variations (not constrained by impedance matching) are intentionally included in our study so that we can test the impact of reflections on the first wave equation migration RTM algorithms. The major objectives of this article are to advance our understanding and to provide concepts, added imaging capabilities, and new algorithms for RTM. Although our objective of extracting useful subsurface information from recorded data is not different from that of well-known previous RTM publications, our method is different. Although all current methods utilize the wave equation, the imaging condition they call upon, the time and space coincidence of up- and down-going waves, ultimately results in an asymptotic approximate imaging algorithm. All current industry applied RTM algorithms do not correspond to predicting a coincident source and receiver experiment at depth at t = 0. That imaging principle is the defining property of wave equation migration (WEM). The method of this paper represents WEM for RTM. In this paper, we present the first WEM RTM imaging tests, with a discontinuous reference medium and outputting the correct image locations and distinct reflection coefficients from above and below each reflector, with primaries and internal multiples in the data. There is "no cross talk" or any other artifacts as reported by other methods that seek to migrate data with primaries and multiples. That is an implementation and analysis of Weglein et al. (2011a,b) with primaries and internal multiples in the data.