Hybrid Scheme for Simulation of Seismic Wave Propagation in Presence of Anisotropy

Abstract eng:
In this paper we focus on the wave propagation in realistic geological models. One of the typical features of rock is anisotropy which is widely spread in the Earth’s interior. However, numerical algorithms, in particular those based on finite differences, used to simulate seismic wave propagation in anisotropic media are several times more CPU time and memory consuming than those used for isotropic media. A simple estimation shows that in order to perform simulation inside a domain of the size of 500 by 500 by 250 wavelength (rather standard sizes for modern applications) one needs about 42 Tb of RAM or about 24000 cores of modern high-performance computer if the model is isotropic and the standard staggered grid scheme (SSGS) [1] is used. At the same time, in case of anisotropy this amount increases up to 200 Tb of RAM if either rotated staggered grid scheme [2]or Lebedev scheme (LS) [3] is applied. On the other hand anisotropic formations typically take relatively small part of the model (about 10%) and present in subhorizontal layers, such as fractured reservoirs, finely-layered formations etc. Thus it seems reasonable to design an algorithm combining anisotropy-oriented memory consuming schemes, in particular Lebedev scheme, with the standard staggered grid scheme, so that the LS to be used only in subdomain surrounding anisotropic formation, while efficient SSGS is applied in the major part of the model. Coming back to the presented example one may derive, that if anisotropic (Lebedev) part of the model is about 10% then the simulation by means of the hybrid scheme requires about 60 Tb of RAM which is only 27% of RAM that would be demanded by pure LS simulations. At the same time all the peculiarities of the wave propagation in anisotropic formation are fully taken into account and simulated properly. The research was supported by the Russian Foundation for Basic Research grans no. 11-05-00947, 11-0512022, 12-05-31008, 13-05-00076, and the scholarship program of the President of Russian Federation no. SP-150.2012.5.

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