2.5-dimensional crosshole acoustic response: a variable density approach

Abstract

SUMMARY This paper presents the development of a 2.5-D simulation technique for acoustic wave propagation in media with variable density and velocity. A comparative study of the 2-D and 2.5-D responses of a model reveals the spatially and temporally damped nature of the 2.5-D acoustic wave equations. The simulated results for constant and variable density models show that the density variation aVects only the reflectivity of the layer. The computational cost for variable density models is 2.17 and 2.26 times that for constant density models for the 2.5-D and 2-D cases, respectively. Furthermore, the 2.5-D computational cost in the time domain is only about 10‐15 per cent more than that for two dimensions, so this modest increase in computational cost can avoid the exorbitant 3-D computational cost. Snapshots for a crosshole geometry were computed at various times in order to study the eVect of heterogeneity on the amplitude and shape of the wave front. Extensive analysis of an oil-bearing reservoir with and without the inclusion of a gas zone was performed using a point source as well as multiple sources. In addition, the eVects of the thickness of a low-velocity layer (oil-bearing) and of the location of the source have been studied. It is concluded from the numerical response that the waveguide action of the low-velocity layer depends on its thickness in terms of the dominant wavelength. Trapping of waves was not observed when the source was outside the low-velocity layer. Furthermore, the presence of heterogeneity in the low-velocity layer contributes considerably to the leakage of energy in the adjacent layers due to scattering/diVraction. It was found that, in the 2.5-D numerical simulation, the stability condition and the requirement of the number of grid points per wavelength to avoid grid dispersion are the same as for the 2-D case.