A major challenge in carbonates environments is to map heterogeneities which have a strong impact on oil and gas production. For example in many carbonate reservoirs, matrix porosity contains the oil in place but the permeability is mainly provided by fracture corridors. In some carbonate reservoirs, such as Kashagan field in Kazakhstan, the oil in place is essentially contained primarily in karstic caves and conduits. Therefore being able to precisely locate these heterogeneities and possibly characterize their properties is essential in these environments.

Various techniques have been developed recently to locate and characterize these heterogeneities, by detailed analysis of the elastic signals recorded in seismic experiments. Among them one can think of the scattering index presented by Willis et al (2004) or all the imaging techniques developed recently under the generic name of interferometry.

The first step in all processing or inversion procedures is to be able to accurately simulate the forward problem, and it is therefore of paramount importance to be able to accurately model the scattering related to fractures and caves. The numerical and computer constrains even on very large clusters limit the resolution at which a model can be described. The current practice for finite difference modeling is to use 20m grid cells for acoustic modeling and spatial discretization leading to cells 10m in size for elastic modeling. In these cases, heterogeneity associated with fracturing on smaller scales must be upscaled and distributed in an equivalent medium, which will reproduce varaiations in traveltimes and changes in reflection coefficient but will neglect the scattered wavefields that are the subject of the recently developed methods for characterizing fracture distributions. In this paper, we present a full waveform modeling technique based on a new approach of finite differences which allows simultaneous simulation of both macro- and micro-scale heterogeneities. This algorithm is based on a multi grid approach that models the seismic response of a shot point over a large size model containing micro scale heterogeneities in a reasonable time frame (i.e., several hours on a modern cluster). We show various examples of the signals related to fractures and their importance in terms of heterogeneities interpretation, and we also examine results of simulations using 3-D modeling based on the Born approximation to help interpret and explain the synthetic seismograms.

These new numerical results will have significant advantages over previous results that rely on approaches that replace the detailed spatial variations of elastic properties with media with altered velocities and densities.

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