3-D Finite Di erence Modeling for Borehole and Reservoir Applications

ERL’s in-house finite difference code (Krasovec et al., 2003) has undergone several upgrades in the past year. Most notably, a stretched grid can now be used to greatly reduce the amount of RAM memory needed by certain types of models. Improvements have been made in the GUI front end, allowing more freedom and ease in building the model, source or source array, and receiver array. The finite difference code has contributed to several different research projects at ERL in the past year. A few of these projects, including borehole seismics, reservoir delineation, and source mechanics, are shown in this report. Introduction In an effort to expand the modeling tools available at ERL, we have updated a finite difference code first developed by Cheng (1994) to model seismic waves in anisotropic, viscoelastic media. The wave equation is discretized in velocity and stress on a staggered grid, is 2nd order in time and 4th order in space, and models anisotropy with up to nine elastic constants. Two types of boundary conditions can be used: those of Cerjan et al. (1987) or Higdon (1986, 1987). The method of Emmerich and Korn (1987) can be used to include attenuation in the calculations, with three relaxation frequencies, as discussed in Krasovec et al. (2003). Originally written in Fortran, the code has been converted to MPI C to allow it to run large models on a PC cluster. A front end of Matlab graphic user interfaces (GUIs) have also been developed to make the code easier to use. A 2D version of the code was released at ERL’s 2003 Consortium. This year, the 3D version, including the Matlab GUIs, the Matlab mex version, a standalone serial version, a parallel MPI C version, a number of accompanying Matlab scripts, a tutorial, and a manual are included in the software release. Upgrades to the GUIs can best be experienced by going through the tutorial. This paper focuses on the output of the code as opposed to its usage. First, we show a comparison of the finite difference code to discrete wavenumber results for a 3D fluid filled borehole. Second, we show a more complicated borehole geometry: finite difference modeling results of ERL’s scaled down LWD tool. Moving away from the borehole geometry, the third example looks for shear wave splitting in synthetic micro earthquake data due to the presence of fractures in a reservoir layer. The final example shows how an empty cylindrical cavity located next to an explosion source can scatter the source energy into shear waves, a problem of interest in monitoring for the Comprehensive Test Ban Treaty. The Stretched Grid Some models can be made more computationally efficient by using a stretched grid. For example, borehole models need small grid elements in the borehole, because the fluid velocity is low, hence the wavelength