Borehole Acoustics –New Approaches to Old Problems - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 388

Figure 10.8f. Electric field for eccentered resistivity tool in conductive mud
showing how wide annular space above tool contributes little to logging signal.
Figure 10.8g. Computational grid for wells with adjacent shale lense
developed for a cross-well seismic application.
10.3.3 Applications to borehole geophysics.
In 2005, the United States Department of Energy, through its Small
Business Innovation Research (SBIR) program, supported the author' s extension
of the grid generation ideas described above to geophysical applications, in
Borehole Seismic Modeling Using Curvilinear Boundary-Conforming Meshes.
The results led to new ways to handle borehole geophysical problems
encountered in the drilling of deviate and horizontal wells. These numerically
based methods could not provide results as elegant as Equation 10.1, but they do
handle eccentricity and multiple radial-vertical layering satisfactorily. The wide
body of work that resulted will be published separately, but it is possible to give
an outline of the philosophies and mathematical techniques developed to exploit
the added resolution provided by our powerful gridding methodologies.