Efficient 3D Borehole Modeling of the Reflected Wave Field While Drilling

Based on a closed form explicit expression for the 3D scattered elastic wave field resulting from an arbitrary multipole force source excitation in an unbounded, homogeneous and isotropic elastic medium with a plane scatterer, we have developed a numerical implementation to verify the validity of the full elastodynamic Born approximation. The concept for this new fast and efficient 3D elastodynamic forward modeling technique was developed with focus on borehole measurements and therefore aims to include the fluid-filled borehole, but it is not limited to these configurations. We present the details and specific features of the numerical implementation and show a comparison with a quasi analytic solution. Furthermore we show a convergence test to establish a sufficient discretization criterion. For simplicity we restrict ourselves to the PP reflection in a zero-offset configuration with a single force source excitation. The results are promising as it seems that the developed method is fast and accurate enough to properly model the scattered wave field (including converted waves).