Esh3D, an Analytical and Numerical Hybrid Code for Full Space and Half‐Space Eshelby's Inclusion Problems. Issue 3 (2nd March 2019) - Meng, C.
Abstract : I present an open source code Esh3D that evaluates the quasi‐static elastic displacement and stress fields perturbed by ellipsoidal inclusions, known as the Eshelby solution. The improvement over my previous work includes obtaining solutions in half‐space by numerically canceling the traction to stage a free surface. The discrete numerical domain allows nonplanar surface. I first briefly introduce the ellipsoidal inclusion problem and solution evaluation. Then, I describe the traction cancellation method in forming the half‐space solutions. Next, I emulate a planar fault with a low aspect ratio ellipsoid and compare the half‐space solution against the well‐known Okada solution for flat and topographic surfaces. Finally, I provide comparisons between the full space and half‐space solutions to illustrate the free surface effects on the displacement and stress fields. Plain Language Summary: In a number of geophysical applications, our code presented in Meng et al. (2012, https://doi.org/10.1016/j.cageo.2011.07.008 ) is adopted. Among those, people sometimes use the code to fit surface deformation/strain data. However, the original code is for full space without considering the free surface. Now I extend the code to cover both the full space and half surface cases. In the last figure, I show that the free surface effect cannot be neglected even at depth of 4 km. Key Points: Esh3D evaluates Eshelby solution for ellipsoidal inclusions in full or half‐space Half space Eshelby solution is obtained seminumerically by traction cancellation The half‐space solution allows nonplanar surface