Cartesian Meshing Spherical Earth (CMSE): A Code Package to Incorporate the Spherical Earth in SPECFEM3D Cartesian Simulations

The SPECFEM3D_Cartesian code package is widely used in simulating seismic wave propagation on local and regional scales due to its computational efficiency compared with the one-chunk version of the SPECFEM3D_Globe code. In SPECFEM3D_Cartesian, the built-in meshing tool maps a spherically curved cube to a rectangular cube using the Universal Transverse Mercator projection (UTM). Meanwhile, the geodetic east, north, and up directions are assigned as the local x-y-z directions. This causes coordinate orientation issues in simulating waveform propagation in regions larger than 6 degrees x 6 degrees or near the Earth's polar regions. In this study, we introduce a new code package, named Cartesian Meshing Spherical Earth (CMSE), that can accurately mesh the 3D geometry of the Earth's surface under the Cartesian coordinate frame, while retaining the geodetic directions. To benchmark our new package, we calculate the residual amplitude of the CMSE synthetics with respect to the reference synthetics calculated by SPECFEM3D_Globe. In the regional scale simulations with an area of 1300 km x 1300 km, we find a maximum of 5% amplitude residual for the SPECFEM3D_Cartesian synthetics using the mesh generated by the CMSE, much smaller than the maximum amplitude residual of 100% for the synthetics based on its built-in meshing tool. Therefore, our new meshing tool CMSE overcomes the limitations of the internal mesher used by SPECFEM3D_Cartesian and can be used for more accurate waveform simulations in larger regions beyond one UTM zone. Furthermore, CMSE can deal with regions at the south and north poles that cannot be handled by the UTM projection. Although other external code packages can be used to mesh the curvature of the Earth, the advantage of the CMSE code is that it is open-source, easy to use, and fully integrated with SPECFEM3D_Cartesian.